============================================
== make qtest ==============================
============================================
== Fri, Jul 24, 2020 10:27:09 PM

============================================
== Test non-reentrant qset.c with mem.c ====
============================================
bin/testqset 10000
qh_meminitbuffers: memory initialized with alignment 8
qh_memsize: quick memory of 16 bytes
qh_memsize: quick memory of 24 bytes
qh_memsize: quick memory of 32 bytes
qh_memsize: quick memory of 40 bytes
SETelemsize is 4 bytes for pointer-to-int


Testing qh_setappend 0..9999.  Test i0 i1 i2 i3 i4 i5 i6 i7 i8 i9 i10 i100 i1000 i9999

Testing qh_settruncate 5000 and 0.  Test n0

Testing qh_setappend2ndlast 0,0..9999.  Test 0 i0 i1 i2 i3 i4 i5 i6 i7 i8 i9 i10 i100 i1000 i9999

Testing SETtruncate_ 5000 and 0.  Test n0

Testing qh_setdelnthsorted and qh_setaddnth 1..9999. Test j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j100 j1000 j9999

Testing qh_setappend_set 0..9999. Test j0 j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j100 j1000 j9999

Testing qh_setcompact and qh_setcopy 0..9999. Test j0 j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j100 j1000 j9999

Testing qh_setequal*, qh_setin*, qh_setdel, qh_setdelnth, and qh_setlarger 0..9999. Test j0 j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j100 j1000 j9999

Testing qh_settemp* 0..9999. Test j0 j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j100 j1000 j9999

Testing qh_setlast, qh_setnew_delnthsorted, qh_setunique, and qh_setzero 0..9999. Test j0 j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j100 j1000 j9999

Testing qh_setdel*, qh_setaddsorted, and  0..9999. Test j0 j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j100 j1000 j9999

Not testing qh_setduplicate and qh_setfree2.  These routines use heap-allocated,
set contents.  See qhull tests in eg/q_test and bin/qhulltest.

qh_memcheck: check size of freelists on qhmem
qh_memcheck: A segmentation fault indicates an overwrite of qhmem
qh_memcheck: total size of freelists totfree is the same as qhmem.totfree

memory statistics:
    124 quick allocations
     25 short allocations
   8230 long allocations
    148 short frees
   8230 long frees
     24 bytes of short memory in use
    760 bytes of short memory in freelists
 130280 bytes of dropped short memory
     68 bytes of unused short memory (estimated)
 105548 bytes of long memory allocated (max, except for input)
      0 bytes of long memory in use (in 0 pieces)
 131064 bytes of short memory buffers (minus links)
  65536 bytes per short memory buffer (initially 131072 bytes)
   1135 calls to qh_setlarger
5.6e+02     average copy size
  freelists(bytes->count): 16->3 24->5 32->6 40->10


testqset: OK


============================================
== Test reentrant qset_r.c with mem_r.c ====
============================================
bin/testqset_r 10000
qh_meminitbuffers: memory initialized with alignment 8
qh_memsize: quick memory of 16 bytes
qh_memsize: quick memory of 24 bytes
qh_memsize: quick memory of 32 bytes
qh_memsize: quick memory of 40 bytes
SETelemsize is 4 bytes for pointer-to-int


Testing qh_setappend 0..9999.  Test i0 i1 i2 i3 i4 i5 i6 i7 i8 i9 i10 i100 i1000 i9999

Testing qh_settruncate 5000 and 0.  Test n0

Testing qh_setappend2ndlast 0,0..9999.  Test 0 i0 i1 i2 i3 i4 i5 i6 i7 i8 i9 i10 i100 i1000 i9999

Testing SETtruncate_ 5000 and 0.  Test n0

Testing qh_setdelnthsorted and qh_setaddnth 1..9999. Test j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j100 j1000 j9999

Testing qh_setappend_set 0..9999. Test j0 j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j100 j1000 j9999

Testing qh_setcompact and qh_setcopy 0..9999. Test j0 j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j100 j1000 j9999

Testing qh_setequal*, qh_setin*, qh_setdel, qh_setdelnth, and qh_setlarger 0..9999. Test j0 j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j100 j1000 j9999

Testing qh_settemp* 0..9999. Test j0 j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j100 j1000 j9999

Testing qh_setlast, qh_setnew_delnthsorted, qh_setunique, and qh_setzero 0..9999. Test j0 j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j100 j1000 j9999

Testing qh_setdel*, qh_setaddsorted, and  0..9999. Test j0 j1 j2 j3 j4 j5 j6 j7 j8 j9 j10 j100 j1000 j9999

Not testing qh_setduplicate and qh_setfree2.  These routines use heap-allocated,
set contents.  See qhull tests in eg/q_test and bin/qhulltest.

qh_memcheck: check size of freelists on qh->qhmem
qh_memcheck: A segmentation fault indicates an overwrite of qh->qhmem
qh_memcheck: total size of freelists totfree is the same as qh->qhmem.totfree

memory statistics:
    124 quick allocations
     25 short allocations
   8230 long allocations
    148 short frees
   8230 long frees
     24 bytes of short memory in use
    760 bytes of short memory in freelists
 130280 bytes of dropped short memory
     68 bytes of unused short memory (estimated)
 105548 bytes of long memory allocated (max, except for input)
      0 bytes of long memory in use (in 0 pieces)
 131064 bytes of short memory buffers (minus links)
  65536 bytes per short memory buffer (initially 131072 bytes)
   1135 calls to qh_setlarger
5.6e+02     average copy size
  freelists(bytes->count): 16->3 24->5 32->6 40->10


testqset_r: OK


============================================
== Run the qhull smoketest ====
============================================
bin/rbox D4 | bin/qhull Tv

Starting the rbox smoketest for qhull.  An immediate failure indicates
that non-reentrant rbox was linked to reentrant routines.  An immediate
failure of qhull may indicate that qhull was linked to the wrong
qhull library.  Also try 'rbox D4 | qhull T1'

Convex hull of 50 points in 4-d:

  Number of vertices: 50
  Number of facets: 260

Statistics for: rbox D4 | qhull Tv

  Number of points processed: 50
  Number of hyperplanes created: 711
  Number of distance tests for qhull: 1432
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 2.8e-15 of
all facets.  Will make 13000 distance computations.
============================================
== make test, after running qtest ==========
============================================

==============================
========= rbox/qhull =======
==============================
bin/rbox D4 | bin/qhull Tv

Starting the rbox smoketest for qhull.  An immediate failure indicates
that non-reentrant rbox was linked to reentrant routines.  An immediate
failure of qhull may indicate that qhull was linked to the wrong
qhull library.  Also try 'rbox D4 | qhull T1'

Convex hull of 50 points in 4-d:

  Number of vertices: 50
  Number of facets: 260

Statistics for: rbox D4 | qhull Tv

  Number of points processed: 50
  Number of hyperplanes created: 711
  Number of distance tests for qhull: 1432
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 2.8e-15 of
all facets.  Will make 13000 distance computations.

==============================
========= qconvex ============
==============================
bin/rbox 10 | bin/qconvex Tv 

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 10 | qconvex Tv

  Number of points processed: 10
  Number of hyperplanes created: 26
  Number of distance tests for qhull: 43
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 2e-15 of
all facets.  Will make 160 distance computations.

==============================
========= qdelaunay ==========
==============================
bin/rbox 10 | bin/qdelaunay Tv 

Delaunay triangulation by the convex hull of 10 points in 4-d:

  Number of input sites: 10
  Number of Delaunay regions: 15

Statistics for: rbox 10 | qdelaunay Tv

  Number of points processed: 10
  Number of hyperplanes created: 47
  Number of facets in hull: 25
  Number of distance tests for qhull: 68
  CPU seconds to compute hull (after input): 0.001


Output completed.  Verifying that all points are below 3e-15 of
all facets.  Will make 150 distance computations.

==============================
========= qhalf ==============
==============================
bin/rbox 10 | bin/qconvex FQ FV n Tv | bin/qhalf Tv

Output completed.  Verifying that all points are below 2e-15 of
all facets.  Will make 160 distance computations.

Halfspace intersection by the convex hull of 16 points in 3-d:

  Number of halfspaces: 16
  Number of non-redundant halfspaces: 16
  Number of intersection points: 10
  Number of non-simplicial intersection points: 10

Statistics for: rbox 10 | qconvex FQ FV n Tv | qhalf Tv

  Number of points processed: 16
  Number of hyperplanes created: 29
  Number of distance tests for qhull: 99
  Number of distance tests for merging: 300
  Number of distance tests for checking: 188
  Number of merged facets: 18
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 160 distance computations.

==============================
========= qvoronoi ===========
==============================
bin/rbox 10 | bin/qvoronoi Tv

Voronoi diagram by the convex hull of 10 points in 4-d:

  Number of Voronoi regions: 10
  Number of Voronoi vertices: 15

Statistics for: rbox 10 | qvoronoi Tv

  Number of points processed: 10
  Number of hyperplanes created: 47
  Number of facets in hull: 25
  Number of distance tests for qhull: 68
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 3e-15 of
all facets.  Will make 150 distance computations.

=================================
========= user_eg ===============
== if fails under Windows =======
== cp lib/libqhull_r.dll bin/ ==
=================================
bin/user_eg

========
user_eg 'cube qhull options' 'Delaunay options' 'halfspace options'

This is the output from user_eg_r.c.  It shows how qhull() may be called from
an application, via Qhull's shared, reentrant library.  user_eg is not part of
Qhull itself.  If user_eg fails immediately, user_eg_r.c was incorrectly linked
to Qhull's non-reentrant library, libqhull.
Try -- user_eg 'T1' 'T1' 'T1'


========
compute convex hull of cube after rotating input
input
    -1     -1     -1 
     1     -1     -1 
    -1      1     -1 
     1      1     -1 
    -1     -1      1 
     1     -1      1 
    -1      1      1 
     1      1      1 

Convex hull of 8 points in 3-d:

  Number of vertices: 8
  Number of facets: 6
  Number of non-simplicial facets: 6

Statistics for:  | qhull s Tcv 

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 96
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.

8 vertices and 6 facets with normals:
    -0     -0     -1 
     0     -1      0 
     1     -0     -0 
    -1     -0     -0 
     0      1     -0 
    -0     -0      1 

========
compute 3-d Delaunay triangulation
seed: 1595644031
input
-0.801 0.00317 -0.695 
-0.358 -0.422  0.394 
-0.893 -0.345 -0.494 
-0.548  0.646  0.388 
-0.0159  0.604  0.693 
  0.43  0.224  0.755 
0.0381  -0.37  -0.66 
-0.737  0.146 -0.926 

Delaunay triangulation by the convex hull of 8 points in 4-d:

  Number of input sites: 8
  Number of Delaunay regions: 8

Statistics for:  | qhull s d Tcv 

  Number of points processed: 8
  Number of hyperplanes created: 25
  Number of facets in hull: 16
  Number of distance tests for qhull: 27
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 8.6e-15 of
all facets.  Will make 64 distance computations.

8 vertices and 16 facets with normals:
  0.44  -0.53 -0.014   0.72 
  0.34  -0.77   0.14   0.52 
-0.071  -0.12   0.39   0.91 
  -0.2 -0.037   0.42   0.88 
 -0.31  -0.32   0.65   0.62 
 -0.38  -0.28   0.66   0.58 
  0.62   0.65  -0.45   0.03 
  0.31   0.76  -0.47  -0.32 
  0.17    0.3 -0.021  -0.94 
  0.03   0.36 -0.071  -0.93 
 -0.76   0.11 -0.041  -0.64 
 -0.55  -0.11  -0.29  -0.78 
 -0.43   0.24  -0.24  -0.84 
 -0.94    0.3  0.069   0.11 
 -0.36  -0.39  -0.78  -0.34 
 -0.13    0.6  -0.48  -0.63 

find 3-d Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...]
-0.02  0.60  0.69 
 0.04 -0.37 -0.66 
-0.74  0.15 -0.93 
-0.55  0.65  0.39 

========
Compute a new triangulation as a separate instance of Qhull
seed: 1595644032
input
-0.801  0.266  0.816 
 0.559  0.644  0.832 
-0.799 -0.987  0.864 
-0.678 -0.587 -0.573 
-0.354  0.674    0.8 
-0.511 -0.433   0.77 
 0.805 -0.236  0.175 
 0.637 -0.676  0.935 

Delaunay triangulation by the convex hull of 8 points in 4-d:

  Number of input sites: 8
  Number of Delaunay regions: 12

Statistics for:  | qhull s d Tcv 

  Number of points processed: 8
  Number of hyperplanes created: 29
  Number of facets in hull: 18
  Number of distance tests for qhull: 28
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1.4e-14 of
all facets.  Will make 96 distance computations.

8 vertices and 18 facets with normals:
 -0.24   0.52  -0.46   0.68 
 -0.91  -0.24   0.12  -0.31 
 -0.49    0.2  -0.02  -0.85 
 -0.27   0.19 -0.052  -0.94 
 0.063   -0.9  0.065  -0.43 
 0.028  -0.92  0.075  -0.39 
-0.086 -0.048   0.99  -0.11 
-0.033 0.0066   0.98  -0.18 
  0.13  0.076   0.69  -0.71 
  0.23 -0.066   0.78  -0.58 
 0.024  0.013   0.96  -0.26 
 0.099   0.71  -0.66  -0.24 
  0.46   0.12  -0.63   0.61 
 -0.12    0.5  -0.48   0.71 
  0.32   0.15  -0.57   0.74 
-0.074    0.2   0.95   0.21 
-0.039  0.091   0.99  0.068 
-0.033  0.076      1 -0.0011 

========
Free memory allocated by the new instance of Qhull, and redisplay the old results.



8 vertices and 16 facets with normals:
  0.44  -0.53 -0.014   0.72 
  0.34  -0.77   0.14   0.52 
-0.071  -0.12   0.39   0.91 
  -0.2 -0.037   0.42   0.88 
 -0.31  -0.32   0.65   0.62 
 -0.38  -0.28   0.66   0.58 
  0.62   0.65  -0.45   0.03 
  0.31   0.76  -0.47  -0.32 
  0.17    0.3 -0.021  -0.94 
  0.03   0.36 -0.071  -0.93 
 -0.76   0.11 -0.041  -0.64 
 -0.55  -0.11  -0.29  -0.78 
 -0.43   0.24  -0.24  -0.84 
 -0.94    0.3  0.069   0.11 
 -0.36  -0.39  -0.78  -0.34 
 -0.13    0.6  -0.48  -0.63 

========
compute halfspace intersection about the origin for a diamond
input as halfspace coefficients + offsets
    -1     -1     -1     -1 
     1     -1     -1     -1 
    -1      1     -1     -1 
     1      1     -1     -1 
    -1     -1      1     -1 
     1     -1      1     -1 
    -1      1      1     -1 
     1      1      1     -1 

Halfspace intersection by the convex hull of 8 points in 3-d:

  Number of halfspaces: 8
  Number of non-redundant halfspaces: 8
  Number of intersection points: 6
  Number of non-simplicial intersection points: 6

Statistics for:  | qhull H0 s Tcv Fp

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 96
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0

3
6
     0      0     -1 
     0     -1      0 
     1      0      0 
    -1      0      0 
     0      1      0 
     0      0      1 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.

8 vertices and 6 facets with normals:
    -0     -0     -1 
     0     -1      0 
     1     -0     -0 
    -1     -0     -0 
     0      1     -0 
    -0     -0      1 

==============================
========= user_eg2 ===========
==============================
bin/user_eg2

========
user_eg2 'cube qhull options' 'Delaunay options' 'halfspace options'

This is the output from user_eg2_r.c.  It shows how qhull() may be called from
an application, via Qhull's static, reentrant library.  user_eg2 is not part
of Qhull itself. If user_eg2 fails immediately, user_eg2_r.c was incorrectly
linked to Qhull's non-reentrant library, libqhullstatic.
Try -- user_eg2 'T1' 'T1' 'T1'


========
compute triangulated convex hull of cube after rotating input

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 96 distance computations.

8 vertices and 12 facets with normals:
    -0     -0     -1 
    -0     -0     -1 
     0     -1      0 
     0     -1      0 
     1     -0     -0 
     1     -0     -0 
    -1     -0     -0 
    -1     -0     -0 
     0      1     -0 
     0      1     -0 
    -0     -0      1 
    -0     -0      1 

add points in a diamond
9 vertices and 14 facets
10 vertices and 16 facets
11 vertices and 16 facets
12 vertices and 16 facets
13 vertices and 14 facets
14 vertices and 12 facets

14 vertices and 12 facets with normals:
  0.71  -0.71     -0 
 -0.71  -0.71      0 
 -0.71   0.71     -0 
  0.71   0.71     -0 
 -0.71     -0  -0.71 
    -0   0.71  -0.71 
     0  -0.71  -0.71 
  0.71      0  -0.71 
    -0  -0.71   0.71 
 -0.71      0   0.71 
  0.71      0   0.71 
    -0   0.71   0.71 

Convex hull of 14 points in 3-d:

  Number of vertices: 14
  Number of facets: 12
  Number of non-simplicial facets: 12

Statistics for: user_eg2 cube example | qhull s Tcv Q11  

  Number of points processed: 14
  Number of hyperplanes created: 23
  Number of distance tests for qhull: 64
  Number of distance tests for merging: 276
  Number of distance tests for checking: 324
  Number of merged facets: 18
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 168 distance computations.

========
compute 2-d Delaunay triangulation
seed: 1595644031

8 vertices and 12 facets with normals:
 -0.17   0.61   0.77 
  0.39  -0.56   0.73 
  0.19  -0.23  -0.95 
   0.4   0.75  -0.52 
  0.63  -0.77  0.026 
  0.21  -0.24  -0.95 
 -0.23   0.64   0.73 
 -0.44   0.78   0.45 
 -0.45  -0.16  -0.88 
 -0.57 -0.097  -0.82 
 -0.69  -0.58  -0.42 
 -0.83   -0.2  -0.53 

Delaunay triangulation by the convex hull of 8 points in 3-d:

  Number of input sites: 8
  Number of Delaunay regions: 7

Statistics for: user_eg2 Delaunay example | qhull s d Tcv 

  Number of points processed: 8
  Number of hyperplanes created: 18
  Number of facets in hull: 12
  Number of distance tests for qhull: 34
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 3.8e-15 of
all facets.  Will make 56 distance computations.

========
add points to triangulation
added point p8:        -1  -0.7369    1.543
9 points, 0 extra points, 9 vertices, and 14 facets in total
added point p9:    0.5112  -0.0827   0.2682
10 points, 0 extra points, 10 vertices, and 16 facets in total
added point p10:   0.06553  -0.5621   0.3202
11 points, 0 extra points, 11 vertices, and 18 facets in total
added point p11:   -0.9059   0.3577   0.9486
12 points, 0 extra points, 12 vertices, and 20 facets in total
added point p12:    0.3586   0.8694   0.8844
13 points, 0 extra points, 13 vertices, and 22 facets in total
added point p13:    -0.233  0.03883   0.0558
14 points, 0 extra points, 14 vertices, and 24 facets in total

find Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...]
 0.36  0.87 
 0.65  0.39 
-0.02  0.60 

Delaunay triangulation by the convex hull of 14 points in 3-d:

  Number of input sites: 14
  Number of Delaunay regions: 20

Statistics for: user_eg2 Delaunay example | qhull s d Tcv 

  Number of points processed: 14
  Number of hyperplanes created: 53
  Number of facets in hull: 24
  Number of distance tests for qhull: 84
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 3.8e-15 of
all facets.  Will make 280 distance computations.

========
compute halfspace intersection about the origin for a diamond

Halfspace intersection by the convex hull of 8 points in 3-d:

  Number of halfspaces: 8
  Number of non-redundant halfspaces: 8
  Number of intersection points: 6
  Number of non-simplicial intersection points: 6

Statistics for: user_eg2 halfspace example | qhull H0 s Tcv 

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 96
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input): 0.001


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.

========
add halfspaces for cube to intersection
added offset -1 and normal    1.732        0        0
8 points, 1 extra points, 9 vertices, and 9 facets in total
added offset -1 and normal   -1.732        0        0
8 points, 2 extra points, 10 vertices, and 12 facets in total
added offset -1 and normal        0    1.732        0
8 points, 3 extra points, 11 vertices, and 15 facets in total
added offset -1 and normal        0   -1.732        0
8 points, 4 extra points, 12 vertices, and 18 facets in total
added offset -1 and normal        0        0    1.732
8 points, 5 extra points, 13 vertices, and 21 facets in total
added offset -1 and normal        0        0   -1.732
8 points, 6 extra points, 14 vertices, and 24 facets in total

Halfspace intersection by the convex hull of 14 points in 3-d:

  Number of halfspaces: 14
  Number of non-redundant halfspaces: 14
  Number of intersection points: 24

Statistics for: user_eg2 halfspace example | qhull H0 s Tcv 

  Number of points processed: 14
  Number of hyperplanes created: 35
  Number of distance tests for qhull: 58
  Number of distance tests for merging: 248
  Number of distance tests for checking: 256
  Number of merged facets: 6
  CPU seconds to compute hull (after input): 0.001


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 192 distance computations.

==============================
========= user_eg3 ===========
==============================
bin/user_eg3

========
user_eg3 commands... -- demonstrate calling rbox and qhull from C++.

user_eg3 is statically linked to qhullcpp and reentrant qhull.  If user_eg3
fails immediately, it is probably linked to the non-reentrant qhull library.

Commands:
  eg-100               Run the example in qh-code.htm
  eg-convex            'rbox d | qconvex o' with std::vector and C++ classes
  eg-delaunay          'rbox y c | qdelaunay o' with std::vector and C++ classes
  eg-voronoi           'rbox y c | qvoronoi o' with std::vector and C++ classes
  eg-fifo              'rbox y c | qvoronoi FN Fi Fo' with QhullUser and qh_fprintf

Rbox and Qhull commands:
  rbox "200 D4" ...    Generate points from rbox
  qhull "d p" ...      Run qhull with options and produce output
  qhull-cout "o" ...   Run qhull with options and produce output to cout
  qhull "T1" ...       Run qhull with level-1 trace to cerr
  qhull-cout "T1z" ... Run qhull with level-1 trace to cout
  facets               Print qhull's facets when done

For example
  user_eg3 rbox qhull
  user_eg3 rbox qhull T1
  user_eg3 rbox qhull d
  user_eg3 rbox D2 10 2 "s r 5" qhull "s p" facets
  user_eg3 eg-convex
  user_eg3 rbox 10 eg-delaunay qhull "d o"
  user_eg3 rbox D5 c P2 qhull d eg-delaunay
  user_eg3 rbox "D5 c P2" qhull v eg-voronoi o
  user_eg3 rbox D2 10 qhull "v" eg-fifo p Fi Fo
bin/user_eg3 rbox "10 D2"  "2 D2" qhull "s p" facets
rbox 10 D2
rbox 2 D2

Results of s p

Convex hull of 12 points in 2-d:

  Number of vertices: 5
  Number of facets: 5

Statistics for: rbox "10 D2" "2 D2 D2" | qhull s p

  Number of points processed: 5
  Number of hyperplanes created: 8
  Number of distance tests for qhull: 56
  CPU seconds to compute hull (after input):  0

2
5
-0.02222276248244826 -0.4979727817680433 
-0.4285431913366012 0.4745826469497594 
0.3790312361708201 0.3779794437605696 
0.3443122672329771 -0.1437312230875075 
-0.4999921736307369 -0.3684622117955817 

Facets created by Qhull::runQhull()
- f2
    - flags: top simplicial
    - normal:  -0.996428 0.0844484
    - offset:  -0.46709
    - vertices: p1(v3) p10(v1)
    - neighboring facets: f4 f3
- f3
    - flags: bottom simplicial
    - normal:  0.118775 0.992921
    - offset:  -0.420323
    - vertices: p1(v3) p4(v2)
    - neighboring facets: f6 f2
- f4
    - flags: bottom simplicial
    - normal:  -0.261631 -0.965168
    - offset:  -0.486442
    - vertices: p0(v4) p10(v1)
    - neighboring facets: f2 f7
- f6
    - flags: top simplicial
    - normal:  0.997793 -0.0664014
    - offset:  -0.353096
    - vertices: p8(v5) p4(v2)
    - neighboring facets: f3 f7
- f7
    - flags: bottom simplicial
    - normal:  0.694945 -0.719063
    - offset:  -0.34263
    - vertices: p8(v5) p0(v4)
    - neighboring facets: f4 f6
================================================
== make testall, after running qtest and test ==
================================================
== Fri, Jul 24, 2020 10:27:12 PM

eg/q_eg
eg/q_eg: Temporarily add "$PWD/bin" to $PATH for access to qconvex,etc.
==============================
========= eg/q_eg ============
== Create geomview examples ==
==============================

rbox c D3 | qconvex s G >eg/eg.01.cube

Convex hull of 8 points in 3-d:

  Number of vertices: 8
  Number of facets: 6
  Number of non-simplicial facets: 6

Statistics for: rbox c D3 | qconvex s G

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 90
  Number of distance tests for checking: 48
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0

rbox c d G2.0 | qconvex s G >eg/eg.02.diamond.cube

Convex hull of 14 points in 3-d:

  Number of vertices: 6
  Number of facets: 8

Statistics for: rbox c d G2.0 | qconvex s G

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 88
  Number of distance tests for merging: 51
  Number of distance tests for checking: 48
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0

rbox s 100 D3 | qconvex s G >eg/eg.03.sphere

Convex hull of 100 points in 3-d:

  Number of vertices: 100
  Number of facets: 196

Statistics for: rbox s 100 D3 | qconvex s G

  Number of points processed: 100
  Number of hyperplanes created: 502
  Number of distance tests for qhull: 1630
  CPU seconds to compute hull (after input):  0

rbox s 100 D2 | qconvex s G >eg/eg.04.circle

Convex hull of 100 points in 2-d:

  Number of vertices: 100
  Number of facets: 100

Statistics for: rbox s 100 D2 | qconvex s G

  Number of points processed: 100
  Number of hyperplanes created: 198
  Number of distance tests for qhull: 890
  CPU seconds to compute hull (after input):  0

rbox 10 l | qconvex s G >eg/eg.05.spiral 

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 10 l | qconvex s G

  Number of points processed: 10
  Number of hyperplanes created: 25
  Number of distance tests for qhull: 39
  CPU seconds to compute hull (after input):  0

rbox 1000 D2 | qconvex s C-0.03 Qc Gapcv >eg/eg.06.merge.square

Convex hull of 1000 points in 2-d:

  Number of vertices: 4
  Number of coplanar points: 103
  Number of facets: 4

Statistics for: rbox 1000 D2 | qconvex s C-0.03 Qc Gapcv

  Number of points processed: 6
  Number of hyperplanes created: 7
  Number of distance tests for qhull: 11448
  Number of distance tests for merging: 41
  Number of distance tests for checking: 3540
  Number of merged facets: 2
  CPU seconds to compute hull (after input):  0
  Maximum distance of point above facet: 0.019 (0.3x)
  Maximum distance of vertex below facet: -0.019 (0.3x)

rbox 1000 D3 | qconvex s G >eg/eg.07.box 

Convex hull of 1000 points in 3-d:

  Number of vertices: 73
  Number of facets: 142

Statistics for: rbox 1000 D3 | qconvex s G

  Number of points processed: 81
  Number of hyperplanes created: 367
  Number of distance tests for qhull: 12879
  CPU seconds to compute hull (after input): 0.001

rbox c G0.4 s 500 | qconvex s G >eg/eg.08a.cube.sphere

Convex hull of 508 points in 3-d:

  Number of vertices: 63
  Number of facets: 122

Statistics for: rbox c G0.4 s 500 | qconvex s G

  Number of points processed: 99
  Number of hyperplanes created: 443
  Number of distance tests for qhull: 9651
  CPU seconds to compute hull (after input):  0

rbox d G0.6 s 500 | qconvex s G >eg/eg.08b.diamond.sphere

Convex hull of 506 points in 3-d:

  Number of vertices: 397
  Number of facets: 790

Statistics for: rbox d G0.6 s 500 | qconvex s G

  Number of points processed: 407
  Number of hyperplanes created: 2053
  Number of distance tests for qhull: 9900
  Number of distance tests for merging: 8243
  Number of distance tests for checking: 4671
  Number of merged facets: 1
  CPU seconds to compute hull (after input): 0.002

rbox 100 L3 G0.5 s | qconvex s G >eg/eg.09.lens

Convex hull of 100 points in 3-d:

  Number of vertices: 100
  Number of facets: 196

Statistics for: rbox 100 L3 G0.5 s | qconvex s G

  Number of points processed: 100
  Number of hyperplanes created: 483
  Number of distance tests for qhull: 1641
  CPU seconds to compute hull (after input):  0

rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG0 >eg/eg.10a.sphere.visible

Convex hull of 100 points in 3-d:

  Number of vertices: 100
  Number of facets: 196
  Number of 'good' facets: 44

Statistics for: rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG0

  Number of points processed: 100
  Number of hyperplanes created: 512
  Number of distance tests for qhull: 1703
  CPU seconds to compute hull (after input):  0

rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG-0 >eg/eg.10b.sphere.beyond

Convex hull of 100 points in 3-d:

  Number of vertices: 100
  Number of facets: 196
  Number of 'good' facets: 152

Statistics for: rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG-0

  Number of points processed: 100
  Number of hyperplanes created: 512
  Number of distance tests for qhull: 1703
  CPU seconds to compute hull (after input):  0

rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG0 PG >eg/eg.10c.sphere.horizon

Convex hull of 100 points in 3-d:

  Number of vertices: 100
  Number of facets: 196
  Number of 'good' facets: 44

Statistics for: rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG0 PG

  Number of points processed: 100
  Number of hyperplanes created: 512
  Number of distance tests for qhull: 1703
  CPU seconds to compute hull (after input):  0

rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QV0 PgG >eg/eg.10d.sphere.cone

Convex hull of 101 points in 3-d:

  Number of vertices: 85
  Number of facets: 166
  Number of 'good' facets: 14

Statistics for: rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QV0 PgG

  Number of points processed: 88
  Number of hyperplanes created: 429
  Number of distance tests for qhull: 1586
  CPU seconds to compute hull (after input):  0

rbox 100 s P0.5,0.5,0.5 | qconvex s Ga >eg/eg.10e.sphere.new

Convex hull of 101 points in 3-d:

  Number of vertices: 85
  Number of facets: 166

Statistics for: rbox 100 s P0.5,0.5,0.5 | qconvex s Ga

  Number of points processed: 88
  Number of hyperplanes created: 429
  Number of distance tests for qhull: 1586
  CPU seconds to compute hull (after input):  0

rbox 100 s P0.5,0.5,0.5 | qhull s Ga QV0g Q0 >eg/eg.14.sphere.corner

Convex hull of 101 points in 3-d:

  Number of vertices: 42
  Number of facets: 80
  Number of 'good' facets: 14

Statistics for: rbox 100 s P0.5,0.5,0.5 | qhull s Ga QV0g Q0

  Number of points processed: 45
  Number of hyperplanes created: 194
  Number of distance tests for qhull: 1426
  CPU seconds to compute hull (after input):  0

rbox 500 W0 | qconvex s QR0 Qc Gvp >eg/eg.15a.surface

Convex hull of 500 points in 3-d:

  Number of vertices: 66
  Number of coplanar points: 434
  Number of facets: 80
  Number of non-simplicial facets: 6

Statistics for: rbox 500 W0 | qconvex s QR0 Qc Gvp QR1595644033

  Number of points processed: 73
  Number of hyperplanes created: 223
  Number of distance tests for qhull: 8533
  Number of distance tests for merging: 2022
  Number of distance tests for checking: 6699
  Number of merged facets: 62
  CPU seconds to compute hull (after input): 0.001

rbox 500 W0 | qconvex s QR0 Qt Qc Gvp >eg/eg.15b.triangle

Convex hull of 500 points in 3-d:

  Number of vertices: 66
  Number of coplanar points: 434
  Number of facets: 128
  Number of triangulated facets: 6

Statistics for: rbox 500 W0 | qconvex s QR0 Qt Qc Gvp QR1595644033

  Number of points processed: 73
  Number of hyperplanes created: 223
  Number of distance tests for qhull: 8533
  Number of distance tests for merging: 2022
  Number of distance tests for checking: 6699
  Number of merged facets: 62
  CPU seconds to compute hull (after input):  0

rbox 500 W0 | qconvex s QR0 QJ5e-2 Qc Gvp >eg/eg.15c.joggle

Convex hull of 500 points in 3-d:

  Number of vertices: 76
  Number of coplanar points: 424
  Number of facets: 148

Statistics for: rbox 500 W0 | qconvex s QR0 QJ5e-2 Qc Gvp QR1595644033

  Number of points processed: 89
  Number of hyperplanes created: 409
  Number of distance tests for qhull: 18381
  CPU seconds to compute hull (after input):  0
  Input joggled by: 0.05

echo 2 = rbox 6 r s D2, rbox 15 B0.3 W0.25, c G0.5 >eg/eg.data.17
echo 25 >>eg/eg.data.17
rbox 15 D2 B0.3 W0.25 c G0.5 | tail -n +3 >>eg/eg.data.17
rbox 6 r s D2 B0.2 | tail -n +3 >>eg/eg.data.17
qdelaunay s Qt <eg/eg.data.17 GnraD2 >eg/eg.17a.delaunay.2

Delaunay triangulation by the convex hull of 25 points in 3-d:

  Number of input sites: 25
  Number of Delaunay regions: 44
  Number of triangulated facets: 1

Statistics for: = rbox 6 r s D2, rbox 15 B0.3 W0.25, c G0.5 | qdelaunay s Qt GnraD2

  Number of points processed: 25
  Number of hyperplanes created: 89
  Number of facets in hull: 46
  Number of distance tests for qhull: 287
  Number of distance tests for merging: 487
  Number of distance tests for checking: 282
  Number of merged facets: 4
  CPU seconds to compute hull (after input):  0

qdelaunay s <eg/eg.data.17 GnraD2 >eg/eg.17b.delaunay.2i

Delaunay triangulation by the convex hull of 25 points in 3-d:

  Number of input sites: 25
  Number of Delaunay regions: 41
  Number of non-simplicial Delaunay regions: 1

Statistics for: = rbox 6 r s D2, rbox 15 B0.3 W0.25, c G0.5 | qdelaunay s GnraD2

  Number of points processed: 25
  Number of hyperplanes created: 89
  Number of facets in hull: 42
  Number of distance tests for qhull: 287
  Number of distance tests for merging: 487
  Number of distance tests for checking: 282
  Number of merged facets: 4
  CPU seconds to compute hull (after input):  0

qdelaunay s <eg/eg.data.17 C-0 Ga >eg/eg.17c.delaunay.2-3

Delaunay triangulation by the convex hull of 25 points in 3-d:

  Number of input sites: 25
  Number of Delaunay regions: 0
  Number of non-simplicial Delaunay regions: 2

Statistics for: = rbox 6 r s D2, rbox 15 B0.3 W0.25, c G0.5 | qdelaunay s C-0 Ga

  Number of points processed: 25
  Number of hyperplanes created: 89
  Number of facets in hull: 42
  Number of distance tests for qhull: 287
  Number of distance tests for merging: 487
  Number of distance tests for checking: 282
  Number of merged facets: 4
  CPU seconds to compute hull (after input):  0

qvoronoi s QJ <eg/eg.data.17 Gna >eg/eg.17d.voronoi.2

Voronoi diagram by the convex hull of 25 points in 3-d:

  Number of Voronoi regions: 25
  Number of Voronoi vertices: 44

Statistics for: = rbox 6 r s D2, rbox 15 B0.3 W0.25, c G0.5 | qvoronoi s QJ Gna

  Number of points processed: 25
  Number of hyperplanes created: 110
  Number of facets in hull: 46
  Number of distance tests for qhull: 281
  CPU seconds to compute hull (after input): 0.001
  Input joggled by: 4.2e-11

qvoronoi s <eg/eg.data.17 Gna >eg/eg.17e.voronoi.2i

Voronoi diagram by the convex hull of 25 points in 3-d:

  Number of Voronoi regions: 25
  Number of Voronoi vertices: 41
  Number of non-simplicial Voronoi vertices: 1

Statistics for: = rbox 6 r s D2, rbox 15 B0.3 W0.25, c G0.5 | qvoronoi s Gna

  Number of points processed: 25
  Number of hyperplanes created: 89
  Number of facets in hull: 42
  Number of distance tests for qhull: 287
  Number of distance tests for merging: 487
  Number of distance tests for checking: 282
  Number of merged facets: 4
  CPU seconds to compute hull (after input):  0

rbox c G0.1 d | qdelaunay Gt Qz >eg/eg.17f.delaunay.3
rbox 10 D2 d | qdelaunay s Qu G >eg/eg.18a.furthest.2-3

Furthest-site Delaunay triangulation by the convex hull of 14 points in 3-d:

  Number of input sites: 14
  Number of Delaunay regions: 0

Statistics for: rbox 10 D2 d | qdelaunay s Qu G

  Number of points processed: 14
  Number of hyperplanes created: 50
  Number of facets in hull: 24
  Number of distance tests for qhull: 96
  Number of distance tests for merging: 229
  Number of distance tests for checking: 138
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0

rbox 10 D2 d | qdelaunay s Qu Pd2 G >eg/eg.18b.furthest-up.2-3

Furthest-site Delaunay triangulation by the convex hull of 14 points in 3-d:

  Number of input sites: 14
  Number of Delaunay regions: 7

Statistics for: rbox 10 D2 d | qdelaunay s Qu Pd2 G

  Number of points processed: 14
  Number of hyperplanes created: 50
  Number of facets in hull: 24
  Number of distance tests for qhull: 96
  Number of distance tests for merging: 229
  Number of distance tests for checking: 138
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0

rbox 10 D2 d | qvoronoi s Qu Gv >eg/eg.18c.furthest.2 

Furthest-site Voronoi vertices by the convex hull of 14 points in 3-d:

  Number of Voronoi regions: 14
  Number of Voronoi vertices: 7

Statistics for: rbox 10 D2 d | qvoronoi s Qu Gv

  Number of points processed: 14
  Number of hyperplanes created: 50
  Number of facets in hull: 24
  Number of distance tests for qhull: 96
  Number of distance tests for merging: 229
  Number of distance tests for checking: 138
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0

rbox 10 D3 | qvoronoi s FQ QV5 p | qconvex s G >eg/eg.19.voronoi.region.3

Voronoi diagram by the convex hull of 10 points in 4-d:

  Number of Voronoi regions: 10
  Number of 'good' Voronoi vertices: 10

Statistics for: rbox 10 D3 | qvoronoi s FQ QV5 p

  Number of points processed: 10
  Number of hyperplanes created: 43
  Number of facets in hull: 27
  Number of distance tests for qhull: 66
  CPU seconds to compute hull (after input):  0


Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 9
  Number of non-simplicial facets: 5

Statistics for: rbox 10 D3 | qvoronoi s FQ QV5 p | qconvex s G

  Number of points processed: 10
  Number of hyperplanes created: 17
  Number of distance tests for qhull: 44
  Number of distance tests for merging: 135
  Number of distance tests for checking: 79
  Number of merged facets: 7
  CPU seconds to compute hull (after input):  0

rbox r s 20 Z1 G0.2 | qconvex s QR1 G >eg/eg.20.cone

Convex hull of 41 points in 3-d:

  Number of vertices: 41
  Number of facets: 41
  Number of non-simplicial facets: 21

Statistics for: rbox r s 20 Z1 G0.2 | qconvex s QR1 G QR1

  Number of points processed: 41
  Number of hyperplanes created: 117
  Number of distance tests for qhull: 630
  Number of distance tests for merging: 1607
  Number of distance tests for checking: 680
  Number of merged facets: 61
  CPU seconds to compute hull (after input):  0

rbox 200 s | qconvex s Qc R0.014 Gpav >eg/eg.21b.roundoff.fixed

Convex hull of 200 points in 3-d:

  Number of vertices: 65
  Number of coplanar points: 135
  Number of facets: 59
  Number of non-simplicial facets: 41

Statistics for: rbox 200 s | qconvex s Qc R0.014 Gpav

  Number of points processed: 71
  Number of hyperplanes created: 298
  Number of distance tests for qhull: 11700
  Number of distance tests for merging: 4151
  Number of distance tests for checking: 5318
  Number of merged facets: 153
  CPU seconds to compute hull (after input): 0.001
  Maximum distance of point above facet: 0.047 (0.8x)
  Maximum distance of vertex below facet: -0.075 (1.3x)

rbox 1000 s| qconvex s C0.01 Qc Gcrp >eg/eg.22a.merge.sphere.01

Convex hull of 1000 points in 3-d:

  Number of vertices: 224
  Number of coplanar points: 776
  Number of facets: 119
  Number of non-simplicial facets: 117

Statistics for: rbox 1000 s | qconvex s C0.01 Qc Gcrp

  Number of points processed: 1000
  Number of hyperplanes created: 5544
  Number of distance tests for qhull: 122395
  Number of distance tests for merging: 77744
  Number of distance tests for checking: 7926
  Number of merged facets: 1877
  CPU seconds to compute hull (after input): 0.009
  Maximum distance of vertex below facet: -0.041 (1.4x)

rbox 1000 s| qconvex s C-0.01 Qc Gcrp >eg/eg.22b.merge.sphere.-01

Convex hull of 1000 points in 3-d:

  Number of vertices: 103
  Number of coplanar points: 897
  Number of facets: 96
  Number of non-simplicial facets: 77

Statistics for: rbox 1000 s | qconvex s C-0.01 Qc Gcrp

  Number of points processed: 105
  Number of hyperplanes created: 447
  Number of distance tests for qhull: 60561
  Number of distance tests for merging: 6257
  Number of distance tests for checking: 21333
  Number of merged facets: 240
  CPU seconds to compute hull (after input): 0.002
  Maximum distance of point above facet: 0.025 (0.8x)
  Maximum distance of vertex below facet: -0.03 (1.0x)

rbox 1000 s| qconvex s C0.05 Qc Gcrpv >eg/eg.22c.merge.sphere.05

Convex hull of 1000 points in 3-d:

  Number of vertices: 36
  Number of coplanar points: 964
  Number of facets: 20
  Number of non-simplicial facets: 20

Statistics for: rbox 1000 s | qconvex s C0.05 Qc Gcrpv

  Number of points processed: 1000
  Number of hyperplanes created: 5544
  Number of distance tests for qhull: 50001
  Number of distance tests for merging: 82257
  Number of distance tests for checking: 7446
  Number of merged facets: 1976
  CPU seconds to compute hull (after input): 0.015
  Maximum distance of vertex below facet: -0.21 (1.4x)

rbox 1000 s| qconvex s C-0.05 Qc Gcrpv >eg/eg.22d.merge.sphere.-05

Convex hull of 1000 points in 3-d:

  Number of vertices: 18
  Number of coplanar points: 982
  Number of facets: 15
  Number of non-simplicial facets: 13

Statistics for: rbox 1000 s | qconvex s C-0.05 Qc Gcrpv

  Number of points processed: 22
  Number of hyperplanes created: 68
  Number of distance tests for qhull: 41237
  Number of distance tests for merging: 1029
  Number of distance tests for checking: 12702
  Number of merged facets: 41
  CPU seconds to compute hull (after input): 0.002
  Maximum distance of point above facet: 0.14 (0.9x)
  Maximum distance of vertex below facet: -0.15 (1.0x)

rbox 1000 | qconvex s Gcprvah C0.1 Qc >eg/eg.23.merge.cube

Convex hull of 1000 points in 3-d:

  Number of vertices: 8
  Number of coplanar points: 743
  Number of facets: 6
  Number of non-simplicial facets: 6

Statistics for: rbox 1000 | qconvex s Gcprvah C0.1 Qc

  Number of points processed: 95
  Number of hyperplanes created: 453
  Number of distance tests for qhull: 59218
  Number of distance tests for merging: 5460
  Number of distance tests for checking: 6022
  Number of merged facets: 146
  CPU seconds to compute hull (after input): 0.002
  Maximum distance of vertex below facet: -0.18 (0.6x)

rbox 5000 D4 | qconvex s GD0v Pd0:0.5 C-0.02 C0.1 >eg/eg.24.merge.cube.4d-in-3d

Convex hull of 5000 points in 4-d:

  Number of vertices: 16
  Number of facets: 8
  Number of 'good' facets: 1
  Number of 'good' non-simplicial facets: 1

Statistics for: rbox 5000 D4 | qconvex s GD0v Pd0:0.5 C-0.02 C0.1

  Number of points processed: 28
  Number of hyperplanes created: 161
  Number of distance tests for qhull: 606114
  Number of distance tests for merging: 8562
  Number of distance tests for checking: 40020
  Number of merged facets: 159
  CPU seconds to compute hull (after input): 0.012
  Maximum distance of point above facet: 0.14 (0.4x)
  Maximum distance of vertex below facet: -0.28 (0.7x)

rbox 5000 D4 | qconvex s s C-0.02 C0.1 Gh >eg/eg.30.4d.merge.cube

Convex hull of 5000 points in 4-d:

  Number of vertices: 16
  Number of facets: 8
  Number of non-simplicial facets: 8

Statistics for: rbox 5000 D4 | qconvex s s C-0.02 C0.1 Gh

  Number of points processed: 28
  Number of hyperplanes created: 161
  Number of distance tests for qhull: 606114
  Number of distance tests for merging: 8562
  Number of distance tests for checking: 40020
  Number of merged facets: 159
  CPU seconds to compute hull (after input): 0.012
  Maximum distance of point above facet: 0.14 (0.4x)
  Maximum distance of vertex below facet: -0.28 (0.7x)

rbox 20 D3 | qdelaunay s G >eg/eg.31.4d.delaunay

Delaunay triangulation by the convex hull of 20 points in 4-d:

  Number of input sites: 20
  Number of Delaunay regions: 0

Statistics for: rbox 20 D3 | qdelaunay s G

  Number of points processed: 20
  Number of hyperplanes created: 162
  Number of facets in hull: 81
  Number of distance tests for qhull: 303
  CPU seconds to compute hull (after input):  0

rbox 30 s D4 | qconvex s G Pd0d1d2D3 >eg/eg.32.4d.octant

Convex hull of 30 points in 4-d:

  Number of vertices: 30
  Number of facets: 138
  Number of 'good' facets: 9

Statistics for: rbox 30 s D4 | qconvex s G Pd0d1d2D3

  Number of points processed: 30
  Number of hyperplanes created: 340
  Number of distance tests for qhull: 649
  CPU seconds to compute hull (after input):  0

rbox 10 r s Z1 G0.3 | qconvex G >eg/eg.33a.cone
rbox 10 r s Z1 G0.3 | qconvex FQ FV n | qhalf G >eg/eg.33b.cone.dual
rbox 10 r s Z1 G0.3 | qconvex FQ FV n | qhalf FQ s Fp | qconvex G >eg/eg.33c.cone.halfspace

Halfspace intersection by the convex hull of 21 points in 3-d:

  Number of halfspaces: 21
  Number of non-redundant halfspaces: 21
  Number of intersection points: 21
  Number of non-simplicial intersection points: 11

Statistics for: rbox 10 r s Z1 G0.3 | qconvex FQ FV n | qhalf FQ s Fp

  Number of points processed: 21
  Number of hyperplanes created: 49
  Number of distance tests for qhull: 170
  Number of distance tests for merging: 445
  Number of distance tests for checking: 240
  Number of merged facets: 17
  CPU seconds to compute hull (after input):  0


echo ==the following should generate flipped and concave facets== >/dev/null
rbox 200 s | qhull Q0 s R0.014 Gav Po >eg/eg.21a.roundoff.errors
QH6136 qhull precision error: facet f577 is flipped, distance= 0.444437742328
QH6136 qhull precision error: facet f598 is flipped, distance= 0.397912421371
QH6115 qhull precision error: f136 is concave to f206, since p13(v33) is 0.04846 above f206
QH6115 qhull precision error: f175 is concave to f491, since p63(v41) is 0.02842 above f491
QH6115 qhull precision error: f188 is concave to f357, since p13(v33) is 0.05044 above f357
QH6115 qhull precision error: f192 is concave to f430, since p165(v44) is 0.01805 above f430
QH6115 qhull precision error: f206 is concave to f136, since p51(v47) is 0.007003 above f136
QH6115 qhull precision error: f231 is concave to f495, since p53(v5) is 0.01049 above f495
QH6115 qhull precision error: f264 is concave to f539, since p70(v31) is 0.02908 above f539
QH6115 qhull precision error: f275 is concave to f442, since p176(v60) is 0.03539 above f442
QH6115 qhull precision error: f276 is concave to f256, since p131(v61) is 0.01036 above f256
QH6115 qhull precision error: f294 is concave to f465, since p13(v33) is 0.009524 above f465
QH6115 qhull precision error: f307 is concave to f485, since p99(v67) is 0.0106 above f485
QH6115 qhull precision error: f311 is concave to f476, since p87(v16) is 0.03213 above f476
QH6115 qhull precision error: f345 is concave to f344, since p13(v33) is 0.01277 above f344
QH6115 qhull precision error: f357 is concave to f188, since p23(v76) is 0.008612 above f188
QH6115 qhull precision error: f381 is concave to f512, since p161(v13) is 0.05502 above f512
QH6115 qhull precision error: f386 is concave to f532, since p152(v82) is 0.01786 above f532
QH6115 qhull precision error: f436 is concave to f461, since p173(v92) is 0.007229 above f461
QH6115 qhull precision error: f436 is concave to f591, since p109(v11) is 0.04018 above f591
QH6115 qhull precision error: f488 is concave to f487, since p180(v32) is 0.01013 above f487
QH6115 qhull precision error: f539 is concave to f264, since p90(v113) is 0.01548 above f264
QH6115 qhull precision error: f549 is concave to f592, since p81(v95) is 0.0117 above f592
QH6115 qhull precision error: f562 is concave to f460, since p21(v117) is 0.007454 above f460
QH6115 qhull precision error: f563 is concave to f595, since p91(v49) is 0.03273 above f595
QH6115 qhull precision error: f569 is concave to f329, since p62(v119) is 0.007692 above f329
QH6113 qhull precision error: f577 is flipped (interior point is outside)
QH6113 qhull precision error: f598 is flipped (interior point is outside)
QH6115 qhull precision error: f603 is concave to f605, since p79(v52) is 0.01194 above f605

Convex hull of 200 points in 3-d:

  Number of vertices: 128
  Number of facets: 252

Statistics for: rbox 200 s | qhull Q0 s R0.014 Gav Po

  Number of points processed: 128
  Number of hyperplanes created: 610
  Number of distance tests for qhull: 4539
  CPU seconds to compute hull (after input):  0


precision problems (corrected unless 'Q0' or an error)
    101 coplanar half ridges in output
     25 concave half ridges in output
      2 flipped facets
    112 coplanar horizon facets for new vertices
     72 coplanar points during partitioning
echo ==the preceding should report flipped and concave facets== >/dev/null
echo END eg/q_eg >/dev/null



eg/q_egtest
eg/q_egtest: Temporarily add "$PWD/bin" to $PATH for access to qconvex,etc.
==============================
========= eg/q_egtest ========
== Create geomview tests =====
==============================

rbox d D3 | qconvex s Gnrv Tc Tv >eg/eg.t01.spheres.3

Convex hull of 6 points in 3-d:

  Number of vertices: 6
  Number of facets: 8

Statistics for: rbox d D3 | qconvex s Gnrv Tc Tv

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 10
  Number of distance tests for merging: 59
  Number of distance tests for checking: 54
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.
rbox d D2 | qconvex s Gnv  Tc Tv >eg/eg.t02.spheres.2

Convex hull of 4 points in 2-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox d D2 | qconvex s Gnv Tc Tv

  Number of points processed: 4
  Number of hyperplanes created: 5
  Number of distance tests for qhull: 3
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1.3e-15 of
all facets.  Will make 16 distance computations.
rbox d D3 | qconvex s Gnrp Tc Tv >eg/eg.t03.points.3

Convex hull of 6 points in 3-d:

  Number of vertices: 6
  Number of facets: 8

Statistics for: rbox d D3 | qconvex s Gnrp Tc Tv

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 10
  Number of distance tests for merging: 59
  Number of distance tests for checking: 54
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.
rbox d D2 | qconvex s Gnp Tc Tv >eg/eg.t04.points.2

Convex hull of 4 points in 2-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox d D2 | qconvex s Gnp Tc Tv

  Number of points processed: 4
  Number of hyperplanes created: 5
  Number of distance tests for qhull: 3
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1.3e-15 of
all facets.  Will make 16 distance computations.
rbox c D4 | qconvex s C0.05 GnpcD3 Pd3:0.5 Tc Tv >eg/eg.t05.centrum.points.4-3

Convex hull of 16 points in 4-d:

  Number of vertices: 16
  Number of facets: 8
  Number of 'good' facets: 1
  Number of 'good' non-simplicial facets: 1

Statistics for: rbox c D4 | qconvex s C0.05 GnpcD3 Pd3:0.5 Tc Tv

  Number of points processed: 16
  Number of hyperplanes created: 25
  Number of distance tests for qhull: 167
  Number of distance tests for merging: 565
  Number of distance tests for checking: 532
  Number of merged facets: 36
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 16 distance computations.
rbox d D3 | qconvex s Gnrc Tc Tv >eg/eg.t06.centrums.3.precise

Convex hull of 6 points in 3-d:

  Number of vertices: 6
  Number of facets: 8

Statistics for: rbox d D3 | qconvex s Gnrc Tc Tv

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 10
  Number of distance tests for merging: 59
  Number of distance tests for checking: 54
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.
rbox d D3 | qconvex s C0.05 Gnrc Tc Tv >eg/eg.t07.centrums.3

Convex hull of 6 points in 3-d:

  Number of vertices: 6
  Number of facets: 8

Statistics for: rbox d D3 | qconvex s C0.05 Gnrc Tc Tv

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 10
  Number of distance tests for merging: 93
  Number of distance tests for checking: 130
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.
rbox d D2 | qconvex s C0.05 Gc Tc Tv >eg/eg.t08.centrums.2

Convex hull of 4 points in 2-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox d D2 | qconvex s C0.05 Gc Tc Tv

  Number of points processed: 4
  Number of hyperplanes created: 5
  Number of distance tests for qhull: 3
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 16 distance computations.
rbox d D3 | qconvex s Gnha Tc Tv >eg/eg.t09.intersect.3

Convex hull of 6 points in 3-d:

  Number of vertices: 6
  Number of facets: 8

Statistics for: rbox d D3 | qconvex s Gnha Tc Tv

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 10
  Number of distance tests for merging: 59
  Number of distance tests for checking: 54
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.
rbox d D3 | qconvex s GaD0 Pd0 Tc Tv >eg/eg.t10.faces.3-2

Convex hull of 6 points in 3-d:

  Number of vertices: 6
  Number of facets: 8
  Number of 'good' facets: 4

Statistics for: rbox d D3 | qconvex s GaD0 Pd0 Tc Tv

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 10
  Number of distance tests for merging: 59
  Number of distance tests for checking: 54
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 24 distance computations.
rbox d D3 | qconvex s GnrpD0 Pd0 Tc Tv >eg/eg.t11.points.3-2

Convex hull of 6 points in 3-d:

  Number of vertices: 6
  Number of facets: 8
  Number of 'good' facets: 4

Statistics for: rbox d D3 | qconvex s GnrpD0 Pd0 Tc Tv

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 10
  Number of distance tests for merging: 59
  Number of distance tests for checking: 54
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 24 distance computations.
rbox d D3 | qconvex s C0.05 GnrcD0 Pd0 Tc Tv >eg/eg.t12.centrums.3-2

Convex hull of 6 points in 3-d:

  Number of vertices: 6
  Number of facets: 8
  Number of 'good' facets: 4

Statistics for: rbox d D3 | qconvex s C0.05 GnrcD0 Pd0 Tc Tv

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 10
  Number of distance tests for merging: 93
  Number of distance tests for checking: 130
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 24 distance computations.
rbox d D3 | qconvex s GnhaD0 Pd0 Tc Tv >eg/eg.t13.intersect.3-2

Convex hull of 6 points in 3-d:

  Number of vertices: 6
  Number of facets: 8
  Number of 'good' facets: 4

Statistics for: rbox d D3 | qconvex s GnhaD0 Pd0 Tc Tv

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 10
  Number of distance tests for merging: 59
  Number of distance tests for checking: 54
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 24 distance computations.
rbox d D3 | qconvex s GnrvD0 Pd0 Tc Tv >eg/eg.t14.spheres.3-2

Convex hull of 6 points in 3-d:

  Number of vertices: 6
  Number of facets: 8
  Number of 'good' facets: 4

Statistics for: rbox d D3 | qconvex s GnrvD0 Pd0 Tc Tv

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 10
  Number of distance tests for merging: 59
  Number of distance tests for checking: 54
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 24 distance computations.
rbox c D4 | qconvex s GvD0 Pd0:0.5 Tc Tv >eg/eg.t15.spheres.4-3

Convex hull of 16 points in 4-d:

  Number of vertices: 16
  Number of facets: 8
  Number of 'good' facets: 1
  Number of 'good' non-simplicial facets: 1

Statistics for: rbox c D4 | qconvex s GvD0 Pd0:0.5 Tc Tv

  Number of points processed: 16
  Number of hyperplanes created: 25
  Number of distance tests for qhull: 167
  Number of distance tests for merging: 510
  Number of distance tests for checking: 412
  Number of merged facets: 36
  CPU seconds to compute hull (after input): 0.001


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 16 distance computations.
rbox c D4 | qhull s Q0 C0 GpD0 Pd0:0.5 Tc Tv >eg/eg.t16.points.4-3

Convex hull of 16 points in 4-d:

  Number of vertices: 16
  Number of facets: 8
  Number of 'good' facets: 1
  Number of 'good' non-simplicial facets: 1

Statistics for: rbox c D4 | qhull s Q0 C0 GpD0 Pd0:0.5 Tc Tv

  Number of points processed: 16
  Number of hyperplanes created: 61
  Number of distance tests for qhull: 162
  Number of distance tests for merging: 1272
  Number of distance tests for checking: 244
  Number of merged facets: 36
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 16 distance computations.
rbox c D4 | qconvex s GahD0 Pd0:0.5 Tc Tv >eg/eg.t17.intersect.4-3

Convex hull of 16 points in 4-d:

  Number of vertices: 16
  Number of facets: 8
  Number of 'good' facets: 1
  Number of 'good' non-simplicial facets: 1

Statistics for: rbox c D4 | qconvex s GahD0 Pd0:0.5 Tc Tv

  Number of points processed: 16
  Number of hyperplanes created: 25
  Number of distance tests for qhull: 167
  Number of distance tests for merging: 510
  Number of distance tests for checking: 412
  Number of merged facets: 36
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 16 distance computations.
rbox 100 s | qconvex s C-0.05 Qc Gicvprh Tc Tv >eg/eg.t18.imprecise.3

Convex hull of 100 points in 3-d:

  Number of vertices: 18
  Number of coplanar points: 82
  Number of facets: 16
  Number of non-simplicial facets: 12

Statistics for: rbox 100 s | qconvex s C-0.05 Qc Gicvprh Tc Tv

  Number of points processed: 18
  Number of hyperplanes created: 60
  Number of distance tests for qhull: 3110
  Number of distance tests for merging: 784
  Number of distance tests for checking: 1502
  Number of merged facets: 29
  CPU seconds to compute hull (after input): 0.001
  Maximum distance of point above facet: 0.092 (0.6x)
  Maximum distance of vertex below facet: -0.14 (0.9x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 1600 distance computations.
rbox 30 s D4 | qconvex s GhD0 Pd0d1d2D3 Tc >eg/eg.t19.intersect.precise.4-3

Convex hull of 30 points in 4-d:

  Number of vertices: 30
  Number of facets: 138
  Number of 'good' facets: 9

Statistics for: rbox 30 s D4 | qconvex s GhD0 Pd0d1d2D3 Tc

  Number of points processed: 30
  Number of hyperplanes created: 340
  Number of distance tests for qhull: 649
  CPU seconds to compute hull (after input):  0

rbox 100 s P1,1,1 | qconvex s QG-0 Pgp Tc G >eg/eg.t20.notvisible

Convex hull of 100 points in 3-d:

  Number of vertices: 100
  Number of facets: 196
  Number of 'good' facets: 125

Statistics for: rbox 100 s P1,1,1 | qconvex s QG-0 Pgp Tc G

  Number of points processed: 100
  Number of hyperplanes created: 502
  Number of distance tests for qhull: 1630
  CPU seconds to compute hull (after input): 0.001

rbox 100 s | qconvex s QV-10 Pgp Tc G  >eg/eg.t21.notvertex

Convex hull of 100 points in 3-d:

  Number of vertices: 100
  Number of facets: 196
  Number of 'good' facets: 191

Statistics for: rbox 100 s | qconvex s QV-10 Pgp Tc G

  Number of points processed: 100
  Number of hyperplanes created: 494
  Number of distance tests for qhull: 1640
  CPU seconds to compute hull (after input): 0.002

rbox 100 r D2 P1,1 | qhull s Pd0:0.7 PD0:0.8 QgG0 G Tv >eg/eg.t22.split

Convex hull of 100 points in 2-d:

  Number of vertices: 42
  Number of facets: 42
  Number of 'good' facets: 3

Statistics for: rbox 100 r D2 P1,1 | qhull s Pd0:0.7 PD0:0.8 QgG0 G Tv

  Number of points processed: 42
  Number of hyperplanes created: 176
  Number of distance tests for qhull: 1099
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 2.6e-15 of
all good facets.  Will make 303 distance computations.
rbox 100 D2 c G1.0 | qvoronoi s A-0.95 Gna Tv >eg/eg.t23.voronoi.imprecise

Voronoi diagram by the convex hull of 104 points in 3-d:

  Number of Voronoi regions: 16
  Total number of nearly incident points: 88
  Number of Voronoi vertices: 11
  Number of non-simplicial Voronoi vertices: 8

Statistics for: rbox 100 D2 c G1.0 | qvoronoi s A-0.95 Gna Tv

  Number of points processed: 16
  Number of hyperplanes created: 48
  Number of facets in hull: 12
  Number of distance tests for qhull: 2378
  Number of distance tests for merging: 614
  Number of distance tests for checking: 920
  Number of merged facets: 23
  CPU seconds to compute hull (after input):  0
  Maximum distance of point above facet: 0.046
  Maximum distance of vertex below facet: -0.1 (0.1x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 1144 distance computations.
rbox 30 s D4 | qconvex s Gh Pd0d1d2D3 Tc >eg/eg.t24.intersect.precise.4d

Convex hull of 30 points in 4-d:

  Number of vertices: 30
  Number of facets: 138
  Number of 'good' facets: 9

Statistics for: rbox 30 s D4 | qconvex s Gh Pd0d1d2D3 Tc

  Number of points processed: 30
  Number of hyperplanes created: 340
  Number of distance tests for qhull: 649
  CPU seconds to compute hull (after input):  0


echo ==the following generates an error== >/dev/null
rbox 1000 D4 | qhull Q0 s Po R0.005 Ga Tc Tv >eg/eg.t25.neighbors.4d
QH6107 qhull topology error: facets f394, f412 and f396 meet at a ridge with more than 2 neighbors.  Can not continue due to no qh.PREmerge and no 'Qx' (MERGEexact)
ERRONEOUS FACET:
- f394
    - flags: bottom simplicial newfacet
    - offset:          0
    - vertices: p938(v40) p381(v18) p241(v7) p327(v3)
    - neighboring facets: f121 f396 f398 f395
ERRONEOUS OTHER FACET:
- f412
    - flags: bottom simplicial newfacet
    - offset:          0
    - vertices: p938(v40) p241(v7) p837(v6) p327(v3)
    - neighboring facets: f121 f398
ERRONEOUS and NEIGHBORING FACETS to output

While executing: rbox 1000 D4 | qhull Q0 s Po R0.005 Ga Tc Tv
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213546123  Q0-no-premerge  summary  Poutput-forced
  Random-perturb 0.005  Gall-points  Tcheck-frequently  Tverify  _max-width  1
  Error-roundoff 0.0025  Visible-distance 0.0025  U-max-coplanar 0.0025
  Width-outside 0.005  _wide-facet 0.015  _maxoutside 0.025
Last point added to hull was p938.

Convex hull of 1000 points in 4-d:

  Number of vertices: 38
  Number of facets: 180

Statistics for: rbox 1000 D4 | qhull Q0 s Po R0.005 Ga Tc Tv

  Number of points processed: 39
  Number of hyperplanes created: 394
  Number of distance tests for qhull: 21752


precision problems (corrected unless 'Q0' or an error)
      1 flipped facets
     13 coplanar horizon facets for new vertices
    103 coplanar points during partitioning
      4 degenerate hyperplanes recomputed with gaussian elimination

Precision problems were detected during construction of the convex hull.
This occurs because convex hull algorithms assume that calculations are
exact, but floating-point arithmetic has roundoff errors.

To correct for precision problems, do not use 'Q0'.  By default, Qhull
selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',
Qhull joggles the input to prevent precision problems.  See "Imprecision
in Qhull" (qh-impre.htm).

If you use 'Q0', the output may include
coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,
Qhull may produce a ridge with four neighbors or two facets with the same 
vertices.  Qhull reports these events when they occur.  It stops when a
concave ridge, flipped facet, or duplicate facet occurs.

If you need triangular output:
  - use option 'Qt' to triangulate the output
  - use option 'QJ' to joggle the input points and remove precision errors
  - use option 'Ft'.  It triangulates non-simplicial facets with added points.

If you must use 'Q0',
try one or more of the following options.  They can not guarantee an output.
  - use 'QbB' to scale the input to a cube.
  - use 'Po' to produce output and prevent partitioning for flipped facets
  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff
  - use 'En' to specify a maximum roundoff error less than 0.0025.
  - options 'Qf', 'Qbb', and 'QR0' may also help

To guarantee simplicial output:
  - use option 'Qt' to triangulate the output
  - use option 'QJ' to joggle the input points and remove precision errors
  - use option 'Ft' to triangulate the output by adding points
  - use exact arithmetic (see "Imprecision in Qhull", qh-impre.htm)
echo ==the previous should generate an error== >/dev/null
echo END eg/q_egtest >/dev/null

bash -c eg/q_test
eg/q_test: Temporarily add "$PWD/bin" to $PATH for access to qconvex,etc.

Convex hull of 8 points in 3-d:

  Number of vertices: 8
  Number of facets: 6
  Number of non-simplicial facets: 6

Statistics for:  | qhull s Tcv 

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 96
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.

Delaunay triangulation by the convex hull of 8 points in 4-d:

  Number of input sites: 8
  Number of Delaunay regions: 10

Statistics for:  | qhull s d Tcv 

  Number of points processed: 8
  Number of hyperplanes created: 28
  Number of facets in hull: 18
  Number of distance tests for qhull: 28
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1e-14 of
all facets.  Will make 80 distance computations.

Delaunay triangulation by the convex hull of 8 points in 4-d:

  Number of input sites: 8
  Number of Delaunay regions: 10

Statistics for:  | qhull s d Tcv 

  Number of points processed: 8
  Number of hyperplanes created: 26
  Number of facets in hull: 17
  Number of distance tests for qhull: 28
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1e-14 of
all facets.  Will make 80 distance computations.

Halfspace intersection by the convex hull of 8 points in 3-d:

  Number of halfspaces: 8
  Number of non-redundant halfspaces: 8
  Number of intersection points: 6
  Number of non-simplicial intersection points: 6

Statistics for:  | qhull H0 s Tcv Fp

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 96
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.
==============================
========= eg/q_test ==========
== Check qhull programs ======
==============================

qhull => qhull_r 8.0.1 (2020.2.r 2020/07/24)
qconvex => qhull 8.0.1 (2020.2 2020/07/24)
qvoronoi => qhull 8.0.1 (2020.2 2020/07/24)
qdelaunay => qhull 8.0.1 (2020.2 2020/07/24)
qhalf => qhull 8.0.1 (2020.2 2020/07/24)
-rwxr-xr-x 1 bbarber 197121 344064 Jul 24 21:06 /d/bash/local/qhull/bin/qconvex
-rwxr-xr-x 1 bbarber 197121 344576 Jul 24 21:06 /d/bash/local/qhull/bin/qdelaunay
-rwxr-xr-x 1 bbarber 197121 344576 Jul 24 21:06 /d/bash/local/qhull/bin/qhalf
-rwxr-xr-x 1 bbarber 197121 339968 Jul 24 21:06 /d/bash/local/qhull/bin/qhull
-rwxr-xr-x 1 bbarber 197121 343552 Jul 24 21:06 /d/bash/local/qhull/bin/qvoronoi
-rwxr-xr-x 1 bbarber 197121  13312 Jul 24 21:06 /d/bash/local/qhull/bin/user_eg
-rwxr-xr-x 1 bbarber 197121 320000 Jul 24 21:06 /d/bash/local/qhull/bin/user_eg2
-rwxr-xr-x 1 bbarber 197121 468480 Jul 24 21:06 /d/bash/local/qhull/bin/user_eg3
==============================
== check user_eg, user_eg2, and user_eg3
== errors if user_eg and user_eg2 not found
==============================
user_eg

========
user_eg 'cube qhull options' 'Delaunay options' 'halfspace options'

This is the output from user_eg_r.c.  It shows how qhull() may be called from
an application, via Qhull's shared, reentrant library.  user_eg is not part of
Qhull itself.  If user_eg fails immediately, user_eg_r.c was incorrectly linked
to Qhull's non-reentrant library, libqhull.
Try -- user_eg 'T1' 'T1' 'T1'


========
compute convex hull of cube after rotating input
input
    -1     -1     -1 
     1     -1     -1 
    -1      1     -1 
     1      1     -1 
    -1     -1      1 
     1     -1      1 
    -1      1      1 
     1      1      1 

Convex hull of 8 points in 3-d:

  Number of vertices: 8
  Number of facets: 6
  Number of non-simplicial facets: 6

Statistics for:  | qhull s Tcv 

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 96
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.

8 vertices and 6 facets with normals:
    -0     -0     -1 
     0     -1      0 
     1     -0     -0 
    -1     -0     -0 
     0      1     -0 
    -0     -0      1 

========
compute 3-d Delaunay triangulation
seed: 1595644037
input
-0.801 -0.418  0.372 
-0.854 -0.0286 -0.978 
-0.329 -0.199 -0.343 
 0.668 -0.752  0.621 
-0.0443 -0.981 -0.666 
 0.786  0.278  0.847 
 0.639  0.432  0.349 
-0.495 -0.786  0.239 

Delaunay triangulation by the convex hull of 8 points in 4-d:

  Number of input sites: 8
  Number of Delaunay regions: 10

Statistics for:  | qhull s d Tcv 

  Number of points processed: 8
  Number of hyperplanes created: 28
  Number of facets in hull: 18
  Number of distance tests for qhull: 28
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1e-14 of
all facets.  Will make 80 distance computations.

8 vertices and 18 facets with normals:
  0.67   0.27   -0.6   0.35 
  0.51   0.23   -0.8   -0.2 
 -0.47   0.83    0.3  0.072 
 -0.52   0.81   0.13  -0.23 
  0.86 0.0043  -0.48   0.16 
  0.71  -0.35  -0.33  -0.51 
  0.38 -0.011   -0.2    0.9 
 -0.34  -0.07   0.44   0.83 
 -0.38  -0.45   0.29   0.75 
 0.011  -0.16   0.78   -0.6 
  0.27  -0.76  -0.02  -0.59 
 -0.38  -0.49    0.3   0.72 
 -0.64  -0.57  -0.38  -0.34 
 -0.51  -0.56    0.2   0.62 
 -0.75  -0.48   -0.3  -0.35 
-0.0085  -0.17   0.65  -0.74 
  0.12  -0.29   0.58  -0.75 
 0.021  -0.19   0.75  -0.64 

find 3-d Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...]
-0.80 -0.42  0.37 
-0.33 -0.20 -0.34 
 0.64  0.43  0.35 
-0.85 -0.03 -0.98 

========
Compute a new triangulation as a separate instance of Qhull
seed: 1595644038
input
-0.801 -0.155 -0.117 
0.0631 -0.963 -0.541 
-0.235 -0.841 -0.984 
 0.538 0.0146  -0.34 
-0.382 -0.912 -0.559 
-0.155  -0.38  0.862 
-0.594  0.566 -0.816 
 0.878  0.392    0.1 

Delaunay triangulation by the convex hull of 8 points in 4-d:

  Number of input sites: 8
  Number of Delaunay regions: 10

Statistics for:  | qhull s d Tcv 

  Number of points processed: 8
  Number of hyperplanes created: 26
  Number of facets in hull: 17
  Number of distance tests for qhull: 28
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1e-14 of
all facets.  Will make 80 distance computations.

8 vertices and 17 facets with normals:
 -0.27    0.8   0.44  -0.33 
 -0.15   0.61    0.4  -0.67 
-0.064  -0.63  0.081  -0.77 
  0.68  -0.61    0.3  -0.26 
 -0.19   0.77   0.19  -0.58 
 -0.72  -0.05   0.32   0.62 
 -0.23  -0.13  -0.76  -0.59 
  0.51  -0.33   0.37    0.7 
 0.063   0.23   0.34   0.91 
  0.82  -0.23  -0.53  0.074 
  0.55   0.27  -0.78   0.11 
 -0.19  -0.71   0.12  -0.67 
 -0.74  -0.13   0.32   0.58 
-0.024  -0.74   0.42   0.53 
 -0.16   -0.5  -0.37  -0.77 
 -0.22  -0.18  -0.74  -0.61 
-0.097  -0.32  -0.72  -0.61 

========
Free memory allocated by the new instance of Qhull, and redisplay the old results.



8 vertices and 18 facets with normals:
  0.67   0.27   -0.6   0.35 
  0.51   0.23   -0.8   -0.2 
 -0.47   0.83    0.3  0.072 
 -0.52   0.81   0.13  -0.23 
  0.86 0.0043  -0.48   0.16 
  0.71  -0.35  -0.33  -0.51 
  0.38 -0.011   -0.2    0.9 
 -0.34  -0.07   0.44   0.83 
 -0.38  -0.45   0.29   0.75 
 0.011  -0.16   0.78   -0.6 
  0.27  -0.76  -0.02  -0.59 
 -0.38  -0.49    0.3   0.72 
 -0.64  -0.57  -0.38  -0.34 
 -0.51  -0.56    0.2   0.62 
 -0.75  -0.48   -0.3  -0.35 
-0.0085  -0.17   0.65  -0.74 
  0.12  -0.29   0.58  -0.75 
 0.021  -0.19   0.75  -0.64 

========
compute halfspace intersection about the origin for a diamond
input as halfspace coefficients + offsets
    -1     -1     -1     -1 
     1     -1     -1     -1 
    -1      1     -1     -1 
     1      1     -1     -1 
    -1     -1      1     -1 
     1     -1      1     -1 
    -1      1      1     -1 
     1      1      1     -1 

Halfspace intersection by the convex hull of 8 points in 3-d:

  Number of halfspaces: 8
  Number of non-redundant halfspaces: 8
  Number of intersection points: 6
  Number of non-simplicial intersection points: 6

Statistics for:  | qhull H0 s Tcv Fp

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 96
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0

3
6
     0      0     -1 
     0     -1      0 
     1      0      0 
    -1      0      0 
     0      1      0 
     0      0      1 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.

8 vertices and 6 facets with normals:
    -0     -0     -1 
     0     -1      0 
     1     -0     -0 
    -1     -0     -0 
     0      1     -0 
    -0     -0      1 
user_eg  'QR1 p n Qt'  'v p'  'Fp'

========
user_eg 'cube qhull options' 'Delaunay options' 'halfspace options'

This is the output from user_eg_r.c.  It shows how qhull() may be called from
an application, via Qhull's shared, reentrant library.  user_eg is not part of
Qhull itself.  If user_eg fails immediately, user_eg_r.c was incorrectly linked
to Qhull's non-reentrant library, libqhull.
Try -- user_eg 'T1' 'T1' 'T1'


========
compute convex hull of cube after rotating input
input
    -1     -1     -1 
     1     -1     -1 
    -1      1     -1 
     1      1     -1 
    -1     -1      1 
     1     -1      1 
    -1      1      1 
     1      1      1 

Convex hull of 8 points in 3-d:

  Number of vertices: 8
  Number of facets: 12
  Number of triangulated facets: 6

Statistics for:  | qhull s Tcv QR1 p n Qt QR1

  Number of points processed: 8
  Number of hyperplanes created: 12
  Number of distance tests for qhull: 22
  Number of distance tests for merging: 100
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0

3
8
0.9124763375291641 1.390833937612012 -0.4826674750136243 
-0.5764091147442416 0.565375258822974 -1.532352227508615 
-0.1847368907548403 1.250953879569599 1.183632828365285 
-1.673622343028246 0.4254952007805605 0.1339480758702939 
1.673622343028246 -0.4254952007805605 -0.1339480758702939 
0.1847368907548403 -1.250953879569599 -1.183632828365285 
0.5764091147442416 -0.565375258822974 1.532352227508615 
-0.9124763375291641 -1.390833937612012 0.4826674750136243 
4
12
-0.744442726136703 -0.4127293393945193 -0.5248423762474955     -1 
-0.744442726136703 -0.4127293393945193 -0.5248423762474955     -1 
0.380573002749541 -0.9081645691962865 0.1743596995716653     -1 
0.380573002749541 -0.9081645691962865 0.1743596995716653     -1 
-0.5486066141420022 -0.06994002902120684 0.8331501516894545     -1 
-0.5486066141420022 -0.06994002902120684 0.8331501516894545     -1 
0.5486066141420022 0.06994002902120672 -0.8331501516894545     -1 
0.5486066141420022 0.06994002902120672 -0.8331501516894545     -1 
0.7444427261367031 0.4127293393945192 0.5248423762474955     -1 
0.7444427261367031 0.4127293393945192 0.5248423762474955     -1 
-0.380573002749541 0.9081645691962864 -0.1743596995716652     -1 
-0.380573002749541 0.9081645691962864 -0.1743596995716652     -1 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 96 distance computations.

8 vertices and 12 facets with normals:
 -0.74  -0.41  -0.52 
 -0.74  -0.41  -0.52 
  0.38  -0.91   0.17 
  0.38  -0.91   0.17 
 -0.55  -0.07   0.83 
 -0.55  -0.07   0.83 
  0.55   0.07  -0.83 
  0.55   0.07  -0.83 
  0.74   0.41   0.52 
  0.74   0.41   0.52 
 -0.38   0.91  -0.17 
 -0.38   0.91  -0.17 

========
compute 3-d Delaunay triangulation
seed: 1595644038
input
-0.801 -0.155 -0.117 
0.0631 -0.963 -0.541 
-0.235 -0.841 -0.984 
 0.538 0.0146  -0.34 
-0.382 -0.912 -0.559 
-0.155  -0.38  0.862 
-0.594  0.566 -0.816 
 0.878  0.392    0.1 

Voronoi diagram by the convex hull of 8 points in 4-d:

  Number of Voronoi regions: 8
  Number of Voronoi vertices: 10

Statistics for:  | qhull s d Tcv v p

  Number of points processed: 8
  Number of hyperplanes created: 26
  Number of facets in hull: 17
  Number of distance tests for qhull: 28
  CPU seconds to compute hull (after input):  0

3
10
-0.4071479102294318 1.219133029325973 0.6665355448746564 
-0.1108160944725886 0.456025758474877 0.296165826000959 
-0.04172545836103403 -0.4089628768956435 0.05248152588212329 
1.328063758340639 -1.183562100392564 0.5872409889009436 
-0.1590699940723186 0.6580028523373366 0.1606354382946221 
-0.1958933203456756 -0.1120634006329647 -0.6453966139916644 
-0.1391996697363491 -0.532197185823705 0.08861056648935872 
-0.1012641820194624 -0.3207618095382609 -0.2371505242478096 
-0.1847968878329362 -0.150249705715356 -0.6079504566397304 
-0.07956014265606015 -0.2591783977016859 -0.5894629573067639 

Output completed.  Verifying that all points are below 1e-14 of
all facets.  Will make 80 distance computations.

8 vertices and 17 facets with normals:
 -0.27    0.8   0.44  -0.33 
 -0.15   0.61    0.4  -0.67 
-0.064  -0.63  0.081  -0.77 
  0.68  -0.61    0.3  -0.26 
 -0.19   0.77   0.19  -0.58 
 -0.72  -0.05   0.32   0.62 
 -0.23  -0.13  -0.76  -0.59 
  0.51  -0.33   0.37    0.7 
 0.063   0.23   0.34   0.91 
  0.82  -0.23  -0.53  0.074 
  0.55   0.27  -0.78   0.11 
 -0.19  -0.71   0.12  -0.67 
 -0.74  -0.13   0.32   0.58 
-0.024  -0.74   0.42   0.53 
 -0.16   -0.5  -0.37  -0.77 
 -0.22  -0.18  -0.74  -0.61 
-0.097  -0.32  -0.72  -0.61 

find 3-d Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...]
-0.59  0.57 -0.82 
-0.15 -0.38  0.86 
 0.88  0.39  0.10 
-0.80 -0.16 -0.12 

========
Compute a new triangulation as a separate instance of Qhull
seed: 1595644039
input
-0.801  0.108 -0.606 
  0.98  0.102 -0.103 
-0.141  0.517  0.375 
 0.407  0.782  0.698 
 -0.72 -0.842 -0.452 
 0.905  0.963  0.878 
 0.173    0.7 0.0194 
 0.252 -0.431 -0.039 

Voronoi diagram by the convex hull of 8 points in 4-d:

  Number of Voronoi regions: 8
  Number of Voronoi vertices: 10

Statistics for:  | qhull s d Tcv v p

  Number of points processed: 8
  Number of hyperplanes created: 29
  Number of facets in hull: 19
  Number of distance tests for qhull: 34
  CPU seconds to compute hull (after input):  0

3
10
0.6957254548402696 -0.5636294604869319 -2.507464110663786 
0.2747984690652054 0.1906381162276007 -1.008814834585774 
0.9719393512739847 -0.4886296283040745 1.285981228064616 
0.9113330904344364 0.817705195127131 0.1350558690072676 
0.4328681637125205 0.1330532247438454 0.3197206613620017 
0.4651973598805769 0.1012147513913624 0.4233056008080553 
0.466027516489028 0.1682136331316482 0.3670953858444743 
-0.1814376757632739 0.1184692202639611 -0.2296672791600022 
-0.5906767690426418 -0.2360311159460474 0.1939451211897689 
-2.63695386199309 -5.462987868661916 10.22310605930232 

Output completed.  Verifying that all points are below 1.5e-14 of
all facets.  Will make 80 distance computations.

8 vertices and 19 facets with normals:
  0.25  0.099  -0.83   0.49 
  0.26  -0.21  -0.93  -0.18 
  0.41  -0.79   0.41    0.2 
  0.22   0.59  -0.76   0.17 
  0.23   0.16  -0.86  -0.43 
  0.55  -0.28   0.73  -0.28 
  0.69   0.62    0.1  -0.38 
 -0.14  -0.51   0.85 0.0066 
 -0.49   0.87 -0.013  0.069 
  0.58   0.18   0.43  -0.67 
  0.57   0.12   0.52  -0.62 
  0.59   0.21   0.46  -0.63 
 -0.31    0.2  -0.39  -0.85 
  -0.5   0.86  0.013  0.053 
 -0.71  -0.28   0.23   -0.6 
 -0.22  -0.46   0.86 -0.042 
 -0.77   0.12   0.59   0.21 
  -0.7   0.62    0.3   0.15 
 -0.67 -0.036   0.73   0.17 

========
Free memory allocated by the new instance of Qhull, and redisplay the old results.



8 vertices and 17 facets with normals:
 -0.27    0.8   0.44  -0.33 
 -0.15   0.61    0.4  -0.67 
-0.064  -0.63  0.081  -0.77 
  0.68  -0.61    0.3  -0.26 
 -0.19   0.77   0.19  -0.58 
 -0.72  -0.05   0.32   0.62 
 -0.23  -0.13  -0.76  -0.59 
  0.51  -0.33   0.37    0.7 
 0.063   0.23   0.34   0.91 
  0.82  -0.23  -0.53  0.074 
  0.55   0.27  -0.78   0.11 
 -0.19  -0.71   0.12  -0.67 
 -0.74  -0.13   0.32   0.58 
-0.024  -0.74   0.42   0.53 
 -0.16   -0.5  -0.37  -0.77 
 -0.22  -0.18  -0.74  -0.61 
-0.097  -0.32  -0.72  -0.61 

========
compute halfspace intersection about the origin for a diamond
input as halfspace coefficients + offsets
    -1     -1     -1     -1 
     1     -1     -1     -1 
    -1      1     -1     -1 
     1      1     -1     -1 
    -1     -1      1     -1 
     1     -1      1     -1 
    -1      1      1     -1 
     1      1      1     -1 

Halfspace intersection by the convex hull of 8 points in 3-d:

  Number of halfspaces: 8
  Number of non-redundant halfspaces: 8
  Number of intersection points: 6
  Number of non-simplicial intersection points: 6

Statistics for:  | qhull H0 s Tcv Fp

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 96
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0

3
6
     0      0     -1 
     0     -1      0 
     1      0      0 
    -1      0      0 
     0      1      0 
     0      0      1 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.

8 vertices and 6 facets with normals:
    -0     -0     -1 
     0     -1      0 
     1     -0     -0 
    -1     -0     -0 
     0      1     -0 
    -0     -0      1 
user_eg2

========
user_eg2 'cube qhull options' 'Delaunay options' 'halfspace options'

This is the output from user_eg2_r.c.  It shows how qhull() may be called from
an application, via Qhull's static, reentrant library.  user_eg2 is not part
of Qhull itself. If user_eg2 fails immediately, user_eg2_r.c was incorrectly
linked to Qhull's non-reentrant library, libqhullstatic.
Try -- user_eg2 'T1' 'T1' 'T1'


========
compute triangulated convex hull of cube after rotating input

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 96 distance computations.

8 vertices and 12 facets with normals:
    -0     -0     -1 
    -0     -0     -1 
     0     -1      0 
     0     -1      0 
     1     -0     -0 
     1     -0     -0 
    -1     -0     -0 
    -1     -0     -0 
     0      1     -0 
     0      1     -0 
    -0     -0      1 
    -0     -0      1 

add points in a diamond
9 vertices and 14 facets
10 vertices and 16 facets
11 vertices and 16 facets
12 vertices and 16 facets
13 vertices and 14 facets
14 vertices and 12 facets

14 vertices and 12 facets with normals:
  0.71  -0.71     -0 
 -0.71  -0.71      0 
 -0.71   0.71     -0 
  0.71   0.71     -0 
 -0.71     -0  -0.71 
    -0   0.71  -0.71 
     0  -0.71  -0.71 
  0.71      0  -0.71 
    -0  -0.71   0.71 
 -0.71      0   0.71 
  0.71      0   0.71 
    -0   0.71   0.71 

Convex hull of 14 points in 3-d:

  Number of vertices: 14
  Number of facets: 12
  Number of non-simplicial facets: 12

Statistics for: user_eg2 cube example | qhull s Tcv Q11  

  Number of points processed: 14
  Number of hyperplanes created: 23
  Number of distance tests for qhull: 64
  Number of distance tests for merging: 276
  Number of distance tests for checking: 324
  Number of merged facets: 18
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 168 distance computations.

========
compute 2-d Delaunay triangulation
seed: 1595644038

8 vertices and 12 facets with normals:
  0.82   0.37   0.43 
  0.82   0.26   0.52 
  0.77   0.21    0.6 
  0.37 -0.025   0.93 
 -0.96 -0.0085  -0.29 
 -0.66   0.42  -0.62 
 -0.77   0.28  -0.57 
 -0.43  -0.34  -0.83 
 -0.45  -0.61  -0.65 
 -0.54  -0.61  -0.57 
  -0.6  -0.59  -0.53 
 -0.72  -0.46  -0.53 

Delaunay triangulation by the convex hull of 8 points in 3-d:

  Number of input sites: 8
  Number of Delaunay regions: 8

Statistics for: user_eg2 Delaunay example | qhull s d Tcv 

  Number of points processed: 8
  Number of hyperplanes created: 23
  Number of facets in hull: 12
  Number of distance tests for qhull: 32
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 5.2e-15 of
all facets.  Will make 64 distance computations.

========
add points to triangulation
added point p8:        -1  -0.7369    1.543
9 points, 0 extra points, 9 vertices, and 14 facets in total
added point p9:    0.5112  -0.0827   0.2682
10 points, 0 extra points, 10 vertices, and 16 facets in total
added point p10:   0.06553  -0.5621   0.3202
11 points, 0 extra points, 11 vertices, and 18 facets in total
added point p11:   -0.9059   0.3577   0.9486
12 points, 0 extra points, 12 vertices, and 20 facets in total
added point p12:    0.3586   0.8694   0.8844
13 points, 0 extra points, 13 vertices, and 22 facets in total
added point p13:    -0.233  0.03883   0.0558
14 points, 0 extra points, 14 vertices, and 24 facets in total

find Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...]
 0.36  0.87 
 0.51 -0.08 
-0.12  0.06 

Delaunay triangulation by the convex hull of 14 points in 3-d:

  Number of input sites: 14
  Number of Delaunay regions: 19

Statistics for: user_eg2 Delaunay example | qhull s d Tcv 

  Number of points processed: 14
  Number of hyperplanes created: 51
  Number of facets in hull: 24
  Number of distance tests for qhull: 69
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 5.2e-15 of
all facets.  Will make 266 distance computations.

========
compute halfspace intersection about the origin for a diamond

Halfspace intersection by the convex hull of 8 points in 3-d:

  Number of halfspaces: 8
  Number of non-redundant halfspaces: 8
  Number of intersection points: 6
  Number of non-simplicial intersection points: 6

Statistics for: user_eg2 halfspace example | qhull H0 s Tcv 

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 96
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.

========
add halfspaces for cube to intersection
added offset -1 and normal    1.732        0        0
8 points, 1 extra points, 9 vertices, and 9 facets in total
added offset -1 and normal   -1.732        0        0
8 points, 2 extra points, 10 vertices, and 12 facets in total
added offset -1 and normal        0    1.732        0
8 points, 3 extra points, 11 vertices, and 15 facets in total
added offset -1 and normal        0   -1.732        0
8 points, 4 extra points, 12 vertices, and 18 facets in total
added offset -1 and normal        0        0    1.732
8 points, 5 extra points, 13 vertices, and 21 facets in total
added offset -1 and normal        0        0   -1.732
8 points, 6 extra points, 14 vertices, and 24 facets in total

Halfspace intersection by the convex hull of 14 points in 3-d:

  Number of halfspaces: 14
  Number of non-redundant halfspaces: 14
  Number of intersection points: 24

Statistics for: user_eg2 halfspace example | qhull H0 s Tcv 

  Number of points processed: 14
  Number of hyperplanes created: 35
  Number of distance tests for qhull: 58
  Number of distance tests for merging: 248
  Number of distance tests for checking: 256
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 192 distance computations.
user_eg2 'QR1 p'       'v p'  'Fp'

========
user_eg2 'cube qhull options' 'Delaunay options' 'halfspace options'

This is the output from user_eg2_r.c.  It shows how qhull() may be called from
an application, via Qhull's static, reentrant library.  user_eg2 is not part
of Qhull itself. If user_eg2 fails immediately, user_eg2_r.c was incorrectly
linked to Qhull's non-reentrant library, libqhullstatic.
Try -- user_eg2 'T1' 'T1' 'T1'


========
compute triangulated convex hull of cube after rotating input

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 96 distance computations.

8 vertices and 12 facets with normals:
 -0.74  -0.41  -0.52 
 -0.74  -0.41  -0.52 
  0.38  -0.91   0.17 
  0.38  -0.91   0.17 
 -0.55  -0.07   0.83 
 -0.55  -0.07   0.83 
  0.55   0.07  -0.83 
  0.55   0.07  -0.83 
  0.74   0.41   0.52 
  0.74   0.41   0.52 
 -0.38   0.91  -0.17 
 -0.38   0.91  -0.17 

add points in a diamond
9 vertices and 14 facets
10 vertices and 16 facets
11 vertices and 18 facets
12 vertices and 20 facets
13 vertices and 22 facets
14 vertices and 24 facets

14 vertices and 24 facets with normals:
 -0.67   0.63  -0.39 
  0.67  -0.63   0.39 
  -0.1  -0.71    0.7 
 -0.65  -0.65  -0.41 
 -0.62  -0.62  -0.49 
  0.63   -0.7  -0.34 
  0.65  -0.66   0.37 
 -0.65   0.66  -0.37 
   0.1   0.71   -0.7 
 -0.63    0.7   0.34 
  0.62   0.62   0.49 
  0.65   0.65   0.41 
  -0.7  -0.13   -0.7 
 -0.62  -0.49  -0.62 
  0.11    0.7  -0.71 
  0.68   0.29  -0.68 
  0.66  -0.34  -0.67 
  0.67   -0.3  -0.67 
 -0.66   0.34   0.67 
 -0.67    0.3   0.67 
  0.62   0.49   0.62 
   0.7   0.13    0.7 
 -0.11   -0.7   0.71 
 -0.68  -0.29   0.68 

Convex hull of 14 points in 3-d:

  Number of vertices: 14
  Number of facets: 24

Statistics for: user_eg2 cube example | qhull s Tcv Q11 QR1 p  QR1

  Number of points processed: 14
  Number of hyperplanes created: 46
  Number of distance tests for qhull: 68
  Number of distance tests for merging: 284
  Number of distance tests for checking: 244
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0

3
14
0.9124763375291641 1.390833937612012 -0.4826674750136243 
-0.5764091147442416 0.565375258822974 -1.532352227508615 
-0.1847368907548403 1.250953879569599 1.183632828365285 
-1.673622343028246 0.4254952007805605 0.1339480758702939 
1.673622343028246 -0.4254952007805605 -0.1339480758702939 
0.1847368907548403 -1.250953879569599 -1.183632828365285 
0.5764091147442416 -0.565375258822974 1.532352227508615 
-0.9124763375291641 -1.390833937612012 0.4826674750136243 
    -2      0      0 
     2      0      0 
     0     -2      0 
     0      2      0 
     0      0     -2 
     0      0      2 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 192 distance computations.

========
compute 2-d Delaunay triangulation
seed: 1595644038

8 vertices and 12 facets with normals:
  0.82   0.37   0.43 
  0.82   0.26   0.52 
  0.77   0.21    0.6 
  0.37 -0.025   0.93 
 -0.96 -0.0085  -0.29 
 -0.66   0.42  -0.62 
 -0.77   0.28  -0.57 
 -0.43  -0.34  -0.83 
 -0.45  -0.61  -0.65 
 -0.54  -0.61  -0.57 
  -0.6  -0.59  -0.53 
 -0.72  -0.46  -0.53 

Voronoi diagram by the convex hull of 8 points in 3-d:

  Number of Voronoi regions: 8
  Number of Voronoi vertices: 8

Statistics for: user_eg2 Delaunay example | qhull s d Tcv v p

  Number of points processed: 8
  Number of hyperplanes created: 23
  Number of facets in hull: 12
  Number of distance tests for qhull: 32
  CPU seconds to compute hull (after input):  0

2
8
-1.674054922003768 -0.01487922147866316 
-0.5283040369357602 0.3408731556323899 
-0.6811827832457983 0.2470406317137401 
-0.2588235717416882 -0.2062901824864997 
-0.3453635548914167 -0.473499856633778 
-0.4723074028302096 -0.5334617665938058 
-0.5632414635328725 -0.5546706688338812 
-0.6792210384845423 -0.4332097342034502 

Output completed.  Verifying that all points are below 5.2e-15 of
all facets.  Will make 64 distance computations.

========
add points to triangulation
added point p8:        -1  -0.7369    1.543
9 points, 0 extra points, 9 vertices, and 14 facets in total
added point p9:    0.5112  -0.0827   0.2682
10 points, 0 extra points, 10 vertices, and 16 facets in total
added point p10:   0.06553  -0.5621   0.3202
11 points, 0 extra points, 11 vertices, and 18 facets in total
added point p11:   -0.9059   0.3577   0.9486
12 points, 0 extra points, 12 vertices, and 20 facets in total
added point p12:    0.3586   0.8694   0.8844
13 points, 0 extra points, 13 vertices, and 22 facets in total
added point p13:    -0.233  0.03883   0.0558
14 points, 0 extra points, 14 vertices, and 24 facets in total

find Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...]
 0.36  0.87 
 0.51 -0.08 
-0.12  0.06 

Voronoi diagram by the convex hull of 14 points in 3-d:

  Number of Voronoi regions: 14
  Number of Voronoi vertices: 19

Statistics for: user_eg2 Delaunay example | qhull s d Tcv v p

  Number of points processed: 14
  Number of hyperplanes created: 51
  Number of facets in hull: 24
  Number of distance tests for qhull: 69
  CPU seconds to compute hull (after input):  0

2
19
-0.3453635548914167 -0.473499856633778 
-0.4723074028302096 -0.5334617665938058 
-0.5632414635328725 -0.5546706688338812 
-0.6792210384845423 -0.4332097342034502 
-4.056602348809204 -0.06101009284882331 
-0.6560206746168462 -0.6998668839041049 
0.185140444577552 -0.06163295117232724 
-0.2543391922542552 -0.5188303037952583 
0.3503119507232316 -0.379975065066025 
-2.028638855503524 -0.02174467382692347 
-1.591570729265863 -0.04956406204488362 
-0.6808639548265594 0.136484379373769 
0.2852101525160285 0.3693477005974929 
-0.129890132625773 -0.1642796734345424 
-0.2761495329593209 -0.2597875866082675 
-0.5599240949499432 0.2183890070294259 
-0.3236308562463083 0.7169995339075901 
-0.3180575110901469 0.7253864449960007 
-0.3156556110857897 0.7236756129173678 

Output completed.  Verifying that all points are below 5.2e-15 of
all facets.  Will make 266 distance computations.

========
compute halfspace intersection about the origin for a diamond

Halfspace intersection by the convex hull of 8 points in 3-d:

  Number of halfspaces: 8
  Number of non-redundant halfspaces: 8
  Number of intersection points: 6
  Number of non-simplicial intersection points: 6

Statistics for: user_eg2 halfspace example | qhull H0 s Tcv Fp

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 96
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input): 0.001

3
6
     0      0     -1 
     0     -1      0 
     1      0      0 
    -1      0      0 
     0      1      0 
     0      0      1 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.

========
add halfspaces for cube to intersection
added offset -1 and normal    1.732        0        0
8 points, 1 extra points, 9 vertices, and 9 facets in total
added offset -1 and normal   -1.732        0        0
8 points, 2 extra points, 10 vertices, and 12 facets in total
added offset -1 and normal        0    1.732        0
8 points, 3 extra points, 11 vertices, and 15 facets in total
added offset -1 and normal        0   -1.732        0
8 points, 4 extra points, 12 vertices, and 18 facets in total
added offset -1 and normal        0        0    1.732
8 points, 5 extra points, 13 vertices, and 21 facets in total
added offset -1 and normal        0        0   -1.732
8 points, 6 extra points, 14 vertices, and 24 facets in total

Halfspace intersection by the convex hull of 14 points in 3-d:

  Number of halfspaces: 14
  Number of non-redundant halfspaces: 14
  Number of intersection points: 24

Statistics for: user_eg2 halfspace example | qhull H0 s Tcv Fp

  Number of points processed: 14
  Number of hyperplanes created: 35
  Number of distance tests for qhull: 58
  Number of distance tests for merging: 248
  Number of distance tests for checking: 256
  Number of merged facets: 6
  CPU seconds to compute hull (after input): 0.001

3
24
0.5773502691896257      0 -0.4226497308103742 
0.5773502691896257 -0.4226497308103742      0 
0.5773502691896257 0.4226497308103742      0 
0.5773502691896257      0 0.4226497308103742 
-0.5773502691896257      0 -0.4226497308103742 
-0.5773502691896257 -0.4226497308103742      0 
-0.5773502691896257      0 0.4226497308103742 
-0.5773502691896257 0.4226497308103742      0 
     0 0.5773502691896257 -0.4226497308103742 
0.4226497308103742 0.5773502691896257      0 
-0.4226497308103742 0.5773502691896257      0 
     0 0.5773502691896257 0.4226497308103742 
     0 -0.5773502691896257 -0.4226497308103742 
-0.4226497308103742 -0.5773502691896257      0 
     0 -0.5773502691896257 0.4226497308103742 
0.4226497308103742 -0.5773502691896257      0 
     0 -0.4226497308103742 0.5773502691896257 
0.4226497308103742      0 0.5773502691896257 
     0 0.4226497308103742 0.5773502691896257 
-0.4226497308103742      0 0.5773502691896257 
-0.4226497308103742      0 -0.5773502691896257 
     0 -0.4226497308103742 -0.5773502691896257 
     0 0.4226497308103742 -0.5773502691896257 
0.4226497308103742      0 -0.5773502691896257 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 192 distance computations.
user_eg3

========
user_eg3 commands... -- demonstrate calling rbox and qhull from C++.

user_eg3 is statically linked to qhullcpp and reentrant qhull.  If user_eg3
fails immediately, it is probably linked to the non-reentrant qhull library.

Commands:
  eg-100               Run the example in qh-code.htm
  eg-convex            'rbox d | qconvex o' with std::vector and C++ classes
  eg-delaunay          'rbox y c | qdelaunay o' with std::vector and C++ classes
  eg-voronoi           'rbox y c | qvoronoi o' with std::vector and C++ classes
  eg-fifo              'rbox y c | qvoronoi FN Fi Fo' with QhullUser and qh_fprintf

Rbox and Qhull commands:
  rbox "200 D4" ...    Generate points from rbox
  qhull "d p" ...      Run qhull with options and produce output
  qhull-cout "o" ...   Run qhull with options and produce output to cout
  qhull "T1" ...       Run qhull with level-1 trace to cerr
  qhull-cout "T1z" ... Run qhull with level-1 trace to cout
  facets               Print qhull's facets when done

For example
  user_eg3 rbox qhull
  user_eg3 rbox qhull T1
  user_eg3 rbox qhull d
  user_eg3 rbox D2 10 2 "s r 5" qhull "s p" facets
  user_eg3 eg-convex
  user_eg3 rbox 10 eg-delaunay qhull "d o"
  user_eg3 rbox D5 c P2 qhull d eg-delaunay
  user_eg3 rbox "D5 c P2" qhull v eg-voronoi o
  user_eg3 rbox D2 10 qhull "v" eg-fifo p Fi Fo
user_eg3 eg-100
- f24
    - flags: bottom simplicial
    - normal:  -0.721696 -0.658796 -0.212466
    - offset:  -0.549277
    - vertices: p40(v10) p27(v7) p0(v1)
    - neighboring facets: f34 f47 f54
- f32
    - flags: top simplicial
    - normal:  0.389612 -0.428663 0.815138
    - offset:  -0.449315
    - vertices: p22(v12) p13(v6) p82(v2)
    - neighboring facets: f61 f72 f77
- f34
    - flags: top simplicial
    - normal:  -0.452613 -0.760661 0.465335
    - offset:  -0.62552
    - vertices: p22(v12) p27(v7) p0(v1)
    - neighboring facets: f24 f80 f73
- f38
    - flags: top simplicial
    - normal:  0.998285 0.058513 -0.00174787
    - offset:  -0.477764
    - vertices: p90(v13) p48(v8) p82(v2)
    - neighboring facets: f100 f97 f57
- f46
    - flags: bottom simplicial
    - normal:  -0.406035 0.904011 0.133791
    - offset:  -0.547585
    - vertices: p73(v15) p76(v9) p97(v5)
    - neighboring facets: f51 f87 f82
- f47
    - flags: bottom simplicial
    - normal:  -0.992416 -0.0122817 -0.122308
    - offset:  -0.469463
    - vertices: p73(v15) p40(v10) p0(v1)
    - neighboring facets: f24 f81 f88
- f49
    - flags: top simplicial
    - normal:  -0.107843 0.991034 0.0788761
    - offset:  -0.50132
    - vertices: p21(v16) p97(v5) p29(v3)
    - neighboring facets: f116 f66 f51
- f51
    - flags: top simplicial
    - normal:  -0.177935 0.975873 0.126537
    - offset:  -0.506339
    - vertices: p21(v16) p76(v9) p97(v5)
    - neighboring facets: f46 f49 f67
- f52
    - flags: top simplicial
    - normal:  -0.378163 -0.891276 -0.250241
    - offset:  -0.526009
    - vertices: p98(v17) p27(v7) p83(v4)
    - neighboring facets: f75 f53 f54
- f53
    - flags: bottom simplicial
    - normal:  -0.430163 -0.821913 -0.373389
    - offset:  -0.546784
    - vertices: p98(v17) p40(v10) p83(v4)
    - neighboring facets: f108 f52 f54
- f54
    - flags: top simplicial
    - normal:  -0.548096 -0.791241 -0.271162
    - offset:  -0.537299
    - vertices: p98(v17) p40(v10) p27(v7)
    - neighboring facets: f24 f52 f53
- f57
    - flags: bottom simplicial
    - normal:  0.974428 0.137974 -0.177349
    - offset:  -0.521881
    - vertices: p19(v18) p90(v13) p48(v8)
    - neighboring facets: f38 f60 f113
- f59
    - flags: bottom simplicial
    - normal:  0.239508 -0.0103785 -0.970839
    - offset:  -0.517616
    - vertices: p19(v18) p4(v14) p83(v4)
    - neighboring facets: f76 f110 f60
- f60
    - flags: top simplicial
    - normal:  0.567061 -0.0365561 -0.822865
    - offset:  -0.572132
    - vertices: p19(v18) p4(v14) p48(v8)
    - neighboring facets: f85 f57 f59
- f61
    - flags: bottom simplicial
    - normal:  0.433241 -0.284128 0.855321
    - offset:  -0.426268
    - vertices: p37(v19) p13(v6) p82(v2)
    - neighboring facets: f32 f69 f95
- f65
    - flags: top simplicial
    - normal:  -0.198254 0.211674 0.957021
    - offset:  -0.497913
    - vertices: p67(v20) p12(v11) p76(v9)
    - neighboring facets: f79 f67 f68
- f66
    - flags: top simplicial
    - normal:  -0.155514 0.97946 0.128347
    - offset:  -0.504016
    - vertices: p67(v20) p21(v16) p29(v3)
    - neighboring facets: f49 f71 f67
- f67
    - flags: bottom simplicial
    - normal:  -0.16055 0.978089 0.132539
    - offset:  -0.504235
    - vertices: p67(v20) p21(v16) p76(v9)
    - neighboring facets: f51 f65 f66
- f68
    - flags: top simplicial
    - normal:  0.598999 -0.0537935 0.798941
    - offset:  -0.457967
    - vertices: p67(v20) p37(v19) p12(v11)
    - neighboring facets: f96 f65 f69
- f69
    - flags: bottom simplicial
    - normal:  0.69477 -0.0317528 0.718531
    - offset:  -0.45153
    - vertices: p67(v20) p37(v19) p82(v2)
    - neighboring facets: f61 f98 f68
- f71
    - flags: bottom simplicial
    - normal:  0.877687 0.308225 0.366966
    - offset:  -0.494379
    - vertices: p67(v20) p90(v13) p29(v3)
    - neighboring facets: f115 f66 f99
- f72
    - flags: top simplicial
    - normal:  0.245263 -0.887198 0.390801
    - offset:  -0.480731
    - vertices: p41(v21) p22(v12) p82(v2)
    - neighboring facets: f32 f74 f73
- f73
    - flags: bottom simplicial
    - normal:  0.0168085 -0.963019 0.268908
    - offset:  -0.510609
    - vertices: p41(v21) p22(v12) p27(v7)
    - neighboring facets: f34 f75 f72
- f74
    - flags: bottom simplicial
    - normal:  0.227082 -0.964773 0.132845
    - offset:  -0.464868
    - vertices: p41(v21) p4(v14) p82(v2)
    - neighboring facets: f84 f72 f76
- f75
    - flags: bottom simplicial
    - normal:  0.0345717 -0.998303 0.0468616
    - offset:  -0.47919
    - vertices: p41(v21) p27(v7) p83(v4)
    - neighboring facets: f52 f76 f73
- f76
    - flags: top simplicial
    - normal:  0.137757 -0.987556 0.0758723
    - offset:  -0.471349
    - vertices: p41(v21) p4(v14) p83(v4)
    - neighboring facets: f59 f75 f74
- f77
    - flags: bottom simplicial
    - normal:  -0.323398 -0.00535492 0.946248
    - offset:  -0.501516
    - vertices: p15(v22) p22(v12) p13(v6)
    - neighboring facets: f32 f78 f80
- f78
    - flags: top simplicial
    - normal:  -0.20543 0.0915675 0.974379
    - offset:  -0.474687
    - vertices: p15(v22) p12(v11) p13(v6)
    - neighboring facets: f94 f77 f79
- f79
    - flags: bottom simplicial
    - normal:  -0.218614 0.160888 0.962457
    - offset:  -0.484859
    - vertices: p15(v22) p12(v11) p76(v9)
    - neighboring facets: f65 f82 f78
- f80
    - flags: top simplicial
    - normal:  -0.593167 -0.119334 0.796186
    - offset:  -0.544059
    - vertices: p15(v22) p22(v12) p0(v1)
    - neighboring facets: f34 f81 f77
- f81
    - flags: bottom simplicial
    - normal:  -0.974282 0.088044 0.20742
    - offset:  -0.50771
    - vertices: p15(v22) p73(v15) p0(v1)
    - neighboring facets: f47 f80 f82
- f82
    - flags: top simplicial
    - normal:  -0.826328 0.394399 0.402034
    - offset:  -0.559684
    - vertices: p15(v22) p73(v15) p76(v9)
    - neighboring facets: f46 f79 f81
- f84
    - flags: top simplicial
    - normal:  0.82988 -0.542609 -0.129903
    - offset:  -0.585213
    - vertices: p57(v23) p4(v14) p82(v2)
    - neighboring facets: f74 f101 f85
- f85
    - flags: bottom simplicial
    - normal:  0.906692 -0.29884 -0.297664
    - offset:  -0.57209
    - vertices: p57(v23) p4(v14) p48(v8)
    - neighboring facets: f60 f102 f84
- f86
    - flags: top simplicial
    - normal:  -0.85363 0.243861 -0.460269
    - offset:  -0.522928
    - vertices: p11(v24) p40(v10) p97(v5)
    - neighboring facets: f89 f87 f88
- f87
    - flags: bottom simplicial
    - normal:  -0.890339 0.291001 -0.350165
    - offset:  -0.531756
    - vertices: p11(v24) p73(v15) p97(v5)
    - neighboring facets: f46 f86 f88
- f88
    - flags: top simplicial
    - normal:  -0.987894 0.0156004 -0.154345
    - offset:  -0.477251
    - vertices: p11(v24) p73(v15) p40(v10)
    - neighboring facets: f47 f86 f87
- f89
    - flags: bottom simplicial
    - normal:  -0.492188 0.332666 -0.804416
    - offset:  -0.526118
    - vertices: p25(v25) p40(v10) p97(v5)
    - neighboring facets: f86 f114 f109
- f94
    - flags: bottom simplicial
    - normal:  0.368779 -0.208614 0.905805
    - offset:  -0.440207
    - vertices: p7(v26) p12(v11) p13(v6)
    - neighboring facets: f78 f95 f96
- f95
    - flags: top simplicial
    - normal:  0.417114 -0.259346 0.871066
    - offset:  -0.429768
    - vertices: p7(v26) p37(v19) p13(v6)
    - neighboring facets: f61 f94 f96
- f96
    - flags: bottom simplicial
    - normal:  0.469304 -0.162419 0.867971
    - offset:  -0.446808
    - vertices: p7(v26) p37(v19) p12(v11)
    - neighboring facets: f68 f94 f95
- f97
    - flags: top simplicial
    - normal:  0.911891 0.1675 0.374697
    - offset:  -0.446013
    - vertices: p28(v27) p90(v13) p82(v2)
    - neighboring facets: f38 f98 f99
- f98
    - flags: bottom simplicial
    - normal:  0.888791 0.148029 0.433749
    - offset:  -0.448933
    - vertices: p28(v27) p67(v20) p82(v2)
    - neighboring facets: f69 f97 f99
- f99
    - flags: top simplicial
    - normal:  0.903592 0.183305 0.387197
    - offset:  -0.447956
    - vertices: p28(v27) p67(v20) p90(v13)
    - neighboring facets: f71 f97 f98
- f100
    - flags: bottom simplicial
    - normal:  0.93763 -0.294784 -0.184262
    - offset:  -0.546054
    - vertices: p42(v28) p48(v8) p82(v2)
    - neighboring facets: f38 f101 f102
- f101
    - flags: top simplicial
    - normal:  0.933493 -0.306605 -0.185968
    - offset:  -0.547862
    - vertices: p42(v28) p57(v23) p82(v2)
    - neighboring facets: f84 f100 f102
- f102
    - flags: bottom simplicial
    - normal:  0.928146 -0.300441 -0.219729
    - offset:  -0.55469
    - vertices: p42(v28) p57(v23) p48(v8)
    - neighboring facets: f85 f100 f101
- f108
    - flags: top simplicial
    - normal:  0.00135876 0.0103445 -0.999946
    - offset:  -0.494086
    - vertices: p5(v30) p40(v10) p83(v4)
    - neighboring facets: f53 f110 f109
- f109
    - flags: top simplicial
    - normal:  -0.106214 0.129184 -0.985916
    - offset:  -0.504323
    - vertices: p5(v30) p25(v25) p40(v10)
    - neighboring facets: f89 f108 f111
- f110
    - flags: bottom simplicial
    - normal:  0.125474 0.0262996 -0.991748
    - offset:  -0.496467
    - vertices: p5(v30) p19(v18) p83(v4)
    - neighboring facets: f59 f108 f111
- f111
    - flags: bottom simplicial
    - normal:  0.0358445 0.163534 -0.985886
    - offset:  -0.514407
    - vertices: p5(v30) p25(v25) p19(v18)
    - neighboring facets: f112 f110 f109
- f112
    - flags: top simplicial
    - normal:  0.0769357 0.958704 -0.273801
    - offset:  -0.543222
    - vertices: p78(v31) p25(v25) p19(v18)
    - neighboring facets: f111 f113 f114
- f113
    - flags: top simplicial
    - normal:  0.129005 0.982313 -0.135717
    - offset:  -0.512909
    - vertices: p78(v31) p19(v18) p90(v13)
    - neighboring facets: f57 f115 f112
- f114
    - flags: bottom simplicial
    - normal:  -0.0450665 0.957786 -0.283929
    - offset:  -0.551711
    - vertices: p78(v31) p25(v25) p97(v5)
    - neighboring facets: f89 f116 f112
- f115
    - flags: top simplicial
    - normal:  0.102483 0.993113 -0.0567803
    - offset:  -0.497056
    - vertices: p78(v31) p90(v13) p29(v3)
    - neighboring facets: f71 f116 f113
- f116
    - flags: bottom simplicial
    - normal:  -0.00662022 0.999903 -0.0122926
    - offset:  -0.49314
    - vertices: p78(v31) p97(v5) p29(v3)
    - neighboring facets: f49 f115 f114
user_eg3 eg-convex

A 3-d diamond (rbox d)
3 rbox "d"
6
0 0 -0.5 
0 0 0.5 
0 -0.5 0 
0 0.5 0 
-0.5 0 0 
0.5 0 0 

Input points and facetlist of its convex hull (qhull o)
3
6 8 12
     0      0   -0.5 
     0      0    0.5 
     0   -0.5      0 
     0    0.5      0 
  -0.5      0      0 
   0.5      0      0 
3 2 0 4 
3 0 2 5 
3 1 2 4 
3 2 1 5 
3 3 0 5 
3 0 3 4 
3 1 3 5 
3 3 1 4 

Input points and facetlist using std::vector and C++ classes
3
6 8 12
     0      0   -0.5
     0      0    0.5
     0   -0.5      0
     0    0.5      0
  -0.5      0      0
   0.5      0      0
3 2 0 4 
3 0 2 5 
3 1 2 4 
3 2 1 5 
3 3 0 5 
3 0 3 4 
3 1 3 5 
3 3 1 4 

Its outward pointing normals as vector plus offset (qhull n)
4
8
-0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.2886751345948129 
0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.2886751345948129 
-0.5773502691896258 -0.5773502691896258 0.5773502691896258 -0.2886751345948129 
0.5773502691896258 -0.5773502691896258 0.5773502691896258 -0.2886751345948129 
0.5773502691896258 0.5773502691896258 -0.5773502691896258 -0.2886751345948129 
-0.5773502691896258 0.5773502691896258 -0.5773502691896258 -0.2886751345948129 
0.5773502691896258 0.5773502691896258 0.5773502691896258 -0.2886751345948129 
-0.5773502691896258 0.5773502691896258 0.5773502691896258 -0.2886751345948129 
user_eg3 eg-delaunay

A 2-d triangle in a square (rbox y c D2)
2 rbox "y c D2"
7
0.0795233 -0.451105 
0.279706 0.0133225 
-0.0888864 0.0861965 
-0.5 -0.5 
-0.5 0.5 
0.5 -0.5 
0.5 0.5 

The 2-d input sites are lifted to a 3-d paraboloid.
A Delaunay region is a facet of the paraboloid's convex hull.

The Delaunay triangulation as input sites and Delaunay regions (qhull d o)
3
7 8 12
0.07952334739223432 -0.4511049142583319 0.209819606448483 
0.2797056779076398 0.01332249167684696 0.07841275503825199 
-0.08888640449278651 0.08619647248293871 0.01533062477215727 
  -0.5   -0.5    0.5 
  -0.5    0.5    0.5 
   0.5   -0.5    0.5 
   0.5    0.5    0.5 
3 2 4 3 
3 2 6 4 
3 5 0 3 
3 0 2 3 
3 6 1 5 
3 1 6 2 
3 1 0 5 
3 0 1 2 

The same results using std::vector and C++ classes
3
7 8 12
0.0795233 -0.451105 0.20982 
0.279706 0.0133225 0.0784128 
-0.0888864 0.0861965 0.0153306 
-0.5 -0.5 0.5 
-0.5 0.5 0.5 
0.5 -0.5 0.5 
0.5 0.5 0.5 
3 2 4 3 
3 2 6 4 
3 5 0 3 
3 0 2 3 
3 6 1 5 
3 1 6 2 
3 1 0 5 
3 0 1 2 
user_eg3 eg-voronoi

A 2-d triangle in a square (rbox y c D2)
2 rbox "y c D2"
7
0.0795233 -0.451105 
0.279706 0.0133225 
-0.0888864 0.0861965 
-0.5 -0.5 
-0.5 0.5 
0.5 -0.5 
0.5 0.5 

Its Voronoi diagram as vertices and regions (qhull v o)
The Voronoi diagram is the dual of the Delaunay triangulation
Voronoi vertices are Delaunay regions, and Voronoi regions are Delaunay input sites
The Voronoi vertex at infinity is represented as '-10.101 -10.101'
2
9 7 1
-10.101 -10.101 
-0.5894591914795221 -2.775557561562891e-17 
     0 0.5856274089010268 
-1.387778780781446e-17 -2.967377898513707 
-0.2290343684408742 -0.2527745420948135 
0.9568726986640038 2.081668171172169e-17 
0.1571419516493774 0.3619977084558904 
0.3129256373384354 -0.2763523586794005 
0.05307821633938364 -0.1643502208872393 
4 8 4 3 7
4 8 6 5 7
5 8 4 1 2 6
4 4 1 0 3
3 2 0 1
4 7 3 0 5
4 6 2 0 5

The same results using std::vector and C++ classes
Qhull::prepareVoronoi assigns facetT.visit_id and vertexT.neighbors
The Voronoi regions are rotated by one Voronoi vertex (prepareVoronoi occurs twice)
2
9 7 1
-10.101 -10.101 
-0.589459 -2.77556e-17 
0 0.585627 
-1.38778e-17 -2.96738 
-0.229034 -0.252775 
0.956873 2.08167e-17 
0.157142 0.361998 
0.312926 -0.276352 
0.0530782 -0.16435 
4 7 8 4 3
4 7 8 6 5
5 6 8 4 1 2
4 3 4 1 0
3 1 2 0
4 5 7 3 0
4 5 6 2 0
user_eg3 eg-fifo

A 2-d triangle in a square (rbox y c D2)
2 rbox "y c D2"
7
0.0795233 -0.451105 
0.279706 0.0133225 
-0.0888864 0.0861965 
-0.5 -0.5 
-0.5 0.5 
0.5 -0.5 
0.5 0.5 

Its Voronoi vertices (qhull v p)
This is the first part of eg-voronoi, but without infinity
2
8
-0.5894591914795221 -2.775557561562891e-17 
     0 0.5856274089010268 
-1.387778780781446e-17 -2.967377898513707 
-0.2290343684408742 -0.2527745420948135 
0.9568726986640038 2.081668171172169e-17 
0.1571419516493774 0.3619977084558904 
0.3129256373384354 -0.2763523586794005 
0.05307821633938364 -0.1643502208872393 

Its Voronoi regions (qhull v FN)
This is the second part of eg-voronoi, with ids one less
Regions are ordered by the corresponding input site.
7
4 7 3 2 6
4 7 5 4 6
5 7 3 0 1 5
4 3 0 -1 2
3 1 -1 0
4 6 2 -1 4
4 5 1 -1 4

The same results as 'qhull v p FN' using std::vector and C++ classes
Qhull::prepareVoronoi assigns facet.visit_id and vertex.neighbors
prepareVoronoi is also called by q.outputQhull("FN"), hence the rotated vertices
2
8
-0.589459 -2.77556e-17 
0 0.585627 
-1.38778e-17 -2.96738 
-0.229034 -0.252775 
0.956873 2.08167e-17 
0.157142 0.361998 
0.312926 -0.276352 
0.0530782 -0.16435 
7
4 6 7 3 2
4 6 7 5 4
5 5 7 3 0 1
4 2 3 0 -1
3 0 1 -1
4 4 6 2 -1
4 4 5 1 -1

Hyperplanes for bounded facets between Voronoi regions (qhull v Fi)
Each hyperplane is the perpendicular bisector of 2 input sites.
10
5 0 1 0.3958261856523667 0.9183254492563615 0.1299172425168069 
5 0 5 0.9933067158065388 -0.1155065726858348 -0.3427516509210134 
5 0 2 -0.2990888272252211 0.954225273941663 0.1727022360246516 
5 0 3 -0.9964596398753636 -0.08407250501478321 -0.2494748932535505 
5 1 5 0.3943714145865591 -0.9189511343684148 -0.3773632397513814 
5 1 2 -0.9810105005095815 0.1939546284313432 0.08394677360204827 
5 1 6 0.4123709353479589 0.9110160326142727 -0.3945864897570009 
5 2 6 0.8181972788475073 0.5749375730342683 -0.3366992011759034 
5 2 3 -0.574189571650573 -0.8187223801800775 -0.3384613206611199 
5 2 4 -0.7047972640762143 0.7094087795838752 -0.4154492254393445 

Hyperplanes for unbounded rays of unbounded facets (qhull v Fo)
Each ray goes through the midpoint of 2 input sites, oriented outwards
4
5 3 5      1 -5.624508437144599e-18 -2.812254218572297e-18 
5 3 4 -3.10259629632159e-16      1 -1.551298148160795e-16 
5 4 6      1     -0     -0 
5 5 6 -4.55634179336919e-17      1 2.278170896684595e-17 

The same result as 'qhull v Fi' using QhullUser and its custom qh_fprintf
qh_fprintf captures the output from qh_eachvoronoi in io_r.c (qhull v Fi Fo Ta)
10
5 0 1  0.395826 0.918325 0.129917 
5 0 5  0.993307 -0.115507 -0.342752 
5 0 2  -0.299089 0.954225 0.172702 
5 0 3  -0.99646 -0.0840725 -0.249475 
5 1 5  0.394371 -0.918951 -0.377363 
5 1 2  -0.981011 0.193955 0.0839468 
5 1 6  0.412371 0.911016 -0.394586 
5 2 6  0.818197 0.574938 -0.336699 
5 2 3  -0.57419 -0.818722 -0.338461 
5 2 4  -0.704797 0.709409 -0.415449 

The same result as 'qhull v Fo' using QhullUser and its custom qh_fprintf
4
5 3 5       1 -5.62451e-18 -2.81225e-18 
5 3 4  -3.1026e-16      1 -1.5513e-16 
5 4 6       1     -0     -0 
5 5 6  -4.55634e-17      1 2.27817e-17 

Message codes captured by qh_fprintf in QhullUser.cpp (qhull v Fo Ta):
9231 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 
user_eg3 rbox qhull

Results of qhull

Convex hull of 10 points in 2-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox "10 D2" | qhull 

  Number of points processed: 4
  Number of hyperplanes created: 5
  Number of distance tests for qhull: 51
  CPU seconds to compute hull (after input):  0

user_eg3 rbox qhull T1

Results of T1
[QH0013]qh_initqhull_globals: for rbox "10 D2" | qhull T1
qh_meminitbuffers: memory initialized with alignment 8
qh_maxmin: dim             min             max           width    nearzero  min-point  max-point
             0 -4.28543191e-01  3.79031236e-01  8.07574428e-01  7.6125e-15  p1         p4
             1 -4.97972782e-01  4.74582647e-01  9.72555429e-01  1.6458e-14  p0         p1
qh_maxmin: found the max and min points (by dim): p1 p4 p0 p1
[QH1002]qh_maxsimplex: selected point p0 for 3`th initial vertex, det=0.7462, targetdet=0.7854, mindet=0.007854
[QH1028]qh_createsimplex: created simplex
qh_initialhull: qh.interior_point p-2:  -0.02391   0.1182
[QH1027]qh_checkpolygon: check all facets from f1, qh.NEWtentative? 0
[QH1064]qh_checkconvex: check that facets are not-flipped and for qh.ZEROcentrum that simplicial vertices are below their neighbor (dist<0.0)
qh_initialhull: simplex constructed
[QH1042]qh_partitionall: partition all points into outside sets

Trace level T0, IStracing 1, point TP-3, merge TM0, dist TW1.8e+308, qh.tracefacet_id -1, traceridge_id -1, tracevertex_id -1, last qh.RERUN 0, rbox "10 D2" | qhull T1
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213562930  _pre-merge  _zero-centrum  _max-width 0.97
  Error-roundoff 4.3e-16  _one-merge 2.1e-15  _near-inside 1.1e-14
  Visible-distance 8.5e-16  U-max-coplanar 8.5e-16  Width-outside 1.7e-15
  _wide-facet 5.1e-15
[QH1029]qh_furthestnext: made f3 next facet(dist 0.19)
[QH1030]qh_initbuild: initial hull created and points partitioned
[QH1037]qh_buildhull: start build hull
[QH1049]qh_addpoint: add p8(v4) 0.19 above f3 to hull of 3 facets, 0 merges, 3 outside at    0 CPU secs.  Previous p-1(v3) delta    0 CPU, 3 facets, 0 merges, 3 hyperplanes, 61 distplanes, 0 retries
[QH1040]qh_findhorizon: find horizon for point p8 facet f3
[QH1041]qh_findhorizon: 2 horizon facets(good 2), 1 visible(good 1), 0 coplanar
[QH1032]qh_makenewfacets: created 2 new facets f4..f5 from point p8 to horizon
[QH1019]qh_matchnewfacets: match neighbors for new facets.
[QH1043]qh_partitionvisible: partitioned 2 points from outsidesets, 0 points from coplanarsets, and 0 deleted vertices
[QH1018]qh_deletevisible: delete 1 visible facets and 0 vertices
[QH1039]qh_buildhull: completed the hull construction
[QH1036]Qhull: algorithm completed
[QH1027]qh_checkpolygon: check all facets from f1, qh.NEWtentative? 0
[QH1064]qh_checkconvex: check that facets are not-flipped and for qh.ZEROcentrum that simplicial vertices are below their neighbor (dist<0.0)

Convex hull of 10 points in 2-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox "10 D2" | qhull T1

  Number of points processed: 4
  Number of hyperplanes created: 5
  Number of distance tests for qhull: 51
  CPU seconds to compute hull (after input):  0

user_eg3 rbox qhull d

Results of d

Delaunay triangulation by the convex hull of 10 points in 3-d:

  Number of input sites: 10
  Number of Delaunay regions: 14

Statistics for: rbox "10 D2" | qhull d

  Number of points processed: 10
  Number of hyperplanes created: 28
  Number of facets in hull: 16
  Number of distance tests for qhull: 47
  CPU seconds to compute hull (after input):  0

user_eg3 rbox y c
rbox y
rbox c
3 rbox "y" "c"
12
-0.306292 0.149266 -0.289011 
-0.409906 -0.282924 -0.0983473 
0.0770774 0.440163 -0.185531 
-0.212802 0.438723 -0.375664 
-0.5 -0.5 -0.5 
-0.5 -0.5 0.5 
-0.5 0.5 -0.5 
-0.5 0.5 0.5 
0.5 -0.5 -0.5 
0.5 -0.5 0.5 
0.5 0.5 -0.5 
0.5 0.5 0.5 
user_eg3 rbox D2 10 2 "s r 5"  qhull 's p' facets
rbox D2
rbox 10
rbox 2
rbox s r 5

Results of s p

Convex hull of 17 points in 2-d:

  Number of vertices: 7
  Number of facets: 7

Statistics for: rbox "10 D2" "2 D2" "s r 5 D2" | qhull s p

  Number of points processed: 7
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 78
  CPU seconds to compute hull (after input):  0

2
7
-0.02222276248244826 -0.4979727817680433 
-0.4285431913366012 0.4745826469497594 
0.3790312361708201 0.3779794437605696 
0.1545084971874737 0.4755282581475768 
-0.4045084971874738 -0.2938926261462365 
0.1545084971874736 -0.4755282581475768 
   0.5 -1.224646799147353e-16 

Facets created by Qhull::runQhull()
- f5
    - flags: bottom simplicial
    - normal:  0.952413 0.304811
    - offset:  -0.476206
    - vertices: p4(v4) p16(v2)
    - neighboring facets: f8 f11
- f6
    - flags: bottom simplicial
    - normal:  -0.999511 -0.0312605
    - offset:  -0.413498
    - vertices: p14(v5) p1(v1)
    - neighboring facets: f10 f7
- f7
    - flags: top simplicial
    - normal:  -0.470938 -0.882167
    - offset:  -0.44976
    - vertices: p14(v5) p0(v3)
    - neighboring facets: f9 f6
- f8
    - flags: top simplicial
    - normal:  0.809017 -0.587785
    - offset:  -0.404508
    - vertices: p15(v6) p16(v2)
    - neighboring facets: f5 f9
- f9
    - flags: bottom simplicial
    - normal:  0.125986 -0.992032
    - offset:  -0.491205
    - vertices: p15(v6) p0(v3)
    - neighboring facets: f7 f8
- f10
    - flags: top simplicial
    - normal:  -0.00162183 0.999999
    - offset:  -0.475277
    - vertices: p12(v7) p1(v1)
    - neighboring facets: f6 f11
- f11
    - flags: bottom simplicial
    - normal:  0.398486 0.917174
    - offset:  -0.497712
    - vertices: p12(v7) p4(v4)
    - neighboring facets: f5 f10
user_eg3 rbox "10 D2" eg-convex
rbox 10 D2

Input points and facetlist for convex hull of rbox "10 D2" via C++ classes
2
10 4 4
-0.0222228 -0.497973
-0.428543 0.474583
0.31054 0.240018
-0.0188396 0.363026
0.379031 0.377979
-0.299496 0.377661
0.347182 0.0836553
-0.0048582 0.348268
0.344312 -0.143731
0.309331 -0.077581
2 4 1 
2 1 0 
2 8 4 
2 0 8 
user_eg3 rbox '10 D2' qhull s eg-convex
rbox 10 D2

Results of s

Convex hull of 10 points in 2-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox "10 D2" | qhull s

  Number of points processed: 4
  Number of hyperplanes created: 5
  Number of distance tests for qhull: 51
  CPU seconds to compute hull (after input):  0


Input points and facetlist for 'qhull s' via C++ classes
2
10 4 4
-0.0222228 -0.497973
-0.428543 0.474583
0.31054 0.240018
-0.0188396 0.363026
0.379031 0.377979
-0.299496 0.377661
0.347182 0.0836553
-0.0048582 0.348268
0.344312 -0.143731
0.309331 -0.077581
2 4 1 
2 1 0 
2 8 4 
2 0 8 
user_eg3 rbox 10 eg-delaunay qhull 'd o'
rbox 10

Delaunay triangulation of 10 points as 4-d paraboloid via C++ classes
4
10 15 30
-0.374949 0.224726 -0.0378235 0.192519 
0.300492 0.369454 0.421096 0.404114 
0.364148 0.233952 0.0348979 0.188555 
-0.470713 -0.281065 0.135495 0.318928 
0.264275 -0.326571 0.317506 0.2773 
0.318323 0.0506033 0.489822 0.343815 
0.433436 -0.248039 0.203767 0.290911 
-0.285595 -0.00222701 -0.42931 0.265876 
-0.40759 -0.362593 -0.0978938 0.307186 
-0.301385 -0.378685 0.434172 0.422741 
4 5 2 1 6 
4 5 4 2 6 
4 2 4 7 6 
4 4 0 5 2 
4 0 5 2 1 
4 0 4 9 3 
4 4 0 9 5 
4 0 9 5 1 
4 4 8 7 6 
4 4 8 9 3 
4 8 0 7 3 
4 0 8 4 3 
4 4 8 2 7 
4 8 0 2 7 
4 8 0 4 2 

Results of d o
4
10 15 30
-0.374949442106252 0.2247255418679914 -0.03782349642163468 0.1925192701852094 
0.3004920247946792 0.3694544596313075 0.4210962191420572 0.4041140804824029 
0.3641479121187217 0.2339522165562512 0.03489791698278666 0.1885552061417448 
-0.4707134565997063 -0.2810653003687648 0.1354949890035158 0.3189277533404903 
0.2642752088273644 -0.3265712199048802 0.3175057017407433 0.2773000183087906 
0.3183227589524563 0.05060330969337679 0.4898217078203537 0.3438153792710754 
0.4334355904100794 -0.2480392830893763 0.2037671452423252 0.2909109464698327 
-0.2855954200826543 -0.002227006947833121 -0.4293096679535784 0.2658764945305452 
-0.4075898489985521 -0.3625928418362446 -0.09789381697577781 0.3071862533596335 
-0.3013850588364387 -0.3786854184034145 0.4341719447953365 0.4227408774485775 
4 5 2 1 6 
4 5 4 2 6 
4 2 4 7 6 
4 4 0 5 2 
4 0 5 2 1 
4 0 4 9 3 
4 4 0 9 5 
4 0 9 5 1 
4 4 8 7 6 
4 4 8 9 3 
4 8 0 7 3 
4 0 8 4 3 
4 4 8 2 7 
4 8 0 2 7 
4 8 0 4 2 
user_eg3 rbox D5 c P2 qhull d eg-delaunay
rbox D5
rbox c
rbox P2

Results of d

Delaunay triangulation by the convex hull of 33 points in 6-d:

  Number of input sites: 33
  Number of Delaunay regions: 2
  Number of non-simplicial Delaunay regions: 2

Statistics for: rbox "c D5" "P2 D5" | qhull d

  Number of points processed: 33
  Number of hyperplanes created: 87
  Number of facets in hull: 11
  Number of distance tests for qhull: 826
  Number of distance tests for merging: 3868
  Number of distance tests for checking: 363
  Number of merged facets: 296
  CPU seconds to compute hull (after input): 0.001


Vertices and Delaunay regions of paraboloid from 'qhull d' via C++ classes
6
33 2 6
-0.5 -0.5 -0.5 -0.5 -0.5 1.25 
-0.5 -0.5 -0.5 -0.5 0.5 1.25 
-0.5 -0.5 -0.5 0.5 -0.5 1.25 
-0.5 -0.5 -0.5 0.5 0.5 1.25 
-0.5 -0.5 0.5 -0.5 -0.5 1.25 
-0.5 -0.5 0.5 -0.5 0.5 1.25 
-0.5 -0.5 0.5 0.5 -0.5 1.25 
-0.5 -0.5 0.5 0.5 0.5 1.25 
-0.5 0.5 -0.5 -0.5 -0.5 1.25 
-0.5 0.5 -0.5 -0.5 0.5 1.25 
-0.5 0.5 -0.5 0.5 -0.5 1.25 
-0.5 0.5 -0.5 0.5 0.5 1.25 
-0.5 0.5 0.5 -0.5 -0.5 1.25 
-0.5 0.5 0.5 -0.5 0.5 1.25 
-0.5 0.5 0.5 0.5 -0.5 1.25 
-0.5 0.5 0.5 0.5 0.5 1.25 
0.5 -0.5 -0.5 -0.5 -0.5 1.25 
0.5 -0.5 -0.5 -0.5 0.5 1.25 
0.5 -0.5 -0.5 0.5 -0.5 1.25 
0.5 -0.5 -0.5 0.5 0.5 1.25 
0.5 -0.5 0.5 -0.5 -0.5 1.25 
0.5 -0.5 0.5 -0.5 0.5 1.25 
0.5 -0.5 0.5 0.5 -0.5 1.25 
0.5 -0.5 0.5 0.5 0.5 1.25 
0.5 0.5 -0.5 -0.5 -0.5 1.25 
0.5 0.5 -0.5 -0.5 0.5 1.25 
0.5 0.5 -0.5 0.5 -0.5 1.25 
0.5 0.5 -0.5 0.5 0.5 1.25 
0.5 0.5 0.5 -0.5 -0.5 1.25 
0.5 0.5 0.5 -0.5 0.5 1.25 
0.5 0.5 0.5 0.5 -0.5 1.25 
0.5 0.5 0.5 0.5 0.5 1.25 
2 0 0 0 0 4 
32 17 18 3 20 5 6 24 9 10 12 19 21 22 7 25 26 11 28 13 14 23 27 29 30 15 31 16 1 2 4 8 0 
17 17 18 20 24 19 21 22 25 26 28 23 27 29 30 31 16 32 
user_eg3 rbox '10 D2' eg-voronoi
rbox 10 D2

Voronoi vertices and regions for rbox "10 D2" via C++ classes
2
15 10 1
-10.101 -10.101 
-0.129438 -0.0724741 
0.0826769 -0.239764 
0.129526 1.71603 
0.174036 0.531752 
0.185142 0.388255 
-0.906594 -0.296296 
-0.195481 -0.0711189 
-0.140758 0.723386 
-0.16763 0.208062 
0.0586831 0.0663207 
0.0880634 0.105408 
0.476159 -0.0316837 
3.09421 -0.0647219 
0.541052 0.211562 
5 7 1 2 0 6
4 8 3 0 6
3 14 5 11
4 9 4 3 8
6 14 5 4 3 0 13
4 9 7 6 8
5 14 11 10 12 13
7 11 5 4 9 7 1 10
4 13 0 2 12
4 12 2 1 10
user_eg3 rbox "D5 c P2" qhull v eg-voronoi o
rbox D5 c P2

Results of v

Voronoi diagram by the convex hull of 33 points in 6-d:

  Number of Voronoi regions: 33
  Number of Voronoi vertices: 2
  Number of non-simplicial Voronoi vertices: 2

Statistics for: rbox "D5 c P2" | qhull v

  Number of points processed: 33
  Number of hyperplanes created: 87
  Number of facets in hull: 11
  Number of distance tests for qhull: 826
  Number of distance tests for merging: 3868
  Number of distance tests for checking: 363
  Number of merged facets: 296
  CPU seconds to compute hull (after input): 0.001


Voronoi vertices and regions for 'qhull v' via C++ classes
5
3 33 1
-10.101 -10.101 -10.101 -10.101 -10.101 
0 0 0 0 0 
0.916667 0 0 0 0 
2 0 2
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2

Results of o
5
3 33 1
-10.101 -10.101 -10.101 -10.101 -10.101 
     0      0      0      0      0 
0.9166666666666667      0      0      0      0 
2 0 2
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
2 0 1
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
3 0 1 2
user_eg3 rbox '10 D2' eg-fifo
rbox 10 D2

Voronoi vertices for rbox "10 D2" via QhullUser and qh_fprintf
2
14
-0.129438 -0.0724741 
0.0826769 -0.239764 
0.129526 1.71603 
0.174036 0.531752 
0.185142 0.388255 
-0.906594 -0.296296 
-0.195481 -0.0711189 
-0.140758 0.723386 
-0.16763 0.208062 
0.0586831 0.0663207 
0.0880634 0.105408 
0.476159 -0.0316837 
3.09421 -0.0647219 
0.541052 0.211562 
10
5 6 0 1 -1 5
4 7 2 -1 5
3 13 4 10
4 8 3 2 7
6 13 4 3 2 -1 12
4 8 6 5 7
5 13 10 9 11 12
7 10 4 3 8 6 0 9
4 12 -1 1 11
4 11 1 0 9

Hyperplanes for bounded facets between Voronoi regions via QhullUser and qh_fprintf
19
5 0 5  -0.301881 0.953346 0.00878913 
5 0 7  0.0205153 0.99979 0.0751143 
5 0 9  0.619259 0.785187 0.137061 
5 1 5  0.799595 -0.600539 0.546971 
5 1 3  0.964872 -0.262721 0.325862 
5 2 6  0.22816 -0.973624 0.0825353 
5 2 4  0.444671 0.895694 -0.430084 
5 2 7  -0.945841 0.32463 0.0490754 
5 3 5  -0.998643 0.0520745 -0.178237 
5 3 7  0.687752 -0.725945 0.26633 
5 3 4  0.999294 0.037557 -0.193884 
5 4 6  -0.107584 -0.994196 0.268542 
5 4 7  -0.997018 -0.0771644 0.214549 
5 5 7  0.995061 -0.0992661 0.187455 
5 6 7  -0.799364 0.600847 0.00706064 
5 6 9  -0.228542 -0.973534 0.077977 
5 6 8  -0.0126184 -0.99992 -0.0256728 
5 7 9  0.593695 -0.80469 0.0185277 
5 8 9  -0.467479 0.884004 0.250603 

Hyperplanes for unbounded facets between Voronoi regions via QhullUser and qh_fprintf
4
5 0 8  0.719063 0.694945 0.107173 
5 0 1  -0.385496 0.92271 -0.076093 
5 1 4  0.992921 -0.118775 0.0752121 
5 4 8  -0.0664014 -0.997793 0.140881 

Message codes captured by qh_fprintf in QhullUser.cpp (qhull v Fo Ta):
9231 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 
user_eg3 rbox D2 10 qhull v eg-fifo p Fi Fo
rbox D2
rbox 10

Results of v

Voronoi diagram by the convex hull of 10 points in 3-d:

  Number of Voronoi regions: 10
  Number of Voronoi vertices: 14

Statistics for: rbox "10 D2" | qhull v

  Number of points processed: 10
  Number of hyperplanes created: 28
  Number of facets in hull: 16
  Number of distance tests for qhull: 47
  CPU seconds to compute hull (after input):  0


Voronoi vertices for 'qhull v' via C++ classes
2
14
-0.129438 -0.0724741 
0.0826769 -0.239764 
0.129526 1.71603 
0.174036 0.531752 
0.185142 0.388255 
-0.906594 -0.296296 
-0.195481 -0.0711189 
-0.140758 0.723386 
-0.16763 0.208062 
0.0586831 0.0663207 
0.0880634 0.105408 
0.476159 -0.0316837 
3.09421 -0.0647219 
0.541052 0.211562 
10
5 6 0 1 -1 5
4 7 2 -1 5
3 13 4 10
4 8 3 2 7
6 13 4 3 2 -1 12
4 8 6 5 7
5 13 10 9 11 12
7 10 4 3 8 6 0 9
4 12 -1 1 11
4 11 1 0 9

Hyperplanes for bounded facets between Voronoi regions via QhullUser and qh_fprintf
19
5 0 5  -0.301881 0.953346 0.00878913 
5 0 7  0.0205153 0.99979 0.0751143 
5 0 9  0.619259 0.785187 0.137061 
5 1 5  0.799595 -0.600539 0.546971 
5 1 3  0.964872 -0.262721 0.325862 
5 2 6  0.22816 -0.973624 0.0825353 
5 2 4  0.444671 0.895694 -0.430084 
5 2 7  -0.945841 0.32463 0.0490754 
5 3 5  -0.998643 0.0520745 -0.178237 
5 3 7  0.687752 -0.725945 0.26633 
5 3 4  0.999294 0.037557 -0.193884 
5 4 6  -0.107584 -0.994196 0.268542 
5 4 7  -0.997018 -0.0771644 0.214549 
5 5 7  0.995061 -0.0992661 0.187455 
5 6 7  -0.799364 0.600847 0.00706064 
5 6 9  -0.228542 -0.973534 0.077977 
5 6 8  -0.0126184 -0.99992 -0.0256728 
5 7 9  0.593695 -0.80469 0.0185277 
5 8 9  -0.467479 0.884004 0.250603 

Hyperplanes for unbounded facets between Voronoi regions via QhullUser and qh_fprintf
4
5 0 8  0.719063 0.694945 0.107173 
5 0 1  -0.385496 0.92271 -0.076093 
5 1 4  0.992921 -0.118775 0.0752121 
5 4 8  -0.0664014 -0.997793 0.140881 

Message codes captured by qh_fprintf in QhullUser.cpp (qhull v Fo Ta):
9231 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 

Results of p
2
14
-0.1294381801544404 -0.07247409101984709 
0.08267689532419764 -0.2397644955865706 
0.1295260566906467 1.716033573116839 
0.1740355150742391 0.5317519038435656 
0.1851415205797576 0.3882545794457364 
-0.9065939866848106 -0.2962957610652136 
-0.1954805620516264 -0.07111892482963184 
-0.1407581310832469 0.7233857048236081 
-0.1676297826663961 0.2080621273999384 
0.05868313821742954 0.06632066014880161 
0.08806341399736983 0.1054080604689984 
0.4761588899009251 -0.03168366595227294 
3.094213357897476 -0.064721945677682 
0.5410515627308723 0.211561543495592 

Results of Fi
19
5 0 5 -0.301880639203215 0.9533457293522944 0.008789126238507639 
5 0 7 0.02051532578114256 0.9997895385570373 0.0751143044524602 
5 0 9 0.619259133056969 0.7851866823409139 0.1370614663104577 
5 1 5 0.7995952824356682 -0.6005392446015695 0.5469710423089691 
5 1 3 0.9648718030091262 -0.2627211520946076 0.3258622775065155 
5 2 6 0.2281595097543264 -0.9736237661995856 0.0825352874566877 
5 2 4 0.4446710312325422 0.895693962234081 -0.4300843534994401 
5 2 7 -0.9458410914974846 0.324629988810102 0.04907537812572163 
5 3 5 -0.9986432053419565 0.05207445078292225 -0.1782370644858235 
5 3 7 0.6877523324625964 -0.7259454037269318 0.2663295190946446 
5 3 4 0.99929448732669 0.03755699133966526 -0.1938837324602515 
5 4 6 -0.1075842248297359 -0.9941959739245502 0.2685422477498993 
5 4 7 -0.9970183790688238 -0.07716444646969949 0.2145489484590234 
5 5 7 0.995060920624513 -0.09926612839179721 0.1874553677160639 
5 6 7 -0.7993641842155071 0.6008468199079334 0.007060641163779156 
5 6 9 -0.2285415587894344 -0.9735341575446109 0.07797696388863322 
5 6 8 -0.01261839651625044 -0.9999203848653946 -0.02567278177543585 
5 7 9 0.5936952885926361 -0.8046899429612046 0.01852766555277021 
5 8 9 -0.4674785097727935 0.8840044360186254 0.2506025495170938 

Results of Fo
4
5 0 8 0.7190625207842074 0.6949453872092838 0.1071733734620183 
5 0 1 -0.3854955578888163 0.922709691532494 -0.07609298438083834 
5 1 4 0.9929212365203528 -0.1187746524595787 0.0752121188850394 
5 4 8 -0.06640144810487485 -0.9977929883946747 0.1408811441173877 

set +v
=== check front ends and examples Fri, Jul 24, 2020 10:27:18 PM ==================
qconvex -

qconvex -- compute the convex hull
    http://www.qhull.org  2020.2 2020/07/24

input (stdin):
    first lines: dimension and number of points (or vice-versa).
    other lines: point coordinates, best if one point per line
    comments:    start with a non-numeric character

options:
    Qc   - keep coplanar points with nearest facet
    Qi   - keep interior points with nearest facet
    QJ   - joggled input instead of merged facets
    Qt   - triangulated output

Qhull control options:
    Qa   - allow input with fewer or more points than coordinates
    Qbk:n   - scale coord k so that low bound is n
      QBk:n - scale coord k so that upper bound is n (QBk is 0.5)
    QbB  - scale input to unit cube centered at the origin
    Qbk:0Bk:0 - remove k-th coordinate from input
    QJn  - randomly joggle input in range [-n,n]
    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
    Qs   - search all points for the initial simplex

Qhull extra options:
    QGn  - good facet if visible from point n, -n for not visible
    QVn  - good facet if it includes point n, -n if not
    Qw   - allow option warnings
    Q12  - allow wide facets and wide dupridge
    Q14  - merge pinched vertices that create a dupridge

T options:
    TFn  - report summary when n or more facets created
    TI file - input file, may be enclosed in single quotes
    TO file - output file, may be enclosed in single quotes
    Ts   - statistics
    Tv   - verify result: structure, convexity, and in-circle test
    Tz   - send all output to stdout

Trace options:
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
    Ta   - annotate output with message codes
    TAn  - stop qhull after adding n vertices
     TCn - stop qhull after building cone for point n
     TVn - stop qhull after adding point n, -n for before
    Tc   - check frequently during execution
    Tf   - flush each qh_fprintf for debugging segfaults
    TPn  - turn on tracing when point n added to hull
     TMn - turn on tracing at merge n
     TWn - trace merge facets when width > n

Precision options:
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
    Rn   - randomly perturb computations by a factor of [1-n,1+n]
    Un   - max distance below plane for a new, coplanar point
    Wn   - min facet width for outside point (before roundoff)

Output formats (may be combined; if none, produces a summary to stdout):
    f    - facet dump
    G    - Geomview output (see below)
    i    - vertices incident to each facet
    m    - Mathematica output (2-d and 3-d)
    n    - normals with offsets
    o    - OFF file format (dim, points and facets)
    p    - point coordinates 
    s    - summary (stderr)

More formats:
    Fa   - area for each facet
    FA   - compute total area and volume for option 's'
    Fc   - count plus coplanar points for each facet
           use 'Qc' (default) for coplanar and 'Qi' for interior
    FC   - centrum for each facet
    Fd   - use cdd format for input (homogeneous with offset first)
    FD   - use cdd format for numeric output (offset first)
    FF   - facet dump without ridges
    Fi   - inner plane for each facet
    FI   - ID for each facet
    Fm   - merge count for each facet (511 max)
    FM   - Maple output (2-d and 3-d)
    Fn   - count plus neighboring facets for each facet
    FN   - count plus neighboring facets for each point
    Fo   - outer plane (or max_outside) for each facet
    FO   - options and precision constants
    FP   - nearest vertex for each coplanar point
    FQ   - command used for qconvex
    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
                      output: #vertices, #facets, #coplanars, #nonsimplicial
                    #real (2), max outer plane, min vertex
    FS   - sizes:   #int (0) 
                    #real (2) tot area, tot volume
    Ft   - triangulation with centrums for non-simplicial facets (OFF format)
    Fv   - count plus vertices for each facet
    FV   - average of vertices (a feasible point for 'H')
    Fx   - extreme points (in order for 2-d)

Geomview output (2-d, 3-d, and 4-d)
    Ga   - all points as dots
     Gp  -  coplanar points and vertices as radii
     Gv  -  vertices as spheres
    Gc   - centrums
    GDn  - drop dimension n in 3-d and 4-d output
    Gh   - hyperplane intersections
    Gi   - inner planes only
     Gn  -  no planes
     Go  -  outer planes only
    Gr   - ridges

Print options:
    PAn  - keep n largest facets by area
    Pdk:n - drop facet if normal[k] <= n (default 0.0)
    PDk:n - drop facet if normal[k] >= n
    PFn  - keep facets whose area is at least n
    Pg   - print good facets (needs 'QGn' or 'QVn')
    PG   - print neighbors of good facets
    PMn  - keep n facets with most merges
    Po   - force output.  If error, output neighborhood of facet
    Pp   - do not report precision problems

    .    - list of all options
    -    - one line descriptions of all options
    -?   - help with examples
    -V   - version
qconvex .

Qhull 2020.2 2020/07/24
Except for 'F.' and 'PG', upper-case options take an argument.

 facet-dump     Geomview       incidences     mathematica    normals
 off-format     points         summary

 Farea          FArea-total    Fcoplanars     FCentrums      Fd-cdd-in
 FD-cdd-out     FFacets-xridge Finner         FIDs           Fmerges
 FMaple         Fneighbors     FNeigh-vertex  Fouter         FOptions
 FPoint-near    FQhull         Fsummary       FSize          Ftriangles
 Fvertices      FVertex-ave    Fxtremes

 Gall-points    Gcentrums      GDrop-dim      Ghyperplanes   Ginner
 Gno-planes     Gouter         Gpoints        Gridges        Gvertices

 PArea-keep     Pdrop-d0:0D0   PFacet-area-keep  Pgood       PGood-neighbors
 PMerge-keep    Poutput-forced Pprecision-not

 Qallow-short   QbBound-0:0.5  QbB-scale-box  Qcoplanar      QGood-point
 Qinterior      QJoggle        QRotate        Qsearch-all    Qtriangulate
 QVertex-good   Qwarn-allow    Q12-allow-wide Q14-merge-pinched

 TFacet-log     TInput-file    TOutput-file   Tstatistics    Tverify
 Tz-stdout

 T4-trace       Tannotate      TAdd-stop      Tcheck-often   TCone-stop
 Tflush         TMerge-trace   TPoint-trace   TVertex-stop   TWide-trace

 Angle-max      Centrum-size   Random-dist    Ucoplanar-max  Wide-outside
qconvex -? # [mar'19] isatty does not work for Git for Windows

qconvex -- compute the convex hull.  Qhull 2020.2 2020/07/24
    input (stdin): dimension, number of points, point coordinates
    comments start with a non-numeric character

options (qconvex.htm):
    Qt   - triangulated output
    QJ   - joggled input instead of merged facets
    Tv   - verify result: structure, convexity, and point inclusion
    .    - concise list of all options
    -    - one-line description of each option
    -?   - this message
    -V   - version

output options (subset):
    s    - summary of results (default)
    i    - vertices incident to each facet
    n    - normals with offsets
    p    - vertex coordinates (if 'Qc', includes coplanar points)
    FA   - report total area and volume
    FS   - total area and volume
    Fx   - extreme points (convex hull vertices)
    G    - Geomview output (2-d, 3-d, and 4-d)
    m    - Mathematica output (2-d and 3-d)
    o    - OFF format (dim, n, points, facets)
    QVn  - print facets that include point n, -n if not
    TI file - input file, may be enclosed in single quotes
    TO file - output file, may be enclosed in single quotes

examples:
    rbox c D2 | qconvex s n                    rbox c D2 | qconvex i
    rbox c D2 | qconvex o                      rbox 1000 s | qconvex s Tv FA
    rbox c d D2 | qconvex s Qc Fx              rbox y 1000 W0 | qconvex Qc s n
    rbox y 1000 W0 | qconvex s QJ              rbox d G1 D12 | qconvex QR0 FA Pp
    rbox c D7 | qconvex FA TF1000

rbox c D3 | qconvex s n Qt 

Convex hull of 8 points in 3-d:

  Number of vertices: 8
  Number of facets: 12
  Number of triangulated facets: 6

Statistics for: rbox c D3 | qconvex s n Qt

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 90
  Number of distance tests for checking: 48
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0

4
12
    -0     -0     -1   -0.5 
    -0     -0     -1   -0.5 
     0     -1      0   -0.5 
     0     -1      0   -0.5 
     1     -0     -0   -0.5 
     1     -0     -0   -0.5 
    -1     -0     -0   -0.5 
    -1     -0     -0   -0.5 
     0      1     -0   -0.5 
     0      1     -0   -0.5 
    -0     -0      1   -0.5 
    -0     -0      1   -0.5 
rbox c D2 | qconvex s i 

Convex hull of 4 points in 2-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox c D2 | qconvex s i

  Number of points processed: 4
  Number of hyperplanes created: 6
  Number of distance tests for qhull: 5
  CPU seconds to compute hull (after input):  0

4
0 2 
1 0 
2 3 
3 1 
rbox c D2 | qconvex s n

Convex hull of 4 points in 2-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox c D2 | qconvex s n

  Number of points processed: 4
  Number of hyperplanes created: 6
  Number of distance tests for qhull: 5
  CPU seconds to compute hull (after input):  0

3
4
    -0     -1   -0.5 
    -1      0   -0.5 
     1     -0   -0.5 
     0      1   -0.5 
rbox c D2 | qconvex o
2
4 4 4
  -0.5   -0.5 
  -0.5    0.5 
   0.5   -0.5 
   0.5    0.5 
2 0 2 
2 1 0 
2 2 3 
2 3 1 
rbox 1000 s | qconvex s Tv FA

Convex hull of 1000 points in 3-d:

  Number of vertices: 1000
  Number of facets: 1996

Statistics for: rbox 1000 s | qconvex s Tv FA

  Number of points processed: 1000
  Number of hyperplanes created: 5544
  Number of distance tests for qhull: 25487
  CPU seconds to compute hull (after input): 0.003
  Total facet area:   3.1201951
  Total volume:       0.51650274


qhull output completed.  Verifying that 1000 points are
below 2.1e-15 of the nearest facet.
rbox c d D2 | qconvex s Qc Fx

Convex hull of 8 points in 2-d:

  Number of vertices: 4
  Number of coplanar points: 4
  Number of facets: 4

Statistics for: rbox c d D2 | qconvex s Qc Fx

  Number of points processed: 4
  Number of hyperplanes created: 6
  Number of distance tests for qhull: 35
  CPU seconds to compute hull (after input):  0

4
0
2
3
1
rbox y 1000 W0 | qconvex Qc s n 

Convex hull of 1004 points in 3-d:

  Number of vertices: 4
  Number of coplanar points: 1000
  Number of facets: 4

Statistics for: rbox y 1000 W0 | qconvex Qc s n

  Number of points processed: 4
  Number of hyperplanes created: 4
  Number of distance tests for qhull: 11000
  CPU seconds to compute hull (after input): 0.001

4
4
0.2135848119563837 0.1168704340428168 0.9699086708284446 -0.09806074564261894 
0.08553875579270347 -0.8316435307282575 -0.5486822022403076 -0.1234144150397865 
-0.749541668500822 -0.02779445272382575 -0.6613733859014791 -0.2159556159595279 
0.3120013537900506 0.9498158823230658 -0.02247097950761911 -0.02453689035981485 
rbox y 1000 W0 | qconvex s QJ

Convex hull of 1004 points in 3-d:

  Number of vertices: 51
  Number of facets: 98

Statistics for: rbox y 1000 W0 | qconvex s QJ

  Number of points processed: 52
  Number of hyperplanes created: 180
  Number of distance tests for qhull: 6420
  CPU seconds to compute hull (after input):  0
  Input joggled by: 2.1e-11

rbox d G1 D12 | qconvex QR0 FA

Convex hull of 24 points in 12-d:

  Number of vertices: 24
  Number of facets: 4096

Statistics for: rbox d G1 D12 | qconvex QR0 FA QR1595644039

  Number of points processed: 24
  Number of hyperplanes created: 4107
  Number of distance tests for qhull: 4215
  Number of distance tests for merging: 121142
  Number of distance tests for checking: 98304
  Number of merged facets: 2036
  CPU seconds to compute hull (after input): 0.024
  Approximate facet area:   0.00035546337
  Approximate volume:       8.5511197e-06

rbox c D6 | qconvex s FA TF500

At 22:27:19 & 0.003 CPU secs, qhull has created 543 facets and merged 289.
 The current hull contains 91 facets and 23 vertices.  There are 41
 outside points.  Next is point p27(v24), 0.64 above f107.

At 22:27:19 & 0.004 CPU secs, qhull has created 1061 facets and merged 737.
 The current hull contains 69 facets and 33 vertices.  There are 31
 outside points.  Next is point p22(v34), 0.52 above f610.

At 22:27:19 & 0.006 CPU secs, qhull has created 1567 facets and merged 1216.
 The current hull contains 37 facets and 48 vertices.  There are 16
 outside points.  Next is point p9(v49), 0.45 above f1061.

At 22:27:19 & 0.006 CPU secs, qhull has created 1819 facets and merged 1462.
 The current hull contains 12 facets and 64 vertices.  Last point was p11

Convex hull of 64 points in 6-d:

  Number of vertices: 64
  Number of facets: 12
  Number of non-simplicial facets: 12

Statistics for: rbox c D6 | qconvex s FA TF500

  Number of points processed: 64
  Number of hyperplanes created: 358
  Number of distance tests for qhull: 2515
  Number of distance tests for merging: 14300
  Number of distance tests for checking: 0
  Number of merged facets: 1462


First post-merge with 'C3.5e-15' and 'A1.8e+308'

At 22:27:19 & 0.006 CPU secs, qhull has created 1819 facets and merged 1462.
 The current hull contains 12 facets and 64 vertices.  Last point was p11

Testing all coplanar points.
computing area of each facet and volume of the convex hull

Convex hull of 64 points in 6-d:

  Number of vertices: 64
  Number of facets: 12
  Number of non-simplicial facets: 12

Statistics for: rbox c D6 | qconvex s FA TF500

  Number of points processed: 64
  Number of hyperplanes created: 358
  Number of distance tests for qhull: 2515
  Number of distance tests for merging: 14420
  Number of distance tests for checking: 768
  Number of merged facets: 1462
  CPU seconds to compute hull (after input): 0.006
  Approximate facet area:   12
  Approximate volume:        1

rbox c D7 | qconvex s FA TF1000

At 22:27:19 & 0.003 CPU secs, qhull has created 1048 facets and merged 469.
 The current hull contains 230 facets and 24 vertices.  There are 104
 outside points.  Next is point p79(v25), 0.66 above f145.

At 22:27:19 & 0.005 CPU secs, qhull has created 2146 facets and merged 1272.
 The current hull contains 273 facets and 31 vertices.  There are 97
 outside points.  Next is point p120(v32), 0.54 above f437.

At 22:27:19 & 0.008 CPU secs, qhull has created 3310 facets and merged 2244.
 The current hull contains 243 facets and 36 vertices.  There are 92
 outside points.  Next is point p60(v37), 0.54 above f1338.

At 22:27:19 & 0.01 CPU secs, qhull has created 4322 facets and merged 3099.
 The current hull contains 249 facets and 42 vertices.  There are 86
 outside points.  Next is point p30(v43), 0.54 above f2005.

At 22:27:19 & 0.013 CPU secs, qhull has created 5491 facets and merged 4196.
 The current hull contains 186 facets and 48 vertices.  There are 80
 outside points.  Next is point p21(v49), 0.5 above f2995.

At 22:27:19 & 0.015 CPU secs, qhull has created 6589 facets and merged 5175.
 The current hull contains 194 facets and 53 vertices.  There are 75
 outside points.  Next is point p56(v54), 0.28 above f3731.

At 22:27:19 & 0.018 CPU secs, qhull has created 7867 facets and merged 6337.
 The current hull contains 203 facets and 60 vertices.  There are 68
 outside points.  Next is point p76(v61), 0.29 above f5879.

At 22:27:19 & 0.021 CPU secs, qhull has created 8971 facets and merged 7362.
 The current hull contains 179 facets and 67 vertices.  There are 61
 outside points.  Next is point p80(v68), 0.23 above f7175.

At 22:27:19 & 0.024 CPU secs, qhull has created 9984 facets and merged 8352.
 The current hull contains 104 facets and 77 vertices.  There are 51
 outside points.  Next is point p96(v78), 0.41 above f6748.

At 22:27:19 & 0.028 CPU secs, qhull has created 10990 facets and merged 9326.
 The current hull contains 54 facets and 90 vertices.  There are 38
 outside points.  Next is point p18(v91), 0.41 above f10178.

At 22:27:19 & 0.03 CPU secs, qhull has created 11996 facets and merged 10295.
 The current hull contains 34 facets and 114 vertices.  There are 14
 outside points.  Next is point p19(v115), 0.38 above f11792.

At 22:27:19 & 0.032 CPU secs, qhull has created 12860 facets and merged 11072.
 The current hull contains 14 facets and 128 vertices.  Last point was p77

Convex hull of 128 points in 7-d:

  Number of vertices: 128
  Number of facets: 14
  Number of non-simplicial facets: 14

Statistics for: rbox c D7 | qconvex s FA TF1000

  Number of points processed: 128
  Number of hyperplanes created: 1789
  Number of distance tests for qhull: 10122
  Number of distance tests for merging: 87203
  Number of distance tests for checking: 0
  Number of merged facets: 11072


First post-merge with 'C4.4e-15' and 'A1.8e+308'

At 22:27:19 & 0.033 CPU secs, qhull has created 12860 facets and merged 11072.
 The current hull contains 14 facets and 128 vertices.  Last point was p77

Testing all coplanar points.
computing area of each facet and volume of the convex hull

Convex hull of 128 points in 7-d:

  Number of vertices: 128
  Number of facets: 14
  Number of non-simplicial facets: 14

Statistics for: rbox c D7 | qconvex s FA TF1000

  Number of points processed: 128
  Number of hyperplanes created: 1789
  Number of distance tests for qhull: 10122
  Number of distance tests for merging: 87371
  Number of distance tests for checking: 1792
  Number of merged facets: 11072
  CPU seconds to compute hull (after input): 0.033
  Approximate facet area:   14
  Approximate volume:        1

rbox d G1 D12 | qconvex QR0 FA Pp

Convex hull of 24 points in 12-d:

  Number of vertices: 24
  Number of facets: 4096

Statistics for: rbox d G1 D12 | qconvex QR0 FA Pp QR1595644039

  Number of points processed: 24
  Number of hyperplanes created: 4107
  Number of distance tests for qhull: 4215
  Number of distance tests for merging: 121142
  Number of distance tests for checking: 98304
  Number of merged facets: 2036
  CPU seconds to compute hull (after input): 0.022
  Approximate facet area:   0.00035546337
  Approximate volume:       8.5511197e-06

rbox c P0 d D2 | qconvex p Fa Fc FP FI Fn FN FS Fv Fx 
2
8
  -0.5   -0.5 
  -0.5    0.5 
   0.5   -0.5 
   0.5    0.5 
     0   -0.5 
     0    0.5 
  -0.5      0 
   0.5      0 
4
     1 
     1 
     1 
     1 
4
1 5
1 7
1 8
1 6
4
3 5 1    0.5 
2 7 2    0.5 
4 8 4    0.5 
4 6 5    0.5 
4
1
2
4
5
4
2 1 2
2 0 3
2 0 3
2 1 2
9
0
2 0 1
2 1 3
2 2 0
2 3 2
1 0
1 3
1 1
1 2
0
2      4      1 
4
2 3 1
2 2 1
2 4 3
2 4 2
4
1
3
4
2
rbox c d D2 | qconvex s i QV0

Convex hull of 8 points in 2-d:

  Number of vertices: 4
  Number of facets: 4
  Number of 'good' facets: 2

Statistics for: rbox c d D2 | qconvex s i QV0

  Number of points processed: 4
  Number of hyperplanes created: 6
  Number of distance tests for qhull: 35
  CPU seconds to compute hull (after input):  0

2
0 2 
1 0 
rbox c | qconvex Q0
QH6029 qhull option error: option 'Q0' is not used with this program.
             It may be used with qhull.

While executing:  | qconvex Q0
Options selected for Qhull 2020.2 2020/07/24:
  run-id 213579737  _maxoutside  0
qvoronoi -

qvoronoi -- compute the Voronoi diagram
    http://www.qhull.org  2020.2 2020/07/24

input (stdin):
    first lines: dimension and number of points (or vice-versa).
    other lines: point coordinates, best if one point per line
    comments:    start with a non-numeric character

options:
    Qu   - compute furthest-site Voronoi diagram

Qhull control options:
    Qa   - allow input with fewer or more points than coordinates
    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
    Qs   - search all points for the initial simplex
    Qz   - add point-at-infinity to Voronoi diagram

Qhull extra options:
    QGn  - Voronoi vertices if visible from point n, -n if not
    QVn  - Voronoi vertices for input point n, -n if not
    Qw   - allow option warnings
    Q12  - allow wide facets and wide dupridge
    Q14  - merge pinched vertices that create a dupridge

T options:
    TFn  - report summary when n or more facets created
    TI file - input file, may be enclosed in single quotes
    TO file - output file, may be enclosed in single quotes
    Ts   - statistics
    Tv   - verify result: structure, convexity, and in-circle test
    Tz   - send all output to stdout

Trace options:
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
    Ta   - annotate output with message codes
    TAn  - stop qhull after adding n vertices
     TCn - stop qhull after building cone for point n
     TVn - stop qhull after adding point n, -n for before
    Tc   - check frequently during execution
    Tf   - flush each qh_fprintf for debugging segfaults
    TPn  - turn on tracing when point n added to hull
     TMn - turn on tracing at merge n
     TWn - trace merge facets when width > n

Precision options:
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
    Rn   - randomly perturb computations by a factor of [1-n,1+n]
    Wn   - min facet width for non-coincident point (before roundoff)

Output formats (may be combined; if none, summary to stdout):
    p    - Voronoi vertices
    s    - summary to stderr
    f    - facet dump
    i    - Delaunay regions (use 'Pp' to avoid warning)
    o    - OFF format (dim, Voronoi vertices, and Voronoi regions)

More formats:
    Fc   - count plus coincident points (by Voronoi vertex)
    Fd   - use cdd format for input (homogeneous with offset first)
    FD   - use cdd format for output (offset first)
    FF   - facet dump without ridges
    Fi   - separating hyperplanes for bounded Voronoi regions
    FI   - ID for each Voronoi vertex
    Fm   - merge count for each Voronoi vertex (511 max)
    Fn   - count plus neighboring Voronoi vertices for each Voronoi vertex
    FN   - count and Voronoi vertices for each Voronoi region
    Fo   - separating hyperplanes for unbounded Voronoi regions
    FO   - options and precision constants
    FP   - nearest point and distance for each coincident point
    FQ   - command used for qvoronoi
    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
                    for output: #Voronoi regions, #Voronoi vertices,
                                #coincident points, #non-simplicial regions
                    #real (2), max outer plane and min vertex
    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites
    Fx   - extreme points of Delaunay triangulation (on convex hull)

Geomview output (2-d only)
    Ga   - all points as dots
     Gp  -  coplanar points and vertices as radii
     Gv  -  vertices as spheres
    Gc   - centrums
    GDn  - drop dimension n in 3-d and 4-d output
    Gh   - hyperplane intersections
    Gi   - inner planes only
     Gn  -  no planes
     Go  -  outer planes only
    Gr   - ridges

Print options:
    PAn  - keep n largest Voronoi vertices by 'area'
    Pdk:n - drop facet if normal[k] <= n (default 0.0)
    PDk:n - drop facet if normal[k] >= n
    PFn  - keep Voronoi vertices whose 'area' is at least n
    Pg   - print good Voronoi vertices (needs 'QGn' or 'QVn')
    PG   - print neighbors of good Voronoi vertices
    PMn  - keep n Voronoi vertices with most merges
    Po   - force output.  If error, output neighborhood of facet
    Pp   - do not report precision problems

    .    - list of all options
    -    - one line descriptions of all options
    -?   - help with examples
    -V   - version
qvoronoi .

Qhull 2020.2 2020/07/24
Except for 'F.' and 'PG', upper-case options take an argument.

 facet-dump     Geomview       i-delaunay     off-format     p-vertices
 summary

 Fcoincident    Fd-cdd-in      FD-cdd-out     FF-dump-xridge Fi-bounded
 FIDs           Fmerges        Fneighbors     FNeigh-region  Fo-unbounded
 FOptions       FPoint-near    FQvoronoi      Fsummary       Fvoronoi
 Fxtremes

 Gall-points    Gcentrums      GDrop-dim      Ghyperplanes   Ginner
 Gno-planes     Gouter         Gpoints        Gridges        Gvertices

 PArea-keep     Pdrop-d0:0D0   PFacet-area-keep  Pgood       PGood-neighbors
 PMerge-keep    Poutput-forced Pprecision-not

 Qallow-short   QG-vertex-good QRotate        Qsearch-all    Qupper-voronoi
 QV-point-good  Qwarn-allow    Qzinfinite     Q12-allow-wide Q14-merge-pinched

 TFacet-log     TInput-file    TOutput-file   Tstatistics    Tverify
 Tz-stdout

 T4-trace       Tannotate      TAdd-stop      Tcheck-often   TCone-stop
 Tflush         TMerge-trace   TPoint-trace   TVertex-stop   TWide-trace

 Angle-max      Centrum-size   Random-dist    Wide-outside
qvoronoi -? # [mar'19] isatty does not work for Git for Windows

qvoronoi -- compute the Voronoi diagram.  Qhull 2020.2 2020/07/24
    input (stdin): dimension, number of points, point coordinates
    comments start with a non-numeric character

options (qvoronoi.htm):
    Qu   - compute furthest-site Voronoi diagram
    Tv   - verify result: structure, convexity, and in-circle test
    .    - concise list of all options
    -    - one-line description of all options
    -?   - this message
    -V   - version

output options (subset):
    Fi   - separating hyperplanes for bounded regions, 'Fo' for unbounded
    FN   - count and Voronoi vertices for each Voronoi region
    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites
    G    - Geomview output (2-d only)
    o    - OFF file format (dim, Voronoi vertices, and Voronoi regions)
    p    - Voronoi vertices
    QVn  - Voronoi vertices for input point n, -n if not
    s    - summary of results (default)
    TI file - input file, may be enclosed in single quotes
    TO file - output file, may be enclosed in single quotes

examples:
    rbox c P0 D2 | qvoronoi s o         rbox c P0 D2 | qvoronoi Fi
    rbox c P0 D2 | qvoronoi Fo          rbox c P0 D2 | qvoronoi Fv
    rbox c P0 D2 | qvoronoi s Qu Fv     rbox c P0 D2 | qvoronoi Qu Fo
    rbox c G1 d D2 | qvoronoi s p       rbox c P0 D2 | qvoronoi s Fv QV0

rbox c P0 D2 | qvoronoi s o

Voronoi diagram by the convex hull of 5 points in 3-d:

  Number of Voronoi regions: 5
  Number of Voronoi vertices: 4

Statistics for: rbox c P0 D2 | qvoronoi s o

  Number of points processed: 5
  Number of hyperplanes created: 6
  Number of facets in hull: 5
  Number of distance tests for qhull: 7
  Number of distance tests for merging: 34
  Number of distance tests for checking: 25
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0

2
5 5 1
-10.101 -10.101 
     0   -0.5 
  -0.5      0 
   0.5      0 
     0    0.5 
4 4 2 1 3
3 2 0 1
3 4 0 2
3 3 0 1
3 4 0 3
rbox c P0 D2 | qvoronoi Fi Tv
4
5 0 3 0.7071067811865475 -0.7071067811865475 -0.3535533905932737 
5 0 1 -0.7071067811865475 -0.7071067811865475 -0.3535533905932737 
5 0 2 -0.7071067811865475 0.7071067811865475 -0.3535533905932737 
5 0 4 0.7071067811865475 0.7071067811865475 -0.3535533905932737 

Voronoi ridge statistics
      4 bounded ridges
      0   max. distance of midpoint to ridge
      4 bounded ridges with ok normal
2.2e-16   ave. angle to ridge
2.2e-16   max. angle to ridge

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 20 distance computations.
rbox c P0 D2 | qvoronoi Fo Tv
4
5 1 2     -1      0   -0.5 
5 1 3      1     -0     -0 
5 2 4      1     -0     -0 
5 3 4     -1      0    0.5 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 20 distance computations.
rbox c P0 D2 | qvoronoi Fv
8
4 0 3 1 3
4 0 1 1 2
4 0 2 2 4
4 0 4 3 4
4 1 2 0 2
4 1 3 0 1
4 2 4 0 4
4 3 4 0 3
rbox c P0 D2 | qvoronoi s Qu Fv

Furthest-site Voronoi vertices by the convex hull of 5 points in 3-d:

  Number of Voronoi regions: 5
  Number of Voronoi vertices: 1
  Number of non-simplicial Voronoi vertices: 1

Statistics for: rbox c P0 D2 | qvoronoi s Qu Fv

  Number of points processed: 5
  Number of hyperplanes created: 6
  Number of facets in hull: 5
  Number of distance tests for qhull: 7
  Number of distance tests for merging: 34
  Number of distance tests for checking: 25
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0

4
4 1 2 0 1
4 1 3 0 1
4 2 4 0 1
4 3 4 0 1
rbox c P0 D2 | qvoronoi s Qu Qt Fv

Furthest-site Voronoi vertices by the convex hull of 5 points in 3-d:

  Number of Voronoi regions: 5
  Number of Voronoi vertices: 2
  Number of triangulated facets: 1

Statistics for: rbox c P0 D2 | qvoronoi s Qu Qt Fv

  Number of points processed: 5
  Number of hyperplanes created: 6
  Number of facets in hull: 6
  Number of distance tests for qhull: 7
  Number of distance tests for merging: 34
  Number of distance tests for checking: 25
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0

4
4 1 3 0 2
4 1 2 0 1
4 2 4 0 1
4 3 4 0 2
rbox c P0 D2 | qvoronoi Qu Fo
4
5 1 2     -0      1      0 
5 1 3      1     -0     -0 
5 2 4      1     -0     -0 
5 3 4     -0      1     -0 
rbox c G1 d D2 | qvoronoi s p 

Voronoi diagram by the convex hull of 8 points in 3-d:

  Number of Voronoi regions: 8
  Number of Voronoi vertices: 9
  Number of non-simplicial Voronoi vertices: 1

Statistics for: rbox c G1 d D2 | qvoronoi s p

  Number of points processed: 8
  Number of hyperplanes created: 16
  Number of facets in hull: 10
  Number of distance tests for qhull: 41
  Number of distance tests for merging: 108
  Number of distance tests for checking: 72
  Number of merged facets: 3
  CPU seconds to compute hull (after input):  0

2
9
     0  -1.75 
 -1.75      0 
-0.5833333333333334 -0.5833333333333333 
     0   1.75 
-0.5833333333333333 0.5833333333333334 
  1.75      0 
0.5833333333333334 -0.5833333333333333 
0.5833333333333334 0.5833333333333333 
     0      0 
rbox c G1 d D2 | qvoronoi QJ p 
2
10
-2.57276422388486e-11 1.749999999802917 
-2.05463598231932e-11 -1.750000000331276 
0.5833333333083517 -0.5833333333052267 
1.862254794815499e-11 -7.815052443180038e-11 
1.750000000002628 3.498100747664324e-11 
0.5833333333132078 0.5833333333796981 
-0.5833333332888888 0.5833333333317835 
-7.592293460589872e-11 -7.815050692933323e-11 
-1.750000000049026 2.293196879294717e-11 
-0.5833333333977307 -0.5833333333229861 
rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN 

Voronoi diagram by the convex hull of 7 points in 3-d:

  Number of Voronoi regions: 6
  Number of nearly incident points: 1
  Number of Voronoi vertices: 4
  Number of non-simplicial Voronoi vertices: 2

Statistics for: rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN

  Number of points processed: 6
  Number of hyperplanes created: 7
  Number of facets in hull: 5
  Number of distance tests for qhull: 31
  Number of distance tests for merging: 54
  Number of distance tests for checking: 36
  Number of merged facets: 3
  CPU seconds to compute hull (after input):  0

4
0
1 1
0
0
1
2 1 8      0 
rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN
4
3 -1 2 3
3 -1 2 3
4 -1 0 3 1
4 0 -1 2 1
7
3 3 2 0
1 1
3 3 1 2
3 0 -1 2
3 3 -1 0
3 1 -1 2
3 1 -1 3
rbox P0 c D2 | qvoronoi s Fv QV0

Voronoi diagram by the convex hull of 5 points in 3-d:

  Number of Voronoi regions: 5
  Number of 'good' Voronoi vertices: 4

Statistics for: rbox P0 c D2 | qvoronoi s Fv QV0

  Number of points processed: 5
  Number of hyperplanes created: 6
  Number of facets in hull: 5
  Number of distance tests for qhull: 7
  Number of distance tests for merging: 34
  Number of distance tests for checking: 25
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0

4
4 0 3 1 3
4 0 1 1 2
4 0 2 2 4
4 0 4 3 4
qdelaunay -

qdelaunay -- compute the Delaunay triangulation
    http://www.qhull.org  2020.2 2020/07/24

input (stdin):
    first lines: dimension and number of points (or vice-versa).
    other lines: point coordinates, best if one point per line
    comments:    start with a non-numeric character

options:
    QJ   - joggled input instead of merged facets
    Qt   - triangulated output
    Qu   - compute furthest-site Delaunay triangulation

Qhull control options:
    Qa   - allow input with fewer or more points than coordinates
    QJn  - randomly joggle input in range [-n,n]
    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
    Qs   - search all points for the initial simplex
    Qz   - add point-at-infinity to Delaunay triangulation

Qhull extra options:
    QGn  - print Delaunay region if visible from point n, -n if not
    QVn  - print Delaunay regions that include point n, -n if not
    Qw   - allow option warnings
    Q12  - allow wide facets and wide dupridge
    Q14  - merge pinched vertices that create a dupridge

T options:
    TFn  - report summary when n or more facets created
    TI file - input file, may be enclosed in single quotes
    TO file - output file, may be enclosed in single quotes
    Ts   - statistics
    Tv   - verify result: structure, convexity, and in-circle test
    Tz   - send all output to stdout

Trace options:
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
    Ta   - annotate output with message codes
    TAn  - stop qhull after adding n vertices
     TCn - stop qhull after building cone for point n
     TVn - stop qhull after adding point n, -n for before
    Tc   - check frequently during execution
    Tf   - flush each qh_fprintf for debugging segfaults
    TPn  - turn on tracing when point n added to hull
     TMn - turn on tracing at merge n
     TWn - trace merge facets when width > n

Precision options:
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
    Rn   - randomly perturb computations by a factor of [1-n,1+n]
    Wn   - min facet width for outside point (before roundoff)

Output formats (may be combined; if none, produces a summary to stdout):
    f    - facet dump
    G    - Geomview output (see below)
    i    - vertices incident to each Delaunay region
    m    - Mathematica output (2-d only, lifted to a paraboloid)
    o    - OFF format (dim, points, and facets as a paraboloid)
    p    - point coordinates (lifted to a paraboloid)
    s    - summary (stderr)

More formats:
    Fa   - area for each Delaunay region
    FA   - compute total area for option 's'
    Fc   - count plus coincident points for each Delaunay region
    Fd   - use cdd format for input (homogeneous with offset first)
    FD   - use cdd format for numeric output (offset first)
    FF   - facet dump without ridges
    FI   - ID of each Delaunay region
    Fm   - merge count for each Delaunay region (511 max)
    FM   - Maple output (2-d only, lifted to a paraboloid)
    Fn   - count plus neighboring region for each Delaunay region
    FN   - count plus neighboring region for each point
    FO   - options and precision constants
    FP   - nearest point and distance for each coincident point
    FQ   - command used for qdelaunay
    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
                    output: #vertices, #Delaunay regions,
                                #coincident points, #non-simplicial regions
                    #real (2), max outer plane, min vertex
    FS   - sizes:   #int (0)
                    #real (2), tot area, 0
    Fv   - count plus vertices for each Delaunay region
    Fx   - extreme points of Delaunay triangulation (on convex hull)

Geomview output (2-d and 3-d points lifted to a paraboloid)
    Ga   - all points as dots
     Gp  -  coplanar points and vertices as radii
     Gv  -  vertices as spheres
    Gc   - centrums
    GDn  - drop dimension n in 3-d and 4-d output
    Gh   - hyperplane intersections
    Gi   - inner planes only
     Gn  -  no planes
     Go  -  outer planes only
    Gr   - ridges
    Gt   - transparent outer ridges to view 3-d Delaunay

Print options:
    PAn  - keep n largest Delaunay regions by area
    Pdk:n - drop facet if normal[k] <= n (default 0.0)
    PDk:n - drop facet if normal[k] >= n
    PFn  - keep Delaunay regions whose area is at least n
    Pg   - print good Delaunay regions (needs 'QGn' or 'QVn')
    PG   - print neighbors of good regions (needs 'QGn' or 'QVn')
    PMn  - keep n Delaunay regions with most merges
    Po   - force output.  If error, output neighborhood of facet
    Pp   - do not report precision problems

    .    - list of all options
    -    - one line descriptions of all options
    -?   - help with examples
    -V   - version
qdelaunay .

Qhull 2020.2 2020/07/24
Except for 'F.' and 'PG', upper-case options take an argument.

 facet-dump     Geomview       incidences     mathematica    off-format
 points-lifted  summary

 Farea          FArea-total    Fcoincident    Fd-cdd-in      FD-cdd-out
 FF-dump-xridge FIDs           Fmerges        FMaple         Fneighbors
 FNeigh-vertex  FOptions       FPoint-near    FQdelaun       Fsummary
 FSize          Fvertices      Fxtremes

 Gall-points    Gcentrums      GDrop-dim      Ghyperplanes   Ginner
 Gno-planes     Gouter         Gpoints        Gridges        Gtransparent
 Gvertices

 PArea-keep     Pdrop-d0:0D0   PFacet-area-keep  Pgood       PGood-neighbors
 PMerge-keep    Poutput-forced Pprecision-not

 Qallow-short   QGood-point    QJoggle        Qrotate        Qsearch-all
 Qtriangulate   QupperDelaunay QVertex-good   Qwarn-allow    Qzinfinite
 Q12-allow-wide Q14-merge-pinched

 TFacet-log     TInput-file    TOutput-file   Tstatistics    Tverify
 Tz-stdout

 T4-trace       Tannotate      TAdd-stop      Tcheck-often   TCone-stop
 Tflush         TMerge-trace   TPoint-trace   TVertex-stop   TWide-trace

 Angle-max      Centrum-size   Random-dist    Wide-outside
qdelaunay -? # [mar'19] isatty does not work for Git for Windows

qdelaunay -- compute the Delaunay triangulation.  Qhull 2020.2 2020/07/24
    input (stdin): dimension, number of points, point coordinates
    comments start with a non-numeric character

options (qdelaun.htm):
    Qu   - furthest-site Delaunay triangulation
    Qt   - triangulated output
    QJ   - joggled input instead of merged facets
    Tv   - verify result: structure, convexity, and in-circle test
    .    - concise list of all options
    -    - one-line description of each option
    -?   - this message
    -V   - version

output options (subset):
    s    - summary of results (default)
    i    - vertices incident to each Delaunay region
    Fx   - extreme points (vertices of the convex hull)
    G    - Geomview output (2-d and 3-d points lifted to a paraboloid)
    m    - Mathematica output (2-d inputs lifted to a paraboloid)
    o    - OFF format (shows the points lifted to a paraboloid)
    QVn  - print Delaunay regions that include point n, -n if not
    TI file - input file, may be enclosed in single quotes
    TO file - output file, may be enclosed in single quotes

examples:
    rbox c P0 D2 | qdelaunay s o          rbox c P0 D2 | qdelaunay i
    rbox c P0 D2 | qdelaunay Fv           rbox c P0 D2 | qdelaunay s Qu Fv
    rbox c G1 d D2 | qdelaunay s i        rbox c G1 d D2 | qdelaunay Qt
    rbox M3,4 z 100 D2 | qdelaunay s      rbox M3,4 z 100 D2 | qdelaunay s Qt

rbox c P0 D2 | qdelaunay s o

Delaunay triangulation by the convex hull of 5 points in 3-d:

  Number of input sites: 5
  Number of Delaunay regions: 4

Statistics for: rbox c P0 D2 | qdelaunay s o

  Number of points processed: 5
  Number of hyperplanes created: 6
  Number of facets in hull: 5
  Number of distance tests for qhull: 7
  Number of distance tests for merging: 34
  Number of distance tests for checking: 25
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0

3
5 4 6
     0      0      0 
  -0.5   -0.5    0.5 
  -0.5    0.5    0.5 
   0.5   -0.5    0.5 
   0.5    0.5    0.5 
3 3 0 1 
3 0 2 1 
3 4 0 3 
3 0 4 2 
rbox c P0 D2 | qdelaunay i
4
3 0 1 
0 2 1 
4 0 3 
0 4 2 
rbox c P0 D2 | qdelaunay Fv
4
3 0 3 1
3 0 2 1
3 4 0 3
3 4 0 2
rbox c P0 D2 | qdelaunay s Qu Qt Fv

Furthest-site Delaunay triangulation by the convex hull of 5 points in 3-d:

  Number of input sites: 5
  Number of Delaunay regions: 2
  Number of triangulated facets: 1

Statistics for: rbox c P0 D2 | qdelaunay s Qu Qt Fv

  Number of points processed: 5
  Number of hyperplanes created: 6
  Number of facets in hull: 6
  Number of distance tests for qhull: 7
  Number of distance tests for merging: 34
  Number of distance tests for checking: 25
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0

2
3 4 2 1
3 4 3 1
rbox c G1 d D2 | qdelaunay s i

Delaunay triangulation by the convex hull of 8 points in 3-d:

  Number of input sites: 8
  Number of Delaunay regions: 9
  Number of non-simplicial Delaunay regions: 1

Statistics for: rbox c G1 d D2 | qdelaunay s i

  Number of points processed: 8
  Number of hyperplanes created: 16
  Number of facets in hull: 10
  Number of distance tests for qhull: 41
  Number of distance tests for merging: 108
  Number of distance tests for checking: 72
  Number of merged facets: 3
  CPU seconds to compute hull (after input):  0

9
2 4 0 
6 1 0 
4 6 0 
5 3 1 
6 5 1 
3 7 2 
7 4 2 
5 7 3 
4 7 5 6 
rbox c G1 d D2 | qhull d Qbb Ft
2
9 12 14
    -1     -1 
    -1      1 
     1     -1 
     1      1 
     0   -0.5 
     0    0.5 
  -0.5      0 
   0.5      0 
     0      0 
3 2 4 0 
3 6 1 0 
3 4 6 0 
3 5 3 1 
3 6 5 1 
3 3 7 2 
3 7 4 2 
3 5 7 3 
3 8 5 6 
3 8 6 4 
3 8 7 5 
3 8 4 7 
rbox c G1 d D2 | qhull d Qbb QJ s Ft

Delaunay triangulation by the convex hull of 8 points in 3-d:

  Number of input sites: 8
  Number of Delaunay regions: 10

Statistics for: rbox c G1 d D2 | qhull d Qbb QJ s Ft

  Number of points processed: 8
  Number of hyperplanes created: 19
  Number of facets in hull: 12
  Number of distance tests for qhull: 31
  CPU seconds to compute hull (after input):  0
  Input joggled by: 8.3e-11

2
8 10 15
-1.000000000061343 -0.999999999957446 
-0.9999999999945448 0.9999999999532114 
1.000000000029778 -0.9999999999701502 
0.9999999999806051 1.000000000003233 
-7.748592400792811e-11 -0.5000000000743411 
2.849349704487493e-11 0.49999999991804 
-0.5000000000721135 -1.37371989142159e-11 
0.5000000000148132 7.166044474310069e-11 
3 1 5 3 
3 2 4 0 
3 7 4 2 
3 4 7 5 
3 3 7 2 
3 5 7 3 
3 1 6 5 
3 6 4 5 
3 6 1 0 
3 4 6 0 
rbox M3,4 z 100 D2 | qdelaunay s

Delaunay triangulation by the convex hull of 100 points in 3-d:

  Number of input sites: 100
  Number of Delaunay regions: 81
  Number of non-simplicial Delaunay regions: 81

Statistics for: rbox M3,4 z 100 D2 | qdelaunay s

  Number of points processed: 100
  Number of hyperplanes created: 251
  Number of facets in hull: 86
  Number of distance tests for qhull: 1650
  Number of distance tests for merging: 2765
  Number of distance tests for checking: 1248
  Number of merged facets: 155
  CPU seconds to compute hull (after input):  0

rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN

Delaunay triangulation by the convex hull of 7 points in 3-d:

  Number of input sites: 6
  Number of nearly incident points: 1
  Number of Delaunay regions: 4
  Number of non-simplicial Delaunay regions: 2

Statistics for: rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN

  Number of points processed: 6
  Number of hyperplanes created: 7
  Number of facets in hull: 5
  Number of distance tests for qhull: 31
  Number of distance tests for merging: 54
  Number of distance tests for checking: 35
  Number of merged facets: 3
  CPU seconds to compute hull (after input):  0
  Approximate facet area:    1

4
4
3
6
5
4
   0.2 
   0.2 
   0.3 
   0.3 
4
0
1 1
0
0
1
2 1 8      0 
rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN
4
3 -1 2 3
3 -1 2 3
4 -1 0 3 1
4 0 -1 2 1
7
3 3 2 0
1 1
3 3 1 2
3 0 -1 2
3 3 -1 0
3 1 -1 2
3 1 -1 3
rbox P0 P0 c D2 | qdelaunay s FP QV0

Delaunay triangulation by the convex hull of 6 points in 3-d:

  Number of input sites: 5
  Number of nearly incident points: 1
  Number of 'good' Delaunay regions: 4

Statistics for: rbox P0 P0 c D2 | qdelaunay s FP QV0

  Number of points processed: 5
  Number of hyperplanes created: 6
  Number of facets in hull: 5
  Number of distance tests for qhull: 18
  Number of distance tests for merging: 34
  Number of distance tests for checking: 30
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0

1
0 1 2      0 
qhalf -

qhalf -- compute the intersection of halfspaces about a point
    http://www.qhull.org  2020.2 2020/07/24

input (stdin):
    optional interior point: dimension, 1, coordinates
    first lines: dimension+1 and number of halfspaces
    other lines: halfspace coefficients followed by offset
    comments:    start with a non-numeric character

options:
    Hn,n - specify coordinates of interior point
    Qc   - keep coplanar halfspaces
    Qi   - keep other redundant halfspaces
    QJ   - joggled input instead of merged facets
    Qt   - triangulated output

Qhull control options:
    Qa   - allow input with fewer or more points than coordinates
    Qbk:0Bk:0 - remove k-th coordinate from input
    QJn  - randomly joggle input in range [-n,n]
    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
    Qs   - search all halfspaces for the initial simplex

Qhull extra options:
    QGn  - print intersection if visible to halfspace n, -n for not
    QVn  - print intersections for halfspace n, -n if not
    Qw   - allow option warnings
    Q12  - allow wide facets and wide dupridge
    Q14  - merge pinched vertices that create a dupridge

T options:
    TFn  - report summary when n or more facets created
    TI file - input file, may be enclosed in single quotes
    TO file - output file, may be enclosed in single quotes
    Ts   - statistics
    Tv   - verify result: structure, convexity, and in-circle test
    Tz   - send all output to stdout

Trace options:
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
    Ta   - annotate output with message codes
    TAn  - stop qhull after adding n vertices
     TCn - stop qhull after building cone for point n
     TVn - stop qhull after adding point n, -n for before
    Tc   - check frequently during execution
    Tf   - flush each qh_fprintf for debugging segfaults
    TPn - turn on tracing when point n added to hull
    TMn  - turn on tracing at merge n
    TWn  - trace merge facets when width > n

Precision options:
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
    Rn   - randomly perturb computations by a factor of [1-n,1+n]
    Un   - max distance below plane for a new, coplanar halfspace
    Wn   - min facet width for outside halfspace (before roundoff)

Output formats (may be combined; if none, produces a summary to stdout):
    f    - facet dump
    G    - Geomview output (dual convex hull)
    i    - non-redundant halfspaces incident to each intersection
    m    - Mathematica output (dual convex hull)
    o    - OFF format (dual convex hull: dimension, points, and facets)
    p    - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi')
    s    - summary (stderr)

More formats:
    Fc   - count plus redundant halfspaces for each intersection
         -   Qc (default) for coplanar and Qi for other redundant
    Fd   - use cdd format for input (homogeneous with offset first)
    FF   - facet dump without ridges
    FI   - ID of each intersection
    Fm   - merge count for each intersection (511 max)
    FM   - Maple output (dual 2-d or 3-d convex hull)
    Fn   - count plus neighboring intersections for each intersection
    FN   - count plus intersections for each halfspace
    FO   - options and precision constants
    Fp   - dim, count, and intersection coordinates
    FP   - nearest halfspace and distance for each redundant halfspace
    FQ   - command used for qhalf
    Fs   - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections
                      output: #non-redundant, #intersections, #coplanar
                                  halfspaces, #non-simplicial intersections
                    #real (2), max outer plane, min vertex
    Fv   - count plus non-redundant halfspaces for each intersection
    Fx   - non-redundant halfspaces

Geomview output (2-d, 3-d and 4-d; dual convex hull)
    Ga   - all points (i.e., transformed halfspaces) as dots
     Gp  -  coplanar points and vertices as radii
     Gv  -  vertices (i.e., non-redundant halfspaces) as spheres
    Gc   - centrums
    GDn  - drop dimension n in 3-d and 4-d output
    Gh   - hyperplane intersections
    Gi   - inner planes (i.e., halfspace intersections) only
     Gn  -  no planes
     Go  -  outer planes only
    Gr   - ridges

Print options:
    PAn  - keep n largest facets (i.e., intersections) by area
    Pdk:n- drop facet if normal[k] <= n (default 0.0)
    PDk:n- drop facet if normal[k] >= n
    PFn  - keep facets whose area is at least n
    Pg   - print good facets (needs 'QGn' or 'QVn')
    PG   - print neighbors of good facets
    PMn  - keep n facets with most merges
    Po   - force output.  If error, output neighborhood of facet
    Pp   - do not report precision problems

    .    - list of all options
    -    - one line descriptions of all options
    -?   - help with examples
    -V   - version
qhalf .

Qhull 2020.2 2020/07/24
Except for 'F.' and 'PG', upper_case options take an argument.

 facet-dump     Geomview       H0,0-interior incidences      mathematica
 off-format     point-dual     summary

 Fc-redundant   Fd-cdd-in      FF-dump-xridge FIDs           Fmerges
 FMaple         Fneighbors     FN-intersect   FOptions       Fp-coordinates
 FP-nearest     FQhalf         Fsummary       Fv-halfspace   Fx-non-redundant

 Gall-points    Gcentrums      GDrop-dim      Ghyperplanes   Ginner
 Gno-planes     Gouter         Gpoints        Gridges        Gvertices

 PArea-keep     Pdrop-d0:0D0   PFacet-area-keep  Pgood       PGood-neighbors
 PMerge-keep    Poutput-forced Pprecision-not

 Qallow-short   Qbk:0Bk:0-drop Qcoplanar      QG-half-good   Qi-redundant
 QJoggle        QRotate        Qsearch-all    Qtriangulate   QVertex-good
 Qwarn-allow    Q12-allow-wide Q14-merge-pinched

 TFacet-log     TInput-file    TOutput-file   Tstatistics    Tverify
 Tz-stdout

 T4-trace       Tannotate      TAdd-stop      Tcheck-often   TCone-stop
 Tflush         TMerge-trace   TPoint-trace   TVertex-stop   TWide-trace

 Angle-max      Centrum-size   Random-dist    Ucoplanar-max  Wide-outside
qhalf -? # [mar'19] isatty does not work for Git for Windows

qhalf -- halfspace intersection about a point.  Qhull 2020.2 2020/07/24
    input (stdin): [dimension, 1, interior point]
                       dimension+1, number of halfspaces, coefficients+offset
    comments start with a non-numeric character

options (qhalf.htm):
    Hn,n - specify coordinates of interior point
    Qt   - triangulated output
    QJ   - joggled input instead of merged facets
    Tv   - verify result: structure, convexity, and redundancy
    .    - concise list of all options
    -    - one-line description of each option
    -?   - this message
    -V   - version

output options (subset):
    s    - summary of results (default)
    Fp   - intersection coordinates
    Fv   - non-redundant halfspaces incident to each intersection
    Fx   - non-redundant halfspaces
    G    - Geomview output (dual convex hull)
    m    - Mathematica output (dual convex hull)
    o    - OFF file format (dual convex hull)
    QVn  - print intersections for halfspace n, -n if not
    TI file - input file, may be enclosed in single quotes
    TO file - output file, may be enclosed in single quotes

examples:
    rbox d | qconvex FQ n | qhalf s H0,0,0 Fp
    rbox c | qconvex FQ FV n | qhalf s i
    rbox c | qconvex FQ FV n | qhalf s o

rbox d | qhull FQ n | qhalf s Qt H0,0,0 Fp

Halfspace intersection by the convex hull of 8 points in 3-d:

  Number of halfspaces: 8
  Number of non-redundant halfspaces: 8
  Number of intersection points: 12
  Number of triangulated facets: 6

Statistics for: rbox d | qhull FQ n | qhalf s Qt H0,0,0 Fp

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 32
  Number of distance tests for merging: 101
  Number of distance tests for checking: 48
  Number of merged facets: 7
  CPU seconds to compute hull (after input):  0

3
12
     0      0   -0.5 
     0      0   -0.5 
     0   -0.5      0 
     0   -0.5      0 
  -0.5      0      0 
  -0.5      0      0 
   0.5      0      0 
   0.5      0      0 
     0    0.5      0 
     0    0.5      0 
     0      0    0.5 
     0      0    0.5 
rbox c | qhull FQ FV n | qhalf s i

Halfspace intersection by the convex hull of 6 points in 3-d:

  Number of halfspaces: 6
  Number of non-redundant halfspaces: 6
  Number of intersection points: 8

Statistics for: rbox c | qhull FQ FV n | qhalf s i

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 10
  Number of distance tests for merging: 51
  Number of distance tests for checking: 48
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0

8
1 0 3 
0 1 2 
5 1 3 
1 5 2 
4 0 2 
0 4 3 
5 4 2 
4 5 3 
rbox c | qhull FQ FV n | qhalf o
3
6 8 12
    -0     -0     -2 
     0     -2      0 
     2     -0     -0 
    -2     -0     -0 
     0      2     -0 
    -0     -0      2 
3 1 0 3 
3 0 1 2 
3 5 1 3 
3 1 5 2 
3 4 0 2 
3 0 4 3 
3 5 4 2 
3 4 5 3 
rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx

Halfspace intersection by the convex hull of 4 points in 2-d:

  Number of halfspaces: 4
  Number of non-redundant halfspaces: 4
  Number of intersection points: 4

Statistics for: rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx

  Number of points processed: 4
  Number of hyperplanes created: 6
  Number of distance tests for qhull: 5
  CPU seconds to compute hull (after input):  0

4
0
0
0
0
0
4
2 1 2
2 0 3
2 0 3
2 1 2
4
2 0 1
2 2 0
2 1 3
2 3 2
rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx
4
2 1 0
2 2 0
2 3 1
2 3 2
4
0
1
3
2
# qhull - printed at end
qhull .

Qhull 2020.2.r 2020/07/24
Except for 'F.' and 'PG', upper-case options take an argument.

 delaunay       facet-dump     Geomview       H0,0-interior  Halfspace
 incidences     mathematica    normals        off-format     points
 summary        voronoi

 Farea          FArea-total    Fcoplanars     FCentrums      Fd-cdd-in
 FD-cdd-out     FFacets-xridge Finner         FIDs           Fmerges
 FMaple         Fneighbors     FNeigh-vertex  Fouter         FOptions
 Fpoint-intersect  FPoint-near FQhull         Fsummary       FSize
 Ftriangles     Fvertices      Fvoronoi       FVertex-ave    Fxtremes

 Gall-points    Gcentrums      GDrop-dim      Ghyperplanes   Ginner
 Gno-planes     Gouter         Gpoints        Gridges        Gtransparent
 Gvertices

 PArea-keep     Pdrop-d0:0D0   PFacet-area-keep  Pgood       PGood-neighbors
 PMerge-keep    Poutput-forced Pprecision-not

 Qallow-short   QbBound-0:0.5  QbB-scale-box  Qbb-scale-last Qbk:0Bk:0-drop
 Qcoplanar      Qinterior      QJoggle        QRotate        Qsearch-all
 Qtriangulate   QupperDelaunay Qwarn-allow    Qxact-merge    Qzinfinite

 Qfurthest      Qgood-only     QGood-point    Qmax-outside   Qrandom
 Qvneighbors    QVertex-good

 Q0-no-premerge Q1-angle-merge     Q2-no-independ  Q3-no-redundant
 Q4-no-old      Q5-no-check-out    Q6-no-concave   Q7-depth-first
 Q8-no-near-in  Q9-pick-furthest   Q10-no-narrow   Q11-trinormals
 Q12-allow-wide Q14-merge-pinched  Q15-duplicates

 TFacet-log     TInput-file    TOutput-file   Tstatistics    Tverify
 Tz-stdout

 T4-trace       Tannotate      TAdd-stop      Tcheck-often   TCone-stop
 Tflush         TMerge-trace   TPoint-trace   TRerun         TVertex-stop
 TWide-trace

 Angle-max      Centrum-size   Error-round    Random-dist    Ucoplanar-max
 Visible-min    Wide-outside
qhull -? # [mar'19] isatty does not work for Git for Windows

qhull -- compute convex hulls and related structures.  Qhull 2020.2.r 2020/07/24
    input (stdin): dimension, number of points, point coordinates
    comments start with a non-numeric character
    halfspace: use dim+1 and put offsets after coefficients

options (qh-quick.htm):
    d    - Delaunay triangulation by lifting points to a paraboloid
    d Qu - furthest-site Delaunay triangulation (upper convex hull)
    v    - Voronoi diagram as the dual of the Delaunay triangulation
    v Qu - furthest-site Voronoi diagram
    H1,1 - Halfspace intersection about [1,1,0,...] via polar duality
    Qt   - triangulated output
    QJ   - joggled input instead of merged facets
    Tv   - verify result: structure, convexity, and point inclusion
    .    - concise list of all options
    -    - one-line description of each option
    -?   - this message
    -V   - version

Output options (subset):
    s    - summary of results (default)
    i    - vertices incident to each facet
    n    - normals with offsets
    p    - vertex coordinates (if 'Qc', includes coplanar points)
           if 'v', Voronoi vertices
    FA   - report total area and volume
    Fp   - halfspace intersections
    FS   - total area and volume
    Fx   - extreme points (convex hull vertices)
    G    - Geomview output (2-d, 3-d and 4-d)
    m    - Mathematica output (2-d and 3-d)
    o    - OFF format (if 'v', outputs Voronoi regions)
    QVn  - print facets that include point n, -n if not
    TI file - input file, may be enclosed in single quotes
    TO file - output file, may be enclosed in single quotes

examples:
    rbox D4 | qhull Tv                        rbox 1000 s | qhull Tv s FA
    rbox 10 D2 | qhull d QJ s i TO result     rbox 10 D2 | qhull v Qbb Qt p
    rbox 10 D2 | qhull d Qu QJ m              rbox 10 D2 | qhull v Qu QJ o
    rbox c d D2 | qhull Qc s f Fx | more      rbox c | qhull FV n | qhull H Fp
    rbox d D12 | qhull QR0 FA                 rbox c D7 | qhull FA TF1000
    rbox y 1000 W0 | qhull Qc                 rbox c | qhull n

rbox 1000 s | qhull Tv s FA

Convex hull of 1000 points in 3-d:

  Number of vertices: 1000
  Number of facets: 1996

Statistics for: rbox 1000 s | qhull Tv s FA

  Number of points processed: 1000
  Number of hyperplanes created: 5544
  Number of distance tests for qhull: 25487
  CPU seconds to compute hull (after input): 0.003
  Total facet area:   3.1201951
  Total volume:       0.51650274


qhull output completed.  Verifying that 1000 points are
below 2.1e-15 of the nearest facet.
rbox 10 D2 | qhull d QJ s i TO q_test.log.1

Delaunay triangulation by the convex hull of 10 points in 3-d:

  Number of input sites: 10
  Number of Delaunay regions: 14

Statistics for: rbox 10 D2 | qhull d QJ s i TO q_test.log.1

  Number of points processed: 10
  Number of hyperplanes created: 28
  Number of facets in hull: 16
  Number of distance tests for qhull: 47
  CPU seconds to compute hull (after input):  0
  Input joggled by: 4e-11

cat q_test.log.1
14
9 7 0 
8 9 0 
3 4 1 
3 7 4 
7 2 4 
0 5 1 
7 5 0 
5 3 1 
3 5 7 
6 7 9 
6 2 7 
8 6 9 
6 8 4 
2 6 4 
rbox 10 D2 | qhull v Qbb Qt p
2
14
-0.1294381801544404 -0.07247409101984714 
0.08267689532419747 -0.2397644955865706 
0.1295260566906465 1.716033573116837 
0.1740355150742391 0.5317519038435655 
0.1851415205797575 0.3882545794457364 
-0.9065939866848107 -0.2962957610652135 
-0.1954805620516266 -0.07111892482963184 
-0.1407581310832468 0.7233857048236082 
-0.1676297826663962 0.2080621273999375 
0.05868313821742954 0.06632066014880154 
0.08806341399736994 0.1054080604689985 
0.4761588899009253 -0.03168366595227294 
3.094213357897477 -0.064721945677682 
0.5410515627308725 0.2115615434955919 
rbox 10 D2 | qhull d Qu QJ m              
{
Polygon[{{      0.37903124,       0.37797944,       0.29963416},
{     -0.02222276,      -0.49797278,       0.23792952},
{     -0.42854319,       0.47458265,       0.49797278}}],
Polygon[{{      0.34431227,      -0.14373122,       0.06080143},
{     -0.02222276,      -0.49797278,       0.23792952},
{      0.37903124,       0.37797944,       0.29963416}}]}
rbox 10 D2 | qhull v Qu QJ o
2
3 10 1
-10.101 -10.101 
-0.06934933488573394 0.05349366577046777 
-0.3051278692468022 0.16149850548211 
3 0 2 1
2 0 1
0
0
3 0 1 2
0
0
0
2 0 2
0
rbox c d D2 | qhull Qc s f Fx      

Convex hull of 8 points in 2-d:

  Number of vertices: 4
  Number of coplanar points: 4
  Number of facets: 4

Statistics for: rbox c d D2 | qhull Qc s f Fx

  Number of points processed: 4
  Number of hyperplanes created: 6
  Number of distance tests for qhull: 35
  CPU seconds to compute hull (after input):  0

Vertices and facets:
- p2(v2):   0.5  -0.5
- p0(v1):  -0.5  -0.5
- p1(v3):  -0.5   0.5
- p3(v4):   0.5   0.5
- f1
    - flags: bottom simplicial
    - normal:        -0       -1
    - offset:       -0.5
    - coplanar set(furthest p4):
      p4:         0     -0.5
      furthest distance=  0
    - vertices: p2(v2) p0(v1)
    - neighboring facets: f2 f4
- f2
    - flags: top simplicial
    - normal:        -1        0
    - offset:       -0.5
    - coplanar set(furthest p6):
      p6:      -0.5        0
      furthest distance=  0
    - vertices: p1(v3) p0(v1)
    - neighboring facets: f1 f5
- f4
    - flags: bottom simplicial
    - normal:         1       -0
    - offset:       -0.5
    - coplanar set(furthest p7):
      p7:       0.5        0
      furthest distance=  0
    - vertices: p3(v4) p2(v2)
    - neighboring facets: f1 f5
- f5
    - flags: top simplicial
    - normal:         0        1
    - offset:       -0.5
    - coplanar set(furthest p5):
      p5:         0      0.5
      furthest distance=  0
    - vertices: p3(v4) p1(v3)
    - neighboring facets: f2 f4
4
0
2
3
1
rbox c | qhull FV n | qhull H Fp
3
8
  -0.5   -0.5   -0.5 
   0.5   -0.5   -0.5 
  -0.5   -0.5    0.5 
   0.5   -0.5    0.5 
   0.5    0.5   -0.5 
  -0.5    0.5   -0.5 
   0.5    0.5    0.5 
  -0.5    0.5    0.5 
rbox d D12 | qhull QR0 FA                 

Convex hull of 24 points in 12-d:

  Number of vertices: 24
  Number of facets: 4096

Statistics for: rbox d D12 | qhull QR0 FA QR1595644042

  Number of points processed: 24
  Number of hyperplanes created: 4107
  Number of distance tests for qhull: 4215
  Number of distance tests for merging: 121142
  Number of distance tests for checking: 98304
  Number of merged facets: 2036
  CPU seconds to compute hull (after input): 0.023
  Approximate facet area:   1.735661e-07
  Approximate volume:       2.0876757e-09

rbox c D7 | qhull FA TF1000

At 22:27:22 & 0.003 CPU secs, qhull has created 1048 facets and merged 469.
 The current hull contains 230 facets and 24 vertices.  There are 104
 outside points.  Next is point p79(v25), 0.66 above f145.

At 22:27:22 & 0.005 CPU secs, qhull has created 2146 facets and merged 1272.
 The current hull contains 273 facets and 31 vertices.  There are 97
 outside points.  Next is point p120(v32), 0.54 above f437.

At 22:27:22 & 0.008 CPU secs, qhull has created 3310 facets and merged 2244.
 The current hull contains 243 facets and 36 vertices.  There are 92
 outside points.  Next is point p60(v37), 0.54 above f1338.

At 22:27:22 & 0.01 CPU secs, qhull has created 4322 facets and merged 3099.
 The current hull contains 249 facets and 42 vertices.  There are 86
 outside points.  Next is point p30(v43), 0.54 above f2005.

At 22:27:22 & 0.012 CPU secs, qhull has created 5491 facets and merged 4196.
 The current hull contains 186 facets and 48 vertices.  There are 80
 outside points.  Next is point p21(v49), 0.5 above f2995.

At 22:27:22 & 0.015 CPU secs, qhull has created 6589 facets and merged 5175.
 The current hull contains 194 facets and 53 vertices.  There are 75
 outside points.  Next is point p56(v54), 0.28 above f3731.

At 22:27:22 & 0.018 CPU secs, qhull has created 7867 facets and merged 6337.
 The current hull contains 203 facets and 60 vertices.  There are 68
 outside points.  Next is point p76(v61), 0.29 above f5879.

At 22:27:22 & 0.021 CPU secs, qhull has created 8971 facets and merged 7362.
 The current hull contains 179 facets and 67 vertices.  There are 61
 outside points.  Next is point p80(v68), 0.23 above f7175.

At 22:27:22 & 0.023 CPU secs, qhull has created 9984 facets and merged 8352.
 The current hull contains 104 facets and 77 vertices.  There are 51
 outside points.  Next is point p96(v78), 0.41 above f6748.

At 22:27:22 & 0.027 CPU secs, qhull has created 10990 facets and merged 9326.
 The current hull contains 54 facets and 90 vertices.  There are 38
 outside points.  Next is point p18(v91), 0.41 above f10178.

At 22:27:22 & 0.031 CPU secs, qhull has created 11996 facets and merged 10295.
 The current hull contains 34 facets and 114 vertices.  There are 14
 outside points.  Next is point p19(v115), 0.38 above f11792.

At 22:27:22 & 0.034 CPU secs, qhull has created 12860 facets and merged 11072.
 The current hull contains 14 facets and 128 vertices.  Last point was p77

Convex hull of 128 points in 7-d:

  Number of vertices: 128
  Number of facets: 14
  Number of non-simplicial facets: 14

Statistics for: rbox c D7 | qhull FA TF1000

  Number of points processed: 128
  Number of hyperplanes created: 1789
  Number of distance tests for qhull: 10122
  Number of distance tests for merging: 87203
  Number of distance tests for checking: 0
  Number of merged facets: 11072


First post-merge with 'C4.4e-15' and 'A1.8e+308'

At 22:27:22 & 0.034 CPU secs, qhull has created 12860 facets and merged 11072.
 The current hull contains 14 facets and 128 vertices.  Last point was p77

Testing all coplanar points.
computing area of each facet and volume of the convex hull

Convex hull of 128 points in 7-d:

  Number of vertices: 128
  Number of facets: 14
  Number of non-simplicial facets: 14

Statistics for: rbox c D7 | qhull FA TF1000

  Number of points processed: 128
  Number of hyperplanes created: 1789
  Number of distance tests for qhull: 10122
  Number of distance tests for merging: 87371
  Number of distance tests for checking: 1792
  Number of merged facets: 11072
  CPU seconds to compute hull (after input): 0.034
  Approximate facet area:   14
  Approximate volume:        1

rbox y 1000 W0 | qhull Qc                 

Convex hull of 1004 points in 3-d:

  Number of vertices: 4
  Number of coplanar points: 1000
  Number of facets: 4

Statistics for: rbox y 1000 W0 | qhull Qc

  Number of points processed: 4
  Number of hyperplanes created: 4
  Number of distance tests for qhull: 11000
  CPU seconds to compute hull (after input): 0.001

rbox c | qhull n
4
6
    -0     -0     -1   -0.5 
     0     -1      0   -0.5 
     1     -0     -0   -0.5 
    -1     -0     -0   -0.5 
     0      1     -0   -0.5 
    -0     -0      1   -0.5 
rbox c | qhull TA1

Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.
Convex hull of 8 points in 3-d:

  Number of vertices: 5
  Number of facets: 6

Statistics for: rbox c | qhull TA1

  Number of points processed: 5
  Number of hyperplanes created: 8
  Number of distance tests for qhull: 25
  CPU seconds to compute hull (after input):  0

rbox 10 s | qhull C1e-5 T1P-1f
[QH1008]qh_readpoints: read in 10 3-dimensional points
[QH0013]qh_initqhull_globals: for rbox 10 s | qhull C1e-5 T1P-1f

Trace level T1, IStracing 0, point TP-1, merge TM0, dist TW1.8e+308, qh.tracefacet_id -1, traceridge_id -1, tracevertex_id -1, last qh.RERUN 0, rbox 10 s | qhull C1e-5 T1P-1f
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213630158  Centrum-postmerge 1e-05  Trace-point -1  Tflush  _pre-merge
  _max-width 0.88  Error-roundoff 6.7e-16  _one-merge 3e-05
  _near-inside 0.00015  Visible-distance 1.3e-15  U-max-coplanar 1.3e-15
  Width-outside 2.7e-15  _wide-facet 8e-15
[QH2112]qh_qhull: finished qh_buildhull and qh_postmerge, start tracing (TP-1)
[QH1022]qh_check_maxout: check and update qh.min_vertex -6.7e-16 and qh.max_outside 1.1e-16
[QH1055]qh_check_maxout: determine actual maxoutside
[QH1024]qh_check_maxout:  p7(v6) is qh.min_vertex -6.7e-16 below facet f4.  Point p2 for f4 is qh.max_outside 1.1e-16 above f4.  0 points are outside of not-good facets
[QH1036]Qhull: algorithm completed
[QH1027]qh_checkpolygon: check all facets from f4, qh.NEWtentative? 0
[QH1062]qh_checkconvex: check that facets are not-flipped and that their centrums are convex by qh.DISTround ('En', 'Rn') 

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 10 s | qhull C1e-5 T1P-1f

  Number of points processed: 10
  Number of hyperplanes created: 27
  Number of distance tests for qhull: 51
  CPU seconds to compute hull (after input):  0

[QH1006]qh_freeqhull: free global memory
[QH1005]qh_freebuild: free memory from qh_inithull and qh_buildhull
[QH1061]qh_freeqhull: clear qhT except for qh.qhmem and qh.qhstat

set +v
=== check quality of Qhull for kelwyn Fri, Jul 24, 2020 10:27:22 PM
rbox 1000 W0 | qhull QR2 QJ s Fs Tv

Convex hull of 1000 points in 3-d:

  Number of vertices: 144
  Number of facets: 284

Statistics for: rbox 1000 W0 | qhull QR2 QJ s Fs Tv QR2

  Number of points processed: 171
  Number of hyperplanes created: 1233
  Number of distance tests for qhull: 33543
  CPU seconds to compute hull (after input): 0.005
  After 1 retries, input joggled by: 2.9e-11

10 3 1000 144 284 144 284 0 0 33 0
2 5.045982607091333e-11 -5.045982607091333e-11

Output completed.  Verifying that all points are below 2.9e-15 of
all facets.  Will make 284000 distance computations.
rbox 1000 W0 | qhull QR2 s Fs Tv

Convex hull of 1000 points in 3-d:

  Number of vertices: 84
  Number of facets: 98
  Number of non-simplicial facets: 6

Statistics for: rbox 1000 W0 | qhull QR2 s Fs Tv QR2

  Number of points processed: 97
  Number of hyperplanes created: 299
  Number of distance tests for qhull: 18050
  Number of distance tests for merging: 3163
  Number of distance tests for checking: 15481
  Number of merged facets: 92
  CPU seconds to compute hull (after input): 0.001

10 3 1000 84 98 84 98 0 6 13 0
2 1.942124858599573e-15 -1.241679291552168e-15

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 98000 distance computations.
rbox 1000 s | qhull C0.02 Qc Tv

Convex hull of 1000 points in 3-d:

  Number of vertices: 110
  Number of coplanar points: 890
  Number of facets: 57
  Number of non-simplicial facets: 57

Statistics for: rbox 1000 s | qhull C0.02 Qc Tv

  Number of points processed: 1000
  Number of hyperplanes created: 5544
  Number of distance tests for qhull: 81537
  Number of distance tests for merging: 80708
  Number of distance tests for checking: 8256
  Number of merged facets: 1939
  CPU seconds to compute hull (after input): 0.011
  Maximum distance of vertex below facet: -0.079 (1.3x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 57000 distance computations.
rbox 500 s D4 | qhull C0.01 Qc Tv

Convex hull of 500 points in 4-d:

  Number of vertices: 462
  Number of coplanar points: 38
  Number of facets: 345
  Number of non-simplicial facets: 332

Statistics for: rbox 500 s D4 | qhull C0.01 Qc Tv

  Number of points processed: 500
  Number of hyperplanes created: 11283
  Number of distance tests for qhull: 42789
  Number of distance tests for merging: 217345
  Number of distance tests for checking: 12552
  Number of merged facets: 2821
  CPU seconds to compute hull (after input): 0.019
  Maximum distance of vertex below facet: -0.08 (2.0x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 172500 distance computations.
rbox 1000 s | qhull C-0.02 Qc Tv

Convex hull of 1000 points in 3-d:

  Number of vertices: 52
  Number of coplanar points: 948
  Number of facets: 47
  Number of non-simplicial facets: 38

Statistics for: rbox 1000 s | qhull C-0.02 Qc Tv

  Number of points processed: 53
  Number of hyperplanes created: 214
  Number of distance tests for qhull: 47444
  Number of distance tests for merging: 2943
  Number of distance tests for checking: 19555
  Number of merged facets: 107
  CPU seconds to compute hull (after input): 0.002
  Maximum distance of point above facet: 0.039 (0.7x)
  Maximum distance of vertex below facet: -0.057 (0.9x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 47000 distance computations.
rbox 1000 s D4 | qhull C-0.01 Qc Tv

Convex hull of 1000 points in 4-d:

  Number of vertices: 126
  Number of coplanar points: 874
  Number of facets: 206
  Number of non-simplicial facets: 148

Statistics for: rbox 1000 s D4 | qhull C-0.01 Qc Tv

  Number of points processed: 126
  Number of hyperplanes created: 1371
  Number of distance tests for qhull: 414344
  Number of distance tests for merging: 73447
  Number of distance tests for checking: 124140
  Number of merged facets: 1331
  CPU seconds to compute hull (after input): 0.02
  Maximum distance of point above facet: 0.068 (1.7x)
  Maximum distance of vertex below facet: -0.1 (2.6x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 206000 distance computations.
rbox 200 s D5 | qhull C-0.01 Qx Qc Tv 

Convex hull of 200 points in 5-d:

  Number of vertices: 161
  Number of coplanar points: 39
  Number of facets: 416
  Number of non-simplicial facets: 365

Statistics for: rbox 200 s D5 | qhull C-0.01 Qx Qc Tv

  Number of points processed: 161
  Number of hyperplanes created: 4552
  Number of distance tests for qhull: 229096
  Number of distance tests for merging: 309308
  Number of distance tests for checking: 54701
  Number of merged facets: 6165
  CPU seconds to compute hull (after input): 0.039
  Maximum distance of point above facet: 0.059 (1.2x)
  Maximum distance of vertex below facet: -0.1 (2.1x)

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 83200 distance computations.
rbox 100 s D6 | qhull C-0.001 Qx Qc Tv

Convex hull of 100 points in 6-d:

  Number of vertices: 100
  Number of facets: 4454
  Number of non-simplicial facets: 809

Statistics for: rbox 100 s D6 | qhull C-0.001 Qx Qc Tv

  Number of points processed: 100
  Number of hyperplanes created: 19805
  Number of distance tests for qhull: 33228
  Number of distance tests for merging: 330047
  Number of distance tests for checking: 88758
  Number of merged facets: 3862
  CPU seconds to compute hull (after input): 0.057
  Maximum distance of point above facet: 0.003 (0.5x)
  Maximum distance of vertex below facet: -0.014 (2.3x)

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 445400 distance computations.
rbox 1000 W1e-4 | qhull C-1e-6 Qc Tv

Convex hull of 1000 points in 3-d:

  Number of vertices: 145
  Number of coplanar points: 87
  Number of facets: 243
  Number of non-simplicial facets: 29

Statistics for: rbox 1000 W1e-4 | qhull C-1e-6 Qc Tv

  Number of points processed: 185
  Number of hyperplanes created: 940
  Number of distance tests for qhull: 40788
  Number of distance tests for merging: 7744
  Number of distance tests for checking: 6136
  Number of merged facets: 143
  CPU seconds to compute hull (after input): 0.002
  Maximum distance of point above facet: 8.3e-07 (0.3x)
  Maximum distance of vertex below facet: -3.9e-06 (1.3x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 243000 distance computations.
rbox 1000 W5e-4 D4 | qhull C-1e-5 Qc Tv

Convex hull of 1000 points in 4-d:

  Number of vertices: 291
  Number of coplanar points: 645
  Number of facets: 1273
  Number of non-simplicial facets: 151

Statistics for: rbox 1000 W5e-4 D4 | qhull C-1e-5 Qc Tv

  Number of points processed: 365
  Number of hyperplanes created: 6252
  Number of distance tests for qhull: 173357
  Number of distance tests for merging: 90805
  Number of distance tests for checking: 56693
  Number of merged facets: 1351
  CPU seconds to compute hull (after input): 0.013
  Maximum distance of point above facet: 0.00013 (3.3x)
  Maximum distance of vertex below facet: -0.00021 (5.4x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 1273000 distance computations.
rbox 400 W1e-3 D5 | qhull C-1e-5 Qx Qc Tv

Convex hull of 400 points in 5-d:

  Number of vertices: 306
  Number of coplanar points: 33
  Number of facets: 5557
  Number of non-simplicial facets: 287

Statistics for: rbox 400 W1e-3 D5 | qhull C-1e-5 Qx Qc Tv

  Number of points processed: 338
  Number of hyperplanes created: 24498
  Number of distance tests for qhull: 262194
  Number of distance tests for merging: 271065
  Number of distance tests for checking: 90075
  Number of merged facets: 1472
  CPU seconds to compute hull (after input): 0.045
  Maximum distance of point above facet: 5.5e-05 (1.1x)
  Maximum distance of vertex below facet: -0.0001 (2.1x)

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 2222800 distance computations.

set +v
=== check input format etc. Fri, Jul 24, 2020 10:27:23 PM
qhull <<EOF
2 4 input comment
1 0 1 1 1 2  0 0
EOF

Convex hull of 4 points in 2-d:

  Number of vertices: 3
  Number of facets: 3

Statistics for: input comment | qhull

  Number of points processed: 3
  Number of hyperplanes created: 4
  Number of distance tests for qhull: 8
  CPU seconds to compute hull (after input):  0

qhull <<EOF
2 4 input comment
1 0 1 1 1 2  0 0 0
EOF
QH6410 qhull error: instead of 4 points in 2-d, input contains 4 points and 1 extra coordinates.
    Line 1 is the first comment.
    Line 2 is the first point.
    Line 2 is the first long line.
    Override with option 'Qa' (allow-short)

While executing: input comment | qhull
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213646965  _maxoutside  0
qhull Qa <<EOF
2 4 input comment
1 0 1 1 1 2  0 0 0
EOF
QH7073 qhull warning: instead of 4 points in 2-d, input contains 4 points and 1 extra coordinates.
    Line 1 is the first comment.
    Line 2 is the first point.
    Line 2 is the first long line.
    Continuing with 4 points.

Convex hull of 4 points in 2-d:

  Number of vertices: 3
  Number of facets: 3

Statistics for: input comment | qhull Qa

  Number of points processed: 3
  Number of hyperplanes created: 4
  Number of distance tests for qhull: 8
  CPU seconds to compute hull (after input):  0

qhull <<EOF
2 4 input comment
1 0 1 1 1 2  0
EOF
QH6410 qhull error: instead of 4 points in 2-d, input contains 3 points and 1 extra coordinates.
    Line 1 is the first comment.
    Line 2 is the first point.
    Line 2 is the first long line.
    Override with option 'Qa' (allow-short)

While executing: input comment | qhull
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213646965  _maxoutside  0
qhull Qa <<EOF
2 4 input comment
1 0 1 1 1 2  0
EOF
QH7073 qhull warning: instead of 4 points in 2-d, input contains 3 points and 1 extra coordinates.
    Line 1 is the first comment.
    Line 2 is the first point.
    Line 2 is the first long line.
    Continuing with 3 points.
QH6013 qhull input error: input is less than 2-dimensional since all points have the same x coordinate    1

While executing: input comment | qhull Qa
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213663772  Qallow-short  _pre-merge  _zero-centrum  _max-width  2
  Error-roundoff 1.7e-15  _one-merge 8.6e-15  _near-inside 4.3e-14
  Visible-distance 3.4e-15  U-max-coplanar 3.4e-15  Width-outside 6.9e-15
  _wide-facet 2.1e-14  _maxoutside 1e-14
qhull <<EOF
2 
4 input comment
1 #another comment
0 1 1 1 2  0
EOF
QH6410 qhull error: instead of 4 points in 2-d, input contains 3 points and 1 extra coordinates.
    Line 2 is the first comment.
    Line 3 is the first point.
    Line 3 is the first short line.
    Line 4 is the first long line.
    Override with option 'Qa' (allow-short)

While executing: input comment | qhull
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213663772  _maxoutside  0
qhull <<EOF
2 4  1 0  1 1  1 2  0 0
EOF

Convex hull of 4 points in 2-d:

  Number of vertices: 3
  Number of facets: 3

Statistics for:  | qhull

  Number of points processed: 3
  Number of hyperplanes created: 4
  Number of distance tests for qhull: 8
  CPU seconds to compute hull (after input):  0

qhull d Qz <<EOF
2 5  1 0  1 1  0 1  0 0  0
EOF
QH6410 qhull error: instead of 5 points in 2-d, input contains 4 points and 1 extra coordinates.
    Line 1 is the first point.
    Line 1 is the first long line.
    Override with option 'Qa' (allow-short)

While executing:  | qhull d Qz
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213663772  delaunay  Qz-infinity-point  _maxoutside  0
qhull d Q8 Qz <<EOF
2 5  1 0  1 1  0 1  0 0  0
EOF
QH6410 qhull error: instead of 5 points in 2-d, input contains 4 points and 1 extra coordinates.
    Line 1 is the first point.
    Line 1 is the first long line.
    Override with option 'Qa' (allow-short)

While executing:  | qhull d Q8 Qz
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213663772  delaunay  Q8-no-near-inside  Qz-infinity-point
  _maxoutside  0
rbox d h | qhull Fd FV n FD Tcv | qhull Fd H Fp Tcv

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.
3
6
     0      0   -0.5 
     0   -0.5      0 
  -0.5      0      0 
   0.5      0      0 
     0    0.5      0 
     0      0    0.5 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.
rbox 10 h | qhull Fd FD p Tcv | qhull Fd d Tcv 

Output completed.  Verifying that all points are below 1.7e-15 of
all facets.  Will make 140 distance computations.

Delaunay triangulation by the convex hull of 9 points in 4-d:

  Number of input sites: 9
  Number of Delaunay regions: 11

Statistics for: rbox 10 h | qhull Fd FD p Tcv | qhull Fd d Tcv

  Number of points processed: 9
  Number of hyperplanes created: 34
  Number of facets in hull: 22
  Number of distance tests for qhull: 45
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 2.5e-15 of
all facets.  Will make 99 distance computations.

set +v
=== check rbox Fri, Jul 24, 2020 10:27:24 PM
rbox 3 n D2
2
3
0.2234321234034673 0.2236923805658635 
-0.4021654933711192 -0.1954478539484067 
0.1079163058734651 -0.2506519423338137 
rbox 3 D2
2 rbox 3 D2
3
-0.3570490315156514 0.07692619792830779 
-0.1013959339832849 -0.1614655765345931 
0.2480525339469802 0.01893219260399437 
rbox 3 h D2
rbox 3 h D2
begin
        3 3 real
     1 0.16093073846859 -0.2370837309743126 
     1 0.3337314574362071 0.02459860548805315 
     1 0.4287583324394733 0.141286041719174 
end
hull
rbox 3 z D2
2 rbox 3 z D2
3
696870 290489 
252081 728918 
932465 -69056 
rbox 3 z h D2
rbox 3 z h D2
begin
        3 3 integer
1 -951655 -464136 
1 -741320 630989 
1 -964370 -171508 
end
hull
rbox 3 B10 D2
2 rbox 3 B10 D2
3
6.07777520648928 9.167769643634342 
2.704250554278727 -9.661033665445665 
7.007182209759188 9.71126632738045 
rbox 3 B10 D2 C2,1E-13,1
2 rbox 3 B10 D2 C2,1E-13,1
5
-9.999843472614739 -7.369244235911633 
-9.999843472614687 -7.369244235911641 
-9.999843472614732 -7.369244235911689 
-9.05910767527214 3.577294343688799 
3.585928123058684 8.693857927521558 
rbox 3 z B10 D2
2 rbox 3 z B10 D2
3
5 2 
5 -1 
3 9 
rbox 4 L2 r D2
2 rbox 4 L2 r D2
6
   0.5      0
0.1736481776669304 0.1187823492277694
0.1736481776669304 -0.1187823492277694
-0.1736481776669304 0.1187823492277694
-0.1736481776669304 -0.1187823492277694
  -0.5      0
rbox 8 L2 r D2
2 rbox 8 L2 r D2
14
   0.5      0
0.365341024366395 0.06484834485976565
0.365341024366395 -0.06484834485976565
0.2225209339563144 0.108902508397385
0.2225209339563144 -0.108902508397385
0.07473009358642427 0.1311783933967415
0.07473009358642427 -0.1311783933967415
-0.07473009358642424 0.1311783933967415
-0.07473009358642424 -0.1311783933967415
-0.2225209339563144 0.108902508397385
-0.2225209339563144 -0.108902508397385
-0.365341024366395 0.06484834485976565
-0.365341024366395 -0.06484834485976565
  -0.5      0
rbox 8 L2 D2 C1,1E-13,2
2 rbox 8 L2 D2 C1,1E-13,2
10
-0.4014722424908947 -0.04984578721860422 
-0.4014722424908402 -0.04984578721870322 
-0.3537770307209493 0.06930438433003638 
-0.353777030720961 0.06930438433002231 
-0.4536521880095642 -0.02515341795345205 
0.09926382627500697 0.1290357464938974 
0.4803069842605469 -0.01107504705944207 
-0.4407884497398482 0.03158561585376829 
-0.43365738760839 -0.03505243423659854 
0.1399579896503841 -0.1241320388139711 
rbox 4 L4 r D3
3 rbox 4 L4 r D3
12
   0.5      0      0
  0.25      0 0.04782181019473453
  0.25      0 -0.04782181019473453
3.061616997868383e-17    0.5      0
1.530808498934192e-17   0.25 0.04782181019473453
1.530808498934192e-17   0.25 -0.04782181019473453
  -0.5 6.123233995736766e-17      0
 -0.25 3.061616997868383e-17 0.04782181019473453
 -0.25 3.061616997868383e-17 -0.04782181019473453
-9.184850993605148e-17   -0.5      0
-4.592425496802574e-17  -0.25 0.04782181019473453
-4.592425496802574e-17  -0.25 -0.04782181019473453
rbox 4 L4 s D5 W1e-3 
5 rbox 4 L4 s D5 W1e-3
4
-0.1779876601833928 -0.1311655069863711 0.09099061083332423 -0.0147197628642461 0.0491007664448838 
0.08530477699633816 0.08551065958609008 0.2073152333839907 -0.05556059038062115 0.04824638578429845 
-0.2043906348252541 0.01359444539903207 0.07833891569611255 -0.2253375927975145 0.03863248544102459 
0.07678497944972421 0.03657959246981071 0.1769587053753909 0.1423142450665639 -0.04874898497507386 
rbox 4 L4 s D5 W1e-3 C1,1E-12
5 rbox 4 L4 s D5 W1e-3 C1,1E-12
8
0.0002946652970602764 0.01409557808797486 -0.004433138692070485 0.02830701320254122 0.06321803825410263 
0.0002946652976213024 0.01409557808713995 -0.004433138692549452 0.02830701320252706 0.0632180382541969 
0.0395007958298621 0.08424796754402081 0.05096384542027204 -0.09702947578293189 -0.05829868829611209 
0.03950079583077567 0.08424796754434548 0.05096384542100907 -0.0970294757837081 -0.05829868829594329 
-0.04232294908783042 0.03923635869829208 -0.002523757174853624 -0.007690531229328437 -0.06262981797685649 
-0.04232294908753993 0.0392363586986717 -0.00252375717458491 -0.007690531229051642 -0.06262981797676299 
-0.1462855747417375 0.02301178389047249 0.1483804611920676 -0.1253035217565061 -0.04852571310121132 
-0.1462855747427029 0.0230117838896562 0.1483804611927586 -0.1253035217563368 -0.04852571310078617 
rbox y
3 rbox y
4
-0.3062920647731908 0.1492658412542808 -0.2890111205997049 
-0.4099055704752966 -0.2829236833219637 -0.09834729097629646 
0.07707741817187275 0.4401626986825491 -0.1855306003107974 
-0.2128018845923262 0.4387234094913336 -0.3756640258949846 
rbox 10 M3,4 
3 rbox 10 M3,4
10
     0      0      0 
     3      4      0 
     6      8      0 
    -4      3      0 
    -1      7      0 
     2     11      0 
    -8      6      0 
    -5     10      0 
    -2     14      0 
     0      0      5 
rbox 10 M3,4 C1,1E-14
3 rbox 10 M3,4 C1,1E-14
20
     0      0      0 
2.814732056869875e-15 7.201579527185838e-15 -3.053021210295168e-15 
     3      4      0 
3.000000000000008 3.999999999999992 4.994823238807566e-15 
     6      8      0 
6.000000000000008 7.999999999999996 1.743024766205834e-15 
    -4      3      0 
-4.000000000000005 2.999999999999993 -4.748389036160324e-15 
    -1      7      0 
-1.000000000000006 7.000000000000004 -1.260957588684708e-16 
     2     11      0 
2.000000000000001 11.00000000000001 2.063112521602872e-16 
    -8      6      0 
-7.999999999999993 6.000000000000001 6.666691421220716e-16 
    -5     10      0 
-4.999999999999996 9.999999999999991 4.071436025268804e-15 
    -2     14      0 
-1.999999999999991     14 -7.015196799314765e-15 
     0      0      5 
-4.412629440811118e-15 -3.063055438048258e-15 4.999999999999999 
rbox 27 M1,0,1
3 rbox 27 M1,0,1
27
     0      0      0 
     1      0      0 
     2      0      0 
     0      1      0 
     1      1      0 
     2      1      0 
     0      2      0 
     1      2      0 
     2      2      0 
     0      0      1 
     1      0      1 
     2      0      1 
     0      1      1 
     1      1      1 
     2      1      1 
     0      2      1 
     1      2      1 
     2      2      1 
     0      0      2 
     1      0      2 
     2      0      2 
     0      1      2 
     1      1      2 
     2      1      2 
     0      2      2 
     1      2      2 
     2      2      2 
rbox 10 L4 r D3 | qhull Tcv

Convex hull of 30 points in 3-d:

  Number of vertices: 30
  Number of facets: 22
  Number of non-simplicial facets: 22

Statistics for: rbox 10 L4 r D3 | qhull Tcv

  Number of points processed: 30
  Number of hyperplanes created: 62
  Number of distance tests for qhull: 307
  Number of distance tests for merging: 765
  Number of distance tests for checking: 730
  Number of merged facets: 43
  CPU seconds to compute hull (after input): 0.001


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 660 distance computations.
rbox 10 L4 s D5 W1e-3 | qhull Tcv

Convex hull of 10 points in 5-d:

  Number of vertices: 10
  Number of facets: 40

Statistics for: rbox 10 L4 s D5 W1e-3 | qhull Tcv

  Number of points processed: 10
  Number of hyperplanes created: 64
  Number of distance tests for qhull: 69
  CPU seconds to compute hull (after input):  0

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below 2.2e-15 of
all facets.  Will make 400 distance computations.
rbox 10 L4 s D5 W1e-3 C1,1E-12 | qhull Tcv

Convex hull of 20 points in 5-d:

  Number of vertices: 19
  Number of facets: 144
  Number of non-simplicial facets: 2

Statistics for: rbox 10 L4 s D5 W1e-3 C1,1E-12 | qhull Tcv

  Number of points processed: 19
  Number of hyperplanes created: 269
  Number of distance tests for qhull: 413
  Number of distance tests for merging: 2659
  Number of distance tests for checking: 1264
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0
  Maximum distance of point above facet: 3.9e-15 (0.4x)
  Maximum distance of vertex below facet: -3.2e-15 (0.3x)

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 2880 distance computations.
rbox 10 L6 D3 | qhull Tcv

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 10 L6 D3 | qhull Tcv

  Number of points processed: 10
  Number of hyperplanes created: 28
  Number of distance tests for qhull: 47
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1.7e-15 of
all facets.  Will make 160 distance computations.
rbox 10 L1.1 s D4 | qhull Tcv

Convex hull of 10 points in 4-d:

  Number of vertices: 10
  Number of facets: 26

Statistics for: rbox 10 L1.1 s D4 | qhull Tcv

  Number of points processed: 10
  Number of hyperplanes created: 44
  Number of distance tests for qhull: 52
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 2.4e-15 of
all facets.  Will make 260 distance computations.
rbox y r 100 W0 O0.5 | qhull s p Tcv

Convex hull of 104 points in 3-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox y r 100 W0 O0.5 | qhull s p Tcv

  Number of points processed: 4
  Number of hyperplanes created: 5
  Number of distance tests for qhull: 1100
  CPU seconds to compute hull (after input):  0

3
4
     1    0.5    0.5 
   0.5      1    0.5 
   0.5    0.5      1 
     0      0      0 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 416 distance computations.
rbox x r 100 W0 O0.5 | qhull s Tcv

Convex hull of 100 points in 3-d:

  Number of vertices: 27
  Number of facets: 35
  Number of non-simplicial facets: 4

Statistics for: rbox x r 100 W0 O0.5 | qhull s Tcv

  Number of points processed: 27
  Number of hyperplanes created: 76
  Number of distance tests for qhull: 1284
  Number of distance tests for merging: 606
  Number of distance tests for checking: 1052
  Number of merged facets: 15
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 3500 distance computations.
rbox 12 D8 | qhull Tcv

Convex hull of 12 points in 8-d:

  Number of vertices: 12
  Number of facets: 92

Statistics for: rbox 12 D8 | qhull Tcv

  Number of points processed: 12
  Number of hyperplanes created: 132
  Number of distance tests for qhull: 84
  CPU seconds to compute hull (after input):  0

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below 7.9e-15 of
all facets.  Will make 1104 distance computations.
rbox 12 D9 | qhull Tcv

Convex hull of 12 points in 9-d:

  Number of vertices: 12
  Number of facets: 70

Statistics for: rbox 12 D9 | qhull Tcv

  Number of points processed: 12
  Number of hyperplanes created: 88
  Number of distance tests for qhull: 46
  CPU seconds to compute hull (after input):  0

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below 9e-15 of
all facets.  Will make 840 distance computations.
rbox 1000 D4 | qhull s i A-0.97 C0.2 A0.7 Tcv

Convex hull of 1000 points in 4-d:

  Number of vertices: 12
  Number of facets: 7
  Number of non-simplicial facets: 7

Statistics for: rbox 1000 D4 | qhull s i A-0.97 C0.2 A0.7 Tcv

  Number of points processed: 117
  Number of hyperplanes created: 2350
  Number of distance tests for qhull: 498469
  Number of distance tests for merging: 123185
  Number of distance tests for checking: 12444
  Number of merged facets: 1929
  CPU seconds to compute hull (after input): 0.035
  Maximum distance of point above facet: 0.044
  Maximum distance of vertex below facet: -0.91 (0.6x)

68
118 856 380 837 
118 675 639 380 
118 856 675 380 
118 670 675 465 
118 638 856 837 
118 380 639 837 
118 465 856 638 
118 639 465 638 
118 675 670 639 
118 639 638 837 
118 639 670 465 
118 465 675 856 
119 856 465 638 
119 111 771 856 
119 111 856 837 
119 856 638 837 
119 771 465 856 
119 771 111 465 
119 465 111 638 
119 638 111 837 
120 120 771 465 
120 675 465 856 
120 670 120 465 
120 120 670 675 
120 465 771 856 
120 120 675 856 
120 675 670 465 
120 771 120 856 
121 639 380 837 
121 380 750 837 
121 111 750 639 
121 111 638 837 
121 638 639 837 
121 750 111 837 
121 639 750 380 
121 111 639 638 
122 771 120 465 
122 750 120 111 
122 670 639 465 
122 111 771 465 
122 120 750 670 
122 111 465 638 
122 465 639 638 
122 670 750 639 
122 120 771 111 
122 120 670 465 
122 639 111 638 
122 750 111 639 
123 750 670 639 
123 670 675 639 
123 120 750 675 
123 750 120 670 
123 639 675 380 
123 750 639 380 
123 675 750 380 
123 670 120 675 
124 675 120 856 
124 856 111 837 
124 771 120 111 
124 111 750 837 
124 771 111 856 
124 750 675 380 
124 750 120 675 
124 750 380 837 
124 120 771 856 
124 120 750 111 
124 380 856 837 
124 675 856 380 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 7000 distance computations.
rbox 3 D2 | qhull Qb0B1:-2 p 
2
3
  -0.5     -2 
-0.1839506649197531 -0.1614655765345934 
0.2480525339469802 -1.552736350137872 
rbox 100 r D2 | qhull Pd0:0.7 PD0:0.8 Pg n Tcv
3
6
0.7501110696304588 0.6613118653236527 -0.4997532801828658 
0.7071067811865485 0.7071067811865467 -0.4997532801828658 
0.7501110696304543 -0.6613118653236579 -0.4997532801828658 
0.7901550123756914 0.6129070536529753 -0.4997532801828658 
0.7901550123756885 -0.6129070536529789 -0.4997532801828659 
0.707106781186544 -0.7071067811865511 -0.4997532801828658 

Output completed.  Verifying that all points are below 1.3e-15 of
all facets.  Will make 600 distance computations.
rbox 1000 s | qhull  C0.05 Tcv

Convex hull of 1000 points in 3-d:

  Number of vertices: 36
  Number of facets: 20
  Number of non-simplicial facets: 20

Statistics for: rbox 1000 s | qhull C0.05 Tcv

  Number of points processed: 1000
  Number of hyperplanes created: 5544
  Number of distance tests for qhull: 50001
  Number of distance tests for merging: 82277
  Number of distance tests for checking: 23318
  Number of merged facets: 1976
  CPU seconds to compute hull (after input): 0.057
  Maximum distance of vertex below facet: -0.21 (1.4x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 20000 distance computations.
rbox 1000 s t | qhull Qm C0.05 Tcv

Convex hull of 1000 points in 3-d:

  Number of vertices: 46
  Number of facets: 25
  Number of non-simplicial facets: 25

Statistics for: rbox 1000 s t1595644046 | qhull Qm C0.05 Tcv

  Number of points processed: 1000
  Number of hyperplanes created: 5565
  Number of distance tests for qhull: 56798
  Number of distance tests for merging: 82129
  Number of distance tests for checking: 23646
  Number of merged facets: 1971
  CPU seconds to compute hull (after input): 0.045
  Maximum distance of vertex below facet: -0.18 (1.2x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 25000 distance computations.
rbox 500 D2 | qhull n A-0.95 C0.1 Tcv
3
4
0.004814116480453948 0.9999884120741163 -0.4852084337990873 
-0.9999815737204624 -0.006070602898184517 -0.4913197370926178 
-0.006423098021811921 -0.9999793716931376 -0.4958250456626817 
0.9999972817907392 0.002331611273993484 -0.4974344499395051 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 2000 distance computations.
rbox 500 s P1,1,1 | qhull QgG0 Pp Tcv

Convex hull of 500 points in 3-d:

  Number of vertices: 226
  Number of facets: 448
  Number of 'good' facets: 340

Statistics for: rbox 500 s P1,1,1 | qhull QgG0 Pp Tcv

  Number of points processed: 226
  Number of hyperplanes created: 1612
  Number of distance tests for qhull: 9967
  CPU seconds to compute hull (after input): 0.007

rbox d | qhull m
{
Polygon[{{      0.00000000,      -0.50000000,       0.00000000},
{      0.00000000,       0.00000000,      -0.50000000},
{     -0.50000000,       0.00000000,       0.00000000}}],
Polygon[{{      0.00000000,       0.00000000,      -0.50000000},
{      0.00000000,      -0.50000000,       0.00000000},
{      0.50000000,       0.00000000,       0.00000000}}],
Polygon[{{      0.00000000,       0.00000000,       0.50000000},
{      0.00000000,      -0.50000000,       0.00000000},
{     -0.50000000,       0.00000000,       0.00000000}}],
Polygon[{{      0.00000000,      -0.50000000,       0.00000000},
{      0.00000000,       0.00000000,       0.50000000},
{      0.50000000,       0.00000000,       0.00000000}}],
Polygon[{{      0.00000000,       0.50000000,       0.00000000},
{      0.00000000,       0.00000000,      -0.50000000},
{      0.50000000,       0.00000000,       0.00000000}}],
Polygon[{{      0.00000000,       0.00000000,      -0.50000000},
{      0.00000000,       0.50000000,       0.00000000},
{     -0.50000000,       0.00000000,       0.00000000}}],
Polygon[{{      0.00000000,       0.00000000,       0.50000000},
{      0.00000000,       0.50000000,       0.00000000},
{      0.50000000,       0.00000000,       0.00000000}}],
Polygon[{{      0.00000000,       0.50000000,       0.00000000},
{      0.00000000,       0.00000000,       0.50000000},
{     -0.50000000,       0.00000000,       0.00000000}}]}
rbox d | qhull FM
PLOT3D(POLYGONS(
[[      0.00000000,      -0.50000000,       0.00000000],
[      0.00000000,       0.00000000,      -0.50000000],
[     -0.50000000,       0.00000000,       0.00000000]],
[[      0.00000000,       0.00000000,      -0.50000000],
[      0.00000000,      -0.50000000,       0.00000000],
[      0.50000000,       0.00000000,       0.00000000]],
[[      0.00000000,       0.00000000,       0.50000000],
[      0.00000000,      -0.50000000,       0.00000000],
[     -0.50000000,       0.00000000,       0.00000000]],
[[      0.00000000,      -0.50000000,       0.00000000],
[      0.00000000,       0.00000000,       0.50000000],
[      0.50000000,       0.00000000,       0.00000000]],
[[      0.00000000,       0.50000000,       0.00000000],
[      0.00000000,       0.00000000,      -0.50000000],
[      0.50000000,       0.00000000,       0.00000000]],
[[      0.00000000,       0.00000000,      -0.50000000],
[      0.00000000,       0.50000000,       0.00000000],
[     -0.50000000,       0.00000000,       0.00000000]],
[[      0.00000000,       0.00000000,       0.50000000],
[      0.00000000,       0.50000000,       0.00000000],
[      0.50000000,       0.00000000,       0.00000000]],
[[      0.00000000,       0.50000000,       0.00000000],
[      0.00000000,       0.00000000,       0.50000000],
[     -0.50000000,       0.00000000,       0.00000000]]));
rbox c D2 | qhull Tcv Q0

Convex hull of 4 points in 2-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox c D2 | qhull Tcv Q0

  Number of points processed: 4
  Number of hyperplanes created: 6
  Number of distance tests for qhull: 5
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1.3e-15 of
all facets.  Will make 16 distance computations.
rbox d D2 | qhull Tcv

Convex hull of 4 points in 2-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox d D2 | qhull Tcv

  Number of points processed: 4
  Number of hyperplanes created: 5
  Number of distance tests for qhull: 3
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1.3e-15 of
all facets.  Will make 16 distance computations.
rbox c D3 | qhull Tcv Q0

Convex hull of 8 points in 3-d:

  Number of vertices: 8
  Number of facets: 12

Statistics for: rbox c D3 | qhull Tcv Q0

  Number of points processed: 8
  Number of hyperplanes created: 17
  Number of distance tests for qhull: 34
  CPU seconds to compute hull (after input):  0


precision problems (corrected unless 'Q0' or an error)
     12 coplanar half ridges in output
      6 coplanar horizon facets for new vertices

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 96 distance computations.
rbox d D3 | qhull Tcv

Convex hull of 6 points in 3-d:

  Number of vertices: 6
  Number of facets: 8

Statistics for: rbox d D3 | qhull Tcv

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 10
  Number of distance tests for merging: 59
  Number of distance tests for checking: 54
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.
rbox c D4 | qhull Tcv Q0

Convex hull of 16 points in 4-d:

  Number of vertices: 16
  Number of facets: 44

Statistics for: rbox c D4 | qhull Tcv Q0

  Number of points processed: 16
  Number of hyperplanes created: 61
  Number of distance tests for qhull: 162
  CPU seconds to compute hull (after input):  0


precision problems (corrected unless 'Q0' or an error)
     80 coplanar half ridges in output
     32 coplanar horizon facets for new vertices

Output completed.  Verifying that all points are below 3e-15 of
all facets.  Will make 704 distance computations.
rbox d D4 | qhull Tcv

Convex hull of 8 points in 4-d:

  Number of vertices: 8
  Number of facets: 16

Statistics for: rbox d D4 | qhull Tcv

  Number of points processed: 8
  Number of hyperplanes created: 20
  Number of distance tests for qhull: 23
  Number of distance tests for merging: 146
  Number of distance tests for checking: 154
  Number of merged facets: 4
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 128 distance computations.
rbox c D5 | qhull Tcv Q0

Convex hull of 32 points in 5-d:

  Number of vertices: 32
  Number of facets: 210

Statistics for: rbox c D5 | qhull Tcv Q0

  Number of points processed: 32
  Number of hyperplanes created: 296
  Number of distance tests for qhull: 787
  CPU seconds to compute hull (after input): 0.001


precision problems (corrected unless 'Q0' or an error)
    590 coplanar half ridges in output
    200 coplanar horizon facets for new vertices
    190 nearly singular or axis-parallel hyperplanes
    190 zero divisors during back substitute
    246 zero divisors during gaussian elimination

Output completed.  Verifying that all points are below 4.1e-15 of
all facets.  Will make 6720 distance computations.
rbox d D5 | qhull Tcv

Convex hull of 10 points in 5-d:

  Number of vertices: 10
  Number of facets: 32

Statistics for: rbox d D5 | qhull Tcv

  Number of points processed: 10
  Number of hyperplanes created: 36
  Number of distance tests for qhull: 46
  Number of distance tests for merging: 517
  Number of distance tests for checking: 320
  Number of merged facets: 11
  CPU seconds to compute hull (after input):  0

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 320 distance computations.
rbox c D6 | qhull Tcv Q0

Convex hull of 64 points in 6-d:

  Number of vertices: 64
  Number of facets: 1242

Statistics for: rbox c D6 | qhull Tcv Q0

  Number of points processed: 64
  Number of hyperplanes created: 1760
  Number of distance tests for qhull: 4843
  CPU seconds to compute hull (after input): 0.005


precision problems (corrected unless 'Q0' or an error)
   4752 coplanar half ridges in output
   1382 coplanar horizon facets for new vertices
   1180 nearly singular or axis-parallel hyperplanes
   1180 zero divisors during back substitute
   1593 zero divisors during gaussian elimination

Output completed.  Verifying that all points are below 5.3e-15 of
all facets.  Will make 79488 distance computations.
rbox d D6 | qhull Tcv

Convex hull of 12 points in 6-d:

  Number of vertices: 12
  Number of facets: 64

Statistics for: rbox d D6 | qhull Tcv

  Number of points processed: 12
  Number of hyperplanes created: 69
  Number of distance tests for qhull: 87
  Number of distance tests for merging: 1184
  Number of distance tests for checking: 768
  Number of merged facets: 26
  CPU seconds to compute hull (after input):  0

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 768 distance computations.
rbox d D7 | qhull Tcv

Convex hull of 14 points in 7-d:

  Number of vertices: 14
  Number of facets: 128

Statistics for: rbox d D7 | qhull Tcv

  Number of points processed: 14
  Number of hyperplanes created: 135
  Number of distance tests for qhull: 162
  Number of distance tests for merging: 2645
  Number of distance tests for checking: 1792
  Number of merged facets: 57
  CPU seconds to compute hull (after input): 0.002

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 1792 distance computations.
rbox c D2 | qhull Tcv C-0

Convex hull of 4 points in 2-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox c D2 | qhull Tcv C-0

  Number of points processed: 4
  Number of hyperplanes created: 6
  Number of distance tests for qhull: 5
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1.3e-15 of
all facets.  Will make 16 distance computations.
rbox c D3 | qhull Tcv C-0

Convex hull of 8 points in 3-d:

  Number of vertices: 8
  Number of facets: 6
  Number of non-simplicial facets: 6

Statistics for: rbox c D3 | qhull Tcv C-0

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 96
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.
rbox c D4 | qhull Tcv C-0

Convex hull of 16 points in 4-d:

  Number of vertices: 16
  Number of facets: 8
  Number of non-simplicial facets: 8

Statistics for: rbox c D4 | qhull Tcv C-0

  Number of points processed: 16
  Number of hyperplanes created: 25
  Number of distance tests for qhull: 167
  Number of distance tests for merging: 510
  Number of distance tests for checking: 412
  Number of merged facets: 36
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 128 distance computations.
rbox c D5 | qhull Tcv C-0

Convex hull of 32 points in 5-d:

  Number of vertices: 32
  Number of facets: 10
  Number of non-simplicial facets: 10

Statistics for: rbox c D5 | qhull Tcv C-0

  Number of points processed: 32
  Number of hyperplanes created: 86
  Number of distance tests for qhull: 721
  Number of distance tests for merging: 2647
  Number of distance tests for checking: 1810
  Number of merged facets: 210
  CPU seconds to compute hull (after input): 0.002


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 320 distance computations.
rbox c D6 | qhull Tcv C-0

Convex hull of 64 points in 6-d:

  Number of vertices: 64
  Number of facets: 12
  Number of non-simplicial facets: 12

Statistics for: rbox c D6 | qhull Tcv C-0

  Number of points processed: 64
  Number of hyperplanes created: 354
  Number of distance tests for qhull: 2556
  Number of distance tests for merging: 14301
  Number of distance tests for checking: 8642
  Number of merged facets: 1489
  CPU seconds to compute hull (after input): 0.03


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 768 distance computations.
rbox c D7 | qhull Tv C-0

Convex hull of 128 points in 7-d:

  Number of vertices: 128
  Number of facets: 14
  Number of non-simplicial facets: 14

Statistics for: rbox c D7 | qhull Tv C-0

  Number of points processed: 128
  Number of hyperplanes created: 1816
  Number of distance tests for qhull: 9567
  Number of distance tests for merging: 89582
  Number of distance tests for checking: 1960
  Number of merged facets: 11485
  CPU seconds to compute hull (after input): 0.032


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 1792 distance computations.
rbox 20 l D3 | qhull Tcv

Convex hull of 20 points in 3-d:

  Number of vertices: 20
  Number of facets: 36

Statistics for: rbox 20 l D3 | qhull Tcv

  Number of points processed: 20
  Number of hyperplanes created: 62
  Number of distance tests for qhull: 138
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 720 distance computations.
rbox 100 s D2 | qhull Tcv

Convex hull of 100 points in 2-d:

  Number of vertices: 100
  Number of facets: 100

Statistics for: rbox 100 s D2 | qhull Tcv

  Number of points processed: 100
  Number of hyperplanes created: 198
  Number of distance tests for qhull: 897
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1.3e-15 of
all facets.  Will make 10000 distance computations.
rbox 100 s D3 | qhull Tcv

Convex hull of 100 points in 3-d:

  Number of vertices: 100
  Number of facets: 196

Statistics for: rbox 100 s D3 | qhull Tcv

  Number of points processed: 100
  Number of hyperplanes created: 514
  Number of distance tests for qhull: 1690
  CPU seconds to compute hull (after input): 0.001


Output completed.  Verifying that all points are below 2e-15 of
all facets.  Will make 19600 distance computations.
rbox 100 s D4 | qhull Tcv

Convex hull of 100 points in 4-d:

  Number of vertices: 100
  Number of facets: 584

Statistics for: rbox 100 s D4 | qhull Tcv

  Number of points processed: 100
  Number of hyperplanes created: 1717
  Number of distance tests for qhull: 4090
  CPU seconds to compute hull (after input): 0.005


Output completed.  Verifying that all points are below 2.8e-15 of
all facets.  Will make 58400 distance computations.
rbox 100 s c D4 | qhull Tcv

Convex hull of 116 points in 4-d:

  Number of vertices: 16
  Number of facets: 8
  Number of non-simplicial facets: 8

Statistics for: rbox 100 s c D4 | qhull Tcv

  Number of points processed: 16
  Number of hyperplanes created: 25
  Number of distance tests for qhull: 2025
  Number of distance tests for merging: 510
  Number of distance tests for checking: 412
  Number of merged facets: 36
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 928 distance computations.
rbox 100 s d G1.5 D4 | qhull Tcv

Convex hull of 108 points in 4-d:

  Number of vertices: 8
  Number of facets: 16

Statistics for: rbox 100 s d G1.5 D4 | qhull Tcv

  Number of points processed: 8
  Number of hyperplanes created: 20
  Number of distance tests for qhull: 1487
  Number of distance tests for merging: 146
  Number of distance tests for checking: 154
  Number of merged facets: 4
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 1728 distance computations.
rbox 100 s W1e-2 | qhull Tcv

Convex hull of 100 points in 3-d:

  Number of vertices: 100
  Number of facets: 196

Statistics for: rbox 100 s W1e-2 | qhull Tcv

  Number of points processed: 100
  Number of hyperplanes created: 493
  Number of distance tests for qhull: 1581
  CPU seconds to compute hull (after input): 0.001


Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 19600 distance computations.
rbox 100 | qhull Tcv

Convex hull of 100 points in 3-d:

  Number of vertices: 30
  Number of facets: 56

Statistics for: rbox 100 | qhull Tcv

  Number of points processed: 31
  Number of hyperplanes created: 116
  Number of distance tests for qhull: 1210
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 5600 distance computations.
rbox 100 W1e-3 | qhull Tcv

Convex hull of 100 points in 3-d:

  Number of vertices: 60
  Number of facets: 116

Statistics for: rbox 100 W1e-3 | qhull Tcv

  Number of points processed: 65
  Number of hyperplanes created: 297
  Number of distance tests for qhull: 1748
  CPU seconds to compute hull (after input): 0.001


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 11600 distance computations.
rbox 100 r D2 | qhull Tcv

Convex hull of 100 points in 2-d:

  Number of vertices: 100
  Number of facets: 100

Statistics for: rbox 100 r D2 | qhull Tcv

  Number of points processed: 100
  Number of hyperplanes created: 198
  Number of distance tests for qhull: 854
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1.3e-15 of
all facets.  Will make 10000 distance computations.
rbox 100 r s Z1 | qhull Tcv

Convex hull of 102 points in 3-d:

  Number of vertices: 102
  Number of facets: 200

Statistics for: rbox 100 r s Z1 | qhull Tcv

  Number of points processed: 102
  Number of hyperplanes created: 298
  Number of distance tests for qhull: 1459
  Number of distance tests for merging: 11679
  Number of distance tests for checking: 6438
  Number of merged facets: 97
  CPU seconds to compute hull (after input): 0.005


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 20400 distance computations.
rbox 100 r s Z1 G0.1 | qhull Tcv C-0

Convex hull of 201 points in 3-d:

  Number of vertices: 201
  Number of facets: 201
  Number of non-simplicial facets: 101

Statistics for: rbox 100 r s Z1 G0.1 | qhull Tcv C-0

  Number of points processed: 201
  Number of hyperplanes created: 1003
  Number of distance tests for qhull: 6999
  Number of distance tests for merging: 26735
  Number of distance tests for checking: 22944
  Number of merged facets: 330
  CPU seconds to compute hull (after input): 0.023


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 40401 distance computations.
rbox 100 s Z1 G0.1 | qhull Tcv 

Convex hull of 101 points in 3-d:

  Number of vertices: 101
  Number of facets: 198

Statistics for: rbox 100 s Z1 G0.1 | qhull Tcv

  Number of points processed: 101
  Number of hyperplanes created: 460
  Number of distance tests for qhull: 1621
  CPU seconds to compute hull (after input): 0.001


Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 19998 distance computations.
rbox 100 s Z1e-5 G0.1 | qhull Tc Pp

Convex hull of 101 points in 3-d:

  Number of vertices: 101
  Number of facets: 196
  Number of non-simplicial facets: 2

Statistics for: rbox 100 s Z1e-5 G0.1 | qhull Tc Pp

  Number of points processed: 101
  Number of hyperplanes created: 453
  Number of distance tests for qhull: 1847
  Number of distance tests for merging: 2078
  Number of distance tests for checking: 1209
  Number of merged facets: 3
  CPU seconds to compute hull (after input): 0.002
  Maximum distance of vertex below facet: -1.1e-15 (0.3x)


set +v
=== check qhull option errors Fri, Jul 24, 2020 10:27:28 PM
rbox 10 | qhull d H0
QH6037 qhull option error (qh_readpoints): can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H')

While executing: rbox 10
 | qhull d H0
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213731000  delaunay  Halfspace-about  0  _maxoutside  0
rbox 10 | qhull Zza
QH7094 qhull option warning: unknown option 'Z'(5a)
QH7036 qhull option warning: missing space after option 'Z'(5a), reserved for sub-options, ignoring 'Z' options to next space
QH6035 qhull option error: see previous warnings, use 'Qw' to override: 'qhull Zza' (last offset 6)

While executing:  | qhull Zza
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213731000  _maxoutside  0
rbox 10 | qhull Zza Qw
QH7094 qhull option warning: unknown option 'Z'(5a)
QH7036 qhull option warning: missing space after option 'Z'(5a), reserved for sub-options, ignoring 'Z' options to next space

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 10 | qhull Zza Qw

  Number of points processed: 10
  Number of hyperplanes created: 26
  Number of distance tests for qhull: 43
  CPU seconds to compute hull (after input):  0

rbox 10 | qhull Q999

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 10 | qhull Q999

  Number of points processed: 10
  Number of hyperplanes created: 26
  Number of distance tests for qhull: 43
  CPU seconds to compute hull (after input):  0

rbox 10 | qhull Q999 Qw

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 10 | qhull Q999 Qw

  Number of points processed: 10
  Number of hyperplanes created: 26
  Number of distance tests for qhull: 43
  CPU seconds to compute hull (after input):  0

qhull TIxyzlkajdfhwh
QH6041 qhull option error: cannot open 'TI' file "xyzlkajdfhwh"

While executing:  | qhull TIxyzlkajdfhwh
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213731000  _maxoutside  0
rbox 10 >r.x
qhull TIr.x

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 10 | qhull TIr.x

  Number of points processed: 10
  Number of hyperplanes created: 26
  Number of distance tests for qhull: 43
  CPU seconds to compute hull (after input):  0

qhull p TI    r.x TO x.x
cat x.x
3
10
-0.374949442106252 0.2247255418679914 -0.03782349642163468 
0.3004920247946792 0.3694544596313075 0.4210962191420572 
0.3641479121187217 0.2339522165562512 0.03489791698278666 
-0.4707134565997063 -0.2810653003687648 0.1354949890035158 
0.2642752088273644 -0.3265712199048802 0.3175057017407433 
0.3183227589524563 0.05060330969337679 0.4898217078203537 
0.4334355904100794 -0.2480392830893763 0.2037671452423252 
-0.2855954200826543 -0.002227006947833121 -0.4293096679535784 
-0.4075898489985521 -0.3625928418362446 -0.09789381697577781 
-0.3013850588364387 -0.3786854184034145 0.4341719447953365 

set +v
=== check qhull output formats Fri, Jul 24, 2020 10:27:28 PM
rbox 5 r s D2 | qhull Tcv

Convex hull of 5 points in 2-d:

  Number of vertices: 5
  Number of facets: 5

Statistics for: rbox 5 r s D2 | qhull Tcv

  Number of points processed: 5
  Number of hyperplanes created: 8
  Number of distance tests for qhull: 7
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1.3e-15 of
all facets.  Will make 25 distance computations.
rbox 5 r s D2 | qhull s 

Convex hull of 5 points in 2-d:

  Number of vertices: 5
  Number of facets: 5

Statistics for: rbox 5 r s D2 | qhull s

  Number of points processed: 5
  Number of hyperplanes created: 8
  Number of distance tests for qhull: 7
  CPU seconds to compute hull (after input):  0

rbox 5 r s D2 | qhull s o 

Convex hull of 5 points in 2-d:

  Number of vertices: 5
  Number of facets: 5

Statistics for: rbox 5 r s D2 | qhull s o

  Number of points processed: 5
  Number of hyperplanes created: 8
  Number of distance tests for qhull: 7
  CPU seconds to compute hull (after input):  0

2
5 5 5
0.1545084971874737 0.4755282581475768 
-0.4045084971874737 0.2938926261462366 
-0.4045084971874738 -0.2938926261462365 
0.1545084971874736 -0.4755282581475768 
   0.5 -1.224646799147353e-16 
2 4 0 
2 2 3 
2 3 4 
2 1 2 
2 0 1 
rbox 5 r s D2 | qhull f
Vertices and facets:
- p0(v3):  0.15  0.48
- p4(v2):   0.5 -1.2e-16
- p3(v4):  0.15 -0.48
- p2(v1):  -0.4 -0.29
- p1(v5):  -0.4  0.29
- f3
    - flags: bottom simplicial
    - normal:     0.809   0.5878
    - offset: -0.4045085
    - vertices: p0(v3) p4(v2)
    - neighboring facets: f5 f7
- f4
    - flags: bottom simplicial
    - normal:    -0.309  -0.9511
    - offset: -0.4045085
    - vertices: p3(v4) p2(v1)
    - neighboring facets: f6 f5
- f5
    - flags: top simplicial
    - normal:     0.809  -0.5878
    - offset: -0.4045085
    - vertices: p3(v4) p4(v2)
    - neighboring facets: f3 f4
- f6
    - flags: top simplicial
    - normal:        -1 9.444e-17
    - offset: -0.4045085
    - vertices: p1(v5) p2(v1)
    - neighboring facets: f4 f7
- f7
    - flags: bottom simplicial
    - normal:    -0.309   0.9511
    - offset: -0.4045085
    - vertices: p1(v5) p0(v3)
    - neighboring facets: f3 f6
rbox 5 r s D2 | qhull i 
5
4 0 
2 3 
3 4 
1 2 
0 1 
rbox 5 r s D2 | qhull m 
{
Line[{{      0.50000000,      -0.00000000}, {      0.15450850,       0.47552826}}]
,Line[{{     -0.40450850,      -0.29389263}, {      0.15450850,      -0.47552826}}]
,Line[{{      0.15450850,      -0.47552826}, {      0.50000000,      -0.00000000}}]
,Line[{{     -0.40450850,       0.29389263}, {     -0.40450850,      -0.29389263}}]
,Line[{{      0.15450850,       0.47552826}, {     -0.40450850,       0.29389263}}]
}
rbox 5 r s D2 | qhull FM 
PLOT(CURVES(
[[      0.50000000,      -0.00000000], [      0.15450850,       0.47552826]]
,[[     -0.40450850,      -0.29389263], [      0.15450850,      -0.47552826]]
,[[      0.15450850,      -0.47552826], [      0.50000000,      -0.00000000]]
,[[     -0.40450850,       0.29389263], [     -0.40450850,      -0.29389263]]
,[[      0.15450850,       0.47552826], [     -0.40450850,       0.29389263]]
));
rbox 5 r s D2 | qhull n 
3
5
0.8090169943749476 0.587785252292473 -0.4045084971874737 
-0.3090169943749476 -0.9510565162951536 -0.4045084971874738 
0.8090169943749472 -0.5877852522924732 -0.4045084971874737 
    -1 9.444121133484361e-17 -0.4045084971874738 
-0.3090169943749474 0.9510565162951536 -0.4045084971874738 
rbox 5 r s D2 | qhull p 
2
5
0.1545084971874737 0.4755282581475768 
-0.4045084971874737 0.2938926261462366 
-0.4045084971874738 -0.2938926261462365 
0.1545084971874736 -0.4755282581475768 
   0.5 -1.224646799147353e-16 
rbox 5 r s D2 | qhull o 
2
5 5 5
0.1545084971874737 0.4755282581475768 
-0.4045084971874737 0.2938926261462366 
-0.4045084971874738 -0.2938926261462365 
0.1545084971874736 -0.4755282581475768 
   0.5 -1.224646799147353e-16 
2 4 0 
2 2 3 
2 3 4 
2 1 2 
2 0 1 
rbox 5 r s D2 | qhull Ft
2
5 5 5
0.1545084971874737 0.4755282581475768 
-0.4045084971874737 0.2938926261462366 
-0.4045084971874738 -0.2938926261462365 
0.1545084971874736 -0.4755282581475768 
   0.5 -1.224646799147353e-16 
2 4 0 
2 2 3 
2 3 4 
2 1 2 
2 0 1 
rbox 5 r s D2 | qhull Fx
5
4
0
1
2
3
rbox 5 r s D2 | qhull p n i p p
2
5
0.1545084971874737 0.4755282581475768 
-0.4045084971874737 0.2938926261462366 
-0.4045084971874738 -0.2938926261462365 
0.1545084971874736 -0.4755282581475768 
   0.5 -1.224646799147353e-16 
3
5
0.8090169943749476 0.587785252292473 -0.4045084971874737 
-0.3090169943749476 -0.9510565162951536 -0.4045084971874738 
0.8090169943749472 -0.5877852522924732 -0.4045084971874737 
    -1 9.444121133484361e-17 -0.4045084971874738 
-0.3090169943749474 0.9510565162951536 -0.4045084971874738 
5
4 0 
2 3 
3 4 
1 2 
0 1 
rbox 10 D3 | qhull f Tcv
Vertices and facets:
- p0(v5): -0.022 -0.37  0.33
- p9(v3):  0.38 -0.47 -0.22
- p6(v1): -0.31 -0.011 -0.49
- p1(v4): -0.067 -0.16  0.46
- p7(v2):  0.39 0.045  0.12
- p3(v6):  0.31 0.084  -0.1
- p4(v7):  0.18  0.12 0.049
- p5(v8): -0.12 0.015 -0.14
- p2(v9): 0.028 0.042 0.058
- f5
    - flags: top simplicial
    - normal:   -0.4934  -0.8471  -0.1973
    - offset: -0.2568231
    - vertices: p0(v5) p9(v3) p6(v1)
    - neighboring facets: f9 f6 f7
- f6
    - flags: bottom simplicial
    - normal:   -0.9301  -0.3157   0.1877
    - offset: -0.1977325
    - vertices: p0(v5) p1(v4) p6(v1)
    - neighboring facets: f17 f5 f8
- f7
    - flags: bottom simplicial
    - normal:    0.7008  -0.3956   0.5936
    - offset:  -0.323519
    - vertices: p0(v5) p9(v3) p7(v2)
    - neighboring facets: f10 f8 f5
- f8
    - flags: top simplicial
    - normal:    0.6544   -0.298   0.6949
    - offset: -0.3219447
    - vertices: p0(v5) p1(v4) p7(v2)
    - neighboring facets: f13 f7 f6
- f9
    - flags: bottom simplicial
    - normal:    0.4866   0.2316  -0.8424
    - offset: -0.2582907
    - vertices: p3(v6) p9(v3) p6(v1)
    - neighboring facets: f5 f16 f10
- f10
    - flags: top simplicial
    - normal:     0.943   0.1711  -0.2855
    - offset: -0.3386013
    - vertices: p3(v6) p9(v3) p7(v2)
    - neighboring facets: f7 f14 f9
- f13
    - flags: bottom simplicial
    - normal:   0.08536   0.8035   0.5892
    - offset: -0.1388354
    - vertices: p4(v7) p1(v4) p7(v2)
    - neighboring facets: f8 f14 f20
- f14
    - flags: top simplicial
    - normal:    0.3121    0.948  0.06295
    - offset: -0.1707289
    - vertices: p4(v7) p3(v6) p7(v2)
    - neighboring facets: f10 f13 f16
- f16
    - flags: bottom simplicial
    - normal:  -0.008104   0.9738  -0.2271
    - offset: -0.1026508
    - vertices: p4(v7) p3(v6) p6(v1)
    - neighboring facets: f9 f18 f14
- f17
    - flags: top simplicial
    - normal:   -0.6179   0.7381   0.2709
    - offset: -0.04995414
    - vertices: p5(v8) p1(v4) p6(v1)
    - neighboring facets: f6 f18 f21
- f18
    - flags: bottom simplicial
    - normal:   -0.3978   0.9064   0.1423
    - offset: -0.04320607
    - vertices: p5(v8) p4(v7) p6(v1)
    - neighboring facets: f16 f17 f22
- f20
    - flags: top simplicial
    - normal:   -0.4124   0.8514   0.3242
    - offset: -0.04294297
    - vertices: p2(v9) p4(v7) p1(v4)
    - neighboring facets: f13 f21 f22
- f21
    - flags: bottom simplicial
    - normal:   -0.5086   0.8133   0.2826
    - offset: -0.03620543
    - vertices: p2(v9) p5(v8) p1(v4)
    - neighboring facets: f17 f20 f22
- f22
    - flags: top simplicial
    - normal:    -0.432   0.8759   0.2148
    - offset: -0.03703814
    - vertices: p2(v9) p5(v8) p4(v7)
    - neighboring facets: f18 f20 f21

Output completed.  Verifying that all points are below 2e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D3 | qhull i
14
0 9 6 
1 0 6 
9 0 7 
0 1 7 
9 3 6 
3 9 7 
1 4 7 
4 3 7 
3 4 6 
5 1 6 
4 5 6 
2 4 1 
5 2 1 
2 5 4 
rbox 10 D3 | qhull p 
3
9
-0.0222149361131852 -0.366434993563625 0.3270621312102882 
-0.06676722137887703 -0.1566931052661437 0.4589771055234383 
0.02820502736438535 0.04189077954915421 0.05832764185809314 
0.3126723396709863 0.08400649026409401 -0.1029227018383543 
0.1781470954214661 0.1182274414396169 0.04860343742054274 
-0.1220315663349177 0.01546165115708642 -0.1360330368727753 
-0.3072535691850387 -0.01073880122111998 -0.4870359524963758 
0.3867462923626847 0.04492879989084675 0.118335500935405 
0.3789805913148268 -0.4732086509216658 -0.2177962499836425 
rbox 10 D3 | qhull o 
3
10 14 21
-0.0222149361131852 -0.366434993563625 0.3270621312102882 
-0.06676722137887703 -0.1566931052661437 0.4589771055234383 
0.02820502736438535 0.04189077954915421 0.05832764185809314 
0.3126723396709863 0.08400649026409401 -0.1029227018383543 
0.1781470954214661 0.1182274414396169 0.04860343742054274 
-0.1220315663349177 0.01546165115708642 -0.1360330368727753 
-0.3072535691850387 -0.01073880122111998 -0.4870359524963758 
0.3867462923626847 0.04492879989084675 0.118335500935405 
-0.1352406177997967 0.01093378431250691 -0.2358910583293913 
0.3789805913148268 -0.4732086509216658 -0.2177962499836425 
3 0 9 6 
3 1 0 6 
3 9 0 7 
3 0 1 7 
3 9 3 6 
3 3 9 7 
3 1 4 7 
3 4 3 7 
3 3 4 6 
3 5 1 6 
3 4 5 6 
3 2 4 1 
3 5 2 1 
3 2 5 4 
rbox 10 D3 | qhull Fx
9
0
1
2
3
4
5
6
7
9
rbox 27 M1,0,1 | qhull Qc

Convex hull of 27 points in 3-d:

  Number of vertices: 8
  Number of coplanar points: 18
  Number of facets: 6
  Number of non-simplicial facets: 6

Statistics for: rbox 27 M1,0,1 | qhull Qc

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 297
  Number of distance tests for merging: 90
  Number of distance tests for checking: 168
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0

rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 Pg s p Tcv

Convex hull of 50 points in 3-d:

  Number of vertices: 17
  Number of coplanar points: 33
  Number of facets: 11
  Number of 'good' facets: 1

Statistics for: rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 Pg s p Tcv

  Number of points processed: 50
  Number of hyperplanes created: 236
  Number of distance tests for qhull: 1191
  Number of distance tests for merging: 3250
  Number of distance tests for checking: 1146
  Number of merged facets: 85
  CPU seconds to compute hull (after input): 0.001
  Maximum distance of vertex below facet: -0.24 (0.8x)

3
4
0.4995640899182717 0.005583735684776723 0.02011322848106416 
0.3642936952899509 -0.2163723184172344 -0.2654677445467591 
0.39379735093457 0.04855022442420501 -0.3042474685273066 
0.397166795352245 -0.07497301400429786 -0.2943426300092109 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 50 distance computations.
rbox 10 D2 P0 P1e-15 | qhull d Qc FP s Tcv

Delaunay triangulation by the convex hull of 12 points in 3-d:

  Number of input sites: 11
  Number of nearly incident points: 1
  Number of Delaunay regions: 16

Statistics for: rbox 10 D2 P0 P1e-15 | qhull d Qc FP s Tcv

  Number of points processed: 11
  Number of hyperplanes created: 33
  Number of facets in hull: 18
  Number of distance tests for qhull: 107
  CPU seconds to compute hull (after input):  0

1
0 1 12  1e-15 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 192 distance computations.
rbox 100 s | qhull C-0.003 Qc FP s

Convex hull of 100 points in 3-d:

  Number of vertices: 90
  Number of coplanar points: 10
  Number of facets: 118
  Number of non-simplicial facets: 46

Statistics for: rbox 100 s | qhull C-0.003 Qc FP s

  Number of points processed: 90
  Number of hyperplanes created: 404
  Number of distance tests for qhull: 1996
  Number of distance tests for merging: 3783
  Number of distance tests for checking: 1381
  Number of merged facets: 105
  CPU seconds to compute hull (after input):  0
  Maximum distance of point above facet: 0.0057 (0.6x)
  Maximum distance of vertex below facet: -0.0087 (1.0x)

10
29 92 222 0.05221620842441997 
49 2 292 0.03790045221711884 
99 9 336 0.02993864679572162 
54 84 340 0.06479664045626413 
54 72 226 0.03827167959574595 
96 6 368 0.02282529175708784 
19 1 372 0.01048228658130246 
69 26 409 0.04998878658421259 
19 66 371 0.008281093788857875 
19 45 371 0.04608027722786196 
rbox 100 s D2 | qhull C0.1 i Fx Tcv
6
4 28 
77 70 
6 68 
70 6 
68 4 
28 77 
6
4
28
77
70
6
68

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 600 distance computations.
rbox 4 s D3 | qhull Qc Ghipv Tcv 
{appearance {+edge -evert linewidth 2} LIST # rbox 4 s D3 | qhull Qc Ghipv Tcv
{appearance {-edge -normal normscale 0} {
INST geom {define vsphere OFF
18 32 48

0 0 1
1 0 0
0 1 0
-1 0 0
0 -1 0
0 0 -1
0.707107 0 0.707107
0 -0.707107 0.707107
0.707107 -0.707107 0
-0.707107 0 0.707107
-0.707107 -0.707107 0
0 0.707107 0.707107
-0.707107 0.707107 0
0.707107 0.707107 0
0.707107 0 -0.707107
0 0.707107 -0.707107
-0.707107 0 -0.707107
0 -0.707107 -0.707107

3 0 6 11
3 0 7 6 
3 0 9 7 
3 0 11 9
3 1 6 8 
3 1 8 14
3 1 13 6
3 1 14 13
3 2 11 13
3 2 12 11
3 2 13 15
3 2 15 12
3 3 9 12
3 3 10 9
3 3 12 16
3 3 16 10
3 4 7 10
3 4 8 7
3 4 10 17
3 4 17 8
3 5 14 17
3 5 15 14
3 5 16 15
3 5 17 16
3 6 13 11
3 7 8 6
3 9 10 7
3 11 12 9
3 14 8 17
3 15 13 14
3 16 12 15
3 17 10 16
} transforms { TLIST
0.009951 0 0 0 # v3
 0 0.009951 0 0
0 0 0.009951 0
-0.04234  -0.2077  -0.4529  # p3
1
0.009951 0 0 0 # v2
 0 0.009951 0 0
0 0 0.009951 0
0.004313  -0.4976  0.04904  # p2
1
0.009951 0 0 0 # v1
 0 0.009951 0 0
0 0 0.009951 0
 -0.4876  0.03313  -0.1055  # p0
1
0.009951 0 0 0 # v4
 0 0.009951 0 0
0 0 0.009951 0
 -0.3939  -0.1068  -0.2889  # p1
1
}}}
{ OFF 3 1 1 # f1
-0.04933  -0.2152  -0.4566 
-0.002675  -0.5051  0.04532 
 -0.4946  0.02557  -0.1092 
3 0 1 2   0.1808   0.1547   0.3302 1.0 }
VECT 1 2 1 2 1 # intersect f1 f2
0.004313  -0.4976  0.04904 # projected p2
 -0.4876  0.03313  -0.1055 # projected p0
       0        0        0 1.0
VECT 1 2 1 2 1 # intersect f1 f3
-0.04234  -0.2077  -0.4529 # projected p3
 -0.4876  0.03313  -0.1055 # projected p0
       0        0        0 1.0
VECT 1 2 1 2 1 # intersect f1 f4
-0.04234  -0.2077  -0.4529 # projected p3
0.004313  -0.4976  0.04904 # projected p2
       0        0        0 1.0
{ OFF 3 1 1 # f2
 0.01247  -0.4904  0.04773 
 -0.3857 -0.09961  -0.2902 
 -0.4795  0.04031  -0.1068 
3 0 1 2   0.8726    0.828   0.4402 1.0 }
VECT 1 2 1 2 1 # intersect f2 f3
 -0.3939  -0.1068  -0.2889 # projected p1
 -0.4876  0.03313  -0.1055 # projected p0
       0        0        0 1.0
VECT 1 2 1 2 1 # intersect f2 f4
 -0.3939  -0.1068  -0.2889 # projected p1
0.004313  -0.4976  0.04904 # projected p2
       0        0        0 1.0
{ OFF 3 1 1 # f3
 -0.3931  -0.1153   -0.282 
-0.04157  -0.2162   -0.446 
 -0.4869  0.02464 -0.09863 
3 0 1 2   0.5351   0.1123   0.8138 1.0 }
VECT 1 2 1 2 1 # intersect f3 f4
 -0.3939  -0.1068  -0.2889 # projected p1
-0.04234  -0.2077  -0.4529 # projected p3
       0        0        0 1.0
{ OFF 3 1 1 # f4
-0.03767  -0.1989  -0.4482 
 -0.3892 -0.09803  -0.2843 
0.008983  -0.4888  0.05366 
3 0 1 2   0.7133   0.8999   0.7112 1.0 }
}

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 16 distance computations.
rbox 6 D4 | qhull f Tcv
Vertices and facets:
- p3(v5):   0.1 -0.13 -0.17 -0.42
- p0(v4): -0.33 -0.43 -0.46  0.15
- p2(v3):  0.11   0.4 -0.063 -0.18
- p1(v1): -0.35 -0.24  0.14 -0.18
- p4(v2):  0.14 -0.34 -0.084 0.087
- p5(v6): -0.25  -0.5  0.22 -0.033
- f4
    - flags: bottom simplicial
    - normal:   -0.6536   0.3379   -0.424  -0.5281
    - offset: -0.1850304
    - vertices: p3(v5) p0(v4) p2(v3) p1(v1)
    - neighboring facets: f6 f8 f10 f5
- f5
    - flags: top simplicial
    - normal:    0.6142  0.09488  -0.7743   0.1197
    - offset: -0.1313181
    - vertices: p3(v5) p0(v4) p2(v3) p4(v2)
    - neighboring facets: f7 f9 f11 f4
- f6
    - flags: top simplicial
    - normal:   -0.4209   0.3853   0.2879   0.7691
    - offset: 0.04819078
    - vertices: p5(v6) p0(v4) p2(v3) p1(v1)
    - neighboring facets: f4 f8 f10 f7
- f7
    - flags: bottom simplicial
    - normal:   -0.1759   0.3066   0.2842   0.8912
    - offset: 0.07466537
    - vertices: p5(v6) p0(v4) p2(v3) p4(v2)
    - neighboring facets: f5 f9 f11 f6
- f8
    - flags: bottom simplicial
    - normal:    0.2584  0.07433    0.814   -0.515
    - offset: -0.09844114
    - vertices: p5(v6) p3(v5) p2(v3) p1(v1)
    - neighboring facets: f4 f6 f10 f9
- f9
    - flags: top simplicial
    - normal:    0.6576 -0.06072   0.7252   -0.195
    - offset: -0.03612816
    - vertices: p5(v6) p3(v5) p2(v3) p4(v2)
    - neighboring facets: f5 f7 f11 f8
- f10
    - flags: top simplicial
    - normal:   -0.3537  -0.6003  -0.2017  -0.6883
    - offset: -0.3651888
    - vertices: p5(v6) p3(v5) p0(v4) p1(v1)
    - neighboring facets: f4 f6 f8 f11
- f11
    - flags: bottom simplicial
    - normal:    0.2962   -0.865  -0.2123  -0.3449
    - offset: -0.3220787
    - vertices: p5(v6) p3(v5) p0(v4) p4(v2)
    - neighboring facets: f5 f7 f9 f10

Output completed.  Verifying that all points are below 3e-15 of
all facets.  Will make 48 distance computations.
rbox 6 D4 | qhull i
8
0 3 2 1 
3 0 2 4 
5 0 2 1 
0 5 2 4 
3 5 2 1 
5 3 2 4 
5 3 0 1 
3 5 0 4 
rbox 6 D4 | qhull p 
4
6
-0.3257826863096865 -0.4296101703584289 -0.4581337649916613 0.1458114577883961 
-0.3468340047139991 -0.2391184267952278 0.1365988111464296 -0.1837860440684352 
0.1079548672847029 0.397449696341017 -0.062960620096848 -0.1791453880063681 
0.1034612661259819 -0.1265049433582509 -0.1685859450777862 -0.4239815160855479 
0.1426585555473888 -0.3376619446442108 -0.08430490557505277 0.08744874697872318 
-0.2489141260729303 -0.4997188728300099 0.224904344160952 -0.03269336003129686 
rbox 6 D4 | qhull o
4
6 8 16
-0.3257826863096865 -0.4296101703584289 -0.4581337649916613 0.1458114577883961 
-0.3468340047139991 -0.2391184267952278 0.1365988111464296 -0.1837860440684352 
0.1079548672847029 0.397449696341017 -0.062960620096848 -0.1791453880063681 
0.1034612661259819 -0.1265049433582509 -0.1685859450777862 -0.4239815160855479 
0.1426585555473888 -0.3376619446442108 -0.08430490557505277 0.08744874697872318 
-0.2489141260729303 -0.4997188728300099 0.224904344160952 -0.03269336003129686 
4 0 3 2 1 
4 3 0 2 4 
4 5 0 2 1 
4 0 5 2 4 
4 3 5 2 1 
4 5 3 2 4 
4 5 3 0 1 
4 3 5 0 4 
rbox 1000 s D2 | qhull FA Tcv

Convex hull of 1000 points in 2-d:

  Number of vertices: 1000
  Number of facets: 1000

Statistics for: rbox 1000 s D2 | qhull FA Tcv

  Number of points processed: 1000
  Number of hyperplanes created: 1997
  Number of distance tests for qhull: 13977
  CPU seconds to compute hull (after input): 0.044
  Total facet area:   3.1415592
  Total volume:       0.7853647


qhull output completed.  Verifying that 1000 points are
below 1.3e-15 of the nearest facet.
rbox 1000 s | qhull FA Tcv

Convex hull of 1000 points in 3-d:

  Number of vertices: 1000
  Number of facets: 1996

Statistics for: rbox 1000 s | qhull FA Tcv

  Number of points processed: 1000
  Number of hyperplanes created: 5544
  Number of distance tests for qhull: 25487
  CPU seconds to compute hull (after input): 0.034
  Total facet area:   3.1201951
  Total volume:       0.51650274


qhull output completed.  Verifying that 1000 points are
below 2.1e-15 of the nearest facet.
rbox c D4 | qhull FA Tcv

Convex hull of 16 points in 4-d:

  Number of vertices: 16
  Number of facets: 8
  Number of non-simplicial facets: 8

Statistics for: rbox c D4 | qhull FA Tcv

  Number of points processed: 16
  Number of hyperplanes created: 25
  Number of distance tests for qhull: 167
  Number of distance tests for merging: 510
  Number of distance tests for checking: 412
  Number of merged facets: 36
  CPU seconds to compute hull (after input):  0
  Approximate facet area:    8
  Approximate volume:        1


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 128 distance computations.
rbox c D5 | qhull FA Tcv

Convex hull of 32 points in 5-d:

  Number of vertices: 32
  Number of facets: 10
  Number of non-simplicial facets: 10

Statistics for: rbox c D5 | qhull FA Tcv

  Number of points processed: 32
  Number of hyperplanes created: 86
  Number of distance tests for qhull: 721
  Number of distance tests for merging: 2702
  Number of distance tests for checking: 400
  Number of merged facets: 210
  CPU seconds to compute hull (after input): 0.002
  Approximate facet area:   10
  Approximate volume:        1

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 320 distance computations.
rbox c D5 | qhull FA Qt Tcv

Convex hull of 32 points in 5-d:

  Number of vertices: 32
  Number of facets: 316
  Number of triangulated facets: 10

Statistics for: rbox c D5 | qhull FA Qt Tcv

  Number of points processed: 32
  Number of hyperplanes created: 86
  Number of distance tests for qhull: 721
  Number of distance tests for merging: 2702
  Number of distance tests for checking: 400
  Number of merged facets: 210
  CPU seconds to compute hull (after input): 0.004
  Approximate facet area:   10
  Approximate volume:        1

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 10112 distance computations.
rbox 10 D2 | qhull d FA Tcv

Delaunay triangulation by the convex hull of 10 points in 3-d:

  Number of input sites: 10
  Number of Delaunay regions: 14

Statistics for: rbox 10 D2 | qhull d FA Tcv

  Number of points processed: 10
  Number of hyperplanes created: 28
  Number of facets in hull: 16
  Number of distance tests for qhull: 47
  CPU seconds to compute hull (after input):  0
  Total facet area:   0.46254269


Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D2 | qhull d Qu FA Tcv

Furthest-site Delaunay triangulation by the convex hull of 10 points in 3-d:

  Number of input sites: 10
  Number of Delaunay regions: 2

Statistics for: rbox 10 D2 | qhull d Qu FA Tcv

  Number of points processed: 10
  Number of hyperplanes created: 28
  Number of facets in hull: 16
  Number of distance tests for qhull: 47
  CPU seconds to compute hull (after input):  0
  Total facet area:   0.46254269


Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 20 distance computations.
rbox 10 D2 | qhull FA Tcv

Convex hull of 10 points in 2-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox 10 D2 | qhull FA Tcv

  Number of points processed: 4
  Number of hyperplanes created: 5
  Number of distance tests for qhull: 51
  CPU seconds to compute hull (after input):  0
  Total facet area:   2.8999576
  Total volume:       0.46254269


Output completed.  Verifying that all points are below 1.3e-15 of
all facets.  Will make 40 distance computations.
rbox 10 c D2 | qhull Fx Tcv
4
10
12
13
11

Output completed.  Verifying that all points are below 1.3e-15 of
all facets.  Will make 56 distance computations.
rbox 1000 s | qhull FS Tcv
0
2 3.120195135077461 0.516502736886338 

qhull output completed.  Verifying that 1000 points are
below 2.1e-15 of the nearest facet.
rbox 10 W0 D2 | qhull p Qc FcC Tcv
2
10
-0.3863076515368257    0.5 
-0.05259535978789942    0.5 
0.2626424396993987    0.5 
0.3748708151978168    0.5 
-0.01474997775140219    0.5 
0.1582814042067914    0.5 
  -0.5 0.4508927962285399 
  -0.5 -0.003085198815060031 
-0.3688616616361418   -0.5 
-0.2798755283280048    0.5 
5
0
0
0
0
5 2 4 5 9 1
2
5
0.003004576780837498 -8.023127287351645e-18 
  -0.5 0.2239037987067399 
-0.4344308308180709 -0.25154259940753 
-0.4431538257684129 0.4754463981142699 
-0.005718418169504469    0.5 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 50 distance computations.
rbox 4 z h s D2 | qhull Fd s n FD Tcv

Convex hull of 4 points in 2-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox 4 z h s D2 | qhull Fd s n FD Tcv

  Number of points processed: 4
  Number of hyperplanes created: 5
  Number of distance tests for qhull: 4
  CPU seconds to compute hull (after input):  0

rbox 4 z h s D2 | qhull Fd s n FD Tcv
begin
    4 3 real
107643.7343385944 -0.2650304141580589 -0.964240052876465 
797791.7732245289 -0.6912673062074456 0.7225991360143615 
874890.2679778723 0.9916265954087946 0.1291382796771071 
864878.4439653738 0.3984446264475182 0.9171923896626583 
end

Output completed.  Verifying that all points are below 2.6e-09 of
all facets.  Will make 16 distance computations.
rbox 6 s D3 | qhull C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213781421  Centrum-premerge- 0.1  Qcoplanar-keep  FFacets-xridge
  summary  FQhull  Finner  normals  Fouter  FQhull  FIDs  Fmerges  Fneighbors
  FNeighbors-vertex  FOptions  FQhull  Fsummary  FSize  FVertex-average
  Tcheck-frequently  Tverify  Fvertices  _max-width 0.86
  Error-roundoff 6.6e-16  _one-merge 0.3  _near-inside 1.5
  Visible-distance 0.1  U-max-coplanar 0.1  Width-outside 0.2  _wide-facet 0.6

Convex hull of 6 points in 3-d:

  Number of vertices: 4
  Number of coplanar points: 2
  Number of facets: 4

Statistics for: rbox 6 s D3 | qhull C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv

  Number of points processed: 4
  Number of hyperplanes created: 4
  Number of distance tests for qhull: 22
  CPU seconds to compute hull (after input):  0
  Total facet area:   0.82966766
  Total volume:       0.010511079
  Maximum distance of point above facet: 0.11 (0.4x)

Vertices and facets:
- p1(v3):  -0.3  0.39 -0.092
- p5(v2):   0.4 -0.22  -0.2
- p4(v1): -0.46 -0.19 -0.018
- p2(v4):  0.25  0.28 -0.33
- f1
    - flags: top simplicial isarea
    - area: 0.26
    - normal:    0.2054  0.06987   0.9762
    - offset:   0.125398
    - center: -0.1205015151724569 -0.008790385787885074 -0.1024776532548504 
    - vertices: p1(v3) p5(v2) p4(v1)
    - neighboring facets: f2 f3 f4
- f2
    - flags: bottom simplicial isarea
    - area: 0.23
    - normal:   -0.2032  -0.3001   -0.932
    - offset: -0.1680571
    - center: 0.06430144219370747 -0.04270356053094847 -0.1805812707066012 
    - maxoutside:  0.1132672
    - coplanar set(furthest p3):
      p0:   0.07025  -0.4742   -0.142
      p3:    0.2976  -0.2965  -0.2712
      furthest distance= 0.11
    - vertices: p2(v4) p5(v2) p4(v1)
    - neighboring facets: f1 f3 f4
- f3
    - flags: top simplicial isarea
    - area: 0.18
    - normal:   -0.3912 -0.01238  -0.9202
    - offset: -0.1989549
    - center: -0.1715856748140029 0.1590825675964338 -0.1454013928109104 
    - vertices: p2(v4) p1(v3) p4(v1)
    - neighboring facets: f1 f2 f4
- f4
    - flags: bottom simplicial isarea
    - area: 0.16
    - normal:    0.4184   0.3424   0.8413
    - offset: 0.07254957
    - center: 0.116549362001881 0.1503252206347392 -0.2053893818610149 
    - vertices: p2(v4) p1(v3) p5(v2)
    - neighboring facets: f1 f2 f3
rbox 6 s D3 | qhull C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv
4
4
0.205360378770873 0.06987429109559466 0.976188864039624 0.1253980026939646 
-0.2031613339148238 -0.3001304507855299 -0.9320124381751694 -0.1680570625036091 
-0.3911895500493898 -0.01238286325891905 -0.9202268202077502 -0.1989548866041478 
0.4183781509471984 0.3424157187037644 0.8412557271095321 0.07254956874669725 
4
4
0.205360378770873 0.06987429109559466 0.976188864039624 0.125398002693964 
-0.2031613339148238 -0.3001304507855299 -0.9320124381751694 -0.1680570625036098 
-0.3911895500493898 -0.01238286325891905 -0.9202268202077502 -0.1989548866041485 
0.4183781509471984 0.3424157187037644 0.8412557271095321 0.0725495687466966 
4
4
0.205360378770873 0.06987429109559466 0.976188864039624 0.1253980026939626 
-0.2031613339148238 -0.3001304507855299 -0.9320124381751694 -0.2813242952138535 
-0.3911895500493898 -0.01238286325891905 -0.9202268202077502 -0.1989548866041498 
0.4183781509471984 0.3424157187037644 0.8412557271095321 0.07254956874669528 
rbox 6 s D3 | qhull C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv
4
1
2
3
4
4
0
0
0
0
4
3 1 2 3
3 0 2 3
3 0 1 3
3 0 1 2
6
1 1
3 3 0 2
3 3 1 2
1 1
3 2 0 1
3 3 0 1
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213781421  Centrum-premerge- 0.1  Qcoplanar-keep  FFacets-xridge
  summary  FQhull  Finner  normals  Fouter  FQhull  FIDs  Fmerges  Fneighbors
  FNeighbors-vertex  FOptions  FQhull  Fsummary  FSize  FVertex-average
  Tcheck-frequently  Tverify  Fvertices  _max-width 0.86
  Error-roundoff 6.6e-16  _one-merge 0.3  _near-inside 1.5
  Visible-distance 0.1  U-max-coplanar 0.1  Width-outside 0.2  _wide-facet 0.6
rbox 6 s D3 | qhull C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv
10 3 6 4 4 4 4 2 0 0 0
2 0.1132672327102437 -1.315898280434284e-15
0
2 0.8296676646636063 0.01051107893821417 
3 1
-0.02780909644771785 0.06447846047808484 -0.1584624246583442 
4
3 1 5 4
3 2 5 4
3 2 1 4
3 2 1 5

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 24 distance computations.
rbox P0.5,0.5 P0.5,0.5 W0 5 D2 | qhull d FN Qc
7
5 3 1 0 -4 -8
1 1
5 -10 2 -3 -4 -8
4 2 -3 0 1
3 -4 0 -3
3 -10 -8 3
4 -10 2 1 3
rbox 10 D3 | qhull Fa PA5
5
0.2844546842397038 
0.1170134053930415 
0.1758021655943633 
0.07490600482805046 
0.2087585943133527 
rbox 10 D3 | qhull Fa PF0.4
QH7055 qhull warning: no facets printed
0

set +v
=== test Qt Fri, Jul 24, 2020 10:27:31 PM
rbox c | qhull Qt s o Tcv

Convex hull of 8 points in 3-d:

  Number of vertices: 8
  Number of facets: 12
  Number of triangulated facets: 6

Statistics for: rbox c | qhull Qt s o Tcv

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 96
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0

3
8 12 18
  -0.5   -0.5   -0.5 
  -0.5   -0.5    0.5 
  -0.5    0.5   -0.5 
  -0.5    0.5    0.5 
   0.5   -0.5   -0.5 
   0.5   -0.5    0.5 
   0.5    0.5   -0.5 
   0.5    0.5    0.5 
3 6 2 0 
3 4 6 0 
3 5 4 0 
3 1 5 0 
3 5 6 4 
3 6 5 7 
3 2 3 0 
3 3 1 0 
3 6 3 2 
3 3 6 7 
3 3 5 1 
3 5 3 7 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 96 distance computations.
rbox c | qhull Qt f i
Vertices and facets:
- p6(v6):   0.5   0.5  -0.5
  neighbors: f17 f18 f25 f27 f33 f34
- p2(v3):  -0.5   0.5  -0.5
  neighbors: f17 f29 f33
- p0(v1):  -0.5  -0.5  -0.5
  neighbors: f17 f18 f21 f22 f29 f30
- p4(v2):   0.5  -0.5  -0.5
  neighbors: f18 f21 f25
- p5(v7):   0.5  -0.5   0.5
  neighbors: f21 f22 f25 f27 f37 f38
- p1(v4):  -0.5  -0.5   0.5
  neighbors: f22 f30 f37
- p7(v5):   0.5   0.5   0.5
  neighbors: f27 f34 f38
- p3(v8):  -0.5   0.5   0.5
  neighbors: f29 f30 f33 f34 f37 f38
- f17
    - flags: top simplicial tricoplanar keepcentrum
    - owner of normal & centrum is facet f17
    - normal:        -0       -0       -1
    - offset:       -0.5
    - center:      0      0   -0.5 
    - vertices: p6(v6) p2(v3) p0(v1)
    - neighboring facets: f29 f18 f33
- f18
    - flags: bottom simplicial tricoplanar
    - owner of normal & centrum is facet f17
    - normal:        -0       -0       -1
    - offset:       -0.5
    - center:      0      0   -0.5 
    - vertices: p6(v6) p4(v2) p0(v1)
    - neighboring facets: f21 f17 f25
- f21
    - flags: top simplicial tricoplanar keepcentrum
    - owner of normal & centrum is facet f21
    - normal:         0       -1        0
    - offset:       -0.5
    - center:      0   -0.5      0 
    - vertices: p5(v7) p4(v2) p0(v1)
    - neighboring facets: f18 f22 f25
- f22
    - flags: bottom simplicial tricoplanar
    - owner of normal & centrum is facet f21
    - normal:         0       -1        0
    - offset:       -0.5
    - center:      0   -0.5      0 
    - vertices: p5(v7) p1(v4) p0(v1)
    - neighboring facets: f30 f21 f37
- f25
    - flags: top simplicial tricoplanar keepcentrum
    - owner of normal & centrum is facet f25
    - normal:         1       -0       -0
    - offset:       -0.5
    - center:    0.5      0      0 
    - vertices: p5(v7) p6(v6) p4(v2)
    - neighboring facets: f18 f21 f27
- f27
    - flags: bottom simplicial tricoplanar
    - owner of normal & centrum is facet f25
    - normal:         1       -0       -0
    - offset:       -0.5
    - center:    0.5      0      0 
    - vertices: p5(v7) p6(v6) p7(v5)
    - neighboring facets: f34 f38 f25
- f29
    - flags: bottom simplicial tricoplanar keepcentrum
    - owner of normal & centrum is facet f29
    - normal:        -1       -0       -0
    - offset:       -0.5
    - center:   -0.5      0      0 
    - vertices: p3(v8) p2(v3) p0(v1)
    - neighboring facets: f17 f30 f33
- f30
    - flags: top simplicial tricoplanar
    - owner of normal & centrum is facet f29
    - normal:        -1       -0       -0
    - offset:       -0.5
    - center:   -0.5      0      0 
    - vertices: p3(v8) p1(v4) p0(v1)
    - neighboring facets: f22 f29 f37
- f33
    - flags: bottom simplicial tricoplanar keepcentrum
    - owner of normal & centrum is facet f33
    - normal:         0        1       -0
    - offset:       -0.5
    - center:      0    0.5      0 
    - vertices: p3(v8) p6(v6) p2(v3)
    - neighboring facets: f17 f29 f34
- f34
    - flags: top simplicial tricoplanar
    - owner of normal & centrum is facet f33
    - normal:         0        1       -0
    - offset:       -0.5
    - center:      0    0.5      0 
    - vertices: p3(v8) p6(v6) p7(v5)
    - neighboring facets: f27 f38 f33
- f37
    - flags: top simplicial tricoplanar keepcentrum
    - owner of normal & centrum is facet f37
    - normal:        -0       -0        1
    - offset:       -0.5
    - center:      0      0    0.5 
    - vertices: p3(v8) p5(v7) p1(v4)
    - neighboring facets: f22 f30 f38
- f38
    - flags: bottom simplicial tricoplanar
    - owner of normal & centrum is facet f37
    - normal:        -0       -0        1
    - offset:       -0.5
    - center:      0      0    0.5 
    - vertices: p3(v8) p5(v7) p7(v5)
    - neighboring facets: f27 f34 f37
12
6 2 0 
4 6 0 
5 4 0 
1 5 0 
5 6 4 
6 5 7 
2 3 0 
3 1 0 
6 3 2 
3 6 7 
3 5 1 
5 3 7 
rbox c | qhull Qt m FM n
{
Polygon[{{      0.50000000,       0.50000000,      -0.50000000},
{     -0.50000000,       0.50000000,      -0.50000000},
{     -0.50000000,      -0.50000000,      -0.50000000}}],
Polygon[{{      0.50000000,      -0.50000000,      -0.50000000},
{      0.50000000,       0.50000000,      -0.50000000},
{     -0.50000000,      -0.50000000,      -0.50000000}}],
Polygon[{{      0.50000000,      -0.50000000,       0.50000000},
{      0.50000000,      -0.50000000,      -0.50000000},
{     -0.50000000,      -0.50000000,      -0.50000000}}],
Polygon[{{     -0.50000000,      -0.50000000,       0.50000000},
{      0.50000000,      -0.50000000,       0.50000000},
{     -0.50000000,      -0.50000000,      -0.50000000}}],
Polygon[{{      0.50000000,      -0.50000000,       0.50000000},
{      0.50000000,       0.50000000,      -0.50000000},
{      0.50000000,      -0.50000000,      -0.50000000}}],
Polygon[{{      0.50000000,       0.50000000,      -0.50000000},
{      0.50000000,      -0.50000000,       0.50000000},
{      0.50000000,       0.50000000,       0.50000000}}],
Polygon[{{     -0.50000000,       0.50000000,      -0.50000000},
{     -0.50000000,       0.50000000,       0.50000000},
{     -0.50000000,      -0.50000000,      -0.50000000}}],
Polygon[{{     -0.50000000,       0.50000000,       0.50000000},
{     -0.50000000,      -0.50000000,       0.50000000},
{     -0.50000000,      -0.50000000,      -0.50000000}}],
Polygon[{{      0.50000000,       0.50000000,      -0.50000000},
{     -0.50000000,       0.50000000,       0.50000000},
{     -0.50000000,       0.50000000,      -0.50000000}}],
Polygon[{{     -0.50000000,       0.50000000,       0.50000000},
{      0.50000000,       0.50000000,      -0.50000000},
{      0.50000000,       0.50000000,       0.50000000}}],
Polygon[{{     -0.50000000,       0.50000000,       0.50000000},
{      0.50000000,      -0.50000000,       0.50000000},
{     -0.50000000,      -0.50000000,       0.50000000}}],
Polygon[{{      0.50000000,      -0.50000000,       0.50000000},
{     -0.50000000,       0.50000000,       0.50000000},
{      0.50000000,       0.50000000,       0.50000000}}]}
PLOT3D(POLYGONS(
[[      0.50000000,       0.50000000,      -0.50000000],
[     -0.50000000,       0.50000000,      -0.50000000],
[     -0.50000000,      -0.50000000,      -0.50000000]],
[[      0.50000000,      -0.50000000,      -0.50000000],
[      0.50000000,       0.50000000,      -0.50000000],
[     -0.50000000,      -0.50000000,      -0.50000000]],
[[      0.50000000,      -0.50000000,       0.50000000],
[      0.50000000,      -0.50000000,      -0.50000000],
[     -0.50000000,      -0.50000000,      -0.50000000]],
[[     -0.50000000,      -0.50000000,       0.50000000],
[      0.50000000,      -0.50000000,       0.50000000],
[     -0.50000000,      -0.50000000,      -0.50000000]],
[[      0.50000000,      -0.50000000,       0.50000000],
[      0.50000000,       0.50000000,      -0.50000000],
[      0.50000000,      -0.50000000,      -0.50000000]],
[[      0.50000000,       0.50000000,      -0.50000000],
[      0.50000000,      -0.50000000,       0.50000000],
[      0.50000000,       0.50000000,       0.50000000]],
[[     -0.50000000,       0.50000000,      -0.50000000],
[     -0.50000000,       0.50000000,       0.50000000],
[     -0.50000000,      -0.50000000,      -0.50000000]],
[[     -0.50000000,       0.50000000,       0.50000000],
[     -0.50000000,      -0.50000000,       0.50000000],
[     -0.50000000,      -0.50000000,      -0.50000000]],
[[      0.50000000,       0.50000000,      -0.50000000],
[     -0.50000000,       0.50000000,       0.50000000],
[     -0.50000000,       0.50000000,      -0.50000000]],
[[     -0.50000000,       0.50000000,       0.50000000],
[      0.50000000,       0.50000000,      -0.50000000],
[      0.50000000,       0.50000000,       0.50000000]],
[[     -0.50000000,       0.50000000,       0.50000000],
[      0.50000000,      -0.50000000,       0.50000000],
[     -0.50000000,      -0.50000000,       0.50000000]],
[[      0.50000000,      -0.50000000,       0.50000000],
[     -0.50000000,       0.50000000,       0.50000000],
[      0.50000000,       0.50000000,       0.50000000]]));
4
12
    -0     -0     -1   -0.5 
    -0     -0     -1   -0.5 
     0     -1      0   -0.5 
     0     -1      0   -0.5 
     1     -0     -0   -0.5 
     1     -0     -0   -0.5 
    -1     -0     -0   -0.5 
    -1     -0     -0   -0.5 
     0      1     -0   -0.5 
     0      1     -0   -0.5 
    -0     -0      1   -0.5 
    -0     -0      1   -0.5 
rbox c | qhull Qt p o
3
8
  -0.5   -0.5   -0.5 
  -0.5   -0.5    0.5 
  -0.5    0.5   -0.5 
  -0.5    0.5    0.5 
   0.5   -0.5   -0.5 
   0.5   -0.5    0.5 
   0.5    0.5   -0.5 
   0.5    0.5    0.5 
3
8 12 18
  -0.5   -0.5   -0.5 
  -0.5   -0.5    0.5 
  -0.5    0.5   -0.5 
  -0.5    0.5    0.5 
   0.5   -0.5   -0.5 
   0.5   -0.5    0.5 
   0.5    0.5   -0.5 
   0.5    0.5    0.5 
3 6 2 0 
3 4 6 0 
3 5 4 0 
3 1 5 0 
3 5 6 4 
3 6 5 7 
3 2 3 0 
3 3 1 0 
3 6 3 2 
3 3 6 7 
3 3 5 1 
3 5 3 7 
rbox c | qhull Qt Fx
8
0
1
2
3
4
5
6
7
rbox c | qhull Qt FA s Fa

Convex hull of 8 points in 3-d:

  Number of vertices: 8
  Number of facets: 12
  Number of triangulated facets: 6

Statistics for: rbox c | qhull Qt FA s Fa

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 90
  Number of distance tests for checking: 48
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0
  Approximate facet area:    6
  Approximate volume:        1

12
   0.5 
   0.5 
   0.5 
   0.5 
   0.5 
   0.5 
   0.5 
   0.5 
   0.5 
   0.5 
   0.5 
   0.5 
rbox 6 r s c G0.1 D2 | qhull Qt d FA Tcv

Delaunay triangulation by the convex hull of 10 points in 3-d:

  Number of input sites: 10
  Number of Delaunay regions: 12
  Number of triangulated facets: 3

Statistics for: rbox 6 r s c G0.1 D2 | qhull Qt d FA Tcv

  Number of points processed: 10
  Number of hyperplanes created: 19
  Number of facets in hull: 16
  Number of distance tests for qhull: 48
  Number of distance tests for merging: 170
  Number of distance tests for checking: 164
  Number of merged facets: 7
  CPU seconds to compute hull (after input):  0
  Approximate facet area:   0.64951905


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 120 distance computations.
rbox 6 r s c G0.1 D2 | qhull d FA Tcv

Delaunay triangulation by the convex hull of 10 points in 3-d:

  Number of input sites: 10
  Number of Delaunay regions: 9
  Number of non-simplicial Delaunay regions: 3

Statistics for: rbox 6 r s c G0.1 D2 | qhull d FA Tcv

  Number of points processed: 10
  Number of hyperplanes created: 19
  Number of facets in hull: 10
  Number of distance tests for qhull: 48
  Number of distance tests for merging: 170
  Number of distance tests for checking: 164
  Number of merged facets: 7
  CPU seconds to compute hull (after input):  0
  Approximate facet area:   0.64951905


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 90 distance computations.
rbox 6 r s c G0.1 D2 | qhull Qt v p Tcv
2
12
-0.3359969878447703 -0.1939879513790814 
-0.3359969878447704 0.1939879513790817 
-0.2875      0 
0.3359969878447702 -0.1939879513790819 
0.3359969878447707 0.1939879513790815 
0.2875      0 
-2.220446049250313e-16 -0.3453321730569308 
-2.220446049250313e-16 -0.3453321730569308 
1.110223024625157e-16 0.3453321730569308 
1.110223024625157e-16 0.3453321730569308 
     0      0 
     0      0 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 120 distance computations.
rbox c | qhull Qt C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213798228  Qtriangulate  Centrum-premerge- 0.1  Qcoplanar-keep
  FFacets-xridge  summary  FQhull  Finner  normals  Fouter  FQhull  FIDs
  Fmerges  Fneighbors  FNeighbors-vertex  FOptions  FQhull  Fsummary  FSize
  FVertex-average  Tcheck-frequently  Tverify  Fvertices  _max-width  1
  Error-roundoff 6.9e-16  _one-merge 0.3  _near-inside 1.5
  Visible-distance 0.1  U-max-coplanar 0.1  Width-outside 0.2  _wide-facet 0.6

Convex hull of 8 points in 3-d:

  Number of vertices: 8
  Number of facets: 12
  Number of triangulated facets: 6

Statistics for: rbox c | qhull Qt C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv

  Number of points processed: 8
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 34
  Number of distance tests for merging: 102
  Number of distance tests for checking: 126
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0
  Approximate facet area:    6
  Approximate volume:        1

Vertices and facets:
- p6(v6):   0.5   0.5  -0.5
  neighbors: f17 f18 f25 f27 f33 f34
- p2(v3):  -0.5   0.5  -0.5
  neighbors: f17 f29 f33
- p0(v1):  -0.5  -0.5  -0.5
  neighbors: f17 f18 f21 f22 f29 f30
- p4(v2):   0.5  -0.5  -0.5
  neighbors: f18 f21 f25
- p5(v7):   0.5  -0.5   0.5
  neighbors: f21 f22 f25 f27 f37 f38
- p1(v4):  -0.5  -0.5   0.5
  neighbors: f22 f30 f37
- p7(v5):   0.5   0.5   0.5
  neighbors: f27 f34 f38
- p3(v8):  -0.5   0.5   0.5
  neighbors: f29 f30 f33 f34 f37 f38
- f17
    - flags: top simplicial tricoplanar isarea keepcentrum
    - area: 0.5
    - normal:        -0       -0       -1
    - offset:       -0.5
    - center:      0      0   -0.5 
    - vertices: p6(v6) p2(v3) p0(v1)
    - neighboring facets: f29 f18 f33
- f18
    - flags: bottom simplicial tricoplanar isarea
    - area: 0.5
    - normal:        -0       -0       -1
    - offset:       -0.5
    - center:      0      0   -0.5 
    - vertices: p6(v6) p4(v2) p0(v1)
    - neighboring facets: f21 f17 f25
- f21
    - flags: top simplicial tricoplanar isarea keepcentrum
    - area: 0.5
    - normal:         0       -1        0
    - offset:       -0.5
    - center:      0   -0.5      0 
    - vertices: p5(v7) p4(v2) p0(v1)
    - neighboring facets: f18 f22 f25
- f22
    - flags: bottom simplicial tricoplanar isarea
    - area: 0.5
    - normal:         0       -1        0
    - offset:       -0.5
    - center:      0   -0.5      0 
    - vertices: p5(v7) p1(v4) p0(v1)
    - neighboring facets: f30 f21 f37
- f25
    - flags: top simplicial tricoplanar isarea keepcentrum
    - area: 0.5
    - normal:         1       -0       -0
    - offset:       -0.5
    - center:    0.5      0      0 
    - vertices: p5(v7) p6(v6) p4(v2)
    - neighboring facets: f18 f21 f27
- f27
    - flags: bottom simplicial tricoplanar isarea
    - area: 0.5
    - normal:         1       -0       -0
    - offset:       -0.5
    - center:    0.5      0      0 
    - vertices: p5(v7) p6(v6) p7(v5)
    - neighboring facets: f34 f38 f25
- f29
    - flags: bottom simplicial tricoplanar isarea keepcentrum
    - area: 0.5
    - normal:        -1       -0       -0
    - offset:       -0.5
    - center:   -0.5      0      0 
    - vertices: p3(v8) p2(v3) p0(v1)
    - neighboring facets: f17 f30 f33
- f30
    - flags: top simplicial tricoplanar isarea
    - area: 0.5
    - normal:        -1       -0       -0
    - offset:       -0.5
    - center:   -0.5      0      0 
    - vertices: p3(v8) p1(v4) p0(v1)
    - neighboring facets: f22 f29 f37
- f33
    - flags: bottom simplicial tricoplanar isarea keepcentrum
    - area: 0.5
    - normal:         0        1       -0
    - offset:       -0.5
    - center:      0    0.5      0 
    - vertices: p3(v8) p6(v6) p2(v3)
    - neighboring facets: f17 f29 f34
- f34
    - flags: top simplicial tricoplanar isarea
    - area: 0.5
    - normal:         0        1       -0
    - offset:       -0.5
    - center:      0    0.5      0 
    - vertices: p3(v8) p6(v6) p7(v5)
    - neighboring facets: f27 f38 f33
- f37
    - flags: top simplicial tricoplanar isarea keepcentrum
    - area: 0.5
    - normal:        -0       -0        1
    - offset:       -0.5
    - center:      0      0    0.5 
    - vertices: p3(v8) p5(v7) p1(v4)
    - neighboring facets: f22 f30 f38
- f38
    - flags: bottom simplicial tricoplanar isarea
    - area: 0.5
    - normal:        -0       -0        1
    - offset:       -0.5
    - center:      0      0    0.5 
    - vertices: p3(v8) p5(v7) p7(v5)
    - neighboring facets: f27 f34 f37
rbox c | qhull Qt C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv
4
12
    -0     -0     -1 -0.4999999999999993 
    -0     -0     -1 -0.4999999999999993 
     0     -1      0 -0.4999999999999993 
     0     -1      0 -0.4999999999999993 
     1     -0     -0 -0.4999999999999993 
     1     -0     -0 -0.4999999999999993 
    -1     -0     -0 -0.4999999999999993 
    -1     -0     -0 -0.4999999999999993 
     0      1     -0 -0.4999999999999993 
     0      1     -0 -0.4999999999999993 
    -0     -0      1 -0.4999999999999993 
    -0     -0      1 -0.4999999999999993 
4
12
    -0     -0     -1   -0.5 
    -0     -0     -1   -0.5 
     0     -1      0   -0.5 
     0     -1      0   -0.5 
     1     -0     -0   -0.5 
     1     -0     -0   -0.5 
    -1     -0     -0   -0.5 
    -1     -0     -0   -0.5 
     0      1     -0   -0.5 
     0      1     -0   -0.5 
    -0     -0      1   -0.5 
    -0     -0      1   -0.5 
4
12
    -0     -0     -1 -0.5000000000000013 
    -0     -0     -1 -0.5000000000000013 
     0     -1      0 -0.5000000000000013 
     0     -1      0 -0.5000000000000013 
     1     -0     -0 -0.5000000000000013 
     1     -0     -0 -0.5000000000000013 
    -1     -0     -0 -0.5000000000000013 
    -1     -0     -0 -0.5000000000000013 
     0      1     -0 -0.5000000000000013 
     0      1     -0 -0.5000000000000013 
    -0     -0      1 -0.5000000000000013 
    -0     -0      1 -0.5000000000000013 
rbox c | qhull Qt C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv
12
17
18
21
22
25
27
29
30
33
34
37
38
12
0
0
0
0
0
0
0
0
0
0
0
0
12
3 6 1 8
3 2 0 4
3 1 3 4
3 7 2 10
3 1 2 5
3 9 11 4
3 0 7 8
3 3 6 10
3 0 6 9
3 5 11 8
3 3 7 11
3 5 9 10
8
6 7 3 2 1 0 6
3 10 3 7
3 8 0 6
6 11 9 8 6 7 10
3 4 1 2
6 11 5 4 2 3 10
6 9 5 4 1 0 8
3 11 5 9
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213798228  Qtriangulate  Centrum-premerge- 0.1  Qcoplanar-keep
  FFacets-xridge  summary  FQhull  Finner  normals  Fouter  FQhull  FIDs
  Fmerges  Fneighbors  FNeighbors-vertex  FOptions  FQhull  Fsummary  FSize
  FVertex-average  Tcheck-frequently  Tverify  Fvertices  _max-width  1
  Error-roundoff 6.9e-16  _one-merge 0.3  _near-inside 1.5
  Visible-distance 0.1  U-max-coplanar 0.1  Width-outside 0.2  _wide-facet 0.6
rbox c | qhull Qt C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv
10 3 8 8 12 8 12 0 0 0 6
2 1.387359992873471e-15 -6.936799964367356e-16
0
2      6      1 
3 1
     0      0      0 
12
3 6 2 0
3 6 4 0
3 5 4 0
3 5 1 0
3 5 6 4
3 5 6 7
3 3 2 0
3 3 1 0
3 3 6 2
3 3 6 7
3 3 5 1
3 3 5 7

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 96 distance computations.
rbox 6 r s c G0.1 D2 P0.1,0.1 | qhull s FP d FO Qt
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213798228  summary  FPoint-nearest  delaunay  Qtriangulate  _pre-merge
  _zero-centrum  Pgood  Qcoplanar  _max-width  1  Error-roundoff 6.9e-16
  _one-merge 4.9e-15  _near-inside 2.4e-14  Visible-distance 1.4e-15
  U-max-coplanar 1.4e-15  Width-outside 2.8e-15  _wide-facet 8.3e-15

Delaunay triangulation by the convex hull of 11 points in 3-d:

  Number of input sites: 10
  Number of nearly incident points: 1
  Number of Delaunay regions: 12
  Number of triangulated facets: 3

Statistics for: rbox 6 r s c G0.1 D2 P0.1,0.1 | qhull s FP d FO Qt

  Number of points processed: 10
  Number of hyperplanes created: 19
  Number of facets in hull: 16
  Number of distance tests for qhull: 79
  Number of distance tests for merging: 153
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0

1
0 10 36      0 
rbox 100 W0 | qhull Tv Q11 FO 
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213798228  Tverify  Q11-trinormals Qtriangulate  _pre-merge
  _zero-centrum  _max-width  1  Error-roundoff 6.9e-16  _one-merge 4.9e-15
  _near-inside 2.4e-14  Visible-distance 1.4e-15  U-max-coplanar 1.4e-15
  Width-outside 2.8e-15  _wide-facet 8.3e-15

Convex hull of 100 points in 3-d:

  Number of vertices: 45
  Number of facets: 86
  Number of triangulated facets: 33

Statistics for: rbox 100 W0 | qhull Tv Q11 FO

  Number of points processed: 52
  Number of hyperplanes created: 171
  Number of distance tests for qhull: 1575
  Number of distance tests for merging: 1368
  Number of distance tests for checking: 1131
  Number of merged facets: 41
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 8600 distance computations.

set +v
=== test unbounded intersection Fri, Jul 24, 2020 10:27:32 PM
rbox c | qhull PD0:0.5 n | qhull H0 Fp Tcv
3
5
  -0.5   -0.5   -0.5 
  -0.5    0.5   -0.5 
  -0.5   -0.5    0.5 
  -0.5    0.5    0.5 
-10.101 -10.101 -10.101 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 25 distance computations.
rbox 1000 W1e-3 D3 | qhull PA8 Fa FS s n Tcv 

Convex hull of 1000 points in 3-d:

  Number of vertices: 156
  Number of facets: 308
  Number of 'good' facets: 8

Statistics for: rbox 1000 W1e-3 D3 | qhull PA8 Fa FS s n Tcv

  Number of points processed: 203
  Number of hyperplanes created: 1043
  Number of distance tests for qhull: 21452
  CPU seconds to compute hull (after input): 0.005
  Total facet area:   5.8817432
  Total volume:       0.99685163

8
0.1446087232094601 
0.1622198334884075 
0.2057158590759608 
0.1567143851824352 
0.188985866819172 
0.1580674614313252 
0.1616733826473111 
0.1767351337533958 
0
2 5.881743214947513 0.9968516315221345 
4
8
1.009144997325421e-05 0.9999999999463923 2.319049754624652e-06 -0.4999875785488853 
-1.229609861584452e-05 8.587946880918045e-05 0.9999999962367613 -0.500004859549355 
-1.383340239672454e-05 -0.9999999998842694 6.332306547224586e-06 -0.4999917156571327 
1.802476239613105e-05 -1.901476191096464e-05 0.9999999996567733 -0.4999909156385879 
0.9999999996788914 1.780140020603311e-05 -1.803683546259361e-05 -0.4999971349013697 
3.470111681088057e-06 -3.668365732095583e-05 -0.9999999993211337 -0.4999893476858696 
-1.633273154317779e-05 -0.9999999998072314 1.08985791646657e-05 -0.4999921708899001 
-0.9999999997878146 -2.055073082985623e-05 -1.427680287303445e-06 -0.4999990322171605 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 8000 distance computations.
rbox 1000 W1e-3 D3 | qhull C-0.01 PM10 Fm n Tcv Qc
10
1
1
5
8
6
0
6
2
7
10
4
10
0.6345454980886096 0.2737427089707436 0.7227841587506171 -0.7458921924784656 
-0.00253733560834815 0.666653414016696 0.7453635270845322 -0.6767722083805112 
-0.003237401631533091 0.002761552371517554 -0.9999909464886048 -0.4969398742962436 
-0.0004022623770974538 0.9999997831336711 0.0005214571799133833 -0.5000167453415887 
-0.999601787347817 0.0214081839262726 0.01838359029211947 -0.4985486000821885 
-0.4745617604911457 -0.2935495843214587 0.8298311738084099 -0.7523676152838523 
-0.005480509661076107 -0.9999701072857251 0.005454223027194169 -0.4992904789191579 
-0.9987007292177809 -0.05077399000218431 -0.004342280406757339 -0.5182179901342427 
0.001196850675493193 0.0003334814784797861 0.9999992281689842 -0.4989807987213126 
0.9999992961453315 0.00118637926097064 1.459763172590229e-05 -0.4998611663332402 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 10000 distance computations.
rbox 1000 W1e-3 D3 | qhull C-0.01 PA8 PG n Tcv Qc
4
12
0.6345454980886096 0.2737427089707436 0.7227841587506171 -0.7458921924784656 
-0.00253733560834815 0.666653414016696 0.7453635270845322 -0.6767722083805112 
-0.9785529186794025 -0.009694358843403266 -0.2057673558916428 -0.5832522471275383 
0.8278306348810541 -0.3414688798813042 -0.4450791435520636 -0.7665474225756105 
0.7383776593319754 -0.4655216164679661 0.4879426777814019 -0.7788991125303445 
0.2008161614085187 -0.8823413491644904 0.4256132198037728 -0.6982307124493007 
0.41932306725662 0.6721295192910486 -0.6102541065524131 -0.7755692997856908 
-0.3210285130221472 0.4863414284958994 -0.8126578054478755 -0.7591490151594069 
-0.4745617604911457 -0.2935495843214587 0.8298311738084099 -0.7523676152838523 
-0.8238864443814345 -0.556605789918439 0.1067760337987315 -0.695666244857558 
-0.5357402012449896 -0.5359428531021374 -0.6524934443952053 -0.811263040246498 
0.6755431502353132 -0.2163920762108173 0.7048517017950092 -0.7475007704997935 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 8000 distance computations.
rbox 10 | qhull FO Tz TO q_test.log.1
cat q_test.log.1
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213815035  Tz-stdout  TOutput-file  q_test.log.1  _pre-merge
  _zero-centrum  _max-width 0.92  Error-roundoff 6.8e-16  _one-merge 4.8e-15
  _near-inside 2.4e-14  Visible-distance 1.4e-15  U-max-coplanar 1.4e-15
  Width-outside 2.7e-15  _wide-facet 8.2e-15

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 10 | qhull FO Tz TO q_test.log.1

  Number of points processed: 10
  Number of hyperplanes created: 26
  Number of distance tests for qhull: 43
  CPU seconds to compute hull (after input):  0


set +v
=== check Delaunay/Voronoi Fri, Jul 24, 2020 10:27:33 PM
rbox 10 D2 | qhull d Tcv

Delaunay triangulation by the convex hull of 10 points in 3-d:

  Number of input sites: 10
  Number of Delaunay regions: 14

Statistics for: rbox 10 D2 | qhull d Tcv

  Number of points processed: 10
  Number of hyperplanes created: 28
  Number of facets in hull: 16
  Number of distance tests for qhull: 47
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D2 | qhull d Qz Tcv

Delaunay triangulation by the convex hull of 11 points in 3-d:

  Number of input sites and at-infinity: 11
  Number of Delaunay regions: 14

Statistics for: rbox 10 D2 | qhull d Qz Tcv

  Number of points processed: 11
  Number of hyperplanes created: 30
  Number of facets in hull: 18
  Number of distance tests for qhull: 55
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 154 distance computations.
rbox 10 D3 | qhull d Tcv

Delaunay triangulation by the convex hull of 10 points in 4-d:

  Number of input sites: 10
  Number of Delaunay regions: 18

Statistics for: rbox 10 D3 | qhull d Tcv

  Number of points processed: 10
  Number of hyperplanes created: 43
  Number of facets in hull: 27
  Number of distance tests for qhull: 66
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 2.9e-15 of
all facets.  Will make 180 distance computations.
rbox c | qhull d Qz Ft Tcv
3
10 12 3
  -0.5   -0.5   -0.5 
  -0.5   -0.5    0.5 
  -0.5    0.5   -0.5 
  -0.5    0.5    0.5 
   0.5   -0.5   -0.5 
   0.5   -0.5    0.5 
   0.5    0.5   -0.5 
   0.5    0.5    0.5 
     0      0      0 
     0      0      0 
4 9 1 2 0 
4 9 2 4 0 
4 9 4 1 0 
4 9 7 5 4 
4 9 6 7 4 
4 9 7 6 2 
4 9 2 6 4 
4 9 5 7 1 
4 9 5 1 4 
4 9 7 3 1 
4 9 1 3 2 
4 9 3 7 2 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make  9 distance computations.
rbox 10 s D2 c | qhull d Tcv 

Delaunay triangulation by the convex hull of 14 points in 3-d:

  Number of input sites: 14
  Number of Delaunay regions: 15
  Number of non-simplicial Delaunay regions: 1

Statistics for: rbox 10 s D2 c | qhull d Tcv

  Number of points processed: 14
  Number of hyperplanes created: 32
  Number of facets in hull: 16
  Number of distance tests for qhull: 115
  Number of distance tests for merging: 296
  Number of distance tests for checking: 272
  Number of merged facets: 8
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 210 distance computations.
rbox 10 s D2 | qhull d Tcv Qz Q8

Delaunay triangulation by the convex hull of 11 points in 3-d:

  Number of input sites and at-infinity: 11
  Number of Delaunay regions: 1
  Number of non-simplicial Delaunay regions: 1

Statistics for: rbox 10 s D2 | qhull d Tcv Qz Q8

  Number of points processed: 11
  Number of hyperplanes created: 19
  Number of facets in hull: 11
  Number of distance tests for qhull: 54
  Number of distance tests for merging: 201
  Number of distance tests for checking: 204
  Number of merged facets: 7
  CPU seconds to compute hull (after input):  0

QH7077 qhull input warning: no outer plane check ('Q5') or no processing of near-inside points ('Q8').  Verify may report that a point is outside of a facet.

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 11 distance computations.
rbox 10 D2 | qhull d Tcv p
3
10
-0.02222276248244826 -0.4979727817680433 0.2484707425541546 
-0.4285431913366012 0.4745826469497594 0.4088779556267987 
0.3105396575392593 0.2400179190933871 0.1540434803905201 
-0.01883958887200765 0.3630260628303755 0.13214285240299 
0.3790312361708201 0.3779794437605696 0.2865331378987296 
-0.2994955874043476 0.3776609263174803 0.2323253821416525 
0.3471817493878135 0.08365533089605659 0.1275333814953112 
-0.00485819764887746 0.3482682405489201 0.121314369459436 
0.3443122672329771 -0.1437312230875075 0.1392096018573439 
0.309330780347186 -0.07758103877080702 0.1017043492469565 

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D2 | qhull d Tcv i
14
9 7 0 
8 9 0 
3 4 1 
3 7 4 
7 2 4 
0 5 1 
7 5 0 
5 3 1 
3 5 7 
6 7 9 
6 2 7 
8 6 9 
6 8 4 
2 6 4 

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D2 | qhull d Tcv o
3
10 14 21
-0.02222276248244826 -0.4979727817680433 0.2484707425541546 
-0.4285431913366012 0.4745826469497594 0.4088779556267987 
0.3105396575392593 0.2400179190933871 0.1540434803905201 
-0.01883958887200765 0.3630260628303755 0.13214285240299 
0.3790312361708201 0.3779794437605696 0.2865331378987296 
-0.2994955874043476 0.3776609263174803 0.2323253821416525 
0.3471817493878135 0.08365533089605659 0.1275333814953112 
-0.00485819764887746 0.3482682405489201 0.121314369459436 
0.3443122672329771 -0.1437312230875075 0.1392096018573439 
0.309330780347186 -0.07758103877080702 0.1017043492469565 
3 9 7 0 
3 8 9 0 
3 3 4 1 
3 3 7 4 
3 7 2 4 
3 0 5 1 
3 7 5 0 
3 5 3 1 
3 3 5 7 
3 6 7 9 
3 6 2 7 
3 8 6 9 
3 6 8 4 
3 2 6 4 

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D2 | qhull v Tcv o
2
15 10 1
-10.101 -10.101 
-0.1294381801544404 -0.07247409101984714 
0.08267689532419747 -0.2397644955865706 
0.1295260566906465 1.716033573116837 
0.1740355150742391 0.5317519038435655 
0.1851415205797575 0.3882545794457364 
-0.9065939866848107 -0.2962957610652135 
-0.1954805620516266 -0.07111892482963184 
-0.1407581310832468 0.7233857048236082 
-0.1676297826663962 0.2080621273999375 
0.05868313821742954 0.06632066014880154 
0.08806341399736994 0.1054080604689985 
0.4761588899009253 -0.03168366595227294 
3.094213357897477 -0.064721945677682 
0.5410515627308725 0.2115615434955919 
5 7 1 2 0 6
4 8 3 0 6
3 14 5 11
4 9 4 3 8
6 14 5 4 3 0 13
4 9 7 6 8
5 14 11 10 12 13
7 11 5 4 9 7 1 10
4 13 0 2 12
4 12 2 1 10

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D2 | qhull v Tcv p
2
14
-0.1294381801544404 -0.07247409101984714 
0.08267689532419747 -0.2397644955865706 
0.1295260566906465 1.716033573116837 
0.1740355150742391 0.5317519038435655 
0.1851415205797575 0.3882545794457364 
-0.9065939866848107 -0.2962957610652135 
-0.1954805620516266 -0.07111892482963184 
-0.1407581310832468 0.7233857048236082 
-0.1676297826663962 0.2080621273999375 
0.05868313821742954 0.06632066014880154 
0.08806341399736994 0.1054080604689985 
0.4761588899009253 -0.03168366595227294 
3.094213357897477 -0.064721945677682 
0.5410515627308725 0.2115615434955919 

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D2 | qhull v Tcv G
{appearance {linewidth 3} LIST # rbox 10 D2 | qhull v Tcv G
{appearance {+edge -face} OFF 15 10 1 # Voronoi centers and cells
     0      0  0 # infinity not used
# 1 f8
-0.1294381801544404 -0.07247409101984714  0
# 2 f11
0.08267689532419747 -0.2397644955865706  0
# 3 f12
0.1295260566906465 1.716033573116837  0
# 4 f14
0.1740355150742391 0.5317519038435655  0
# 5 f15
0.1851415205797575 0.3882545794457364  0
# 6 f19
-0.9065939866848107 -0.2962957610652135  0
# 7 f20
-0.1954805620516266 -0.07111892482963184  0
# 8 f21
-0.1407581310832468 0.7233857048236082  0
# 9 f22
-0.1676297826663962 0.2080621273999375  0
# 10 f23
0.05868313821742954 0.06632066014880154  0
# 11 f24
0.08806341399736994 0.1054080604689985  0
# 12 f25
0.4761588899009253 -0.03168366595227294  0
# 13 f26
3.094213357897477 -0.064721945677682  0
# 14 f27
0.5410515627308725 0.2115615434955919  0
4 7 1 2 6 # p0(v3)
3 8 3 6 # p1(v1)
3 14 5 11 # p2(v8)
4 9 4 3 8 # p3(v7)
5 14 5 4 3 13 # p4(v2)
4 9 7 6 8 # p5(v9)
5 14 11 10 12 13 # p6(v10)
7 11 5 4 9 7 1 10 # p7(v5)
3 13 2 12 # p8(v6)
4 12 2 1 10 # p9(v4)
}
}

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D2 | qhull v Tcv Fv
23
4 0 1 0 6
4 0 7 1 7
4 0 9 1 2
4 0 8 0 2
4 0 5 6 7
4 1 4 0 3
4 1 3 3 8
4 1 5 6 8
4 2 7 5 11
4 2 4 5 14
4 2 6 11 14
4 3 4 3 4
4 3 7 4 9
4 3 5 8 9
4 4 8 0 13
4 4 7 4 5
4 4 6 13 14
4 5 7 7 9
4 6 7 10 11
4 6 9 10 12
4 6 8 12 13
4 7 9 1 10
4 8 9 2 12

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D2 | qhull v Tcv Fi
19
5 0 7 0.02051532578114336 0.9997895385570373 0.07511430445246037 
5 0 9 0.619259133056969 0.7851866823409139 0.1370614663104577 
5 0 5 -0.301880639203215 0.9533457293522944 0.008789126238507583 
5 1 3 0.9648718030091262 -0.2627211520946079 0.3258622775065156 
5 1 5 0.7995952824356682 -0.6005392446015695 0.5469710423089692 
5 2 7 -0.9458410914974847 0.3246299888101017 0.04907537812572171 
5 2 4 0.444671031232542 0.8956939622340812 -0.4300843534994401 
5 2 6 0.2281595097543261 -0.9736237661995858 0.08253528745668784 
5 3 4 0.9992944873266901 0.03755699133966539 -0.1938837324602516 
5 3 7 0.6877523324625971 -0.7259454037269313 0.2663295190946441 
5 3 5 -0.9986432053419565 0.05207445078292259 -0.1782370644858237 
5 4 7 -0.9970183790688238 -0.07716444646969993 0.2145489484590235 
5 4 6 -0.1075842248297359 -0.9941959739245502 0.2685422477498993 
5 5 7 0.9950609206245129 -0.09926612839179765 0.187455367716064 
5 6 7 -0.7993641842155074 0.6008468199079334 0.007060641163779212 
5 6 9 -0.2285415587894342 -0.973534157544611 0.07797696388863314 
5 6 8 -0.01261839651625044 -0.9999203848653946 -0.02567278177543585 
5 7 9 0.5936952885926361 -0.8046899429612046 0.01852766555277016 
5 8 9 -0.4674785097727932 0.8840044360186256 0.2506025495170936 

Voronoi ridge statistics
     19 bounded ridges
4.2e-17   ave. distance of midpoint to ridge
1.7e-16   max. distance of midpoint to ridge
     19 bounded ridges with ok normal
5.8e-17   ave. angle to ridge
2.2e-16   max. angle to ridge

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D2 | qhull v Tcv Fo
4
5 0 1 -0.3854955578888161 0.922709691532494 -0.07609298438083822 
5 0 8 0.719062520784207 0.6949453872092842 0.1071733734620186 
5 1 4 0.9929212365203526 -0.1187746524595787 0.07521211888503937 
5 4 8 -0.06640144810487483 -0.9977929883946747 0.1408811441173877 

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D2 | qhull v Qu o Fv Fi Fo Tcv
2
3 10 1
-10.101 -10.101 
-0.06934933486244874 0.05349366577784781 
-0.3051278694340224 0.161498505581022 
3 0 2 1
2 0 1
0
0
3 0 1 2
0
0
0
2 0 2
0
5
4 0 8 0 2
4 0 4 1 2
4 0 1 0 1
4 1 4 0 1
4 4 8 0 2
1
5 0 4 0.4164624817835529 0.9091529031283372 -0.01975252543405325 
4
5 0 8 0.7190625207842071 0.6949453872092841 0.1071733734620185 
5 0 1 -0.3854955578888162 0.922709691532494 -0.07609298438083828 
5 1 4 0.9929212365203528 -0.1187746524595786 0.07521211888503934 
5 4 8 -0.06640144810487485 -0.9977929883946747 0.1408811441173877 

Voronoi ridge statistics
      1 bounded ridges
1.2e-16   ave. distance of midpoint to ridge
1.2e-16   max. distance of midpoint to ridge
      1 bounded ridges with ok normal
      0   max. angle to ridge

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 20 distance computations.
rbox 10 D3 | qhull v Fv Tcv
32
6 0 1 0 17 15 3
7 0 9 0 7 12 11 2
6 0 6 0 7 18 17
5 0 7 0 2 3
6 0 2 2 3 15 11
5 0 8 7 18 12
7 0 5 11 12 18 17 15
5 1 7 0 5 3
6 1 2 3 5 0 15
5 1 5 15 0 17
6 2 3 1 4 13 9
6 2 9 1 2 11 9
7 2 7 1 2 3 5 4
6 2 4 4 5 0 13
7 2 5 9 11 15 0 13
7 3 9 0 6 10 9 1
5 3 7 0 4 1
5 3 6 0 8 6
7 3 4 0 8 14 13 4
6 3 8 6 8 14 10
6 3 5 9 10 14 13
5 4 7 0 5 4
5 4 6 0 16 8
5 4 8 8 16 14
6 4 5 13 0 16 14
6 5 9 9 11 12 10
7 5 8 10 12 18 16 14
6 5 6 0 17 18 16
5 6 9 0 6 7
7 6 8 6 7 18 16 8
5 7 9 0 1 2
6 8 9 6 7 12 10

Output completed.  Verifying that all points are below 2.9e-15 of
all facets.  Will make 180 distance computations.
rbox 10 D3 | qhull v Fi Tcv
13
6 0 2 0.1026012494065408 0.8309156055795224 -0.5468566905731632 0.2399036185798246 
6 0 8 -0.1644981128676535 0.549224308046351 -0.8193247404503221 0.1220237399030437 
6 0 5 -0.1640386761614813 0.6276090456203122 -0.7610507201092116 0.1709974344854015 
6 2 3 0.8628264983391892 0.127742449234631 -0.4890933453107607 -0.1660057988150948 
6 2 9 0.5146151495466437 -0.7556910962035636 -0.4050953159143434 -0.3000434746332832 
6 2 7 0.9862472983740704 0.008356748990702902 0.1650649302430821 -0.2195655184060844 
6 3 8 -0.9471370887617877 -0.1545163381156413 -0.2811690529684558 0.04372902199764667 
6 3 5 -0.9850113492204077 -0.1553182373520528 -0.07502590921037623 0.09265233510028284 
6 4 8 -0.7177135399298967 -0.245721536677967 -0.65154293873383 -0.02974683605231299 
6 5 9 0.7110332662678562 -0.693517783370965 -0.116037831799318 -0.2706062861955821 
6 5 8 -0.1310037283001485 -0.04490613421135446 -0.9903643078593113 -0.2004293237314498 
6 6 8 0.563653077615962 0.07101685912338832 0.8229531054770393 0.4221671959133705 
6 8 9 0.7278413449934529 -0.6852671087526033 0.02561183671604023 -0.2412830130907243 

Voronoi ridge statistics
     15 non-simplicial Voronoi vertices for all ridges
6.9e-17   ave. distance to ridge
1.9e-16   max. distance to ridge
     13 bounded ridges
7.8e-17   ave. distance of midpoint to ridge
  3e-16   max. distance of midpoint to ridge
     13 bounded ridges with ok normal
8.5e-17   ave. angle to ridge
2.2e-16   max. angle to ridge

Output completed.  Verifying that all points are below 2.9e-15 of
all facets.  Will make 180 distance computations.
rbox 10 D3 | qhull v Fo Tcv
19
6 0 1 -0.1769702595802885 0.8331351847724077 0.5239916899325134 0.004105600879712498 
6 0 9 0.5856843296472444 -0.1558732679166009 -0.7954102025713885 -0.1264594278193164 
6 0 6 -0.305501768024369 0.3812318858994052 -0.8725427891556765 -0.04822326899809234 
6 0 7 0.6633910639781613 0.6672883530766242 -0.3385831509130507 0.06175731395259272 
6 1 7 0.7533877382120365 0.334939238848763 -0.5658821628140998 0.06152842458597928 
6 1 2 0.2077539373736714 0.4344067294949102 -0.8764297432625574 0.2556318087147513 
6 1 5 -0.08886729274769822 0.2768317827550689 -0.9568002760954583 0.1656561460661369 
6 2 4 0.8896724708236493 0.4529391082738924 -0.05769799697211265 -0.124969949041603 
6 2 5 -0.6080629223625026 -0.1069684332549473 -0.7866493734408965 -0.05602222006342437 
6 3 9 0.1157648604151236 -0.9728190902550374 -0.2005530222370839 -0.2615067759720444 
6 3 7 0.3131056731324619 -0.1651787990807294 0.9352437125084113 -0.1060546443225209 
6 3 6 -0.8429664438017094 -0.1288333013498811 -0.5223117412882753 -0.1470675860428305 
6 3 4 -0.6546392846048742 0.1665291828386516 0.7373706247980789 0.1638426312062793 
6 4 7 0.8997625993863546 -0.3161631359012113 0.3007792151107228 -0.2534488584590283 
6 4 6 -0.6610636619910346 -0.1756381951302929 -0.7294834194184102 -0.1931488689248214 
6 4 5 -0.8177140658972858 -0.2799433900977097 -0.5029666040348314 0.01966883326066583 
6 5 6 -0.4656867325018191 -0.06587339986788447 -0.8824945112359766 -0.374728122564582 
6 6 9 0.7885740013077054 -0.5314391513195501 0.309392102204163 -0.04784058563315544 
6 7 9 -0.0125726543874506 -0.8388634914110149 -0.5441966291143082 -0.2018836580171401 

Voronoi ridge statistics
     14 non-simplicial Voronoi vertices for all ridges
4.3e-17   ave. distance to ridge
9.7e-17   max. distance to ridge

Output completed.  Verifying that all points are below 2.9e-15 of
all facets.  Will make 180 distance computations.
rbox 10 D3 | qhull v Qu o Fv Fi Fo Tcv
3
10 10 1
-10.101 -10.101 -10.101 
-0.04510412048603351 -0.1962229636993575 -0.06746145990413344 
-0.2032838761823815 -0.3188041900902701 0.1251484339163768 
0.1359785067833994 0.06954805978697726 -0.07249043373758879 
-0.9550934192592715 0.3815223390696589 -0.9370156532984113 
-0.01637948561987637 -0.8836250780525146 -0.03718065630611937 
0.09499885792019704 -0.7038538868165176 -0.181396220925921 
2.128743389186444 -4.06034590041635 -1.2162468947864 
2.789531685277133 -5.393666229616701 -1.494034092231969 
2.640156785601998 -4.796303906482405 -1.459799746992412 
3 0 3 4
7 0 1 3 4 6 7 9
4 0 7 8 9
3 0 2 5
5 0 5 6 7 8
3 0 8 9
9 0 1 2 3 5 6 7 8 9
6 0 1 2 4 5 6
0
5 0 1 2 3 4
18
5 0 1 0 3 4
5 0 9 0 3 4
8 1 6 0 3 1 6 7 9
5 1 2 0 7 9
5 1 4 0 6 7
6 1 7 0 4 1 6
5 1 9 1 3 4
5 2 5 0 9 8
5 2 4 0 7 8
5 2 6 7 9 8
5 3 6 0 5 2
5 3 7 0 2 5
7 4 6 0 5 6 7 8
5 4 7 0 6 5
5 5 6 0 9 8
6 6 9 0 3 1 2
6 6 7 1 2 5 6
6 7 9 0 2 1 4
3
6 1 9 0.5123553720802024 -0.363812082853534 -0.7779027838170592 -0.100757404152973 
6 2 6 -0.5221667006142685 -0.08192192666458321 -0.8488997200501196 -0.2535440955968309 
6 6 7 0.752213645322669 0.06033708575303686 0.6561509489997043 0.09003235761431796 
15
6 0 1 -0.1769702595802886 0.8331351847724078 0.5239916899325134 0.004105600879712498 
6 0 9 0.5856843296472447 -0.1558732679166012 -0.7954102025713884 -0.1264594278193166 
6 1 6 -0.2436653478720986 0.147883680687048 -0.9585184480399009 -0.04663519095132841 
6 1 2 0.2077539373736637 0.4344067294949081 -0.8764297432625605 0.255631808714752 
6 1 4 0.444220078847362 0.4986447037065236 -0.744326528490203 0.1737545932855555 
6 1 7 0.7533877382120362 0.3349392388487629 -0.5658821628141001 0.06152842458597942 
6 2 5 -0.6080629223625006 -0.1069684332549458 -0.7866493734408982 -0.05602222006342417 
6 2 4 0.8896724708236509 0.4529391082738904 -0.0576979969721034 -0.1249699490416035 
6 3 6 -0.8429664438017096 -0.1288333013498811 -0.5223117412882751 -0.1470675860428304 
6 3 7 0.3131056731324613 -0.1651787990807291 0.9352437125084115 -0.1060546443225207 
6 4 6 -0.6610636619910349 -0.1756381951302929 -0.7294834194184099 -0.1931488689248214 
6 4 7 0.8997625993863546 -0.3161631359012115 0.3007792151107228 -0.2534488584590282 
6 5 6 -0.4656867325018176 -0.06587339986788343 -0.8824945112359772 -0.374728122564582 
6 6 9 0.7885740013077054 -0.5314391513195503 0.3093921022041629 -0.04784058563315553 
6 7 9 -0.01257265438745033 -0.8388634914110151 -0.5441966291143079 -0.2018836580171402 

Voronoi ridge statistics
      9 non-simplicial Voronoi vertices for all ridges
1.5e-16   ave. distance to ridge
4.4e-16   max. distance to ridge
      3 bounded ridges
6.4e-16   ave. distance of midpoint to ridge
1.7e-15   max. distance of midpoint to ridge
      3 bounded ridges with ok normal
7.4e-17   ave. angle to ridge
2.2e-16   max. angle to ridge

Output completed.  Verifying that all points are below 2.9e-15 of
all facets.  Will make 90 distance computations.
rbox 5 D2 | qhull v f FnN o
Vertices and facets:
- p3(v5):  0.43 -0.11  0.19
  neighbors: f5 f6 f7 f8
- p2(v2):  0.47 -0.11  0.24
  neighbors: f1 f5 f7
- p4(v1): -0.39  0.45  0.36
  neighbors: f1 f3 f5 f6
- p0(v4): -0.34  0.23  0.17
  neighbors: f3 f6 f8
- p1(v3):  0.32 -0.23  0.16
  neighbors: f1 f3 f7 f8
- f5
    - flags: top simplicial
    - normal:     0.437    0.773  -0.4599
    - offset: -0.01170704
    - center: 0.4751017705052502 0.8404705693422864 
    - vertices: p3(v5) p2(v2) p4(v1)
    - neighboring facets: f1 f6 f7
- f6
    - flags: bottom simplicial
    - normal:    0.3235   0.6691   -0.669
    - offset:     0.0657
    - center: 0.24177356134713 0.5000766029034823 
    - vertices: p3(v5) p0(v4) p4(v1)
    - neighboring facets: f3 f5 f8
- f7
    - flags: top simplicial
    - normal:    0.6288  -0.3317  -0.7033
    - offset: -0.1682885
    - center: 0.4470293595057619 -0.2357835939937328 
    - vertices: p3(v5) p1(v3) p2(v2)
    - neighboring facets: f1 f5 f8
- f8
    - flags: top simplicial
    - normal:    0.1177   0.1841  -0.9758
    - offset:    0.15929
    - center: 0.06029550723695781 0.09433023738340306 
    - vertices: p3(v5) p0(v4) p1(v3)
    - neighboring facets: f3 f7 f6
4
3 -1 1 2
3 -3 0 3
3 -1 0 3
3 -3 2 1
5
3 3 -3 1
4 3 -3 -1 2
3 2 -1 0
4 3 1 0 2
4 1 -3 -1 0
2
5 5 1
-10.101 -10.101 
0.4751017705052502 0.8404705693422864 
0.24177356134713 0.5000766029034823 
0.4470293595057619 -0.2357835939937328 
0.06029550723695781 0.09433023738340306 
3 2 4 0
3 3 4 0
3 1 3 0
4 3 4 2 1
3 1 2 0

set +v
=== check Halfspace and Qhull identity pipeline, showing the input Fri, Jul 24, 2020 10:27:34 PM
=== the Qhull pipeline recreates 100 4-D cospherical points with the same area and volume
rbox 100 s D4 | qhull FA FV s n | head

Convex hull of 100 points in 4-d:

  Number of vertices: 100
  Number of facets: 584

Statistics for: rbox 100 s D4 | qhull FA FV s n

  Number of points processed: 100
  Number of hyperplanes created: 1717
  Number of distance tests for qhull: 4090
  CPU seconds to compute hull (after input): 0.001
  Total facet area:   1.7919449
  Total volume:       0.18640279

4 1
-0.006240661006237819 -0.006198497499885543 -0.0019864189252863 0.03528712962677102 
5
584
-0.4728063044129454 -0.06576180062326932 0.3296766529322419 -0.8145200357250598 -0.4001269961794449 
0.9350657178932537 -0.116181174817606 -0.009048199757790566 0.3347718147035652 -0.3733488931324643 
0.5670388949132408 -0.5323662756300656 -0.3876606744394214 0.4947446227302695 -0.4846392631626165 
0.8393609616706702 -0.1089654738688994 -0.05104156673138016 0.530089105710936 -0.4115455431603698 
0.6753770108964836 -0.1536990905729236 -0.0485198359900459 0.7196445707605155 -0.4414725485817289 
0.20025580309926 0.08170320261530004 0.2334845247641378 0.9480016754748583 -0.4466269780920115 
rbox 100 s D4 | qhull FQ FA FV n s | qhull s H Fp | head

Convex hull of 100 points in 4-d:

  Number of vertices: 100
  Number of facets: 584

Statistics for: rbox 100 s D4 | qhull FQ FA FV n s

  Number of points processed: 100
  Number of hyperplanes created: 1717
  Number of distance tests for qhull: 4090
  CPU seconds to compute hull (after input): 0.001
  Total facet area:   1.7919449
  Total volume:       0.18640279


Halfspace intersection by the convex hull of 584 points in 4-d:

  Number of halfspaces: 584
  Number of non-redundant halfspaces: 584
  Number of intersection points: 100
  Number of non-simplicial intersection points: 100

Statistics for: rbox 100 s D4 | qhull FQ FA FV n s | qhull s H Fp

  Number of points processed: 584
  Number of hyperplanes created: 4013
  Number of distance tests for qhull: 29717
  Number of distance tests for merging: 76955
  Number of distance tests for checking: 18265
  Number of merged facets: 3444
  CPU seconds to compute hull (after input): 0.012
  Maximum distance of point above facet: 2.4e-14 (0.4x)
  Maximum distance of vertex below facet: -1.7e-14 (0.3x)

4
100
-0.1497820974007844 0.4220759056868791 -0.1730594919621551 0.1395265758865447 
-0.1656824599698354 0.2695081565763442 0.2399815540443042 -0.3038478726528215 
-0.1287028906527846 0.3274268489457611 0.1066154632455187 -0.3389105597705839 
0.2152206390581626 0.2489384546335302 -0.342896351704003 0.1553441801811403 
-0.3478218321497436 0.1609400522171699 0.2504669650899252 -0.2009591303498609 
-0.2026608048181584 0.132737676060139 -0.4340855448243784 0.05365675464591807 
-0.1243914612976075 -0.06208848857682957 -0.4348180038806073 -0.2039732517850684 
0.318659177699236 0.2994118752602876 -0.2407753518255607 -0.02891517550426 
rbox 100 s D4 | qhull FQ FA FV n s Tcv | qhull FQ s H Fp Tcv | qhull FA Tcv

Convex hull of 100 points in 4-d:

  Number of vertices: 100
  Number of facets: 584

Statistics for: rbox 100 s D4 | qhull FQ FA FV n s Tcv

  Number of points processed: 100
  Number of hyperplanes created: 1717
  Number of distance tests for qhull: 4090
  CPU seconds to compute hull (after input): 0.007
  Total facet area:   1.7919449
  Total volume:       0.18640279


Output completed.  Verifying that all points are below 2.8e-15 of
all facets.  Will make 58400 distance computations.

Halfspace intersection by the convex hull of 584 points in 4-d:

  Number of halfspaces: 584
  Number of non-redundant halfspaces: 584
  Number of intersection points: 100
  Number of non-simplicial intersection points: 100

Statistics for: rbox 100 s D4 | qhull FQ FA FV n s Tcv | qhull FQ s H Fp Tcv

  Number of points processed: 584
  Number of hyperplanes created: 4013
  Number of distance tests for qhull: 29717
  Number of distance tests for merging: 77055
  Number of distance tests for checking: 51837
  Number of merged facets: 3444
  CPU seconds to compute hull (after input): 0.363
  Maximum distance of point above facet: 2.4e-14 (0.4x)
  Maximum distance of vertex below facet: -1.7e-14 (0.3x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 58400 distance computations.

Convex hull of 100 points in 4-d:

  Number of vertices: 100
  Number of facets: 584

Statistics for: rbox 100 s D4 | qhull FQ FA FV n s Tcv | qhull FQ s H Fp Tcv | qhull FA Tcv

  Number of points processed: 100
  Number of hyperplanes created: 1717
  Number of distance tests for qhull: 4090
  CPU seconds to compute hull (after input): 0.006
  Total facet area:   1.7919449
  Total volume:       0.18640279


Output completed.  Verifying that all points are below 2.8e-15 of
all facets.  Will make 58400 distance computations.
echo === the Qhull pipeline recreates a 3-D tetrahedron
=== the Qhull pipeline recreates a 3-D tetrahedron
rbox d D3 | qhull n FD
rbox d D3 | qhull n FD
begin
    8 4 real
0.2886751345948129 0.5773502691896258 0.5773502691896258 0.5773502691896258 
0.2886751345948129 -0.5773502691896258 0.5773502691896258 0.5773502691896258 
0.2886751345948129 0.5773502691896258 0.5773502691896258 -0.5773502691896258 
0.2886751345948129 -0.5773502691896258 0.5773502691896258 -0.5773502691896258 
0.2886751345948129 -0.5773502691896258 -0.5773502691896258 0.5773502691896258 
0.2886751345948129 0.5773502691896258 -0.5773502691896258 0.5773502691896258 
0.2886751345948129 -0.5773502691896258 -0.5773502691896258 -0.5773502691896258 
0.2886751345948129 0.5773502691896258 -0.5773502691896258 -0.5773502691896258 
end
rbox d D3 | qhull s n FD Tcv | qhull s Fd H0.1,0.1 Fp Tcv

Convex hull of 6 points in 3-d:

  Number of vertices: 6
  Number of facets: 8

Statistics for: rbox d D3 | qhull s n FD Tcv

  Number of points processed: 6
  Number of hyperplanes created: 11
  Number of distance tests for qhull: 10
  Number of distance tests for merging: 59
  Number of distance tests for checking: 54
  Number of merged facets: 1
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.

Halfspace intersection by the convex hull of 8 points in 3-d:

  Number of halfspaces: 8
  Number of non-redundant halfspaces: 8
  Number of intersection points: 6
  Number of non-simplicial intersection points: 6

Statistics for: rbox d D3 | qhull s n FD Tcv | qhull s Fd H0.1,0.1 Fp Tcv

  Number of points processed: 8
  Number of hyperplanes created: 10
  Number of distance tests for qhull: 30
  Number of distance tests for merging: 95
  Number of distance tests for checking: 100
  Number of merged facets: 6
  CPU seconds to compute hull (after input):  0

3
6
-1.387778780781446e-17 -1.387778780781446e-17   -0.5 
-2.775557561562891e-17    0.5      0 
  -0.5      0      0 
   0.5 -2.775557561562891e-17      0 
     0   -0.5      0 
-1.387778780781446e-17 1.387778780781446e-17 0.4999999999999999 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 48 distance computations.
echo === the Qhull pipeline recreates a regular 2-D pentagon
=== the Qhull pipeline recreates a regular 2-D pentagon
rbox 5 r D2 | qhull FQ n
rbox 5 r D2 | qhull FQ n
3
5
0.8090169943749476 0.587785252292473 -0.4045084971874737 
-0.3090169943749476 -0.9510565162951536 -0.4045084971874738 
0.8090169943749472 -0.5877852522924732 -0.4045084971874737 
    -1 9.444121133484361e-17 -0.4045084971874738 
-0.3090169943749474 0.9510565162951536 -0.4045084971874738 
rbox 5 r D2 | qhull s FQ n Tcv | qhull s H0 Fp Tcv

Convex hull of 5 points in 2-d:

  Number of vertices: 5
  Number of facets: 5

Statistics for: rbox 5 r D2 | qhull s FQ n Tcv

  Number of points processed: 5
  Number of hyperplanes created: 8
  Number of distance tests for qhull: 7
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1.3e-15 of
all facets.  Will make 25 distance computations.

Halfspace intersection by the convex hull of 5 points in 2-d:

  Number of halfspaces: 5
  Number of non-redundant halfspaces: 5
  Number of intersection points: 5

Statistics for: rbox 5 r D2 | qhull s FQ n Tcv | qhull s H0 Fp Tcv

  Number of points processed: 5
  Number of hyperplanes created: 7
  Number of distance tests for qhull: 8
  CPU seconds to compute hull (after input):  0

2
5
-0.4045084971874738 -0.2938926261462365 
   0.5 -1.528090898784888e-16 
0.1545084971874736 -0.4755282581475768 
-0.4045084971874737 0.2938926261462366 
0.1545084971874737 0.4755282581475768 

Output completed.  Verifying that all points are below 6.4e-15 of
all facets.  Will make 25 distance computations.

set +v
=== check qhull Fri, Jul 24, 2020 10:27:35 PM
rbox 10 s D3 | qhull Tcv

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 10 s D3 | qhull Tcv

  Number of points processed: 10
  Number of hyperplanes created: 29
  Number of distance tests for qhull: 48
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 2e-15 of
all facets.  Will make 160 distance computations.
rbox 10 s D3 | qhull f Pd0:0.5 Pd2 Pg Tcv
Vertices and facets:
- p7(v8):   0.2 0.093  0.45
- p9(v5):  0.29 -0.16  0.38
- p3(v2):  0.48 -0.13 0.022
- p8(v10):  0.32 0.025 -0.38
- f16
    - flags: bottom simplicial
    - normal:     0.858   0.1759   0.4826
    - offset: -0.4016457
    - vertices: p7(v8) p9(v5) p3(v2)
    - neighboring facets: f7 f27 f23
- f27
    - flags: bottom simplicial
    - normal:     0.646   0.7625  0.03668
    - offset: -0.2138755
    - vertices: p8(v10) p7(v8) p3(v2)
    - neighboring facets: f16 f26 f28

Output completed.  Verifying that all points are below 2e-15 of
all facets.  Will make 20 distance computations.
rbox 10 s D3 | qhull f Tcv PD2:-0.5 Pg 
Vertices and facets:
- p4(v7):  0.23 -0.32 -0.31
- p1(v4): -0.072 0.057 -0.49
- p6(v3): -0.13 -0.47 -0.09
- p0(v9): -0.37 -0.27  0.19
- p8(v10):  0.32 0.025 -0.38
- p5(v6): 0.028  0.16 -0.47
- f12
    - flags: top simplicial
    - normal:   -0.2354  -0.5691  -0.7879
    - offset: -0.3715833
    - vertices: p4(v7) p1(v4) p6(v3)
    - neighboring facets: f21 f11 f25
- f21
    - flags: bottom simplicial
    - normal:   -0.8148  -0.2922  -0.5006
    - offset: -0.2881945
    - vertices: p0(v9) p1(v4) p6(v3)
    - neighboring facets: f12 f19 f20
- f24
    - flags: top simplicial
    - normal:    0.2636 -0.06941  -0.9621
    - offset: -0.4497787
    - vertices: p8(v10) p5(v6) p1(v4)
    - neighboring facets: f9 f25 f28
- f25
    - flags: bottom simplicial
    - normal:    0.2402  -0.2624  -0.9346
    - offset: -0.4268812
    - vertices: p8(v10) p4(v7) p1(v4)
    - neighboring facets: f12 f24 f26

Output completed.  Verifying that all points are below 2e-15 of
all facets.  Will make 40 distance computations.
rbox 10 s D3 | qhull QR-1

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 10 s D3 | qhull QR-1 QR-1595644055

  Number of points processed: 10
  Number of hyperplanes created: 29
  Number of distance tests for qhull: 48
  CPU seconds to compute hull (after input):  0

rbox 10 s D3 | qhull QR-40

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 10 s D3 | qhull QR-40 QR-40

  Number of points processed: 10
  Number of hyperplanes created: 29
  Number of distance tests for qhull: 48
  CPU seconds to compute hull (after input):  0

rbox 1000 D3 | qhull Tcvs
qhull 2020.2.r 2020/07/24 Statistics: rbox 1000 D3 | qhull Tcvs

Convex hull of 1000 points in 3-d:

  Number of vertices: 73
  Number of facets: 142

Statistics for: rbox 1000 D3 | qhull Tcvs

  Number of points processed: 81
  Number of hyperplanes created: 367
  Number of distance tests for qhull: 12879
  CPU seconds to compute hull (after input): 0.001



qhull invoked by: rbox 1000 D3 | qhull Tcvs
  2020.2.r 2020/07/24 with options:
  run-id 213848649  Tcheck-frequently  Tverify  Tstatistics  _pre-merge
  _zero-centrum  _max-width  1  Error-roundoff 6.9e-16  _one-merge 4.9e-15
  _near-inside 2.4e-14  Visible-distance 1.4e-15  U-max-coplanar 1.4e-15
  Width-outside 2.8e-15  _wide-facet 8.3e-15

precision constants:
    0.5 max. abs. coordinate in the (transformed) input ('Qbd:n')
 6.9e-16 max. roundoff error for distance computation ('En')
 6.7e-16 max. roundoff error for angle computations
 2.8e-15 min. distance for outside points ('Wn')
 1.4e-15 min. distance for visible facets ('Vn')
 1.4e-15 max. distance for coplanar facets ('Un')
 8.3e-15 max. facet width for recomputing centrum and area
 2.4e-14 max. distance for near-inside points
 1.4e-15 radius of pre-merge centrum
 4.9e-15 max. distance for merging two simplicial facets
 2.2e-16 max. roundoff error for arithmetic operations
 1.1e-308 min. denominator for division
  zero diagonal for Gauss: 8.88e-15 1.78e-14 2.66e-14 


precision statistics
3.8e-17 ave. distance of a new vertex to a facet
1.7e-16 max. distance of a new vertex to a facet
1.4e-16 max. distance of an output vertex to a facet
-1.7e-16 min. distance of an output vertex to a facet
 0.0026 min. denominator in hyperplane computation

summary information
     73 number of vertices in output
    142 number of facets in output
      3 average number of neighbors per facet
      3 maximum number of neighbors
      3 average number of vertices per facet
      3 maximum number of vertices
  0.001 cpu seconds for qhull after input
     82 vertices created altogether
    367 facets created altogether
      0   maximum merges for a facet (at most 511)
   0.93 average cosine (angle) of facet normals for all ridges
      1   maximum cosine of facet normals (flatest) across a ridge
   0.21   minimum cosine of facet normals (sharpest) across a ridge

build hull statistics
     81 points processed
     73 max. vertices at any one time
   2.78 ave. visible facets per iteration
   0.21   ave. visible facets without an horizon neighbor
   2.78   ave. facets deleted per iteration
      8     maximum
   5.43 ave. visible vertices per iteration
     11     maximum
   4.38 ave. horizon facets per iteration
   4.48 ave. new or merged facets per iteration
     10     maximum (includes initial simplex)
  -0.77 average new facet balance
    1.5   standard deviation
     77   count
      7 determinants for initial hull or voronoi vertices
    503 distance tests for facet visibility
     73 points checked for facets' outer planes
   11.4   ave. distance tests per check
   1668   max visit_id/2
   3125   max vertex_visit/2

partitioning statistics (see previous for outer planes)
      8 total vertices deleted
      1     maximum vertices deleted per iteration
    132 calls to findbest
   2.53  ave. facets tested
      6  max. facets tested
   2048 calls to findbestnew
   4.47  ave. facets tested
     13  max. facets tested
     36  calls due to qh_sharpnewfacets
    927 calls to findhorizon
   3.01  ave. facets tested
      5  max. facets tested
0.00539  ave. clearly better
      5  new bestfacets during qh_findbesthorizon
    919 inside points
      8   inside points that were coplanar with a facet
-2.8e-17 difference in max_outside at final check
   3747 distance tests for initial partition
   3132 partitions of a point
   8553 distance tests for partitioning
    518 distance tests for checking flipped facets
   1160 distance tests for statistics
  16915 total number of distance tests
      8 partitions of coplanar points or deleted vertices
     76    distance tests for these partitions

statistics for matching ridges
    726 total lookups for matching ridges of new facets
  0.583 average number of tests to match a ridge

statistics for determining merges
   1089 distance tests for checking simplicial convexity

statistics for merging
1.7e-16 max distance of vertex or coplanar point above facet (w/roundoff)
-6.9e-16 max distance of vertex below facet (or roundoff)

memory usage statistics (in bytes)
  21584 for facets and their normals, neighbor and vertex sets
   2044 for vertices and their neighbor sets
  31104 for input points, outside and coplanar sets, and qhT

memory statistics:
   1413 quick allocations
    687 short allocations
     69 long allocations
   1445 short frees
     68 long frees
  25680 bytes of short memory in use
   1472 bytes of short memory in freelists
 103912 bytes of dropped short memory
   1364 bytes of unused short memory (estimated)
  10916 bytes of long memory allocated (max, except for input)
     96 bytes of long memory in use (in 1 pieces)
 131064 bytes of short memory buffers (minus links)
  65536 bytes per short memory buffer (initially 131072 bytes)
    100 calls to qh_setlarger
     14     average copy size
  freelists(bytes->count): 16->1 24->13 32->0 48->11 88->7

    size in bytes: merge 48 ridge 20 vertex 28 facet 88
         normal 24 ridge vertices 16 facet vertices or neighbors 20

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 142000 distance computations.
# Test tracing 'Tn', combine stderr/stdout 'Tz', flush fprintf 'Tf'
rbox 100 D3 | qhull T1 Tz Tf TA1 TO q_test.log.1
tail -n -10 q_test.log.1
Statistics for: rbox 100 D3 | qhull T1 Tz Tf TA1 TO q_test.log.1

  Number of points processed: 5
  Number of hyperplanes created: 8
  Number of distance tests for qhull: 456
  CPU seconds to compute hull (after input): 0.001

[QH1006]qh_freeqhull: free global memory
[QH1005]qh_freebuild: free memory from qh_inithull and qh_buildhull
[QH1061]qh_freeqhull: clear qhT except for qh.qhmem and qh.qhstat
rm q_test.log.1
rbox 100 s D3 | qhull TcvA10

Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.
Convex hull of 100 points in 3-d:

  Number of vertices: 14
  Number of facets: 24

Statistics for: rbox 100 s D3 | qhull TcvA10

  Number of points processed: 14
  Number of hyperplanes created: 48
  Number of distance tests for qhull: 599
  CPU seconds to compute hull (after input):  0

rbox 100 s D3 | qhull TcvV-2

Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.
Convex hull of 100 points in 3-d:

  Number of vertices: 78
  Number of facets: 152

Statistics for: rbox 100 s D3 | qhull TcvV-2

  Number of points processed: 78
  Number of hyperplanes created: 390
  Number of distance tests for qhull: 1488
  CPU seconds to compute hull (after input): 0.001

rbox 100 s D3 | qhull TcvC2

Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.
Convex hull of 100 points in 3-d:

  Number of vertices: 79
  Number of facets: 154

Statistics for: rbox 100 s D3 | qhull TcvC2

  Number of points processed: 79
  Number of hyperplanes created: 395
  Number of distance tests for qhull: 1495
  CPU seconds to compute hull (after input): 0.001

rbox 100 s D3 | qhull TcvV2

Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.
Convex hull of 100 points in 3-d:

  Number of vertices: 79
  Number of facets: 154

Statistics for: rbox 100 s D3 | qhull TcvV2

  Number of points processed: 79
  Number of hyperplanes created: 395
  Number of distance tests for qhull: 1495
  CPU seconds to compute hull (after input): 0.001

rbox 100 s D3 | qhull T1cvV2P2
[QH1008]qh_readpoints: read in 100 3-dimensional points
[QH0013]qh_initqhull_globals: for rbox 100 s D3 | qhull T1cvV2P2

Trace level T1, IStracing 0, point TP2, merge TM0, dist TW1.8e+308, qh.tracefacet_id -1, traceridge_id -1, tracevertex_id -1, last qh.RERUN 0, rbox 100 s D3 | qhull T1cvV2P2
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213848649  Tcheck-frequently  Tverify  TV-stop-after-point 2
  Trace-point 2  _pre-merge  _zero-centrum  _max-width 0.94
  Error-roundoff 6.7e-16  _one-merge 4.7e-15  _near-inside 2.3e-14
  Visible-distance 1.3e-15  U-max-coplanar 1.3e-15  Width-outside 2.7e-15
  _wide-facet 8.1e-15
qh_findbest: point p2 starting at f7 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p41, Last merge #0, max_outside 4e-17
qh_findbest: point p2 starting at f15 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p52, Last merge #0, max_outside 1.1e-16
qh_findbest: point p2 starting at f37 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p73, Last merge #0, max_outside 1.1e-16
qh_findbest: point p2 starting at f52 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p87, Last merge #0, max_outside 1.1e-16
qh_findbest: point p2 starting at f72 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p76, Last merge #0, max_outside 1.1e-16
qh_findbest: point p2 starting at f120 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p84, Last merge #0, max_outside 1.1e-16
qh_findbest: point p2 starting at f211 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p10, Last merge #0, max_outside 1.1e-16
qh_findbest: point p2 starting at f289 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p6, Last merge #0, max_outside 1.1e-16
[QH1049]qh_addpoint: add p2(v79) 0.014 above f288 to hull of 152 facets, 0 merges, 22 outside at 0.001 CPU secs.  Previous p56(v78) delta 0.001 CPU, 152 facets, 0 merges, 390 hyperplanes, 3835 distplanes, 0 retries
[QH1040]qh_findhorizon: find horizon for point p2 facet f288
[QH1041]qh_findhorizon: 5 horizon facets(good 5), 3 visible(good 3), 0 coplanar
[QH1032]qh_makenewfacets: created 5 new facets f390..f394 from point p2 to horizon
[QH1019]qh_matchnewfacets: match neighbors for new facets.
[QH1043]qh_partitionvisible: partitioned 0 points from outsidesets, 0 points from coplanarsets, and 0 deleted vertices
[QH1018]qh_deletevisible: delete 3 visible facets and 0 vertices
[QH1027]qh_checkpolygon: check all facets from f62, qh.NEWtentative? 0
[QH1039]qh_buildhull: completed the hull construction
[QH1036]Qhull: algorithm completed
[QH1027]qh_checkpolygon: check all facets from f62, qh.NEWtentative? 0
[QH1064]qh_checkconvex: check that facets are not-flipped and for qh.ZEROcentrum that simplicial vertices are below their neighbor (dist<0.0)

Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.
Convex hull of 100 points in 3-d:

  Number of vertices: 79
  Number of facets: 154

Statistics for: rbox 100 s D3 | qhull T1cvV2P2

  Number of points processed: 79
  Number of hyperplanes created: 395
  Number of distance tests for qhull: 1495
  CPU seconds to compute hull (after input): 0.001

[QH1006]qh_freeqhull: free global memory
[QH1005]qh_freebuild: free memory from qh_inithull and qh_buildhull
[QH1061]qh_freeqhull: clear qhT except for qh.qhmem and qh.qhstat
rbox 100 s D3 | qhull TcvF100

At 22:27:35 & 0.001 CPU secs, qhull has created 102 facets and merged 0.
 The current hull contains 46 facets and 25 vertices.  There are 75
 outside points.  Next is point p55(v26), 0.035 above f44.

At 22:27:35 & 0.001 CPU secs, qhull has created 203 facets and merged 0.
 The current hull contains 86 facets and 45 vertices.  There are 55
 outside points.  Next is point p82(v46), 0.067 above f117.

At 22:27:35 & 0.002 CPU secs, qhull has created 306 facets and merged 0.
 The current hull contains 122 facets and 63 vertices.  There are 37
 outside points.  Next is point p50(v64), 0.042 above f218.

At 22:27:35 & 0.002 CPU secs, qhull has created 412 facets and merged 0.
 The current hull contains 160 facets and 82 vertices.  There are 18
 outside points.  Next is point p60(v83), 0.031 above f307.

Convex hull of 100 points in 3-d:

  Number of vertices: 100
  Number of facets: 196

Statistics for: rbox 100 s D3 | qhull TcvF100

  Number of points processed: 100
  Number of hyperplanes created: 514
  Number of distance tests for qhull: 1690
  CPU seconds to compute hull (after input): 0.002


Output completed.  Verifying that all points are below 2e-15 of
all facets.  Will make 19600 distance computations.
rbox 100 s D3 | qhull Qf Tcv

Convex hull of 100 points in 3-d:

  Number of vertices: 100
  Number of facets: 196

Statistics for: rbox 100 s D3 | qhull Qf Tcv

  Number of points processed: 100
  Number of hyperplanes created: 506
  Number of distance tests for qhull: 4421
  CPU seconds to compute hull (after input): 0.002


Output completed.  Verifying that all points are below 2e-15 of
all facets.  Will make 19600 distance computations.
rbox 100 D3 | qhull Tcv

Convex hull of 100 points in 3-d:

  Number of vertices: 26
  Number of facets: 48

Statistics for: rbox 100 D3 | qhull Tcv

  Number of points processed: 28
  Number of hyperplanes created: 109
  Number of distance tests for qhull: 1163
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 4800 distance computations.
rbox 100 D3 | qhull Qs Tcv

Convex hull of 100 points in 3-d:

  Number of vertices: 26
  Number of facets: 48

Statistics for: rbox 100 D3 | qhull Qs Tcv

  Number of points processed: 29
  Number of hyperplanes created: 105
  Number of distance tests for qhull: 1172
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 4800 distance computations.
rbox 100 D5 | qhull Qs Tcv

Convex hull of 100 points in 5-d:

  Number of vertices: 78
  Number of facets: 1174

Statistics for: rbox 100 D5 | qhull Qs Tcv

  Number of points processed: 85
  Number of hyperplanes created: 4014
  Number of distance tests for qhull: 9050
  CPU seconds to compute hull (after input): 0.01

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 117400 distance computations.
rbox 100 D3 | qhull Qr Tcv

Convex hull of 100 points in 3-d:

  Number of vertices: 26
  Number of facets: 48

Statistics for: rbox 100 D3 | qhull Qr Tcv

  Number of points processed: 56
  Number of hyperplanes created: 293
  Number of distance tests for qhull: 2135


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 4800 distance computations.
rbox 100 D3 | qhull Qxv Tcv

Convex hull of 100 points in 3-d:

  Number of vertices: 26
  Number of facets: 48

Statistics for: rbox 100 D3 | qhull Qxv Tcv

  Number of points processed: 28
  Number of hyperplanes created: 109
  Number of distance tests for qhull: 1163
  CPU seconds to compute hull (after input):  0

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 4800 distance computations.
rbox 100 D3 | qhull Qi f Pd0 Pd1 Pd2 Pg Tcv
Vertices and facets:
- p11(v14): -0.31  0.47  0.07
- p59(v8):  0.44  0.42 -0.11
- p33(v3): -0.067  0.49 -0.11
- p48(v25):  0.25  0.24  0.44
- p37(v15):  0.45  0.26  0.04
- p38(v5):  0.42 -0.25  0.42
- f42
    - flags: bottom simplicial
    - normal:    0.1292   0.9495   0.2858
    - offset: -0.4221543
    - coplanar set(furthest p70):
      p70:   0.04762   0.3507 -0.06712
      furthest distance= -0.1
    - vertices: p11(v14) p59(v8) p33(v3)
    - neighboring facets: f52 f41 f93
- f93
    - flags: top simplicial
    - normal:     0.142   0.9273   0.3463
    - offset: -0.4120445
    - coplanar set(furthest p28):
      p27:    0.1182   0.3419    0.068
      p25:    0.1663   0.2352   0.3516
      p15:    0.2743   0.2665  0.07375
      p44:   -0.1321   0.3861    0.167
      p28:   -0.1003   0.4263  0.07335
      furthest distance= -0.0056
    - vertices: p48(v25) p11(v14) p59(v8)
    - neighboring facets: f42 f94 f95
- f94
    - flags: bottom simplicial
    - normal:    0.7783   0.4631   0.4241
    - offset: -0.4905394
    - vertices: p48(v25) p37(v15) p59(v8)
    - neighboring facets: f47 f93 f97
- f97
    - flags: top simplicial
    - normal:    0.8488   0.2736   0.4523
    - offset: -0.4744876
    - vertices: p48(v25) p37(v15) p38(v5)
    - neighboring facets: f46 f99 f94

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 400 distance computations.
rbox c d | qhull Qc f Tcv
Vertices and facets:
- p6(v6):   0.5   0.5  -0.5
  neighbors: f1 f9 f10
- p2(v3):  -0.5   0.5  -0.5
  neighbors: f1 f3 f10
- p4(v2):   0.5  -0.5  -0.5
  neighbors: f1 f2 f9
- p0(v1):  -0.5  -0.5  -0.5
  neighbors: f1 f2 f3
- p5(v7):   0.5  -0.5   0.5
  neighbors: f2 f9 f13
- p1(v4):  -0.5  -0.5   0.5
  neighbors: f2 f3 f13
- p7(v5):   0.5   0.5   0.5
  neighbors: f10 f13 f9
- p3(v8):  -0.5   0.5   0.5
  neighbors: f3 f10 f13
- f1
    - flags: bottom tested
    - merges: 1
    - normal:        -0       -0       -1
    - offset:       -0.5
    - center:      0      0   -0.5 
    - coplanar set(furthest p8):
      p8:         0        0     -0.5
      furthest distance=  0
    - vertices: p6(v6) p2(v3) p4(v2) p0(v1)
    - neighboring facets: f2 f3 f10 f9
    - ridges:
     - r4 tested simplicialtop simplicialbot
           vertices: p2(v3) p0(v1)
           between f1 and f3
     - r3 tested simplicialtop simplicialbot
           vertices: p4(v2) p0(v1)
           between f2 and f1
     - r1 tested simplicialtop
           vertices: p6(v6) p4(v2)
           between f9 and f1
     - r2 tested simplicialbot
           vertices: p6(v6) p2(v3)
           between f1 and f10
- f2
    - flags: top tested
    - merges: 1
    - normal:         0       -1        0
    - offset:       -0.5
    - center:      0   -0.5      0 
    - coplanar set(furthest p10):
      p10:         0     -0.5        0
      furthest distance=  0
    - vertices: p5(v7) p1(v4) p4(v2) p0(v1)
    - neighboring facets: f1 f3 f13 f9
    - ridges:
     - r3 tested simplicialtop simplicialbot
           vertices: p4(v2) p0(v1)
           between f2 and f1
     - r8 tested simplicialtop simplicialbot
           vertices: p1(v4) p0(v1)
           between f3 and f2
     - r7 tested simplicialtop
           vertices: p5(v7) p1(v4)
           between f13 and f2
     - r6 tested
           vertices: p5(v7) p4(v2)
           between f2 and f9
- f9
    - flags: bottom tested
    - merges: 1
    - normal:         1       -0       -0
    - offset:       -0.5
    - center:    0.5      0      0 
    - coplanar set(furthest p13):
      p13:       0.5        0        0
      furthest distance=  0
    - vertices: p5(v7) p6(v6) p7(v5) p4(v2)
    - neighboring facets: f2 f1 f10 f13
    - ridges:
     - r1 tested simplicialtop
           vertices: p6(v6) p4(v2)
           between f9 and f1
     - r6 tested
           vertices: p5(v7) p4(v2)
           between f2 and f9
     - r10 tested simplicialbot
           vertices: p5(v7) p7(v5)
           between f9 and f13
     - r11 tested simplicialtop simplicialbot
           vertices: p6(v6) p7(v5)
           between f10 and f9
- f3
    - flags: bottom tested
    - merges: 1
    - normal:        -1       -0       -0
    - offset:       -0.5
    - center:   -0.5      0      0 
    - coplanar set(furthest p12):
      p12:      -0.5        0        0
      furthest distance=  0
    - vertices: p3(v8) p1(v4) p2(v3) p0(v1)
    - neighboring facets: f1 f2 f13 f10
    - ridges:
     - r4 tested simplicialtop simplicialbot
           vertices: p2(v3) p0(v1)
           between f1 and f3
     - r13 tested
           vertices: p3(v8) p2(v3)
           between f10 and f3
     - r14 tested
           vertices: p3(v8) p1(v4)
           between f3 and f13
     - r8 tested simplicialtop simplicialbot
           vertices: p1(v4) p0(v1)
           between f3 and f2
- f10
    - flags: top tested
    - merges: 1
    - normal:         0        1       -0
    - offset:       -0.5
    - center:      0    0.5      0 
    - coplanar set(furthest p11):
      p11:         0      0.5        0
      furthest distance=  0
    - vertices: p3(v8) p6(v6) p7(v5) p2(v3)
    - neighboring facets: f3 f1 f9 f13
    - ridges:
     - r2 tested simplicialbot
           vertices: p6(v6) p2(v3)
           between f1 and f10
     - r11 tested simplicialtop simplicialbot
           vertices: p6(v6) p7(v5)
           between f10 and f9
     - r16 tested
           vertices: p3(v8) p7(v5)
           between f13 and f10
     - r13 tested
           vertices: p3(v8) p2(v3)
           between f10 and f3
- f13
    - flags: bottom tested
    - merges: 1
    - normal:        -0       -0        1
    - offset:       -0.5
    - center:      0      0    0.5 
    - coplanar set(furthest p9):
      p9:         0        0      0.5
      furthest distance=  0
    - vertices: p3(v8) p5(v7) p7(v5) p1(v4)
    - neighboring facets: f10 f2 f9 f3
    - ridges:
     - r7 tested simplicialtop
           vertices: p5(v7) p1(v4)
           between f13 and f2
     - r14 tested
           vertices: p3(v8) p1(v4)
           between f3 and f13
     - r16 tested
           vertices: p3(v8) p7(v5)
           between f13 and f10
     - r10 tested simplicialbot
           vertices: p5(v7) p7(v5)
           between f9 and f13

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 84 distance computations.
rbox c d | qhull Qc p Tcv
3
14
  -0.5   -0.5   -0.5 
  -0.5   -0.5    0.5 
  -0.5    0.5   -0.5 
  -0.5    0.5    0.5 
   0.5   -0.5   -0.5 
   0.5   -0.5    0.5 
   0.5    0.5   -0.5 
   0.5    0.5    0.5 
     0      0   -0.5 
     0      0    0.5 
     0   -0.5      0 
     0    0.5      0 
  -0.5      0      0 
   0.5      0      0 

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 84 distance computations.
rbox 100 D3 | qhull QbB FO Tcv
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213865456  QbBound-unit-box 0.5  Tcheck-frequently  Tverify
  _pre-merge  _zero-centrum  _max-width  1  Error-roundoff 6.9e-16
  _one-merge 4.9e-15  _near-inside 2.4e-14  Visible-distance 1.4e-15
  U-max-coplanar 1.4e-15  Width-outside 2.8e-15  _wide-facet 8.3e-15

Convex hull of 100 points in 3-d:

  Number of vertices: 26
  Number of facets: 48

Statistics for: rbox 100 D3 | qhull QbB FO Tcv

  Number of points processed: 28
  Number of hyperplanes created: 109
  Number of distance tests for qhull: 1163
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 4800 distance computations.
rbox 1000 D2 B1e6 | qhull d Qbb FO Tcv
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213865456  delaunay  Qbbound-last  Tcheck-frequently  Tverify
  _pre-merge  _zero-centrum  Pgood  _max-width 2e+06  Error-roundoff 1.4e-09
  _one-merge 9.7e-09  _near-inside 4.9e-08  Visible-distance 2.8e-09
  U-max-coplanar 2.8e-09  Width-outside 5.5e-09  _wide-facet 1.7e-08

Delaunay triangulation by the convex hull of 1000 points in 3-d:

  Number of input sites: 1000
  Number of Delaunay regions: 1982

Statistics for: rbox 1000 D2 B1e6 | qhull d Qbb FO Tcv

  Number of points processed: 1000
  Number of hyperplanes created: 5457
  Number of facets in hull: 1996
  Number of distance tests for qhull: 27959
  CPU seconds to compute hull (after input): 0.036


qhull output completed.  Verifying that 1000 points are
below 4.2e-09 of the nearest facet.
rbox 10 D3 | qhull QbB p Tcv
3
9
-0.08928142660407055 -0.3194671263098747 0.3605569202297553 
-0.1534778158747162 0.03516440701453921    0.5 
-0.01663016790622804 0.3709299907861695 0.0764863283135003 
0.3932651765570926 0.4421392241401818 -0.09396622763110282 
0.199424728304684    0.5 0.06620718432588452 
-0.2331094527352667 0.3262436269787957 -0.128966098672764 
  -0.5 0.2819439085196089   -0.5 
0.4999999999999999 0.3760666748352666 0.1399187075693636 
0.4888102268053206   -0.5 -0.2153953634886358 

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D3 | qhull Qbb p Tcv
QH7040 qhull option warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'
3
9
-0.0222149361131852 -0.366434993563625 0.4072229792632261 
-0.06676722137887703 -0.1566931052661437 0.4732086509216659 
0.02820502736438535 0.04189077954915421 0.272798317696016 
0.3126723396709863 0.08400649026409401 0.1921386936513206 
0.1781470954214661 0.1182274414396169 0.2679341378370068 
-0.1220315663349177 0.01546165115708642 0.1755764518932639 
-0.3072535691850387 -0.01073880122111998      0 
0.3867462923626847 0.04492879989084675 0.3028150683084346 
0.3789805913148268 -0.4732086509216658 0.1346773760895938 

Output completed.  Verifying that all points are below 2e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv
3
9
-5.733970380575339 -0.366434993563625 17.14322461142018 
-6.400761988815288 -0.1566931052661437     20 
-4.97936018866004 0.04189077954915421 11.32346018178493 
-0.7218812392989191 0.08400649026409401 7.831392539952951 
-2.735252796494545 0.1182274414396169 11.11287098934976 
-7.227875597731384 0.01546165115708642 7.114348923589702 
   -10 -0.01073880122111998 -0.4870359524963758 
0.3867462923626847 0.04492879989084675 12.62300161615219 
0.2705209571204694 -0.4732086509216658 5.343669467959105 

Output completed.  Verifying that all points are below 7.5e-14 of
all facets.  Will make 140 distance computations.
rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv | qhull QbB p Tcv

Output completed.  Verifying that all points are below 7.5e-14 of
all facets.  Will make 140 distance computations.
3
9
-0.08928142660407051 -0.3194671263098747 0.3605569202297555 
-0.153477815874716 0.03516440701453921    0.5 
-0.01663016790622796 0.3709299907861695 0.07648632831350011 
0.3932651765570927 0.4421392241401818 -0.09396622763110274 
0.1994247283046841    0.5 0.06620718432588446 
-0.2331094527352668 0.3262436269787957 -0.1289660986727639 
  -0.5 0.2819439085196089 -0.4999999999999999 
   0.5 0.3760666748352666 0.1399187075693635 
0.4888102268053207   -0.5 -0.2153953634886357 

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 126 distance computations.
rbox 10 D3 | qhull Qb1:0B1:0 d Tcv Q8

Delaunay triangulation by the convex hull of 10 points in 3-d:

  Number of input sites: 10
  Number of Delaunay regions: 14

Statistics for: rbox 10 D3 | qhull Qb1:0B1:0 d Tcv Q8

  Number of points processed: 10
  Number of hyperplanes created: 31
  Number of facets in hull: 16
  Number of distance tests for qhull: 61
  CPU seconds to compute hull (after input):  0

QH7077 qhull input warning: no outer plane check ('Q5') or no processing of near-inside points ('Q8').  Verify may report that a point is outside of a facet.

Output completed.  Verifying that all points are below 2e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D3 | qhull Qb1:0B1:0B2:0 d Tcv Q8

Delaunay triangulation by the convex hull of 10 points in 3-d:

  Number of input sites: 10
  Number of Delaunay regions: 14

Statistics for: rbox 10 D3 | qhull Qb1:0B1:0B2:0 d Tcv Q8

  Number of points processed: 10
  Number of hyperplanes created: 31
  Number of facets in hull: 16
  Number of distance tests for qhull: 61
  CPU seconds to compute hull (after input):  0

QH7077 qhull input warning: no outer plane check ('Q5') or no processing of near-inside points ('Q8').  Verify may report that a point is outside of a facet.

Output completed.  Verifying that all points are below 2e-15 of
all facets.  Will make 140 distance computations.
rbox 10 D3 | qhull Qb1:0 d Tcv 

Delaunay triangulation by the convex hull of 10 points in 4-d:

  Number of input sites: 10
  Number of Delaunay regions: 18

Statistics for: rbox 10 D3 | qhull Qb1:0 d Tcv

  Number of points processed: 10
  Number of hyperplanes created: 43
  Number of facets in hull: 27
  Number of distance tests for qhull: 66
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 2.9e-15 of
all facets.  Will make 180 distance computations.
rbox 10 D3 | qhull Qb1:0B1:0  Tcv

Convex hull of 10 points in 2-d:

  Number of vertices: 4
  Number of facets: 4

Statistics for: rbox 10 D3 | qhull Qb1:0B1:0 Tcv

  Number of points processed: 4
  Number of hyperplanes created: 6
  Number of distance tests for qhull: 48
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 1.3e-15 of
all facets.  Will make 40 distance computations.
echo "== next command will error ${d:-`date`} =="
== next command will error Fri, Jul 24, 2020 10:27:36 PM ==
rbox 10 D2 | qhull Qb1:1B1:1 Tcv
QH6154 Qhull precision error: Initial simplex is flat (facet 1 is coplanar with the interior point)

While executing: rbox 10 D2 | qhull Qb1:1B1:1 Tcv
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213865456  Qbound-dim-low 1  1  QBound-dim-high 1  1
  Tcheck-frequently  Tverify  _pre-merge  _zero-centrum  _max-width 0.81
  Error-roundoff 8.6e-16  _one-merge 4.3e-15  _near-inside 2.1e-14
  Visible-distance 1.7e-15  U-max-coplanar 1.7e-15  Width-outside 3.4e-15
  _wide-facet 1e-14  _maxoutside 5.1e-15

The input to qhull appears to be less than 2 dimensional, or a
computation has overflowed.

Qhull could not construct a clearly convex simplex from points:
- p0(v3): -0.022     1
- p4(v2):  0.38     1
- p1(v1): -0.43     1

The center point is coplanar with a facet, or a vertex is coplanar
with a neighboring facet.  The maximum round off error for
computing distances is 8.6e-16.  The center point, facets and distances
to the center point are as follows:

center point -0.02391        1

facet p4 p1 distance=    0
facet p0 p1 distance=    0
facet p0 p4 distance=    0

These points either have a maximum or minimum x-coordinate, or
they maximize the determinant for k coordinates.  Trial points
are first selected from points that maximize a coordinate.

The min and max coordinates for each dimension are:
  0:   -0.4285     0.379  difference= 0.8076
  1:         1         1  difference=    0

If the input should be full dimensional, you have several options that
may determine an initial simplex:
  - use 'QJ'  to joggle the input and make it full dimensional
  - use 'QbB' to scale the points to the unit cube
  - use 'QR0' to randomly rotate the input for different maximum points
  - use 'Qs'  to search all points for the initial simplex
  - use 'En'  to specify a maximum roundoff error less than 8.6e-16.
  - trace execution with 'T3' to see the determinant for each point.

If the input is lower dimensional:
  - use 'QJ' to joggle the input and make it full dimensional
  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should
    pick the coordinate with the least range.  The hull will have the
    correct topology.
  - determine the flat containing the points, rotate the points
    into a coordinate plane, and delete the other coordinates.
  - add one or more points to make the input full dimensional.
rbox 200 L20 D2 t | qhull FO Tcv C-0
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213865456  Tcheck-frequently  Tverify  Centrum-premerge-  0
  _zero-centrum  _max-width 0.98  Error-roundoff 3.4e-16  _one-merge 1.7e-15
  _near-inside 8.5e-15  Visible-distance 6.8e-16  U-max-coplanar 6.8e-16
  Width-outside 1.4e-15  _wide-facet 4.1e-15

Convex hull of 200 points in 2-d:

  Number of vertices: 200
  Number of facets: 200

Statistics for: rbox 200 L20 D2 t1595644056 | qhull FO Tcv C-0

  Number of points processed: 200
  Number of hyperplanes created: 397
  Number of distance tests for qhull: 2118
  CPU seconds to compute hull (after input): 0.002


Output completed.  Verifying that all points are below 1e-15 of
all facets.  Will make 40000 distance computations.
rbox 1000 L20 t | qhull FO Tcv C-0
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213865456  Tcheck-frequently  Tverify  Centrum-premerge-  0
  _zero-centrum  _max-width  1  Error-roundoff 6.9e-16  _one-merge 4.8e-15
  _near-inside 2.4e-14  Visible-distance 1.4e-15  U-max-coplanar 1.4e-15
  Width-outside 2.8e-15  _wide-facet 8.3e-15

Convex hull of 1000 points in 3-d:

  Number of vertices: 49
  Number of facets: 94

Statistics for: rbox 1000 L20 t1595644056 | qhull FO Tcv C-0

  Number of points processed: 63
  Number of hyperplanes created: 272
  Number of distance tests for qhull: 13669
  CPU seconds to compute hull (after input): 0.001


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 94000 distance computations.
rbox 200 L20 D4 t | qhull FO Tcv C-0
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213865456  Tcheck-frequently  Tverify  Centrum-premerge-  0
  _zero-centrum  _max-width 0.99  Error-roundoff 1e-15  _one-merge 9.1e-15
  _near-inside 4.5e-14  Visible-distance 6e-15  U-max-coplanar 6e-15
  Width-outside 1.2e-14  _wide-facet 3.6e-14

Convex hull of 200 points in 4-d:

  Number of vertices: 55
  Number of facets: 261

Statistics for: rbox 200 L20 D4 t1595644056 | qhull FO Tcv C-0

  Number of points processed: 67
  Number of hyperplanes created: 823
  Number of distance tests for qhull: 6036
  CPU seconds to compute hull (after input): 0.002


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 52200 distance computations.
rbox 200 L20 D5 t | qhull FO Tcv Qx
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213865456  Tcheck-frequently  Tverify  Qxact-merge  _zero-centrum
  _max-width 0.99  Error-roundoff 1.4e-15  _one-merge 1.5e-14
  _near-inside 7.5e-14  Visible-distance 8.2e-15  U-max-coplanar 8.2e-15
  Width-outside 1.6e-14  _wide-facet 4.9e-14

Convex hull of 200 points in 5-d:

  Number of vertices: 90
  Number of facets: 1272

Statistics for: rbox 200 L20 D5 t1595644056 | qhull FO Tcv Qx

  Number of points processed: 111
  Number of hyperplanes created: 3928
  Number of distance tests for qhull: 17297
  CPU seconds to compute hull (after input): 0.013

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 254400 distance computations.
rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu Q0
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213882263  delaunay  Tcheck-frequently  Tverify  QupperDelaunay
  Q0-no-premerge  Pgood  _max-width  1  Error-roundoff 6.9e-16
  Visible-distance 6.9e-16  U-max-coplanar 6.9e-16  Width-outside 1.4e-15
  _wide-facet 4.2e-15

Furthest-site Delaunay triangulation by the convex hull of 1000 points in 3-d:

  Number of input sites: 1000
  Number of Delaunay regions: 259

Statistics for: rbox 1000 W1e-3 s D2 t1595644057 | qhull d FO Tcv Qu Q0

  Number of points processed: 1000
  Number of hyperplanes created: 4694
  Number of facets in hull: 1996
  Number of distance tests for qhull: 27601
  CPU seconds to compute hull (after input): 0.037


Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 259000 distance computations.
rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu C-0
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213882263  delaunay  Tcheck-frequently  Tverify  QupperDelaunay
  Centrum-premerge-  0  _zero-centrum  Pgood  _max-width  1
  Error-roundoff 6.9e-16  _one-merge 4.9e-15  _near-inside 2.4e-14
  Visible-distance 1.4e-15  U-max-coplanar 1.4e-15  Width-outside 2.8e-15
  _wide-facet 8.3e-15

Furthest-site Delaunay triangulation by the convex hull of 1000 points in 3-d:

  Number of input sites: 1000
  Number of Delaunay regions: 259

Statistics for: rbox 1000 W1e-3 s D2 t1595644057 | qhull d FO Tcv Qu C-0

  Number of points processed: 1000
  Number of hyperplanes created: 4694
  Number of facets in hull: 1996
  Number of distance tests for qhull: 27601
  CPU seconds to compute hull (after input): 0.035


Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 259000 distance computations.

set +v
=== check joggle and TRn Fri, Jul 24, 2020 10:27:37 PM
rbox 100 W0 | qhull QJ1e-14 Qc TR100 Tv

Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.
Convex hull of 100 points in 3-d:

  Number of vertices: 15
  Number of coplanar points: 4
  Number of facets: 25

Statistics for: rbox 100 W0 | qhull QJ1e-14 Qc TR100 Tv

  Number of points processed: 15
  Number of hyperplanes created: 11218
  Number of distance tests for qhull: 119030
  CPU seconds to compute hull (after input): 0.008
  Percentage of runs with precision errors: 100.0


precision problems (corrected unless 'Q0' or an error)
    100 coplanar horizon facets for new vertices
    400 coplanar points during partitioning
rbox 100 W0 | qhull QJ1e-13 Qc TR100 Tv

Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.
Convex hull of 100 points in 3-d:

  Number of vertices: 28
  Number of coplanar points: 12
  Number of facets: 50

Statistics for: rbox 100 W0 | qhull QJ1e-13 Qc TR100 Tv

  Number of points processed: 28
  Number of hyperplanes created: 24747
  Number of distance tests for qhull: 195826
  CPU seconds to compute hull (after input): 0.016
  Percentage of runs with precision errors: 63.0


precision problems (corrected unless 'Q0' or an error)
     10 coplanar half ridges in output
     53 coplanar horizon facets for new vertices
    119 coplanar points during partitioning
rbox 100 W0 | qhull QJ1e-12 Qc TR100 Tv

Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.
Convex hull of 100 points in 3-d:

  Number of vertices: 40
  Number of coplanar points: 16
  Number of facets: 75

Statistics for: rbox 100 W0 | qhull QJ1e-12 Qc TR100 Tv

  Number of points processed: 40
  Number of hyperplanes created: 29152
  Number of distance tests for qhull: 216487
  CPU seconds to compute hull (after input): 0.017
  Percentage of runs with precision errors:  8.0


precision problems (corrected unless 'Q0' or an error)
      2 coplanar half ridges in output
      6 coplanar horizon facets for new vertices
     17 coplanar points during partitioning
rbox 100 W0 | qhull QJ1e-11 Qc TR100 Tv

Convex hull of 100 points in 3-d:

  Number of vertices: 66
  Number of coplanar points: 34
  Number of facets: 128

Statistics for: rbox 100 W0 | qhull QJ1e-11 Qc TR100 Tv

  Number of points processed: 75
  Number of hyperplanes created: 29577
  Number of distance tests for qhull: 218409
  CPU seconds to compute hull (after input): 0.017
  Percentage of runs with precision errors:  0.0


precision problems (corrected unless 'Q0' or an error)
      3 coplanar points during partitioning

Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 12800 distance computations.
rbox 100 W0 | qhull QJ1e-10 Qc TR100 Tv

Convex hull of 100 points in 3-d:

  Number of vertices: 66
  Number of coplanar points: 34
  Number of facets: 128

Statistics for: rbox 100 W0 | qhull QJ1e-10 Qc TR100 Tv

  Number of points processed: 75
  Number of hyperplanes created: 29583
  Number of distance tests for qhull: 218315
  CPU seconds to compute hull (after input): 0.018
  Percentage of runs with precision errors:  0.0


Output completed.  Verifying that all points are below 2.1e-15 of
all facets.  Will make 12800 distance computations.
rbox 100 | qhull d QJ Qb0:1e4 QB0:1e5 Qb1:1e4 QB1:1e6 Qb2:1e5 QB2:1e7 FO Tv
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213882263  delaunay  Qbound-dim-low 0 1e+04  QBound-dim-high 0 1e+05
  Qbound-dim-low 1 1e+04  QBound-dim-high 1 1e+06  Qbound-dim-low 2 1e+05
  QBound-dim-high 2 1e+07  Tverify  Pgood  _run 1  QJoggle 6.7e+03
  _joggle-seed 16807  _max-width 1e+14  Error-roundoff 0.11
  Visible-distance 0.11  U-max-coplanar 0.11  Width-outside 0.23
  _wide-facet 0.68

Delaunay triangulation by the convex hull of 100 points in 4-d:

  Number of input sites: 100
  Number of Delaunay regions: 488

Statistics for: rbox 100 | qhull d QJ Qb0:1e4 QB0:1e5 Qb1:1e4 QB1:1e6 Qb2:1e5 QB2:1e7 FO Tv

  Number of points processed: 100
  Number of hyperplanes created: 1477
  Number of facets in hull: 560
  Number of distance tests for qhull: 3418
  CPU seconds to compute hull (after input): 0.001
  Input joggled by: 6.7e+03


Output completed.  Verifying that all points are below 0.34 of
all facets.  Will make 48800 distance computations.

set +v
=== check precision options Fri, Jul 24, 2020 10:27:37 PM
rbox 100 D3 s | qhull E0.01 Qx Tcv FO
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213882263  Distance-roundoff 0.01  Qxact-merge  Tcheck-frequently
  Tverify  _zero-centrum  _max-width 0.98  _one-merge 0.07  _near-inside 0.35
  Visible-distance 0.02  U-max-coplanar 0.02  Width-outside 0.04
  _wide-facet 0.12

Convex hull of 100 points in 3-d:

  Number of vertices: 46
  Number of facets: 41
  Number of non-simplicial facets: 29

Statistics for: rbox 100 D3 s | qhull E0.01 Qx Tcv FO

  Number of points processed: 46
  Number of hyperplanes created: 162
  Number of distance tests for qhull: 3834
  Number of distance tests for merging: 1887
  Number of distance tests for checking: 1989
  Number of merged facets: 60
  CPU seconds to compute hull (after input): 0.001
  Maximum distance of point above facet: 0.048 (0.6x)
  Maximum distance of vertex below facet: -0.072 (0.9x)

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 4100 distance computations.
rbox 100 D3 W1e-1 | qhull W1e-3 Tcv

Convex hull of 100 points in 3-d:

  Number of vertices: 33
  Number of facets: 62

Statistics for: rbox 100 D3 W1e-1 | qhull W1e-3 Tcv

  Number of points processed: 37
  Number of hyperplanes created: 169
  Number of distance tests for qhull: 1565
  CPU seconds to compute hull (after input):  0
  Maximum distance of point above facet: 0.00084


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 6200 distance computations.
rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Q0

Convex hull of 100 points in 3-d:

  Number of vertices: 28
  Number of facets: 52

Statistics for: rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Q0

  Number of points processed: 29
  Number of hyperplanes created: 127
  Number of distance tests for qhull: 1691
  CPU seconds to compute hull (after input):  0


precision problems (corrected unless 'Q0' or an error)
     23 coplanar points during partitioning

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 5200 distance computations.
rbox 100 D3 W1e-1 | qhull W1e-2 Tcv 

Convex hull of 100 points in 3-d:

  Number of vertices: 29
  Number of facets: 54

Statistics for: rbox 100 D3 W1e-1 | qhull W1e-2 Tcv

  Number of points processed: 30
  Number of hyperplanes created: 131
  Number of distance tests for qhull: 1720
  CPU seconds to compute hull (after input):  0
  Maximum distance of point above facet: 0.0057


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 5400 distance computations.
rbox 100 D3 W1e-1 | qhull W1e-1 Tcv

Convex hull of 100 points in 3-d:

  Number of vertices: 13
  Number of facets: 22

Statistics for: rbox 100 D3 W1e-1 | qhull W1e-1 Tcv

  Number of points processed: 13
  Number of hyperplanes created: 45
  Number of distance tests for qhull: 2377
  CPU seconds to compute hull (after input):  0
  Maximum distance of point above facet: 0.098


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 2200 distance computations.
rbox 15 D2 P0 P1e-14,1e-14 | qhull d Quc Tcv

Furthest-site Delaunay triangulation by the convex hull of 17 points in 3-d:

  Number of input sites: 17
  Number of Delaunay regions: 5

Statistics for: rbox 15 D2 P0 P1e-14,1e-14 | qhull d Quc Tcv

  Number of points processed: 17
  Number of hyperplanes created: 63
  Number of facets in hull: 28
  Number of distance tests for qhull: 141
  Number of distance tests for merging: 474
  Number of distance tests for checking: 236
  Number of merged facets: 7
  CPU seconds to compute hull (after input):  0
  Maximum distance of point above facet: 1.6e-15 (0.3x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 85 distance computations.
rbox 15 D3 P0 P1e-12,1e-14,1e-14 | qhull d Qcu Tcv

Furthest-site Delaunay triangulation by the convex hull of 17 points in 4-d:

  Number of input sites: 17
  Number of Delaunay regions: 14

Statistics for: rbox 15 D3 P0 P1e-12,1e-14,1e-14 | qhull d Qcu Tcv

  Number of points processed: 17
  Number of hyperplanes created: 123
  Number of facets in hull: 60
  Number of distance tests for qhull: 224
  CPU seconds to compute hull (after input):  0


Output completed.  Verifying that all points are below 2.8e-15 of
all facets.  Will make 238 distance computations.
rbox 1000 s D3 | qhull C-0.01 Tcv Qc

Convex hull of 1000 points in 3-d:

  Number of vertices: 108
  Number of coplanar points: 892
  Number of facets: 95
  Number of non-simplicial facets: 78

Statistics for: rbox 1000 s D3 | qhull C-0.01 Tcv Qc

  Number of points processed: 112
  Number of hyperplanes created: 464
  Number of distance tests for qhull: 62162
  Number of distance tests for merging: 6682
  Number of distance tests for checking: 24376
  Number of merged facets: 264
  CPU seconds to compute hull (after input): 0.007
  Maximum distance of point above facet: 0.021 (0.7x)
  Maximum distance of vertex below facet: -0.029 (1.0x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 95000 distance computations.
rbox 1000 s D3 | qhull C-0.01 V0 Qc Tcv

Convex hull of 1000 points in 3-d:

  Number of vertices: 137
  Number of coplanar points: 863
  Number of facets: 87
  Number of non-simplicial facets: 82

Statistics for: rbox 1000 s D3 | qhull C-0.01 V0 Qc Tcv

  Number of points processed: 466
  Number of hyperplanes created: 2572
  Number of distance tests for qhull: 232429
  Number of distance tests for merging: 47390
  Number of distance tests for checking: 38513
  Number of merged facets: 1818
  CPU seconds to compute hull (after input): 0.046
  Maximum distance of point above facet: 0.026 (0.9x)
  Maximum distance of vertex below facet: -0.075 (2.5x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 87000 distance computations.
rbox 1000 s D3 | qhull C-0.01 U0 Qc Tcv

Convex hull of 1000 points in 3-d:

  Number of vertices: 108
  Number of coplanar points: 892
  Number of facets: 97
  Number of non-simplicial facets: 77

Statistics for: rbox 1000 s D3 | qhull C-0.01 U0 Qc Tcv

  Number of points processed: 112
  Number of hyperplanes created: 505
  Number of distance tests for qhull: 62212
  Number of distance tests for merging: 7315
  Number of distance tests for checking: 24575
  Number of merged facets: 260
  CPU seconds to compute hull (after input): 0.006
  Maximum distance of point above facet: 0.021 (0.7x)
  Maximum distance of vertex below facet: -0.029 (1.0x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 97000 distance computations.
rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv

Convex hull of 1000 points in 3-d:

  Number of vertices: 87
  Number of coplanar points: 913
  Number of facets: 88
  Number of non-simplicial facets: 56

Statistics for: rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv

  Number of points processed: 90
  Number of hyperplanes created: 457
  Number of distance tests for qhull: 46341
  Number of distance tests for merging: 5761
  Number of distance tests for checking: 21602
  Number of merged facets: 192
  CPU seconds to compute hull (after input): 0.005
  Maximum distance of point above facet: 0.032 (1.1x)
  Maximum distance of vertex below facet: -0.041 (1.4x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 88000 distance computations.
rbox 1000 s D3 | qhull C-0.01 Qcm Tcv

Convex hull of 1000 points in 3-d:

  Number of vertices: 101
  Number of coplanar points: 899
  Number of facets: 95
  Number of non-simplicial facets: 69

Statistics for: rbox 1000 s D3 | qhull C-0.01 Qcm Tcv

  Number of points processed: 104
  Number of hyperplanes created: 433
  Number of distance tests for qhull: 59136
  Number of distance tests for merging: 6024
  Number of distance tests for checking: 24116
  Number of merged facets: 232
  CPU seconds to compute hull (after input): 0.006
  Maximum distance of point above facet: 0.023 (0.8x)
  Maximum distance of vertex below facet: -0.031 (1.0x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 95000 distance computations.
rbox 1000 s D3 | qhull C-0.01 Q1 FO Tcv Qc
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213899070  Centrum-premerge- 0.01  Q1-angle-merge  Tcheck-frequently
  Tverify  Qcoplanar-keep  _max-width  1  Error-roundoff 6.9e-16
  _one-merge 0.03  _near-inside 0.15  Visible-distance 0.01
  U-max-coplanar 0.01  Width-outside 0.02  _wide-facet 0.06

Convex hull of 1000 points in 3-d:

  Number of vertices: 107
  Number of coplanar points: 893
  Number of facets: 97
  Number of non-simplicial facets: 80

Statistics for: rbox 1000 s D3 | qhull C-0.01 Q1 FO Tcv Qc

  Number of points processed: 111
  Number of hyperplanes created: 450
  Number of distance tests for qhull: 61776
  Number of distance tests for merging: 6387
  Number of distance tests for checking: 24594
  Number of merged facets: 253
  CPU seconds to compute hull (after input): 0.006
  Maximum distance of point above facet: 0.02 (0.7x)
  Maximum distance of vertex below facet: -0.035 (1.2x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 97000 distance computations.
rbox 1000 s D3 | qhull C-0.01 Q2 FO Tcv Qc
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213899070  Centrum-premerge- 0.01  Q2-no-merge-independent
  Tcheck-frequently  Tverify  Qcoplanar-keep  _max-width  1
  Error-roundoff 6.9e-16  _one-merge 0.03  _near-inside 0.15
  Visible-distance 0.01  U-max-coplanar 0.01  Width-outside 0.02
  _wide-facet 0.06

Convex hull of 1000 points in 3-d:

  Number of vertices: 106
  Number of coplanar points: 894
  Number of facets: 92
  Number of non-simplicial facets: 74

Statistics for: rbox 1000 s D3 | qhull C-0.01 Q2 FO Tcv Qc

  Number of points processed: 110
  Number of hyperplanes created: 451
  Number of distance tests for qhull: 60312
  Number of distance tests for merging: 6396
  Number of distance tests for checking: 23893
  Number of merged facets: 260
  CPU seconds to compute hull (after input): 0.007
  Maximum distance of point above facet: 0.023 (0.8x)
  Maximum distance of vertex below facet: -0.049 (1.6x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 92000 distance computations.
rbox 1000 s D3 | qhull C-0.01 Q3 FO Tcv Qc
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213899070  Centrum-premerge- 0.01  Q3-no-merge-vertices
  Tcheck-frequently  Tverify  Qcoplanar-keep  _max-width  1
  Error-roundoff 6.9e-16  _one-merge 0.03  _near-inside 0.15
  Visible-distance 0.01  U-max-coplanar 0.01  Width-outside 0.02
  _wide-facet 0.06

Convex hull of 1000 points in 3-d:

  Number of vertices: 112
  Number of coplanar points: 888
  Number of facets: 94
  Number of non-simplicial facets: 78

Statistics for: rbox 1000 s D3 | qhull C-0.01 Q3 FO Tcv Qc

  Number of points processed: 112
  Number of hyperplanes created: 468
  Number of distance tests for qhull: 61911
  Number of distance tests for merging: 6879
  Number of distance tests for checking: 24243
  Number of merged facets: 268
  CPU seconds to compute hull (after input): 0.007
  Maximum distance of point above facet: 0.021 (0.7x)
  Maximum distance of vertex below facet: -0.03 (1.0x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 94000 distance computations.
rbox 1000 s D3 | qhull C-0.01 Q4 FO Tcv Qc
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213899070  Centrum-premerge- 0.01  Q4-avoid-old-into-new
  Tcheck-frequently  Tverify  Qcoplanar-keep  _max-width  1
  Error-roundoff 6.9e-16  _one-merge 0.03  _near-inside 0.15
  Visible-distance 0.01  U-max-coplanar 0.01  Width-outside 0.02
  _wide-facet 0.06

Convex hull of 1000 points in 3-d:

  Number of vertices: 108
  Number of coplanar points: 892
  Number of facets: 95
  Number of non-simplicial facets: 78

Statistics for: rbox 1000 s D3 | qhull C-0.01 Q4 FO Tcv Qc

  Number of points processed: 112
  Number of hyperplanes created: 464
  Number of distance tests for qhull: 62162
  Number of distance tests for merging: 6682
  Number of distance tests for checking: 24376
  Number of merged facets: 264
  CPU seconds to compute hull (after input): 0.007
  Maximum distance of point above facet: 0.021 (0.7x)
  Maximum distance of vertex below facet: -0.029 (1.0x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 95000 distance computations.
echo === this may generate an error ${d:-`date`}
=== this may generate an error Fri, Jul 24, 2020 10:27:38 PM
rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv 
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213899070  Centrum-premerge- 0.01  Q5-no-check-outer
  Tcheck-frequently  Tverify  _max-width  1  Error-roundoff 6.9e-16
  _one-merge 0.03  Visible-distance 0.01  U-max-coplanar 0.01
  Width-outside 0.02  _wide-facet 0.06

Convex hull of 1000 points in 3-d:

  Number of vertices: 108
  Number of facets: 95
  Number of non-simplicial facets: 78

Statistics for: rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv

  Number of points processed: 112
  Number of hyperplanes created: 464
  Number of distance tests for qhull: 35756
  Number of distance tests for merging: 6682
  Number of distance tests for checking: 2036
  Number of merged facets: 264
  CPU seconds to compute hull (after input): 0.005
  Maximum distance of point above facet: 0.022 (0.7x)
  Maximum distance of vertex below facet: -0.031 (1.0x)

QH7077 qhull input warning: no outer plane check ('Q5') or no processing of near-inside points ('Q8').  Verify may report that a point is outside of a facet.

Output completed.  Verifying that all points are below 0.022 of
all facets.  Will make 95000 distance computations.
echo === this should generate an error ${d:-`date`}
=== this should generate an error Fri, Jul 24, 2020 10:27:38 PM
rbox 1000 s D3 | qhull C-0.01 Q6 FO Po Tcv Qc
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213899070  Centrum-premerge- 0.01  Q6-no-concave-merge  Poutput-forced
  Tcheck-frequently  Tverify  Qcoplanar-keep  _max-width  1
  Error-roundoff 6.9e-16  _one-merge 0.03  _near-inside 0.15
  Visible-distance 0.01  U-max-coplanar 0.01  Width-outside 0.02
  _wide-facet 0.06
QH6117 qhull precision error: f328 is concave to f329.  Centrum of f328 is 0.001027 above f329
QH6117 qhull precision error: f329 is concave to f328.  Centrum of f329 is 0.004134 above f328
QH6117 qhull precision error: f482 is concave to f484.  Centrum of f482 is 0.0001795 above f484
QH6117 qhull precision error: f484 is concave to f482.  Centrum of f484 is 6.818e-05 above f482

Convex hull of 1000 points in 3-d:

  Number of vertices: 115
  Number of coplanar points: 885
  Number of facets: 184
  Number of non-simplicial facets: 40

Statistics for: rbox 1000 s D3 | qhull C-0.01 Q6 FO Po Tcv Qc

  Number of points processed: 115
  Number of hyperplanes created: 455
  Number of distance tests for qhull: 52081
  Number of distance tests for merging: 1190
  Number of distance tests for checking: 28981
  Number of merged facets: 88
  CPU seconds to compute hull (after input): 0.005
  Maximum distance of point above facet: 0.02 (0.7x)
  Maximum distance of vertex below facet: -0.009 (0.3x)

rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213899070  Centrum-premerge- 0.01  Q7-no-breadth-first
  Tcheck-frequently  Tverify  Qcoplanar-keep  _max-width  1
  Error-roundoff 6.9e-16  _one-merge 0.03  _near-inside 0.15
  Visible-distance 0.01  U-max-coplanar 0.01  Width-outside 0.02
  _wide-facet 0.06

Convex hull of 1000 points in 3-d:

  Number of vertices: 108
  Number of coplanar points: 892
  Number of facets: 99
  Number of non-simplicial facets: 77

Statistics for: rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc

  Number of points processed: 110
  Number of hyperplanes created: 449
  Number of distance tests for qhull: 55287
  Number of distance tests for merging: 6050
  Number of distance tests for checking: 22232
  Number of merged facets: 242
  CPU seconds to compute hull (after input): 0.006
  Maximum distance of point above facet: 0.021 (0.7x)
  Maximum distance of vertex below facet: -0.031 (1.0x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 99000 distance computations.
rbox 1000 s D3 | qhull C-0.01 Qx Tcv Qc

Convex hull of 1000 points in 3-d:

  Number of vertices: 115
  Number of coplanar points: 885
  Number of facets: 101
  Number of non-simplicial facets: 76

Statistics for: rbox 1000 s D3 | qhull C-0.01 Qx Tcv Qc

  Number of points processed: 115
  Number of hyperplanes created: 455
  Number of distance tests for qhull: 89505
  Number of distance tests for merging: 5154
  Number of distance tests for checking: 19846
  Number of merged facets: 171
  CPU seconds to compute hull (after input): 0.006
  Maximum distance of point above facet: 0.02 (0.7x)
  Maximum distance of vertex below facet: -0.034 (1.1x)

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 101000 distance computations.
echo === this may generate an error e.g., t1263080158 ${d:-`date`}
=== this may generate an error e.g., t1263080158 Fri, Jul 24, 2020 10:27:38 PM
rbox 100 s D3 t | qhull R1e-3 Tcv Qc

Convex hull of 100 points in 3-d:

  Number of vertices: 99
  Number of coplanar points: 1
  Number of facets: 173
  Number of non-simplicial facets: 19

Statistics for: rbox 100 s D3 t1595644058 | qhull R1e-3 Tcv Qc

  Number of points processed: 100
  Number of hyperplanes created: 471
  Number of distance tests for qhull: 1627
  Number of distance tests for merging: 2780
  Number of distance tests for checking: 1528
  Number of merged facets: 33
  CPU seconds to compute hull (after input): 0.002
  Maximum distance of point above facet: 0.0017 (0.4x)
  Maximum distance of vertex below facet: -0.0062 (1.6x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 17300 distance computations.
rbox 100 s D3 t | qhull R1e-2 Tcv Qc

Convex hull of 100 points in 3-d:

  Number of vertices: 59
  Number of coplanar points: 41
  Number of facets: 57
  Number of non-simplicial facets: 34

Statistics for: rbox 100 s D3 t1595644059 | qhull R1e-2 Tcv Qc

  Number of points processed: 61
  Number of hyperplanes created: 269
  Number of distance tests for qhull: 3527
  Number of distance tests for merging: 3559
  Number of distance tests for checking: 2604
  Number of merged facets: 120
  CPU seconds to compute hull (after input): 0.002
  Maximum distance of point above facet: 0.034 (0.8x)
  Maximum distance of vertex below facet: -0.061 (1.5x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 5700 distance computations.
rbox 500 s D3 t | qhull R0.05 A-1 Tcv Qc

Convex hull of 500 points in 3-d:

  Number of vertices: 20
  Number of coplanar points: 480
  Number of facets: 15
  Number of non-simplicial facets: 13

Statistics for: rbox 500 s D3 t1595644059 | qhull R0.05 A-1 Tcv Qc

  Number of points processed: 24
  Number of hyperplanes created: 76
  Number of distance tests for qhull: 20339
  Number of distance tests for merging: 1188
  Number of distance tests for checking: 6863
  Number of merged facets: 49
  CPU seconds to compute hull (after input): 0.002
  Maximum distance of point above facet: 0.14 (0.2x)
  Maximum distance of vertex below facet: -0.24 (0.4x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 7500 distance computations.
rbox 100 W0 D3 t | qhull R1e-3 Tcv Qc

Convex hull of 100 points in 3-d:

  Number of vertices: 36
  Number of coplanar points: 64
  Number of facets: 46
  Number of non-simplicial facets: 7

Statistics for: rbox 100 W0 D3 t1595644059 | qhull R1e-3 Tcv Qc

  Number of points processed: 48
  Number of hyperplanes created: 160
  Number of distance tests for qhull: 1898
  Number of distance tests for merging: 1433
  Number of distance tests for checking: 1387
  Number of merged facets: 49
  CPU seconds to compute hull (after input): 0.001
  Maximum distance of point above facet: 0.0018 (0.5x)
  Maximum distance of vertex below facet: -0.0077 (1.9x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 4600 distance computations.
rbox 100 W0 D3 t | qhull R1e-3 Qx Tcv Qc

Convex hull of 100 points in 3-d:

  Number of vertices: 35
  Number of coplanar points: 65
  Number of facets: 46
  Number of non-simplicial facets: 7

Statistics for: rbox 100 W0 D3 t1595644059 | qhull R1e-3 Qx Tcv Qc

  Number of points processed: 48
  Number of hyperplanes created: 157
  Number of distance tests for qhull: 2121
  Number of distance tests for merging: 1562
  Number of distance tests for checking: 1086
  Number of merged facets: 46
  CPU seconds to compute hull (after input): 0.001
  Maximum distance of point above facet: 0.0018 (0.4x)
  Maximum distance of vertex below facet: -0.0041 (1.0x)

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 4600 distance computations.
rbox 100 W0 D3 t | qhull R1e-2 Tcv Qc

Convex hull of 100 points in 3-d:

  Number of vertices: 24
  Number of coplanar points: 76
  Number of facets: 25
  Number of non-simplicial facets: 8

Statistics for: rbox 100 W0 D3 t1595644059 | qhull R1e-2 Tcv Qc

  Number of points processed: 32
  Number of hyperplanes created: 105
  Number of distance tests for qhull: 2303
  Number of distance tests for merging: 1290
  Number of distance tests for checking: 1263
  Number of merged facets: 47
  CPU seconds to compute hull (after input): 0.001
  Maximum distance of point above facet: 0.026 (0.6x)
  Maximum distance of vertex below facet: -0.08 (2.0x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 2500 distance computations.
rbox 100 W0 D3 t | qhull R1e-2 Qx Tcv Qc

Convex hull of 100 points in 3-d:

  Number of vertices: 25
  Number of coplanar points: 75
  Number of facets: 26
  Number of non-simplicial facets: 11

Statistics for: rbox 100 W0 D3 t1595644059 | qhull R1e-2 Qx Tcv Qc

  Number of points processed: 32
  Number of hyperplanes created: 106
  Number of distance tests for qhull: 2604
  Number of distance tests for merging: 1089
  Number of distance tests for checking: 1026
  Number of merged facets: 37
  CPU seconds to compute hull (after input):  0
  Maximum distance of point above facet: 0.026 (0.7x)
  Maximum distance of vertex below facet: -0.051 (1.3x)

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 2600 distance computations.
rbox 500 W0 D3 t | qhull R0.05 A-1 Tcv Qc

Convex hull of 500 points in 3-d:

  Number of vertices: 8
  Number of coplanar points: 492
  Number of facets: 6
  Number of non-simplicial facets: 6

Statistics for: rbox 500 W0 D3 t1595644059 | qhull R0.05 A-1 Tcv Qc

  Number of points processed: 17
  Number of hyperplanes created: 48
  Number of distance tests for qhull: 16359
  Number of distance tests for merging: 670
  Number of distance tests for checking: 3635
  Number of merged facets: 33
  CPU seconds to compute hull (after input): 0.001
  Maximum distance of point above facet: 0.11 (0.2x)
  Maximum distance of vertex below facet: -0.2 (0.3x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 3000 distance computations.
rbox 500 W0 D3 t | qhull R0.05 Qx Tcv Qc

Convex hull of 500 points in 3-d:

  Number of vertices: 8
  Number of coplanar points: 492
  Number of facets: 6
  Number of non-simplicial facets: 6

Statistics for: rbox 500 W0 D3 t1595644059 | qhull R0.05 Qx Tcv Qc

  Number of points processed: 20
  Number of hyperplanes created: 52
  Number of distance tests for qhull: 22372
  Number of distance tests for merging: 729
  Number of distance tests for checking: 3426
  Number of merged facets: 43
  CPU seconds to compute hull (after input): 0.001
  Maximum distance of point above facet: 0.094 (0.5x)
  Maximum distance of vertex below facet: -0.14 (0.7x)

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 3000 distance computations.
rbox 1000 W1e-20 t | qhull Tcv Qc

Convex hull of 1000 points in 3-d:

  Number of vertices: 81
  Number of coplanar points: 919
  Number of facets: 95
  Number of non-simplicial facets: 6

Statistics for: rbox 1000 W1e-20 t1595644059 | qhull Tcv Qc

  Number of points processed: 93
  Number of hyperplanes created: 303
  Number of distance tests for qhull: 18699
  Number of distance tests for merging: 3015
  Number of distance tests for checking: 16676
  Number of merged facets: 87
  CPU seconds to compute hull (after input): 0.002


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 95000 distance computations.
rbox 1000 W1e-20 D4 t | qhull Tcv Qc

Convex hull of 1000 points in 4-d:

  Number of vertices: 287
  Number of coplanar points: 713
  Number of facets: 1029
  Number of non-simplicial facets: 8

Statistics for: rbox 1000 W1e-20 D4 t1595644059 | qhull Tcv Qc

  Number of points processed: 340
  Number of hyperplanes created: 4227
  Number of distance tests for qhull: 69008
  Number of distance tests for merging: 51153
  Number of distance tests for checking: 88363
  Number of merged facets: 997
  CPU seconds to compute hull (after input): 0.086


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 1029000 distance computations.
rbox 500 W1e-20 D5 t | qhull Tv Qc

Convex hull of 500 points in 5-d:

  Number of vertices: 348
  Number of coplanar points: 152
  Number of facets: 5402
  Number of non-simplicial facets: 10

Statistics for: rbox 500 W1e-20 D5 t1595644059 | qhull Tv Qc

  Number of points processed: 405
  Number of hyperplanes created: 27428
  Number of distance tests for qhull: 130100
  Number of distance tests for merging: 299784
  Number of distance tests for checking: 118368
  Number of merged facets: 3468
  CPU seconds to compute hull (after input): 0.045

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 2701000 distance computations.
rbox 100 W1e-20 D6 t | qhull Tv Qc

Convex hull of 100 points in 6-d:

  Number of vertices: 100
  Number of facets: 6076
  Number of non-simplicial facets: 10

Statistics for: rbox 100 W1e-20 D6 t1595644059 | qhull Tv Qc

  Number of points processed: 100
  Number of hyperplanes created: 21104
  Number of distance tests for qhull: 32827
  Number of distance tests for merging: 181994
  Number of distance tests for checking: 62831
  Number of merged facets: 141
  CPU seconds to compute hull (after input): 0.026

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 607600 distance computations.
rbox 50 W1e-20 D6 t | qhull Qv Tv Qc

Convex hull of 50 points in 6-d:

  Number of vertices: 50
  Number of facets: 2067
  Number of non-simplicial facets: 1

Statistics for: rbox 50 W1e-20 D6 t1595644059 | qhull Qv Tv Qc

  Number of points processed: 50
  Number of hyperplanes created: 5952
  Number of distance tests for qhull: 8579
  Number of distance tests for merging: 3400138
  Number of distance tests for checking: 21120
  Number of merged facets: 3
  CPU seconds to compute hull (after input): 0.056

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 103350 distance computations.
rbox 10000 D4 t | qhull QR0 Qc C-0.01 A0.3 Tv

Convex hull of 10000 points in 4-d:

  Number of vertices: 16
  Number of coplanar points: 8483
  Number of facets: 8
  Number of non-simplicial facets: 8

Statistics for: rbox 10000 D4 t1595644059 | qhull QR0 Qc C-0.01 A0.3 Tv QR1595644060

  Number of points processed: 43
  Number of hyperplanes created: 282
  Number of distance tests for qhull: 1406709
  Number of distance tests for merging: 18069
  Number of distance tests for checking: 89655
  Number of merged facets: 291
  CPU seconds to compute hull (after input): 0.032
  Maximum distance of point above facet: 0.053
  Maximum distance of vertex below facet: -0.18 (0.1x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 80000 distance computations.
rbox 1000 D2 t | qhull d QR0 Qc C-1e-8 Qu Tv

Furthest-site Delaunay triangulation by the convex hull of 1000 points in 3-d:

  Number of input sites: 1000
  Number of Delaunay regions: 16

Statistics for: rbox 1000 D2 t1595644060 | qhull d QR0 Qc C-1e-8 Qu Tv QR1595644060

  Number of points processed: 1000
  Number of hyperplanes created: 5585
  Number of facets in hull: 1996
  Number of distance tests for qhull: 30012
  CPU seconds to compute hull (after input): 0.004


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 16000 distance computations.
rbox 300 D5 t |qhull A-0.999 Qx Qc Tcv

Convex hull of 300 points in 5-d:

  Number of vertices: 160
  Number of coplanar points: 23
  Number of facets: 1756
  Number of non-simplicial facets: 471

Statistics for: rbox 300 D5 t1595644060 | qhull A-0.999 Qx Qc Tcv

  Number of points processed: 188
  Number of hyperplanes created: 11314
  Number of distance tests for qhull: 145495
  Number of distance tests for merging: 59109
  Number of distance tests for checking: 31214
  Number of merged facets: 1190
  CPU seconds to compute hull (after input): 0.027
  Maximum distance of vertex below facet: -0.018 (0.2x)

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 526800 distance computations.
rbox 100 D6 t |qhull A-0.9999 Qx Qc Tcv

Convex hull of 100 points in 6-d:

  Number of vertices: 87
  Number of facets: 3852
  Number of non-simplicial facets: 249

Statistics for: rbox 100 D6 t1595644060 | qhull A-0.9999 Qx Qc Tcv

  Number of points processed: 95
  Number of hyperplanes created: 15426
  Number of distance tests for qhull: 36579
  Number of distance tests for merging: 63310
  Number of distance tests for checking: 65746
  Number of merged facets: 597
  CPU seconds to compute hull (after input): 0.03
  Maximum distance of vertex below facet: -0.0061 (0.2x)

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 385200 distance computations.
rbox 50 D7 t |qhull A-0.99999 Qx Qc Tcv W0.1

Convex hull of 50 points in 7-d:

  Number of vertices: 47
  Number of coplanar points: 3
  Number of facets: 5092
  Number of non-simplicial facets: 84

Statistics for: rbox 50 D7 t1595644060 | qhull A-0.99999 Qx Qc Tcv W0.1

  Number of points processed: 47
  Number of hyperplanes created: 15267
  Number of distance tests for qhull: 21958
  Number of distance tests for merging: 67744
  Number of distance tests for checking: 146550
  Number of merged facets: 238
  CPU seconds to compute hull (after input): 0.033
  Maximum distance of point above facet: 0.081
  Maximum distance of vertex below facet: -0.0017 (0.1x)

QH7076 qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx

Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 254600 distance computations.

set +v
=======================================================
=== The following commands may cause errors Fri, Jul 24, 2020 10:27:40 PM
=======================================================

=== check bad cases for Qhull Fri, Jul 24, 2020 10:27:40 PM
rbox 1000 L100000 s G1e-6 t | qhull Tv
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
dimensional (e.g., a square in 3-d instead of a cube)?  Cosine of the minimum
angle is 1.0000000000000000.  If so, Qhull may produce a wide facet.
Options 'Qs' (search all points), 'Qbb' (scale last coordinate), or
'QbB' (scale to unit box) may remove this warning.
See 'Limitations' in qh-impre.htm.  Use 'Pp' to skip this warning.

Convex hull of 1000 points in 3-d:

  Number of vertices: 994
  Number of facets: 1523
  Number of non-simplicial facets: 6

Statistics for: rbox 1000 L100000 s G1e-6 t1595644060 | qhull Tv

  Number of points processed: 994
  Number of hyperplanes created: 3610
  Number of distance tests for qhull: 30049
  Number of distance tests for merging: 128506
  Number of distance tests for checking: 116631
  Number of merged facets: 461
  CPU seconds to compute hull (after input): 0.009
  Maximum distance of point above facet: 2.1e-15 (0.4x)
  Maximum distance of vertex below facet: -4.7e-15 (0.8x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 1523000 distance computations.
rbox 1000 L100000 s G1e-6 t | qhull Tv Q10

Convex hull of 1000 points in 3-d:

  Number of vertices: 994
  Number of facets: 1523
  Number of non-simplicial facets: 6

Statistics for: rbox 1000 L100000 s G1e-6 t1595644060 | qhull Tv Q10

  Number of points processed: 994
  Number of hyperplanes created: 3610
  Number of distance tests for qhull: 30053
  Number of distance tests for merging: 128506
  Number of distance tests for checking: 116638
  Number of merged facets: 461
  CPU seconds to compute hull (after input): 0.008
  Maximum distance of point above facet: 2.1e-15 (0.4x)
  Maximum distance of vertex below facet: -4.7e-15 (0.8x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 1523000 distance computations.
rbox 1000 s Z1 G1e-13 t | qhull Tv

Convex hull of 1001 points in 3-d:

  Number of vertices: 1001
  Number of facets: 1489
  Number of non-simplicial facets: 134

Statistics for: rbox 1000 s Z1 G1e-13 t1595644060 | qhull Tv

  Number of points processed: 1001
  Number of hyperplanes created: 5159
  Number of distance tests for qhull: 32536
  Number of distance tests for merging: 139652
  Number of distance tests for checking: 306125
  Number of merged facets: 2330
  CPU seconds to compute hull (after input): 0.016
  Maximum distance of point above facet: 1.2e-14 (2.1x)
  Maximum distance of vertex below facet: -1.8e-14 (3.2x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 1490489 distance computations.
rbox 1000 s W1e-13 P0 t | qhull d Qbb Qc Q12 Tv

Delaunay triangulation by the convex hull of 1001 points in 4-d:

  Number of input sites: 1001
  Number of Delaunay regions: 1996

Statistics for: rbox 1000 s W1e-13 P0 t1595644060 | qhull d Qbb Qc Q12 Tv

  Number of points processed: 1001
  Number of hyperplanes created: 12921
  Number of facets in hull: 3711
  Number of distance tests for qhull: 56202
  Number of distance tests for merging: 330422
  Number of distance tests for checking: 310646
  Number of merged facets: 3733
  CPU seconds to compute hull (after input): 0.033
  Maximum distance of point above facet: 1.8e-14 (1.8x)
  Maximum distance of vertex below facet: -3.5e-14 (3.5x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 1997996 distance computations.
rbox 1000 s W1e-13 t | qhull d Q12 Tv
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
dimensional (e.g., a square in 3-d instead of a cube)?  Cosine of the minimum
angle is 1.0000000000000000.  If so, Qhull may produce a wide facet.
Options 'Qs' (search all points), 'Qbb' (scale last coordinate), or
'QbB' (scale to unit box) may remove this warning.
See 'Limitations' in qh-impre.htm.  Use 'Pp' to skip this warning.
QH6170 qhull topology error (qh_partitionvisible): all new facets deleted as
       degenerate facets. Can not continue.

While executing: rbox 1000 s W1e-13 t1595644060 | qhull d Q12 Tv
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213932684  delaunay  Q12-allow-wide  Tverify  _pre-merge
  _zero-centrum  Pgood  _max-width  1  Error-roundoff 1e-15  _one-merge 9.1e-15
  _near-inside 4.5e-14  Visible-distance 6e-15  U-max-coplanar 6e-15
  Width-outside 1.2e-14  _wide-facet 3.6e-14  _narrow-hull  0
  _maxoutside 6.4e-13
Last point added to hull was p716.  Last merge was #2225.

At error exit:

Delaunay triangulation by the convex hull of 1000 points in 4-d:

  Number of input sites: 53
  Total number of deleted points due to merging: 184
  Total number of nearly incident points: 763
  Number of Delaunay regions: 31
  Number of non-simplicial Delaunay regions: 11

Statistics for: rbox 1000 s W1e-13 t1595644060 | qhull d Q12 Tv

  Number of points processed: 243
  Number of hyperplanes created: 2811
  Number of facets in hull: 72
  Number of distance tests for qhull: 995247
  Number of distance tests for merging: 231583
  Number of distance tests for checking: 0
  Number of merged facets: 2301
  Maximum distance of point above facet: 6.4e-13 (63.5x)
  Maximum distance of vertex below facet: -1.6e-12 (158.2x)


precision problems (corrected unless 'Q0' or an error)
    235 flipped facets
    394 coplanar horizon facets for new vertices
     11 coplanar points during partitioning
      6 dupridges with flip facet into good neighbor
      1 dupridges with flip facet into good flip neighbor

A Qhull topology error has occurred.  Qhull did not recover from facet merges and vertex merges.
This usually occurs when the input is nearly degenerate and substantial merging has occurred.
See http://www.qhull.org/html/qh-impre.htm#limit
rbox 1000 s W1e-13 t D2 | qhull d Tv
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
dimensional (e.g., a square in 3-d instead of a cube)?  Cosine of the minimum
angle is 1.0000000000000000.  If so, Qhull may produce a wide facet.
Options 'Qs' (search all points), 'Qbb' (scale last coordinate), or
'QbB' (scale to unit box) may remove this warning.
See 'Limitations' in qh-impre.htm.  Use 'Pp' to skip this warning.
QH7086 Qhull precision warning: repartition coplanar point p440 from f817 as an outside point above hidden facet f817 dist 2.8e-13 nearest vertices 0.00052

Delaunay triangulation by the convex hull of 1000 points in 3-d:

  Number of input sites: 977
  Total number of deleted points due to merging: 13
  Total number of nearly incident points: 10
  Number of Delaunay regions: 718
  Number of non-simplicial Delaunay regions: 130

Statistics for: rbox 1000 s W1e-13 D2 t1595644060 | qhull d Tv

  Number of points processed: 990
  Number of hyperplanes created: 3949
  Number of facets in hull: 1457
  Number of distance tests for qhull: 48902
  Number of distance tests for merging: 41502
  Number of distance tests for checking: 74612
  Number of merged facets: 882
  CPU seconds to compute hull (after input): 0.007
  Maximum distance of point above facet: 7.5e-14 (13.5x)
  Maximum distance of vertex below facet: -9.7e-15 (1.7x)


Output completed.  Verifying that all points are below outer planes of
all facets.  Will make 718000 distance computations.

set +v
=== check Qhull without merging Q0 Fri, Jul 24, 2020 10:27:40 PM
rbox c D7 | qhull Q0 Tcv

Convex hull of 128 points in 7-d:

  Number of vertices: 128
  Number of facets: 8666

Statistics for: rbox c D7 | qhull Q0 Tcv

  Number of points processed: 128
  Number of hyperplanes created: 12287
  Number of distance tests for qhull: 26353
  CPU seconds to compute hull (after input): 0.016


precision problems (corrected unless 'Q0' or an error)
  41888 coplanar half ridges in output
  10185 coplanar horizon facets for new vertices
   8389 nearly singular or axis-parallel hyperplanes
   8389 zero divisors during back substitute
  11903 zero divisors during gaussian elimination

qhull output completed.  Verifying that 128 points are
below 6.6e-15 of the nearest facet.
rbox 100 s D3 | qhull Q0 E1e-3 Tc Po
QH6115 qhull precision error: f100 is concave to f247, since p44(v13) is 0.002232 above f247
QH6115 qhull precision error: f139 is concave to f274, since p90(v32) is 0.007128 above f274
QH6115 qhull precision error: f163 is concave to f232, since p5(v6) is 0.001226 above f232
QH6115 qhull precision error: f293 is concave to f389, since p11(v61) is 0.002161 above f389
QH6115 qhull precision error: f307 is concave to f459, since p75(v21) is 0.01537 above f459

Convex hull of 100 points in 3-d:

  Number of vertices: 100
  Number of facets: 196

Statistics for: rbox 100 s D3 | qhull Q0 E1e-3 Tc Po

  Number of points processed: 100
  Number of hyperplanes created: 508
  Number of distance tests for qhull: 1727
  CPU seconds to compute hull (after input): 0.001


precision problems (corrected unless 'Q0' or an error)
     16 coplanar half ridges in output
      5 concave half ridges in output
     18 coplanar horizon facets for new vertices
rbox 100 s D3 | qhull Q0 E1e-2 Tc Po
QH6115 qhull precision error: f123 is concave to f235, since p85(v8) is 0.06092 above f235
QH6115 qhull precision error: f177 is concave to f272, since p98(v20) is 0.03571 above f272
QH6115 qhull precision error: f246 is concave to f252, since p7(v57) is 0.02104 above f252
QH6115 qhull precision error: f261 is concave to f305, since p82(v60) is 0.01847 above f305
QH6115 qhull precision error: f266 is concave to f317, since p82(v60) is 0.02592 above f317

Convex hull of 100 points in 3-d:

  Number of vertices: 72
  Number of facets: 140

Statistics for: rbox 100 s D3 | qhull Q0 E1e-2 Tc Po

  Number of points processed: 72
  Number of hyperplanes created: 321
  Number of distance tests for qhull: 1664
  CPU seconds to compute hull (after input): 0.001


precision problems (corrected unless 'Q0' or an error)
     52 coplanar half ridges in output
      5 concave half ridges in output
     54 coplanar horizon facets for new vertices
     27 coplanar points during partitioning
rbox 100 s D3 | qhull Q0 E1e-1 Tc Po

Convex hull of 100 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 100 s D3 | qhull Q0 E1e-1 Tc Po

  Number of points processed: 10
  Number of hyperplanes created: 27
  Number of distance tests for qhull: 917
  CPU seconds to compute hull (after input):  0


precision problems (corrected unless 'Q0' or an error)
      3 coplanar half ridges in output
      3 coplanar horizon facets for new vertices
     59 coplanar points during partitioning
rbox 100 s D3 | qhull Q0 R1e-3 Tc Po
QH6115 qhull precision error: f94 is concave to f270, since p44(v13) is 0.003303 above f270
QH6115 qhull precision error: f157 is concave to f255, since p5(v6) is 0.005886 above f255
QH6115 qhull precision error: f289 is concave to f386, since p30(v62) is 0.000726 above f386
QH6115 qhull precision error: f381 is concave to f293, since p56(v79) is 0.0006018 above f293

Convex hull of 100 points in 3-d:

  Number of vertices: 100
  Number of facets: 196

Statistics for: rbox 100 s D3 | qhull Q0 R1e-3 Tc Po

  Number of points processed: 100
  Number of hyperplanes created: 498
  Number of distance tests for qhull: 1643
  CPU seconds to compute hull (after input): 0.002


precision problems (corrected unless 'Q0' or an error)
     10 coplanar half ridges in output
      4 concave half ridges in output
     10 coplanar horizon facets for new vertices
rbox 100 s D3 | qhull Q0 R1e-2 Tc Po
QH6115 qhull precision error: f78 is concave to f147, since p57(v1) is 0.01085 above f147
QH6115 qhull precision error: f89 is concave to f194, since p17(v2) is 0.0111 above f194
QH6115 qhull precision error: f106 is concave to f122, since p74(v27) is 0.01501 above f122
QH6115 qhull precision error: f122 is concave to f106, since p95(v30) is 0.00822 above f106
QH6115 qhull precision error: f126 is concave to f213, since p95(v30) is 0.007437 above f213
QH6115 qhull precision error: f141 is concave to f288, since p81(v34) is 0.007157 above f288
QH6115 qhull precision error: f147 is concave to f227, since p90(v19) is 0.1078 above f227
QH6115 qhull precision error: f161 is concave to f252, since p20(v24) is 0.008976 above f252
QH6115 qhull precision error: f176 is concave to f277, since p38(v22) is 0.008285 above f277
QH6115 qhull precision error: f181 is concave to f276, since p73(v12) is 0.02209 above f276
QH6115 qhull precision error: f186 is concave to f291, since p85(v8) is 0.04316 above f291
QH6115 qhull precision error: f194 is concave to f89, since p82(v45) is 0.009743 above f89
QH6115 qhull precision error: f198 is concave to f273, since p82(v45) is 0.01834 above f273
QH6115 qhull precision error: f213 is concave to f126, since p93(v48) is 0.01071 above f126
QH6115 qhull precision error: f227 is concave to f147, since p37(v51) is 0.007006 above f147
QH6115 qhull precision error: f273 is concave to f198, since p29(v60) is 0.006128 above f198
QH6115 qhull precision error: f288 is concave to f141, since p96(v63) is 0.005493 above f141
QH6115 qhull precision error: f291 is concave to f186, since p34(v64) is 0.008643 above f186
QH6115 qhull precision error: f300 is concave to f355, since p30(v66) is 0.006345 above f355
QH6115 qhull precision error: f324 is concave to f384, since p75(v20) is 0.02388 above f384
QH6115 qhull precision error: f361 is concave to f406, since p41(v5) is 0.009438 above f406
QH6115 qhull precision error: f368 is concave to f367, since p11(v69) is 0.007227 above f367
QH6115 qhull precision error: f390 is concave to f391, since p99(v73) is 0.007279 above f391
QH6115 qhull precision error: f391 is concave to f390, since p43(v74) is 0.01052 above f390

Convex hull of 100 points in 3-d:

  Number of vertices: 88
  Number of facets: 172

Statistics for: rbox 100 s D3 | qhull Q0 R1e-2 Tc Po

  Number of points processed: 88
  Number of hyperplanes created: 413
  Number of distance tests for qhull: 1702
  CPU seconds to compute hull (after input): 0.001


precision problems (corrected unless 'Q0' or an error)
     49 coplanar half ridges in output
     24 concave half ridges in output
     53 coplanar horizon facets for new vertices
     12 coplanar points during partitioning
rbox 100 s D3 | qhull Q0 R0.05 Tc
QH6136 qhull precision error: facet f193 is flipped, distance= 0.391655882694
ERRONEOUS FACET:
- f193
    - flags: top simplicial flipped
    - normal:   -0.2813  -0.9389   0.1981
    - offset:  0.2910058
    - vertices: p19(v46) p65(v35) p74(v28)
    - neighboring facets: f183 f194 f195

A flipped facet occurs when its distance to the interior point is
greater than or equal to -0.024, the maximum roundoff error.

While executing: rbox 100 s D3 | qhull Q0 R0.05 Tc
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213949491  Q0-no-premerge  Random-perturb 0.05  Tcheck-frequently
  _max-width 0.94  Error-roundoff 0.024  Visible-distance 0.024
  U-max-coplanar 0.024  Width-outside 0.048  _wide-facet 0.15  _maxoutside 0.19
Last point added to hull was p19.
Qhull has finished constructing the hull.

At error exit:

Convex hull of 100 points in 3-d:

  Number of vertices: 46
  Number of facets: 88

Statistics for: rbox 100 s D3 | qhull Q0 R0.05 Tc

  Number of points processed: 46
  Number of hyperplanes created: 196
  Number of distance tests for qhull: 2023
  CPU seconds to compute hull (after input):  0


precision problems (corrected unless 'Q0' or an error)
      1 flipped facets
     34 coplanar horizon facets for new vertices
     51 coplanar points during partitioning

Precision problems were detected during construction of the convex hull.
This occurs because convex hull algorithms assume that calculations are
exact, but floating-point arithmetic has roundoff errors.

To correct for precision problems, do not use 'Q0'.  By default, Qhull
selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',
Qhull joggles the input to prevent precision problems.  See "Imprecision
in Qhull" (qh-impre.htm).

If you use 'Q0', the output may include
coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,
Qhull may produce a ridge with four neighbors or two facets with the same 
vertices.  Qhull reports these events when they occur.  It stops when a
concave ridge, flipped facet, or duplicate facet occurs.

If you need triangular output:
  - use option 'Qt' to triangulate the output
  - use option 'QJ' to joggle the input points and remove precision errors
  - use option 'Ft'.  It triangulates non-simplicial facets with added points.

If you must use 'Q0',
try one or more of the following options.  They can not guarantee an output.
  - use 'QbB' to scale the input to a cube.
  - use 'Po' to produce output and prevent partitioning for flipped facets
  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff
  - use 'En' to specify a maximum roundoff error less than 0.024.
  - options 'Qf', 'Qbb', and 'QR0' may also help

To guarantee simplicial output:
  - use option 'Qt' to triangulate the output
  - use option 'QJ' to joggle the input points and remove precision errors
  - use option 'Ft' to triangulate the output by adding points
  - use exact arithmetic (see "Imprecision in Qhull", qh-impre.htm)
rbox 100 s D3 | qhull Q0 R0.05 Tc Po
QH6136 qhull precision error: facet f193 is flipped, distance= 0.391655882694
QH6115 qhull precision error: f119 is concave to f134, since p31(v31) is 0.05178 above f134
QH6115 qhull precision error: f124 is concave to f131, since p5(v6) is 0.1065 above f131
QH6115 qhull precision error: f147 is concave to f91, since p69(v36) is 0.0354 above f91
QH6113 qhull precision error: f193 is flipped (interior point is outside)

Convex hull of 100 points in 3-d:

  Number of vertices: 46
  Number of facets: 88

Statistics for: rbox 100 s D3 | qhull Q0 R0.05 Tc Po

  Number of points processed: 46
  Number of hyperplanes created: 196
  Number of distance tests for qhull: 2023
  CPU seconds to compute hull (after input):  0


precision problems (corrected unless 'Q0' or an error)
     35 coplanar half ridges in output
      3 concave half ridges in output
      1 flipped facets
     34 coplanar horizon facets for new vertices
     51 coplanar points during partitioning
rbox 1000 W1e-7 | qhull Q0 Tc Po

Convex hull of 1000 points in 3-d:

  Number of vertices: 164
  Number of facets: 324

Statistics for: rbox 1000 W1e-7 | qhull Q0 Tc Po

  Number of points processed: 221
  Number of hyperplanes created: 1160
  Number of distance tests for qhull: 22590
  CPU seconds to compute hull (after input): 0.006

rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po
QH7088 Qhull precision warning: in post-processing (qh_check_maxout) p0 for f36 is 0.061 above hidden facet f70 nearest vertices 0.15
QH7088 Qhull precision warning: in post-processing (qh_check_maxout) p8 for f38 is 0.26 above hidden facet f145 nearest vertices 0.14
QH6297 Qhull precision error (qh_check_maxout): large increase in qh.max_outside during post-processing dist 0.26 (46669910714866.6x).  See warning QH0032/QH0033.  Allow with 'Q12' (allow-wide) and 'Pp'
ERRONEOUS FACET:
- f145
    - flags: top simplicial
    - normal:   -0.6276   0.1677  -0.7602
    - offset: -0.2196772
    - maxoutside:  0.2588526
    - vertices: p2(v43) p0(v13) p24(v6)
    - neighboring facets: f39 f146 f147
ERRONEOUS and NEIGHBORING FACETS to output

While executing: rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213949491  Q0-no-premerge  Visible 0.05  W-outside 0.01
  Tcheck-frequently  Poutput-forced  _max-width 0.98  Error-roundoff 6.9e-16
  _near-inside 2.4e-14  U-max-coplanar 0.05  _wide-facet 0.3  _maxoutside 0.01
Last point added to hull was p10.

At error exit:

Convex hull of 50 points in 3-d:

  Number of vertices: 50
  Number of facets: 96

Statistics for: rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po

  Number of points processed: 50
  Number of hyperplanes created: 171
  Number of distance tests for qhull: 538


precision problems (corrected unless 'Q0' or an error)
      7 flipped facets
     82 coplanar horizon facets for new vertices

Precision problems were detected during construction of the convex hull.
This occurs because convex hull algorithms assume that calculations are
exact, but floating-point arithmetic has roundoff errors.

To correct for precision problems, do not use 'Q0'.  By default, Qhull
selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',
Qhull joggles the input to prevent precision problems.  See "Imprecision
in Qhull" (qh-impre.htm).

If you use 'Q0', the output may include
coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,
Qhull may produce a ridge with four neighbors or two facets with the same 
vertices.  Qhull reports these events when they occur.  It stops when a
concave ridge, flipped facet, or duplicate facet occurs.

If you need triangular output:
  - use option 'Qt' to triangulate the output
  - use option 'QJ' to joggle the input points and remove precision errors
  - use option 'Ft'.  It triangulates non-simplicial facets with added points.

If you must use 'Q0',
try one or more of the following options.  They can not guarantee an output.
  - use 'QbB' to scale the input to a cube.
  - use 'Po' to produce output and prevent partitioning for flipped facets
  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff
  - use 'En' to specify a maximum roundoff error less than 6.9e-16.
  - options 'Qf', 'Qbb', and 'QR0' may also help

To guarantee simplicial output:
  - use option 'Qt' to triangulate the output
  - use option 'QJ' to joggle the input points and remove precision errors
  - use option 'Ft' to triangulate the output by adding points
  - use exact arithmetic (see "Imprecision in Qhull", qh-impre.htm)
rbox 100 s D5 | qhull Q0 R1e-2 Tc Po
QH6107 qhull topology error: facets f721, f756 and f722 meet at a ridge with more than 2 neighbors.  Can not continue due to no qh.PREmerge and no 'Qx' (MERGEexact)
ERRONEOUS FACET:
- f721
    - flags: bottom simplicial newfacet
    - offset:          0
    - vertices: p84(v29) p2(v19) p58(v12) p3(v7) p9(v2)
    - neighboring facets: f362 f720 f728 f722 f740
ERRONEOUS OTHER FACET:
- f756
    - flags: top simplicial newfacet
    - offset:          0
    - vertices: p84(v29) p40(v26) p2(v19) p58(v12) p9(v2)
    - neighboring facets: f566
ERRONEOUS and NEIGHBORING FACETS to output

While executing: rbox 100 s D5 | qhull Q0 R1e-2 Tc Po
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213949491  Q0-no-premerge  Random-perturb 0.01  Tcheck-frequently
  Poutput-forced  _max-width 0.88  Error-roundoff 0.0045
  Visible-distance 0.0045  U-max-coplanar 0.0045  Width-outside 0.009
  _wide-facet 0.027  _maxoutside 0.054
Last point added to hull was p84.

Convex hull of 100 points in 5-d:

  Number of vertices: 29
  Number of facets: 340

Statistics for: rbox 100 s D5 | qhull Q0 R1e-2 Tc Po

  Number of points processed: 28
  Number of hyperplanes created: 720
  Number of distance tests for qhull: 2275


precision problems (corrected unless 'Q0' or an error)
      1 flipped facets
     24 coplanar horizon facets for new vertices

Precision problems were detected during construction of the convex hull.
This occurs because convex hull algorithms assume that calculations are
exact, but floating-point arithmetic has roundoff errors.

To correct for precision problems, do not use 'Q0'.  By default, Qhull
selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',
Qhull joggles the input to prevent precision problems.  See "Imprecision
in Qhull" (qh-impre.htm).

If you use 'Q0', the output may include
coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,
Qhull may produce a ridge with four neighbors or two facets with the same 
vertices.  Qhull reports these events when they occur.  It stops when a
concave ridge, flipped facet, or duplicate facet occurs.

If you need triangular output:
  - use option 'Qt' to triangulate the output
  - use option 'QJ' to joggle the input points and remove precision errors
  - use option 'Ft'.  It triangulates non-simplicial facets with added points.

If you must use 'Q0',
try one or more of the following options.  They can not guarantee an output.
  - use 'QbB' to scale the input to a cube.
  - use 'Po' to produce output and prevent partitioning for flipped facets
  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff
  - use 'En' to specify a maximum roundoff error less than 0.0045.
  - options 'Qf', 'Qbb', and 'QR0' may also help

To guarantee simplicial output:
  - use option 'Qt' to triangulate the output
  - use option 'QJ' to joggle the input points and remove precision errors
  - use option 'Ft' to triangulate the output by adding points
  - use exact arithmetic (see "Imprecision in Qhull", qh-impre.htm)

set +v
=== check nearly incident points Fri, Jul 24, 2020 10:27:41 PM
rbox L100 2000 D4 s C1,1e-13 t2 | qhull

Convex hull of 4000 points in 4-d:

  Number of vertices: 2096
  Number of facets: 13614
  Number of non-simplicial facets: 52

Statistics for: rbox L100 2000 D4 s C1,1e-13 t2 | qhull

  Number of points processed: 2111
  Number of hyperplanes created: 51581
  Number of distance tests for qhull: 585497
  Number of distance tests for merging: 267217
  Number of distance tests for checking: 152193
  Number of merged facets: 129
  CPU seconds to compute hull (after input): 0.056
  Maximum distance of point above facet: 1.8e-14 (1.9x)
  Maximum distance of vertex below facet: -8.9e-15 (0.9x)

rbox L100 2000 D4 s C1,1e-13 t2 | qhull Q12

Convex hull of 4000 points in 4-d:

  Number of vertices: 2096
  Number of facets: 13614
  Number of non-simplicial facets: 52

Statistics for: rbox L100 2000 D4 s C1,1e-13 t2 | qhull Q12

  Number of points processed: 2111
  Number of hyperplanes created: 51581
  Number of distance tests for qhull: 585497
  Number of distance tests for merging: 267217
  Number of distance tests for checking: 152193
  Number of merged facets: 129
  CPU seconds to compute hull (after input): 0.056
  Maximum distance of point above facet: 1.8e-14 (1.9x)
  Maximum distance of vertex below facet: -8.9e-15 (0.9x)

rbox 50 C1,1E-13 t1447644703 | qhull d
QH6271 qhull topology error (qh_check_dupridge): wide merge (1125070907263.1x wider) due to dupridge between f1143 and f1169 (vertex dist 6.5e-14), merge dist 0.015, while processing p54
- Allow error with option 'Q12'
- Experimental option merge-pinched-vertices ('Q14') may avoid this error.  It merges nearly adjacent vertices.
- A bounding box for the input sites may alleviate this error.
ERRONEOUS FACET:
- f1143
    - flags: bottom upperDelaunay newfacet dupridge mergeridge2 flipped
    - normal:    0.2935   0.3842   0.4668   0.7405
    - offset: 0.05514914
    - vertices: p54(v76) p45(v56) p76(v36) p44(v19)
    - neighboring facets: f405 f1159 f1169 f1144
    - ridges:
     - r576 tested simplicialbot
           vertices: p45(v56) p76(v36) p44(v19)
           between f405 and f1143
     - r1072 simplicialtop simplicialbot
           vertices: p54(v76) p76(v36) p44(v19)
           between f1143 and f1159
     - r1073 simplicialbot
           vertices: p54(v76) p45(v56) p44(v19)
           between f1169 and f1143
     - r1074 simplicialtop simplicialbot
           vertices: p54(v76) p45(v56) p76(v36)
           between f1143 and f1144
ERRONEOUS OTHER FACET:
- f1169
    - flags: bottom upperDelaunay newfacet dupridge mergeridge1 flipped
    - normal:   -0.3214   0.1166   0.5495   0.7623
    - offset:   0.114967
    - vertices: p54(v76) p45(v56) p44(v19) p92(v11)
    - neighboring facets: f405 f1159 f1170 f1143
    - ridges:
     - r561 tested simplicialbot
           vertices: p45(v56) p44(v19) p92(v11)
           between f405 and f1169
     - r1070 simplicialtop simplicialbot
           vertices: p54(v76) p44(v19) p92(v11)
           between f1169 and f1159
     - r1071 simplicialtop simplicialbot
           vertices: p54(v76) p45(v56) p92(v11)
           between f1170 and f1169
     - r1073 simplicialbot
           vertices: p54(v76) p45(v56) p44(v19)
           between f1169 and f1143

While executing: rbox 50 C1,1E-13 t1447644703 | qhull d
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 213949491  delaunay  _pre-merge  _zero-centrum  Pgood  _max-width 0.94
  Error-roundoff 1e-15  _one-merge 9.2e-15  _near-inside 4.6e-14
  Visible-distance 6.1e-15  U-max-coplanar 6.1e-15  Width-outside 1.2e-14
  _wide-facet 3.7e-14  _maxoutside 1.2e-14
Last point added to hull was p54.  Last merge was #247.

At error exit:

Delaunay triangulation by the convex hull of 100 points in 4-d:

  Number of input sites: 76
  Number of nearly incident points: 1
  Number of Delaunay regions: 266
  Number of non-simplicial Delaunay regions: 73

Statistics for: rbox 50 C1,1E-13 t1447644703 | qhull d

  Number of points processed: 76
  Number of hyperplanes created: 1087
  Number of facets in hull: 303
  Number of distance tests for qhull: 5296
  Number of distance tests for merging: 10632
  Number of distance tests for checking: 0
  Number of merged facets: 249
  Maximum distance of point above facet: 1.3e-14 (1.3x)
  Maximum distance of vertex below facet: -1.3e-14 (1.3x)


precision problems (corrected unless 'Q0' or an error)
      4 flipped facets
     73 coplanar horizon facets for new vertices
      1 coplanar points during partitioning
    213 degenerate hyperplanes recomputed with gaussian elimination
     17 nearly singular or axis-parallel hyperplanes
      1 dupridges with multiple neighbors

A wide merge error has occurred.  Qhull has produced a wide facet due to facet merges and vertex merges.
This usually occurs when the input is nearly degenerate and substantial merging has occurred.
See http://www.qhull.org/html/qh-impre.htm#limit
rbox 50 C1,1E-13 t1447644703 | qhull d Q12
QH6271 qhull topology error (qh_check_dupridge): wide merge (1125070907263.1x wider) due to dupridge between f1143 and f1169 (vertex dist 6.5e-14), merge dist 0.015, while processing p54
- Allow error with option 'Q12'
- Experimental option merge-pinched-vertices ('Q14') may avoid this error.  It merges nearly adjacent vertices.
- A bounding box for the input sites may alleviate this error.

Delaunay triangulation by the convex hull of 100 points in 4-d:

  Number of input sites: 99
  Total number of nearly incident points: 1
  Number of Delaunay regions: 307
  Number of non-simplicial Delaunay regions: 133

Statistics for: rbox 50 C1,1E-13 t1447644703 | qhull d Q12

  Number of points processed: 99
  Number of hyperplanes created: 1504
  Number of facets in hull: 345
  Number of distance tests for qhull: 7670
  Number of distance tests for merging: 18284
  Number of distance tests for checking: 7318
  Number of merged facets: 456
  CPU seconds to compute hull (after input): 0.003
  Maximum distance of point above facet: 1.3e-14 (1.3x)
  Maximum distance of vertex below facet: -0.0012 (119810840063.5x)

rbox 50 C1,1E-13 t1447644703 | qhull d Q14

Delaunay triangulation by the convex hull of 100 points in 4-d:

  Number of input sites: 99
  Total number of nearly incident points: 1
  Number of Delaunay regions: 312
  Number of non-simplicial Delaunay regions: 137

Statistics for: rbox 50 C1,1E-13 t1447644703 | qhull d Q14

  Number of points processed: 99
  Number of hyperplanes created: 1487
  Number of facets in hull: 350
  Number of distance tests for qhull: 5360
  Number of distance tests for merging: 17768
  Number of distance tests for checking: 4953
  Number of merged facets: 513
  CPU seconds to compute hull (after input): 0.003
  Maximum distance of point above facet: 1.3e-14 (1.3x)
  Maximum distance of vertex below facet: -1.4e-14 (1.4x)


set +v
=======================================================
=== Testing done. Print documentation
=======================================================

qhull -

qhull -- compute convex hulls and related structures.
    http://www.qhull.org  2020.2.r 2020/07/24

input (stdin):
    first lines: dimension and number of points (or vice-versa).
    other lines: point coordinates, best if one point per line
    comments:    start with a non-numeric character
    halfspaces:  use dim plus one and put offset after coefficients.
                 May be preceded by a single interior point ('H').

options:
    d    - Delaunay triangulation by lifting points to a paraboloid
    d Qu - furthest-site Delaunay triangulation (upper convex hull)
    Hn,n,... - halfspace intersection about point [n,n,0,...]
    Qc   - keep coplanar points with nearest facet
    Qi   - keep interior points with nearest facet
    QJ   - joggled input instead of merged facets
    Qt   - triangulated output
    v    - Voronoi diagram (dual of the Delaunay triangulation)
    v Qu - furthest-site Voronoi diagram

Qhull control options:
    Qa   - allow input with fewer or more points than coordinates
    Qbk:n   - scale coord k so that low bound is n
      QBk:n - scale coord k so that upper bound is n (QBk is 0.5)
    QbB  - scale input to unit cube centered at the origin
    Qbb  - scale last coordinate to [0,m] for Delaunay triangulations
    Qbk:0Bk:0 - remove k-th coordinate from input
    QJn  - randomly joggle input in range [-n,n]
    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
    Qs   - search all points for the initial simplex
    Qu   - for 'd' or 'v', compute upper hull without point at-infinity
              returns furthest-site Delaunay triangulation
    QVn  - good facet if it includes point n, -n if not
    Qx   - exact pre-merges (skips coplanar and angle-coplanar facets)
    Qz   - add point-at-infinity to Delaunay triangulation

Qhull extra options:
    Qf   - partition point to furthest outside facet
    Qg   - only build good facets (needs 'QGn', 'QVn', or 'PdD')
    QGn  - good facet if visible from point n, -n for not visible
    Qm   - only process points that would increase max_outside
    Qr   - process random outside points instead of furthest ones
    Qv   - test vertex neighbors for convexity
    Qw   - allow option warnings
    Q0   - turn off default premerge with 'C-0'/'Qx'
    Q1   - merge by mergetype/angle instead of mergetype/distance
    Q2   - merge all coplanar facets instead of merging independent sets
    Q3   - do not merge redundant vertices
    Q4   - avoid old->new merges
    Q5   - do not correct outer planes at end of qhull
    Q6   - do not pre-merge concave or coplanar facets
    Q7   - depth-first processing instead of breadth-first
    Q8   - do not process near-inside points
    Q9   - process furthest of furthest points
    Q10  - no special processing for narrow distributions
    Q11  - copy normals and recompute centrums for tricoplanar facets
    Q12  - allow wide facets and wide dupridge
    Q14  - merge pinched vertices that create a dupridge
    Q15  - check for duplicate ridges with the same vertices

T options:
    TFn  - report summary when n or more facets created
    TI file - input file, may be enclosed in single quotes
    TO file - output file, may be enclosed in single quotes
    Ts   - statistics
    Tv   - verify result: structure, convexity, and point inclusion
    Tz   - send all output to stdout

Trace options:
    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
    Ta   - annotate output with message codes
    TAn  - stop qhull after adding n vertices
     TCn - stop qhull after building cone for point n
     TVn - stop qhull after adding point n, -n for before
    Tc   - check frequently during execution
    Tf   - flush each qh_fprintf for debugging segfaults
    TPn  - turn on tracing when point n added to hull
     TP-1  turn on tracing after qh_buildhull and qh_postmerge
     TMn - turn on tracing at merge n
     TWn - trace merge facets when width > n
    TRn  - rerun qhull n times for statistics to adjust 'QJn'

Precision options:
    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
    En   - max roundoff error for distance computation
    Rn   - randomly perturb computations by a factor of [1-n,1+n]
    Vn   - min distance above plane for a visible facet (default 3C-n or En)
    Un   - max distance below plane for a new, coplanar point (default Vn)
    Wn   - min facet width for outside point (before roundoff, default 2Vn)

Output formats (may be combined; if none, produces a summary to stdout):
    f    - facet dump
    G    - Geomview output (see below)
    i    - vertices incident to each facet
    m    - Mathematica output (2-d and 3-d)
    n    - normals with offsets
    o    - OFF format (dim, points and facets; Voronoi regions)
    p    - vertex coordinates or Voronoi vertices (coplanar points if 'Qc')
    s    - summary (stderr)

More formats:
    Fa   - area for each facet
    FA   - compute total area and volume for option 's'
    Fc   - count plus coplanar points for each facet
           use 'Qc' (default) for coplanar and 'Qi' for interior
    FC   - centrum or Voronoi center for each facet
    Fd   - use cdd format for input (homogeneous with offset first)
    FD   - use cdd format for numeric output (offset first)
    FF   - facet dump without ridges
    Fi   - inner plane for each facet
           for 'v', separating hyperplanes for bounded Voronoi regions
    FI   - ID of each facet
    Fm   - merge count for each facet (511 max)
    FM   - Maple output (2-d and 3-d)
    Fn   - count plus neighboring facets for each facet
    FN   - count plus neighboring facets for each point
    Fo   - outer plane (or max_outside) for each facet
           for 'v', separating hyperplanes for unbounded Voronoi regions
    FO   - options and precision constants
    Fp   - dim, count, and intersection coordinates (halfspace only)
    FP   - nearest vertex and distance for each coplanar point
    FQ   - command used for qhull
    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
                      output: #vertices, #facets, #coplanars, #nonsimplicial
                    #real (2), max outer plane, min vertex
    FS   - sizes:   #int (0)
                    #real (2) tot area, tot volume
    Ft   - triangulation with centrums for non-simplicial facets (OFF format)
    Fv   - count plus vertices for each facet
           for 'v', Voronoi diagram as Voronoi vertices for pairs of sites
    FV   - average of vertices (a feasible point for 'H')
    Fx   - extreme points (in order for 2-d)

Geomview output (2-d, 3-d, and 4-d; 2-d Voronoi)
    Ga   - all points as dots
     Gp  -  coplanar points and vertices as radii
     Gv  -  vertices as spheres
    Gc   - centrums
    GDn  - drop dimension n in 3-d and 4-d output
    Gh   - hyperplane intersections
    Gi   - inner planes only
     Gn  -  no planes
     Go  -  outer planes only
    Gr   - ridges
    Gt   - for 3-d 'd', transparent outer ridges

Print options:
    PAn  - keep n largest facets by area
    Pdk:n - drop facet if normal[k] <= n (default 0.0)
    PDk:n - drop facet if normal[k] >= n
    PFn  - keep facets whose area is at least n
    Pg   - print good facets (needs 'QGn' or 'QVn')
    PG   - print neighbors of good facets
    PMn  - keep n facets with most merges
    Po   - force output.  If error, output neighborhood of facet
    Pp   - do not report precision problems

    .    - list of all options
    -    - one line descriptions of all options
    -?   - help with examples
    -V   - version
rbox

rbox -- generate various point distributions.  Default is random in cube.

args (any order, space separated):                    Version: 2019/11/10
  3000    number of random points in cube, lens, spiral, sphere or grid
  D3      dimension 3-d
  c       add a unit cube to the output ('c G2.0' sets size)
  d       add a unit diamond to the output ('d G2.0' sets size)
  l       generate a regular 3-d spiral
  r       generate a regular polygon, ('r s Z1 G0.1' makes a cone)
  s       generate cospherical points
  x       generate random points in simplex, may use 'r' or 'Wn'
  y       same as 'x', plus simplex
  Cn,r,m  add n nearly adjacent points within radius r of m points
  Pn,m,r  add point [n,m,r] first, pads with 0, maybe repeated

  Ln      lens distribution of radius n.  Also 's', 'r', 'G', 'W'.
  Mn,m,r  lattice(Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ...
          '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}.  Try 'M3,4 z'.
  W0.1    random distribution within 0.1 of the cube's or sphere's surface
  Z0.5 s  random points in a 0.5 disk projected to a sphere
  Z0.5 s G0.6 same as Z0.5 within a 0.6 gap

  Bn      bounding box coordinates, default 0.5
  h       output as homogeneous coordinates for cdd
  n       remove command line from the first line of output
  On      offset coordinates by n
  t       use time as the random number seed(default is command line)
  tn      use n as the random number seed
  z       print integer coordinates, default 'Bn' is 1e+06
cat html/qhull.txt html/rbox.txt



qhull(1)                                                 qhull(1)


NAME
       qhull  - convex hull, Delaunay triangulation, Voronoi dia-
       gram, halfspace intersection about a point, hull volume, facet area

SYNOPSIS
       qhull- compute convex hulls and related structures
           input (stdin): dimension, #points, point coordinates
           first comment (non-numeric) is listed in the summary
           halfspace: use dim plus one with offsets after coefficients

       options (qh-quick.htm):
           d    - Delaunay triangulation by lifting points to a paraboloid
           d Qu - furthest-site Delaunay triangulation (upper convex hull)
           v    - Voronoi diagram as the dual of the Delaunay triangulation
           v Qu - furthest-site Voronoi diagram
           H1,1 - Halfspace intersection about [1,1,0,...] via polar duality
           Qt   - triangulated output
           QJ   - joggled input instead of merged facets
           Tv   - verify result: structure, convexity, and point inclusion
           .    - concise list of all options
           -    - one-line description of each option
           -?   - this message
           -V   - version

       Output options (subset):
           s    - summary of results (default)
           i    - vertices incident to each facet
           n    - normals with offsets
           p    - vertex coordinates (if 'Qc', includes coplanar points)
                  if 'v', Voronoi vertices
           FA   - report total area and volume
           Fp   - halfspace intersections
           FS   - total area and volume
           Fx   - extreme points (convex hull vertices)
           G    - Geomview output (2-d, 3-d and 4-d)
           m    - Mathematica output (2-d and 3-d)
           o    - OFF format (if 'v', outputs Voronoi regions)
           QVn  - print facets that include point n, -n if not
           TI file - input file, may be enclosed in single quotes
           TO file - output file, may be enclosed in single quotes

       examples:
           rbox D4 | qhull Tv                        rbox 1000 s | qhull Tv s FA
           rbox 10 D2 | qhull d QJ s i TO result     rbox 10 D2 | qhull v Qbb Qt p
           rbox 10 D2 | qhull d Qu QJ m              rbox 10 D2 | qhull v Qu QJ o
           rbox c d D2 | qhull Qc s f Fx | more      rbox c | qhull FV n | qhull H Fp
           rbox d D12 | qhull QR0 FA                 rbox c D7 | qhull FA TF1000
           rbox y 1000 W0 | qhull Qc                 rbox c | qhull n

        - html manual:    html/index.htm
        - installation:   README.txt
        - see also:       COPYING.txt, REGISTER.txt, Changes.txt
        - WWW:            <http://www.qhull.org>
        - GIT:            <git@github.com:qhull/qhull.git>
        - news:           <http://www.qhull.org/news>
        - Geomview:       <http://www.geomview.org>
        - news group:     <news:comp.graphics.algorithms>
        - FAQ:            <http://www.faqs.org/faqs/graphics/algorithms-faq/>
        - email:          qhull@qhull.org
        - bug reports:    qhull_bug@qhull.org




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qhull(1)                                                 qhull(1)


       The sections are:
        - INTRODUCTION
        - DESCRIPTION, a description of Qhull
        - IMPRECISION, how Qhull handles imprecision
        - OPTIONS
        -    Input and output options
        -    Additional input/output formats
        -    Precision options
        -    Geomview options
        -    Print options
        -    Qhull options
        -    Trace options
        - BUGS
        - E-MAIL
        - SEE ALSO
        - AUTHORS
        - ACKNOWLEGEMENTS

       This man page briefly describes all Qhull options.  Please
       report  any  mismatches  with  Qhull's  html  manual  
       (html/index.htm).



INTRODUCTION
       Qhull  is  a  general  dimension code for computing convex
       hulls, Delaunay triangulations, Voronoi diagram, furthest-
       site  Voronoi  diagram,  furthest-site Delaunay triangula-
       tions, and halfspace  intersections  about  a  point.   It
       implements  the Quickhull algorithm for computing the con-
       vex hull.  Qhull handles round-off  errors  from  floating
       point arithmetic.  It can approximate a convex hull.

       The  program includes options for hull volume, facet area,
       partial hulls, input transformations, randomization, trac-
       ing,  multiple  output  formats, and execution statistics.
       The program can be called from  within  your  application.
       You  can  view  the  results  in  2-d,  3-d  and  4-d with
       Geomview.


DESCRIPTION
       The format of input is the following: first line  contains
       the  dimension,  second  line contains the number of input
       points, and point coordinates follow.  The  dimension  and
       number  of  points  can  be  reversed.   Comments and line
       breaks are ignored.  A comment starts with  a  non-numeric
       character  and  continues  to  the end of line.  The first
       comment is reported in summaries  and  statistics.   Error
       reporting is better if there is one point per line.

       The  default printout option is a short summary. There are
       many other output formats.




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qhull(1)                                                 qhull(1)


       Qhull implements the Quickhull algorithm for convex  hull.
       This  algorithm  combines the 2-d Quickhull algorithm with
       the n-d beneath-beyond algorithm [c.f., Preparata & Shamos
       '85].   It  is  similar  to  the  randomized algorithms of
       Clarkson and others  [Clarkson  et  al.  '93].   The  main
       advantages  of Quickhull are output sensitive performance,
       reduced space requirements, and automatic handling of pre-
       cision problems.

       The data structure produced by Qhull consists of vertices,
       ridges, and facets.  A vertex is a point of the input set.
       A ridge is a set of d vertices and two neighboring facets.
       For example in 3-d, a ridge is an edge of the  polyhedron.
       A facet is a set of ridges, a set of neighboring facets, a
       set of incident vertices, and a hyperplane equation.   For
       simplicial  facets, the ridges are defined by the vertices
       and neighboring facets.  When Qhull merges two facets,  it
       produces  a  non-simplicial facet.  A non-simplicial facet
       has more than d neighbors and  may  share  more  than  one
       ridge with a neighbor.


IMPRECISION
       Since Qhull uses floating point arithmetic, roundoff error
       may occur for each calculation.  This causes  problems for
       most geometric algorithms.

       Qhull  automatically  sets  option  'C-0' in 2-d, 3-d, and
       4-d, or option 'Qx' in 5-d and higher.  These options han-
       dle  precision problems by merging facets.  Alternatively,
       use option 'QJ' to joggle the input.

       With 'C-0', Qhull  merges  non-convex  facets  while  con-
       structing  the hull. The remaining facets are clearly con-
       vex. With 'Qx',  Qhull  merges  coplanar  horizon  facets,
       flipped  facets, concave facets and duplicated ridges.  It
       merges coplanar facets after constructing the hull.   With
       'Qx',  coplanar points may be missed, but it appears to be
       unlikely.

       To guarantee triangular  output,  joggle  the  input  with
       option 'QJ'.  Facet merging will not occur.

OPTIONS
       To  get  a  list  of  the  most important options, execute
       'qhull -?'.  To get a  complete  list  of  options,
       execute  'qhull  -'.   To  get a complete, concise list of
       options, execute 'qhull .'.

       Options can be in any order.  Capitalized options take  an
       argument  (except  'PG'  and 'F' options).  Single letters
       are used for output formats and precision constants.   The
       other options are grouped into menus: output formats ('F'), 
       Geomview output ('G'), printing  ('P'),  Qhull control ('Q'), 



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qhull(1)                                                 qhull(1)


       and tracing ('T').

       Main options:

       default
              Compute  the  convex  hull  of  the  input  points.
              Report a summary of the result.

       d      Compute the Delaunay triangulation by  lifting  the
              input  points  to  a  paraboloid.   The  'o' option
              prints the  input  points  and  facets.   The  'QJ'
              option  guarantees  triangular  output.   The  'Ft'
              option prints a triangulation.  It adds points (the
              centrums) to non-simplicial facets.

       v      Compute  the Voronoi diagram from the Delaunay tri-
              angulation.  The 'p' option prints the Voronoi ver-
              tices.   The 'o' option prints the Voronoi vertices
              and the vertices in each Voronoi region.  It  lists
              regions  in  site id order.  The 'Fv' option prints
              each ridge of the Voronoi diagram.   The  first  or
              zero'th  vertex indicates the infinity vertex.  Its
              coordinates are qh_INFINITE  (-10.101).   It  indi-
              cates   unbounded  Voronoi  regions  or  degenerate
              Delaunay triangles.

       Hn,n,...
              Compute halfspace intersection  about  [n,n,0,...].
              The  input  is  a  set of halfspaces defined in the
              same format as 'n', 'Fo', and 'Fi'.   Use  'Fp'  to
              print  the  intersection  points.  Use 'Fv' to list
              the intersection points for  each  halfspace.   The
              other  output formats display the dual convex hull.

              The point [n,n,n,...] is a feasible point  for  the
              halfspaces, i.e., a point that is inside all of the
              halfspaces (Hx+b <=  0).   The  default  coordinate
              value is 0.

              The  input may start with a feasible point.  If so,
              use 'H' by itself.  The input starts with a  feasi-
              ble  point  when the first number is the dimension,
              the second number is "1", and the coordinates  com-
              plete  a line.  The 'FV' option produces a feasible
              point for a convex hull.

       d Qu   Compute the  furthest-site  Delaunay  triangulation
              from  the upper convex hull.  The 'o' option prints
              the input points and facets.  The 'QJ' option guar-
              antees triangular otuput.  You can also use facets.

       v Qu   Compute the furthest-site Voronoi diagram.  The 'p'
              option prints the Voronoi vertices.  The 'o' option
              prints the Voronoi vertices  and  the  vertices  in



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qhull(1)                                                 qhull(1)


              each  Voronoi  region.  The 'Fv' option prints each
              ridge of the Voronoi diagram.  The first or zero'th
              vertex  indicates  the infinity vertex at infinity.
              Its  coordinates  are  qh_INFINITE  (-10.101).   It
              indicates  unbounded Voronoi regions and degenerate
              Delaunay triangles.

       Qt     Triangulated output.


       Input/Output options:

       f      Print all facets and all fields of each  facet.

       G      Output  the hull in Geomview format.  For imprecise
              hulls, Geomview displays the inner and outer  hull.
              Geomview can also display points, ridges, vertices,
              coplanar  points,  and  facet  intersections.   See
              below for a list of options.

              For  Delaunay triangulations, 'G' displays the cor-
              responding paraboloid.  For halfspace intersection,
              'G' displays the dual polytope.

       i      Output the incident vertices for each facet.  Qhull
              prints the number of facets followed  by  the  ver-
              tices  of  each  facet.   One  facet is printed per
              line.  The numbers are the  0-relative  indices  of
              the  corresponding  input  points.   The facets are
              oriented.

              In 4-d and higher, Qhull  triangulates  non-simpli-
              cial  facets.   Each  apex  (the first vertex) is a
              created point that corresponds to the facet's  cen-
              trum.  Its index is greater than the indices of the
              input points.  Each base corresponds to  a  simpli-
              cial  ridge  between two facets.  To print the ver-
              tices without triangulation, use option 'Fv'.  To 
              print the centrum coordinates, use option 'Ft'. The
              centrum indices for option 'i' are one more than 
              the centrum indices for option 'Ft'.


       m      Output  the  hull  in  Mathematica  format.   Qhull
              writes  a  Mathematica  file for 2-d and 3-d convex
              hulls and for 2-d Delaunay triangulations.    Qhull
              produces a list of objects that you can assign to a
              variable in Mathematica,  for  example:  "list=  <<
              <outputfilename> ". If the object is 2-d, it can be
              visualized  by  "Show[Graphics[list]]  ".  For  3-d
              objects the command is "Show[Graphics3D[list]]".

       n      Output  the  normal equation for each facet.  Qhull
              prints the dimension  (plus  one),  the  number  of
              facets,  and  the  normals  for  each  facet.   The
              facet's offset follows its normal coefficients.

       o      Output the facets in OFF file format.  Qhull prints
              the  dimension, number of points, number of facets,
              and  number  of  ridges.   Then   it   prints   the



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qhull(1)                                                 qhull(1)


              coordinates  of  the  input points and the vertices
              for each facet.  Each facet is on a separate  line.
              The  first  number  is the number of vertices.  The
              remainder are  the  indices  of  the  corresponding
              points.  The vertices are oriented in 2-d, 3-d, and
              in simplicial facets.

              For 2-d Voronoi diagrams, the vertices  are  sorted
              by adjacency, but not oriented.  In 3-d and higher,
              the Voronoi vertices are sorted by index.  See  the
              'v' option for more information.

       p      Output the coordinates of each vertex point.  Qhull
              prints the dimension, the number of points, and the
              coordinates  for  each  vertex.   With the 'Gc' and
              'Gi' options, it also prints coplanar and  interior
              points.   For Voronoi diagrams, it prints the coor-
              dinates of each Voronoi vertex.

       s      Print a summary to stderr.  If  no  output  options
              are  specified,  a summary goes to stdout.
              The summary lists the number of input  points,  the
              dimension,  the  number  of  vertices in the convex
              hull, the number of facets in the convex hull,  the
              number of good facets (if 'Pg'), and statistics.

              The  last  two  statistics (if needed) measure the
              maximum distance from a point or vertex to a facet.
              The number in parenthesis (e.g., 2.1x) is the ratio
              between the maximum  distance  and  the  worst-case
              distance due to merging two simplicial facets.


       Precision options

       An     Maximum  angle  given  as  a  cosine.  If the angle
              between a pair of facet normals is greater than n, Qhull
              merges  one  of the facets into a neighbor.  If 'n'
              is negative, Qhull tests angles after  adding  each
              point  to  the hull (pre-merging).  If 'n' is posi-
              tive, Qhull tests  angles  after  constructing  the
              hull  (post-merging).   Both  pre- and post-merging
              can be defined.

              Option 'C0' or 'C-0' is set  if  the  corresponding
              'Cn' or 'C-n' is not set.  If 'Qx' is set, then 'A-
              n' and 'C-n' are checked after  the  hull  is  con-
              structed and before 'An' and 'Cn' are checked.

       Cn     Centrum  radius.  If a centrum is less than n below
              a  neighboring  facet,  Qhull  merges  one  of  the
              facets.   If  'n'  is negative or '-0', Qhull tests
              and merges facets after adding each  point  to  the
              hull.   This  is  called  "pre-merging".  If 'n' is



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qhull(1)                                                 qhull(1)


              positive, Qhull  tests  for  convexity  after  con-
              structing the hull ("post-merging").  Both pre- and
              post-merging can be defined.

              For 5-d and higher, 'Qx' should be used instead  of
              'C-n'.  Otherwise, most or all facets may be merged
              together.

       En     Maximum roundoff error for distance computations.

       Rn     Randomly perturb distance computations up to +/-  n
              *  max_coord.  This option perturbs every distance,
              hyperplane, and angle computation.  To use time  as
              the random number seed, use option 'QR-1'.

       Vn     Minimum  distance  for  a  facet  to be visible.  A
              facet is visible if the distance from the point  to
              the facet is greater than 'Vn'.

              Without  merging, the default value for 'Vn' is the
              round-off error ('En').  With merging, the  default
              value  is  the  pre-merge centrum ('C-n') in 2-d or
              3--d, or three times that in other dimensions.   If
              the outside width is specified ('Wn'), the maximum,
              default value for 'Vn' is 'Wn'.

       Un     Maximum distance below a facet for a  point  to  be
              coplanar  to the facet.  The default value is 'Vn'.

       Wn     Minimum outside width  of  the  hull.   Points  are
              added  to  the convex hull only if they are clearly
              outside of a facet.  A point is outside of a  facet
              if  its distance to the facet is greater than 'Wn'.
              The normal value for 'Wn' is  'En'.   If  the  user
              specifies  pre-merging  and does not set 'Wn', than
              'Wn'  is  set  to  the  premerge  'Cn'  and  maxco-
              ord*(1-An).


       Additional input/output formats

       Fa     Print area for each facet.  For Delaunay triangula-
              tions, the area is the area of the  triangle.   For
              Voronoi  diagrams, the area is the area of the dual
              facet.   Use  'PAn'  for  printing  the  n  largest
              facets, and option 'PFn' for printing facets larger
              than 'n'.

              The area for non-simplicial facets is  the  sum  of
              the areas for each ridge to the centrum.   Vertices
              far below the facet's hyperplane are ignored.   The
              reported  area  may  be significantly less than the
              actual area.




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qhull(1)                                                 qhull(1)


       FA     Compute the total area and volume for  option  's'.
              It  is  an  approximation for non-simplicial facets
              (see 'Fa').

       Fc     Print coplanar points for each facet.   The  output
              starts  with the number of facets.  Then each facet
              is printed one per line.  Each line is  the  number
              of  coplanar  points  followed  by  the  point ids.
              Option 'Qi' includes  the  interior  points.   Each
              coplanar  point (interior point) is assigned to the
              facet it is furthest above (resp., least below).

       FC     Print centrums for each facet.  The  output  starts
              with  the  dimension  followed  by  the  number  of
              facets.  Then each facet centrum  is  printed,  one
              per line.

       Fd     Read  input  in cdd format with homogeneous points.
              The input starts with comments.  The first  comment
              is  reported  in  the summary.  Data starts after a
              "begin" line.  The  next  line  is  the  number  of
              points  followed  by  the dimension+1 and "real" or
              "integer".  Then the  points  are  listed   with  a
              leading  "1" or "1.0".  The data ends with an "end"
              line.

              For halfspaces ('Fd Hn,n,...'), the input format is
              the  same.   Each halfspace starts with its offset.
              The sign of the offset is the opposite  of  Qhull's
              convention.

       FD     Print  normals ('n', 'Fo', 'Fi') or points ('p') in
              cdd format.  The first line  is  the  command  line
              that  invoked  Qhull.   Data  starts with a "begin"
              line.  The next line is the number  of  normals  or
              points  followed  by  the  dimension+1  and "real".
              Then the normals or points  are  listed   with  the
              offset  before  the  coefficients.   The offset for
              points is 1.0.  The  offset  for  normals  has  the
              opposite sign.  The data ends with an "end" line.

       FF     Print  facets  (as  in  'f')  without  printing the
              ridges.

       Fi     Print inner planes for each facet.  The inner plane
              is below all vertices.

       Fi     Print  separating  hyperplanes  for  bounded, inner
              regions of the Voronoi diagram.  The first line  is
              the  number  of  ridges.   Then  each hyperplane is
              printed, one per line.  A line starts with the num-
              ber  of  indices  and floats.  The first pair lists
              adjacent input sites, the next  d  floats  are  the
              normalized coefficients for the hyperplane, and the



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qhull(1)                                                 qhull(1)


              last float is the offset.  The hyperplane  is  ori-
              ented  toward 'QVn' (if defined), or the first input 
              site of the pair.  Use 'Tv' to verify that the 
              hyperplanes are perpendicular  bisectors.   Use  
              'Fo'  for   unbounded regions,  and 'Fv' for the 
              corresponding Voronoi vertices.

       FI     Print facet identifiers.

       Fm     Print number of merges for each facet.  At most 511
              merges  are  reported  for  a facet.  See 'PMn' for
              printing the facets with the most merges.

       FM     Output  the  hull  in  Maple format.  See 'm'

       Fn     Print neighbors for each facet.  The output  starts
              with  the  number  of  facets.   Then each facet is
              printed one per line.  Each line is the  number  of
              neighbors  followed  by an index for each neighbor.
              The indices match the other facet output formats.

              A negative index indicates an unprinted  facet  due
              to  printing  only  good  facets ('Pg').  It is the
              negation of the  facet's  id  (option  'FI').   For
              example,  negative  indices are used for facets "at
              infinity" in the Delaunay triangulation.

       FN     Print vertex neighbors or coplanar facet  for  each
              point.   The  first  line  is the number of points.
              Then each point is printed, one per line.   If  the
              point  is coplanar, the line is "1" followed by the
              facet's id.  If the point is not a selected vertex,
              the  line is "0".  Otherwise, each line is the num-
              ber of  neighbors  followed  by  the  corresponding
              facet indices (see 'Fn').

       Fo     Print  outer planes for each facet in the same for-
              mat as 'n'.  The outer plane is above all points.

       Fo     Print separating hyperplanes for  unbounded,  outer
              regions  of the Voronoi diagram.  The first line is
              the number of  ridges.   Then  each  hyperplane  is
              printed, one per line.  A line starts with the num-
              ber of indices and floats.  The  first  pair  lists
              adjacent  input  sites,  the  next d floats are the
              normalized coefficients for the hyperplane, and the
              last  float  is the offset.  The hyperplane is ori-
              ented  toward 'QVn' (if defined), or the first input 
              site of the pair.  Use 'Tv' to verify that the 
              hyperplanes are perpendicular  bisectors.   Use  
              'Fi'  for bounded regions,  and 'Fv' for the 
              corresponding Voronoi vertices.

       FO     List  all  options to stderr, including the default
              values.  Additional 'FO's are printed to stdout.

       Fp     Print points for  halfspace  intersections  (option
              'Hn,n,...').   Each  intersection  corresponds to a



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qhull(1)                                                 qhull(1)


              facet of the dual polytope.  The  "infinity"  point
              [-10.101,-10.101,...]    indicates   an   unbounded
              intersection.

       FP     For each coplanar point ('Qc') print the  point  id
              of  the nearest vertex, the point id, the facet id,
              and the distance.

       FQ     Print command used for qhull and input.

       Fs     Print a summary.  The first line  consists  of  the
              number  of  integers  ("7"), followed by the dimen-
              sion, the number of points, the number of vertices,
              the  number  of  facets,  the  number  of  vertices
              selected for output, the number of facets  selected
              for  output, the number of coplanar points selected
              for output.

              The second line consists of  the  number  of  reals
              ("2"),  followed by the maxmimum offset to an outer
              plane and and minimum offset  to  an  inner  plane.
              Roundoff  is included.  Later versions of Qhull may
              produce additional integers or reals.

       FS     Print the size of the hull.  The  first  line  con-
              sists  of the number of integers ("0").  The second
              line consists of the number of  reals  ("2"),  fol-
              lowed  by  the total facet area, and the total vol-
              ume.  Later versions of  Qhull  may  produce  addi-
              tional integers or reals.

              The  total volume measures the volume of the inter-
              section of the halfspaces defined  by  each  facet.
              Both  area  and  volume are approximations for non-
              simplicial facets.  See option 'Fa'.

       Ft     Print a triangulation with added  points  for  non-
              simplicial facets.  The first line is the dimension
              and the second line is the number of points and the
              number of facets.  The points follow, one per line,
              then the facets follow as a list of point  indices.
              With option points include the point-at-infinity.

       Fv     Print  vertices  for each facet.  The first line is
              the number of facets.  Then each facet is  printed,
              one  per line.  Each line is the number of vertices
              followed by the corresponding point ids.   Vertices
              are listed in the order they were added to the hull
              (the last one is first).

       Fv     Print all ridges of a Voronoi diagram.   The  first
              line  is  the number of ridges.  Then each ridge is
              printed, one per line.  A line starts with the num-
              ber  of  indices.   The  first  pair lists adjacent



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qhull(1)                                                 qhull(1)


              input sites, the  remaining  indices  list  Voronoi
              vertices.   Vertex  '0'  indicates  the  vertex-at-
              infinity (i.e., an unbounded  ray).   In  3-d,  the
              vertices  are  listed  in order.  See 'Fi' and 'Fo'
              for separating hyperplanes.

       FV     Print average vertex.  The average vertex is a fea-
              sible point for halfspace intersection.

       Fx     List  extreme points (vertices) of the convex hull.
              The first line is the number of points.  The  other
              lines give the indices of the corresponding points.
              The first point is '0'.  In 2-d, the  points  occur
              in counter-clockwise order; otherwise they occur in
              input order.   For  Delaunay  triangulations,  'Fx'
              lists  the  extreme points of the input sites.  The
              points are unordered.


       Geomview options

       G      Produce a file for viewing with Geomview.   Without
              other  options,  Qhull displays edges in 2-d, outer
              planes in 3-d, and ridges in 4-d.  A ridge  can  be
              explicit or implicit.  An explicit ridge is a dim-1
              dimensional simplex between two  facets.   In  4-d,
              the explicit ridges are triangles.  When displaying
              a ridge in 4-d, Qhull projects the ridge's vertices
              to  one  of  its  facets' hyperplanes.  Use 'Gh' to
              project ridges to the intersection of  both  hyper-
              planes.

       Ga     Display all input points as dots.

       Gc     Display  the  centrum  for  each facet in 3-d.  The
              centrum is defined by a green radius sitting  on  a
              blue  plane.   The plane corresponds to the facet's
              hyperplane.  The radius  is  defined  by  'C-n'  or
              'Cn'.

       GDn    Drop  dimension  n  in 3-d or 4-d.  The result is a
              2-d or 3-d object.

       Gh     Display hyperplane intersections in  3-d  and  4-d.
              In  3-d, the intersection is a black line.  It lies
              on two  neighboring  hyperplanes  (c.f.,  the  blue
              squares  associated with centrums ('Gc')).  In 4-d,
              the ridges are projected  to  the  intersection  of
              both hyperplanes.

       Gi     Display  inner  planes  in  2-d and 3-d.  The inner
              plane of a facet is below all of its vertices.   It
              is  parallel  to the facet's hyperplane.  The inner
              plane's color is the opposite (1-r,1-g,1-b) of  the



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qhull(1)                                                 qhull(1)


              outer  plane.  Its edges are determined by the ver-
              tices.

       Gn     Do not display inner or outer planes.  By  default,
              Geomview displays the precise plane (no merging) or
              both inner  and  output  planes  (merging).   Under
              merging,  Geomview does not display the inner plane
              if the the difference between inner  and  outer  is
              too small.

       Go     Display  outer  planes  in  2-d and 3-d.  The outer
              plane of a facet is above all input points.  It  is
              parallel  to  the facet's hyperplane.  Its color is
              determined by the facet's normal, and its edges are
              determined by the vertices.

       Gp     Display  coplanar  points and vertices as radii.  A
              radius defines a  ball  which  corresponds  to  the
              imprecision  of  the point.  The imprecision is the
              maximum of the roundoff error, the centrum  radius,
              and  maxcoord  * (1-An).  It is at least 1/20'th of
              the maximum coordinate, and ignores post-merging if
              pre-merging is done.

       Gr     Display  ridges  in  3-d.  A ridge connects the two
              vertices that are  shared  by  neighboring  facets.
              Ridges are always displayed in 4-d.

       Gt     A  3-d  Delaunay  triangulation looks like a convex
              hull with interior facets.  Option 'Gt' removes the
              outside  ridges to reveal the outermost facets.  It
              automatically sets options 'Gr' and 'GDn'.

       Gv     Display vertices as spheres.   The  radius  of  the
              sphere  corresponds to the imprecision of the data.
              See 'Gp' for determining the radius.


       Print options

       PAn    Only the n  largest  facets  are  marked  good  for
              printing.   Unless  'PG'  is set, 'Pg' is automati-
              cally set.

       Pdk:n  Drop facet from output  if  normal[k]  <=  n.   The
              option 'Pdk' uses the default value of 0 for n.

       PDk:n  Drop  facet  from  output  if  normal[k] >= n.  The
              option 'PDk' uses the default value of 0 for n.

       PFn    Only facets with area at least 'n' are marked  good
              for printing.  Unless 'PG' is set, 'Pg' is automat-
              ically set.




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qhull(1)                                                 qhull(1)


       Pg     Print only good facets.  A  good  facet  is  either
              visible from a point (the 'QGn' option) or includes
              a point (the 'QVn'  option).   It  also  meets  the
              requirements  of  'Pdk'  and 'PDk' options.  Option
              'Pg' is automatically set for  options 'd', 'PAn', 
              'PFn', and 'PMn'

       PG     Print neighbors of good facets.

       PMn    Only  the  n facets with the most merges are marked
              good for printing.  Unless 'PG'  is  set,  'Pg'  is
              automatically set.

       Po     Force output despite precision problems.  Verify  ('Tv')  does    not check
              coplanar points.  Flipped facets are  reported  and
              concave  facets  are  counted.   If  'Po'  is used,
              points are not partitioned into flipped facets  and
              a  flipped  facet  is  always  visible  to a point.
              Also, if an error occurs before the  completion  of
              Qhull  and  tracing  is  not active, 'Po' outputs a
              neighborhood of the erroneous facets (if any).

       Pp     Do not report precision problems.


       Qhull control options

       Qa     Allow input with fewer or more points than coordinates
       
       Qbk:0Bk:0
              Drop dimension  k  from  the  input  points.   This
              allows  the user to take convex hulls of sub-dimen-
              sional objects.  It happens before the Delaunay and
              Voronoi transformation.

       QbB    Scale the input points to fit the unit cube.  After
              scaling, the lower bound will be -0.5 and the upper
              bound  +0.5  in  all  dimensions.  For Delaunay and
              Voronoi diagrams, scaling happens after  projection
              to the paraboloid.  Under precise arithmetic, scal-
              ing does not change  the  topology  of  the  convex
              hull.

       Qbb    Scale  the last coordinate to [0, m] where m is the
              maximum absolute value of  the  other  coordinates.
              For  Delaunay and Voronoi diagrams, scaling happens
              after projection to  the  paraboloid.   It  reduces
              roundoff error for inputs with integer coordinates.
              Under precise arithmetic, scaling does  not  change
              the topology of the convex hull.

       Qbk:n  Scale  the  k'th  coordinate  of  the input points.
              After scaling, the lower bound of the input  points
              will be n.  'Qbk' scales to -0.5.



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qhull(1)                                                 qhull(1)


       QBk:n  Scale  the  k'th  coordinate  of  the input points.
              After scaling, the upper bound will  be  n.   'QBk'
              scales to +0.5.

       Qc     Keep  coplanar points with the nearest facet.  Out-
              put formats 'p', 'f', 'Gp', 'Fc',  'FN',  and  'FP'
              will print the points.

       Qf     Partition points to the furthest outside facet.

       Qg     Only  build  good  facets.   With  the 'Qg' option,
              Qhull will only build those facets that it needs to
              determine  the  good  facets  in  the  output.  See
              'QGn', 'QVn', and 'PdD' for defining  good  facets,
              and  'Pg'  and  'PG'  for  printing good facets and
              their neighbors.

       QGn    A facet is good (see 'Qg' and 'Pg') if it is  visi-
              ble  from point n.  If n < 0, a facet is good if it
              is not visible from point n.  Point n is not  added
              to  the  hull  (unless 'TCn' or 'TPn').  With rbox,
              use the 'Pn,m,r' option to define  your  point;  it
              will be point 0 (QG0).

       Qi     Keep  interior points with the nearest facet.  Out-
              put formats 'p', 'f', 'Gp', 'FN',  'FP',  and  'Fc'
              will print the points.

       QJn    Joggle  each  input  coordinate  by adding a random
              number in [-n,n].  If  a  precision  error  occurs,
              then  qhull  increases  n and tries again.  It does
              not increase n beyond a certain value, and it stops
              after  a  certain  number of attempts [see user.h].
              Option 'QJ' selects a default  value  for  n.   The
              output will be simplicial.  For Delaunay triangula-
              tions, 'QJn' sets 'Qbb' to scale the  last  coordi-
              nate (not if 'Qbk:n' or 'QBk:n' is set).  'QJn' is
              deprecated for Voronoi diagrams.  See also 'Qt'.

       Qm     Only  process  points that would otherwise increase
              max_outside.  Other points are treated as  coplanar
              or interior points.

       Qr     Process  random  outside points instead of furthest
              ones.  This makes Qhull equivalent to  the  random-
              ized  incremental  algorithms.   CPU  time  is  not
              reported since the randomization is inefficient.

       QRn    Randomly rotate the input points.  If n=0, use time
              as  the  random  number seed.  If n>0, use n as the
              random number seed.  If n=-1, don't rotate but  use
              time  as the random number seed.  For Delaunay tri-
              angulations ('d' and 'v'), rotate  about  the  last
              axis.




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qhull(1)                                                 qhull(1)


       Qs     Search all points for the initial simplex.

       Qt     Triangulated output.  Triangulate non-simplicial
              facets. 'Qt' is deprecated for Voronoi diagrams.
              See also 'QJn'

       Qv     Test  vertex  neighbors  for  convexity after post-
              merging.  To use the 'Qv' option, you also need  to
              set a merge option (e.g., 'Qx' or 'C-0').

       QVn    A  good facet (see 'Qg' and 'Pg') includes point n.
              If n<0, then a good facet does not include point n.
              The point is either in the initial simplex or it is
              the first point added to the  hull.   Option  'QVn'
              may not be used with merging.

       Qw     Allow option warnings. Otherwise Qhull returns an 
              error after most option warnings.

       Qx     Perform  exact merges while building the hull.  The
              "exact" merges are merging a point into a  coplanar
              facet  (defined  by 'Vn', 'Un', and 'C-n'), merging
              concave facets, merging duplicate ridges, and merg-
              ing  flipped  facets.   Coplanar  merges  and angle
              coplanar merges ('A-n') are not performed.  Concav-
              ity testing is delayed until a merge occurs.

              After  the  hull  is built, all coplanar merges are
              performed (defined by 'C-n' and 'A-n'), then  post-
              merges are performed (defined by 'Cn' and 'An').

       Qz     Add  a  point  "at  infinity"  that  is  above  the
              paraboloid for Delaunay triangulations and  Voronoi
              diagrams.   This  reduces  precision  problems  and
              allows the triangulation of cospherical points.


       Qhull experiments and speedups

       Q0     Turn off pre-merging as  a  default  option.   With
              'Q0'/'Qx'  and  without explicit pre-merge options,
              Qhull ignores precision issues  while  constructing
              the  convex  hull.   This  may  lead  to  precision
              errors.  If so, a descriptive warning is generated.

       Q1     With 'Q1', Qhull merges by mergetype/angle instead 
              of mergetype/distance.

       Q2     With 'Q2', Qhull merges all facets at once  instead
              of  using  independent  sets  of  merges  and  then
              retesting.

       Q3     With 'Q3', Qhull does  not  remove  redundant  ver-
              tices.

       Q4     With 'Q4', Qhull avoids merges of an old facet into
              a new facet.

       Q5     With 'Q5', Qhull does not correct outer  planes  at
              the  end.  The maximum outer plane is used instead.




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qhull(1)                                                 qhull(1)


       Q6     With 'Q6', Qhull  does  not  pre-merge  concave  or
              coplanar facets.

       Q7     With  'Q7',  Qhull  processes facets in depth-first
              order instead of breadth-first order.

       Q8     With 'Q8' and merging, Qhull does not retain  near-
              interior  points  for adjusting outer planes.  'Qc'
              will probably retain all points that  adjust  outer
              planes.

       Q9     With 'Q9', Qhull processes the furthest of all out-
              side sets at each iteration.

       Q10    With 'Q10', Qhull does not use special processing
              for narrow distributions.

       Q11    With 'Q11', Qhull copies normals and recomputes
              centrums for tricoplanar facets.

       Q12    With 'Q12', Qhull allows wide facets and wide dupridge
       
       Q14    With 'Q14', Qhull merges pinched vertices that create a dupridge.

       Q15    With 'Q15', Qhull checks for duplicate ridges with the same vertices.
       
       Trace options

       Tn     Trace at level n.  Qhull  includes  full  execution
              tracing.   'T-1'  traces  events.   'T1' traces the
              overall execution of the program.   'T2'  and  'T3'
              trace overall execution and geometric and topologi-
              cal  events.   'T4'  traces  the  algorithm.   'T5'
              includes  information  about  memory allocation and
              Gaussian elimination.

       Ta     Annotate output with codes that identify the
              corresponding qh_fprintf() statement.

       TAn    Stop Qhull after adding n vertices.

       Tc     Check frequently during execution.  This will catch
              most inconsistency errors.

       TCn    Stop  Qhull  after  building the cone of new facets
              for point n.  The output for 'f' includes the  cone
              and the old hull.  See also 'TVn'.

       Tf     Flush output after each qh_fprintf.  Use 'Tf' for 
              debugging segfaults.  See 'Tz' for redirecting stderr.
       
       TFn    Report  progress  whenever  more  than n facets are
              created During post-merging, 'TFn' reports progress
              after more than n/2 merges.

       TI file
              Input data from 'file'.  The filename may not include
              spaces or quotes.

       TMn    Turn on tracing at n'th merge.

       TO file
              Output results to 'file'.  The name may be enclosed
              in single quotes.

       TPn    Turn on tracing when point n is added to the  hull.
              Trace partitions of point n. If used with TWn, turn off
              tracing after adding point n to the hull.

       TP-1   Turn on tracing after qh_buildhull and qh_postmerge.

       TRn    Rerun  qhull  n  times.  Usually used with 'QJn' to
              determine the probability that a given joggle  will
              fail.

       Ts     Collect  statistics  and print to stderr at the end
              of execution.

       Tv     Verify the convex hull.  This checks the  topologi-
              cal  structure,  facet  convexity, and point inclu-
              sion.  If precision problems occurred,  facet  con-
              vexity  is  tested whether or not 'Tv' is selected.
              Option 'Tv'  does  not  check  point  inclusion  if


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qhull(1)                                                 qhull(1)


              forcing output with 'Po', or if 'Q5' is set.

              For  point  inclusion  testing, Qhull verifies that
              all points are below all outer planes  (facet->max-
              outside).  Point inclusion is exhaustive if merging
              or if the facet-point product is small enough; oth-
              erwise  Qhull  verifies  each point with a directed
              search (qh_findbest).

              Point inclusion testing occurs after producing out-
              put.   It  prints a message to stderr unless option
              'Pp' is used.  This allows the  user  to  interrupt
              Qhull without changing the output.

       TVn    Stop  Qhull  after  adding point n.  If n < 0, stop
              Qhull before adding point n.  Output shows the hull
              at this time.  See also 'TCn'

       TWn    Trace  merge  facets when the width is greater than
              n.

       Tz     Redirect stderr to stdout.  See 'Tf' for flushing writes.


BUGS
       Please    report    bugs     to     Brad     Barber     at
       qhull_bug@qhull.org.

       If Qhull does not compile, it is due to an incompatibility
       between your system and ours.  The first thing to check is
       that  your compiler is ANSI standard.  If it is, check the
       man page for the best options, or  find  someone  to  help
       you.  If you locate the cause of your problem, please send
       email since it might help others.

       If Qhull compiles but crashes on the test case (rbox  D4),
       there's  still  incompatibility  between  your  system and
       ours.  Typically it's been due to mem.c and memory  align-
       ment.   You  can  use qh_NOmem in mem.h to turn off memory
       management.  Please let us know if you figure out  how  to
       fix these problems.

       If  you  do  find  a  problem,  try  to simplify it before
       reporting the error.  Try different size inputs to  locate
       the  smallest one that causes an error.  You're welcome to
       hunt through the code  using  the  execution  trace  as  a
       guide.   This  is  especially true if you're incorporating
       Qhull into your own program.

       When you do report an error, please attach a data  set  to
       the  end of your message.  This allows us to see the error
       for ourselves.  Qhull is maintained part-time.



Geometry Center              2019/05/03                17





qhull(1)                                                 qhull(1)


E-MAIL
       Please  send  correspondence  to  qhull@qhull.org   and
       report  bugs  to  qhull_bug@qhull.org.  Let us know how
       you use Qhull.  If you mention it in a paper, please  send
       the reference and an abstract.

       If  you would like to get Qhull announcements (e.g., a new
       version) and news (any bugs that get fixed, etc.), let  us
       know  and  we  will  add  you to our mailing list.  If you
       would like to communicate with other Qhull users, we  will
       add you to the qhull_users alias.  For Internet news about
       geometric algorithms and convex hulls, look at comp.graph-
       ics.algorithms and sci.math.num-analysis


SEE ALSO
       rbox(1)

       Barber,  C.  B.,  D.P.  Dobkin,  and  H.T. Huhdanpaa, "The
       Quickhull Algorithm for Convex Hulls," ACM Trans. on Math-
       ematical Software, 22(4):469-483, Dec. 1996.
       http://portal.acm.org/citation.cfm?doid=235815.235821
       http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405


       Clarkson, K.L., K. Mehlhorn, and R. Seidel, "Four  results
       on  randomized  incremental  construction,"  Computational
       Geometry: Theory and Applications,  vol.  3,  p.  185-211,
       1993.

       Preparata,  F.  and  M.  Shamos,  Computational  Geometry,
       Springer-Verlag, New York, 1985.



AUTHORS
         C. Bradford Barber                    Hannu Huhdanpaa
         bradb@shore.net                       hannu@qhull.org



ACKNOWLEDGEMENTS
       A special thanks to Albert Marden, Victor Milenkovic,  the
       Geometry Center, Harvard University, and Endocardial Solu-
       tions, Inc. for supporting this work.

       Qhull 1.0 and 2.0 were developed under National Science Foundation
       grants NSF/DMS-8920161 and NSF-CCR-91-15793 750-7504.  David Dobkin



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qhull(1)                                                 qhull(1)


       guided the original work at Princeton University.  If you find it
       useful, please let us know.

       The Geometry Center was supported by grant DMS-8920161 from the National
       Science Foundation, by grant DOE/DE-FG02-92ER25137 from the Department
       of Energy, by the University of Minnesota, and by Minnesota Technology, Inc.

       Qhull is available from http://www.qhull.org

Geometry Center              2019/05/03                19





rbox(1)                                                   rbox(1)


NAME
       rbox - generate point distributions for qhull

SYNOPSIS
       Command "rbox" (w/o arguments) lists the options.

DESCRIPTION
       rbox  generates random or regular points according to the
       options given, and  outputs  the  points  to  stdout.  The
       points  are  generated in a cube, unless 's' or given. The
       format of the output is the following: first line contains
       the dimension and a comment, second line contains the num-
       ber of points, and the following lines contain the points,
       one  point per line. Points are represented by their coor-
       dinate values.

EXAMPLES
       rbox 10
              10 random points in the unit cube centered  at  the
              origin.

       rbox 10 s D2
              10 random points on a 2-d circle.

       rbox 100 W0
              100 random points on the surface of a cube.

       rbox 1000 s D4
              1000 random points on a 4-d sphere.

       rbox c D5 O0.5
              a 5-d hypercube with one corner at the origin.

       rbox d D10
              a 10-d diamond.

       rbox x 1000 r W0
              100 random points on the surface of a fixed simplex

       rbox y D12
              a 12-d simplex.

       rbox l 10
              10 random points along a spiral

       rbox l 10 r
              10 regular points  along  a  spiral  plus  two  end
              points

       rbox 1000 L10000 D4 s
              1000 random points on the surface of a narrow lens.

       rbox c G2 d G3
              a cube with coordinates +2/-2 and  a  diamond  with



Geometry Center          August 10, 1998                        1





rbox(1)                                                   rbox(1)


              coordinates +3/-3.

       rbox 64 M3,4 z
              a  rotated,  {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lat-
              tice (Mesh) of integer points.

       rbox P0 P0 P0 P0 P0
              5 copies of the origin in 3-d.  Try 'rbox P0 P0  P0
              P0 P0 | qhull QJ'.

       r 100 s Z1 G0.1
              two  cospherical  100-gons plus another cospherical
              point.

       100 s Z1
              a cone of points.

       100 s Z1e-7
              a narrow cone of points with many precision errors.

OPTIONS
       n      number of points

       Dn     dimension n-d (default 3-d)

       Bn     bounding box coordinates (default 0.5)

       l      spiral distribution, available only in 3-d

       Ln     lens  distribution  of  radius n.  May be used with
              's', 'r', 'G', and 'W'.

       Mn,m,r lattice  (Mesh)  rotated  by  {[n,-m,0],   [m,n,0],
              [0,0,r],  ...}.   Use  'Mm,n'  for a rigid rotation
              with r = sqrt(n^2+m^2).  'M1,0'  is  an  orthogonal
              lattice.   For  example,  '27  M1,0'  is  {0,1,2} x
              {0,1,2} x {0,1,2}.

       s      cospherical points randomly generated in a cube and
              projected to the unit sphere

       x      simplicial  distribution.   It  is fixed for option
              'r'.  May be used with 'W'.

       y      simplicial distribution plus a simplex.   Both  'x'
              and 'y' generate the same points.

       Wn     restrict  points  to distance n of the surface of a
              sphere or a cube

       c      add a unit cube to the output

       c Gm   add a cube with all combinations of +m  and  -m  to
              the output



Geometry Center          August 10, 1998                        2





rbox(1)                                                   rbox(1)


       d      add a unit diamond to the output.

       d Gm   add a diamond made of 0, +m and -m to the output
       
       Cn,r,m add n nearly coincident points within radius r of m points

       Pn,m,r add point [n,m,r] to the output first.  Pad coordi-
              nates with 0.0.

       n      Remove the command line from the first line of out-
              put.

       On     offset the data by adding n to each coordinate.

       t      use  time  in  seconds  as  the  random number seed
              (default is command line).

       tn     set the random number seed to n.

       z      generate integer coordinates.  Use 'Bn'  to  change
              the  range.   The  default  is 'B1e6' for six-digit
              coordinates.  In R^4, seven-digit coordinates  will
              overflow hyperplane normalization.

       Zn s   restrict points to a disk about the z+ axis and the
              sphere (default Z1.0).  Includes the opposite pole.
              'Z1e-6'  generates  degenerate  points under single
              precision.

       Zn Gm s
              same as Zn with an empty center (default G0.5).

       r s D2 generate a regular polygon

       r s Z1 G0.1
              generate a regular cone

BUGS
       Some combinations of arguments generate odd results.

       Report bugs to  qhull_bug@qhull.org,     other  correspon-
       dence to qhull@qhull.org

SEE ALSO
       qhull(1)

AUTHOR
       C. Bradford Barber
       bradb@shore.net
       




Geometry Center          August 10, 1998                        3



# end of q_test
eg/q_benchmark test 1 1 1 1
eg/q_benchmark: Temporarily add "$PWD/bin" to $PATH for access to rbox

============================================
== eg/q_benchmark [test] [precision-count] [other-count] [pinched-count] [time-count]
== Time and precision benchmarks for qhull
============================================

[jun'20] Many timing figures 5-10% faster than jun'19 results.  No change to code

'q_benchmark test 1 1 1 1' Fri, Jul 24, 2020 10:27:42 PM

# $Id: //main/2019/qhull/eg/q_benchmark#5 $$DateTime: 2020/06/05 16:33:18 $
# $Id: //main/2019/qhull/eg/qtest.sh#4 $$DateTime: 2019/06/25 15:24:47 $
qhull => qhull_r 8.0.1 (2020.2.r 2020/07/24)
-rwxr-xr-x 1 bbarber 197121 339968 Jul 24 21:06 /d/bash/local/qhull/bin/qhull
rbox => Version: 2019/11/10
-rwxr-xr-x 1 bbarber 197121 32768 Jul 24 21:06 /d/bash/local/qhull/bin/rbox
MINGW64_NT-10.0-19041 kelwyn 3.0.7-338.x86_64 2019-04-30 21:52 UTC x86_64 Msys

Logging to /d/bash/local/qhull/eg/qhull-benchmark.log and eg/qhull-benchmark-show.log

========================
=== test eg/qtest.sh ===
========================

== qtest.sh help

qtest.sh -- test qhull runs
  qtest.sh  N 'rbox c | qhull'         -- N random qhull runs
  qtest.sh  N 'rbox-opts' 'qhull-opts' -- N random rbox|qhull runs
  qtest.sh -N 'rbox c | qhull'         -- N qhull runs
  qtest.sh -N 'rbox opts' 'qhull opts' -- N rbox|qhull runs
execute rbox and qhull
  qtest.sh run 'rbox c | qhull'        -- execute 'qhull command'
  qtest.sh run QR... 'rbox | qhull'    -- execute 'qhull command QR...'
  qtest.sh run t... 'rbox-opts' 'qhull-opts' -- execute 'rbox t... | qhull'
log execution of rbox and qhull
  qtest.sh log 'rbox c | qhull'        -- log qhull to qhull.log/qhull-step.log
  qtest.sh QR... 'rbox c | qhull'      -- log a qhull run
  qtest.sh t... 'rbox-opts' 'qhull-opts' -- log a 'rbox|qhull' run
  qtest.sh grep 'include-regexp'       -- grep qhull.log for events to grep.log
  qtest.sh grep 'include-regexp' 'exclude-regexp'
  qtest.sh grep-merge logfile          -- grep logfile for qh_mergefacet,etc. to stdout
  qtest.sh grep-step logfile           -- grep logfile for steps to stdout
  qtest.sh -v ...                      -- verbose output with environment vars
variables defined in qtest.sh
  QH_TEST_BASE        -- first tNN for negative counts
  QH_TEST_DEST        -- qtest.sh log
  QH_TEST_GREP        --   grep expression for qtest.sh log
  QH_SHOW_DEST        -- qtest.sh show log
  QH_SHOW_GREPX       --   exclude grep for show log
  QH_LOG_DEST         -- qhull log
  QH_LOG_GREP         --   grep expression for qhull log
  QH_STEP_DEST        -- qhull step log
  QH_STEP_GREP        --   grep expression for step log and grep-step
  QH_MERGE_GREP       -- grep expression for grep-merge
  QH_MERGE_GREPX      --   exclude grep for grep-merge
environment variables
  QHULL               -- qhull program, may be qconvex, etc
  QH_APPEND_DEST      -- append qtest.sh log
  QH_APPEND_SHOW      -- append show log
  QH_TEST             -- additional grep expression for qtest.sh log
  QH_TESTX            --   exclude grep for qtest.sh log
  QH_SHOW             -- grep expression for show log
  QH_SHOWX            --   additional exclude grep for show log
  QH_GREP             -- additional grep expression for grep log
  QH_GREPX            --   additional exclude grep for grep log
  Tnz                 -- Trace setting for 'qtest.sh log'
examples
  qtest.sh help
  qtest.sh 25 '1000 W1e-13 D4' ''
  qtest.sh 25 '1000 W0 D4 C2,2e-13' 'Q14'
  qtest.sh 25 '300 D4 C1,2e-13' 'd Q14'
  qtest.sh -10 '10000 D4' ''
  qtest.sh -10 '1000 s D4' ''
  qtest.sh -10 'rbox 1000 s D4 | qhull'
  qtest.sh run QR4 'rbox 1000 s D4 | qhull'
  qtest.sh run t876333 '1000 s D4' ''
  qtest.sh log 'rbox 500 s D4 | qhull'         # qhull.log qhull-step.log
  qtest.sh t876333 '500 s D4' ''
  qtest.sh QR4 'rbox 500 s D4 | qhull'
  qtest.sh grep 'qh_addpoint|qh_mark_dupridges' | head -20 # QH_GREP QH_GREPX
  qtest.sh grep 'qh_addpoint' 'added| qh_addpoint' | head -20
  qtest.sh grep-merge qhull.log | head -20
  qtest.sh grep-step qhull.log >qhull-step.log
  qtest.sh -v -10 '10000 D4' ''                 # verbose

# $Id: //main/2019/qhull/eg/qtest.sh#4 $$DateTime: 2019/06/25 15:24:47 $
== qtest.sh 1 '10' ''

Testing -- rbox 10 t330528 | qhull  >/d/bash/var/tmp/qtest-2020-07-24/qhull-330528.log
Test -- t330528
  CPU seconds to compute hull (after input):  0
== qtest.sh 2 'rbox 10 | qhull'
Testing -- rbox 10 | qhull >/d/bash/var/tmp/qtest-2020-07-24/qhull-864005.log
Test -- QR864005
  CPU seconds to compute hull (after input):  0
Test -- QR864006
  CPU seconds to compute hull (after input):  0
== qtest.sh -3 '10' ''

Testing -- rbox 10 t1 | qhull  >/d/bash/var/tmp/qtest-2020-07-24/qhull-930959.log
Test -- t1
  CPU seconds to compute hull (after input):  0
Test -- t2
  CPU seconds to compute hull (after input):  0
Test -- t3
  CPU seconds to compute hull (after input):  0
1595644068 Test 3 runs in 1 seconds (ave. 333 msec) -- rbox 10 t1 | qhull 
== qtest.sh -3 'rbox 10 | qhull'
Testing -- rbox 10 | qhull >/d/bash/var/tmp/qtest-2020-07-24/qhull-464436.log
Test -- QR1
  CPU seconds to compute hull (after input):  0
Test -- QR2
  CPU seconds to compute hull (after input):  0
Test -- QR3
  CPU seconds to compute hull (after input):  0
1595644069 Test 3 runs in 0 seconds (average 0 msec) -- rbox 10 | qhull
== qtest.sh run t123456 '10' 'Tz'

Convex hull of 10 points in 3-d:

  Number of vertices: 8
  Number of facets: 12

Statistics for: rbox 10 t123456 | qhull Tz

  Number of points processed: 8
  Number of hyperplanes created: 20
  Number of distance tests for qhull: 53
  CPU seconds to compute hull (after input):  0

== qtest.sh run QR123456 'rbox 10 | qhull Tz'

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 10 | qhull Tz QR123456 QR123456

  Number of points processed: 10
  Number of hyperplanes created: 27
  Number of distance tests for qhull: 45
  CPU seconds to compute hull (after input):  0

== qtest.sh log 'rbox 10 | qhull'
qtest.sh: log 'rbox 10 | qhull T4z' to 'qhull.log' and 'qhull-step.log'

==== EXTRA Fri, Jul 24, 2020 10:27:51 PM ====

1801:Convex hull of 10 points in 3-d:
1802:
1803:  Number of vertices: 10
1804:  Number of facets: 16
1805:
1806:Statistics for: rbox 10 | qhull T4z
1807:
1808:  Number of points processed: 10
1809:  Number of hyperplanes created: 26
1810:  Number of distance tests for qhull: 43
1811:  CPU seconds to compute hull (after input): 0.002

qhull.log
qtest.sh: log 'rbox 10 | qhull T4z' to 'qhull.log' and 'qhull-step.log'
kelwyn Fri, Jul 24, 2020 10:27:50 PM
/d/bash/local/qhull
-rwxr-xr-x 1 bbarber 197121 339968 Jul 24 21:06 /d/bash/local/qhull/bin/qhull
qhull_r 8.0.1 (2020.2.r 2020/07/24)
1:qh_initflags: option flags initialized
2:[QH1008]qh_readpoints: read in 10 3-dimensional points
3:[QH0013]qh_initqhull_globals: for rbox 10 | qhull T4z
4:[QH2005]qh_initqhull_globals: initialize globals.  input_dim 3, numpoints 10, malloc? 1, projected 0 to hull_dim 3
5:[QH3024]qh_initqhull_outputflags: qhull T4z
== qtest.sh t123456 '10' ''
qtest.sh: logging 'rbox 10 t123456 | qhull T4sz ' to 'qhull.log' and 'qhull-step.log'

==== EXTRA Fri, Jul 24, 2020 10:27:52 PM ====

1320:Convex hull of 10 points in 3-d:
1321:
1322:  Number of vertices: 8
1323:  Number of facets: 12
1324:
1325:Statistics for: rbox 10 t123456 | qhull T4z
1326:
1327:  Number of points processed: 8
1328:  Number of hyperplanes created: 20
1329:  Number of distance tests for qhull: 53
1330:  CPU seconds to compute hull (after input): 0.003

qhull.log
qtest.sh: logging 'rbox 10 t123456 | qhull T4sz ' to 'qhull.log' and 'qhull-step.log'
Fri, Jul 24, 2020 10:27:51 PM
/d/bash/local/qhull
-rwxr-xr-x 1 bbarber 197121 339968 Jul 24 21:06 /d/bash/local/qhull/bin/qhull
qhull_r 8.0.1 (2020.2.r 2020/07/24)
1:qh_initflags: option flags initialized
2:[QH1008]qh_readpoints: read in 10 3-dimensional points
3:[QH0013]qh_initqhull_globals: for rbox 10 t123456 | qhull T4z
4:[QH2005]qh_initqhull_globals: initialize globals.  input_dim 3, numpoints 10, malloc? 1, projected 0 to hull_dim 3
5:[QH3024]qh_initqhull_outputflags: qhull T4z
== qtest.sh QR123456 'rbox 10 | qhull'
qtest.sh: log 'rbox 10 | qhull T4z QR123456' to 'qhull.log' and 'qhull-step.log'

==== EXTRA Fri, Jul 24, 2020 10:27:53 PM ====

1850:Convex hull of 10 points in 3-d:
1851:
1852:  Number of vertices: 10
1853:  Number of facets: 16
1854:
1855:Statistics for: rbox 10 | qhull T4z QR123456 QR123456
1856:
1857:  Number of points processed: 10
1858:  Number of hyperplanes created: 27
1859:  Number of distance tests for qhull: 45
1860:  CPU seconds to compute hull (after input): 0.004

qhull-step.log
qtest.sh: log 'rbox 10 | qhull T4z QR123456' to 'qhull.log' and 'qhull-step.log'
2:[QH1008]qh_readpoints: read in 10 3-dimensional points
3:[QH0013]qh_initqhull_globals: for rbox 10 | qhull T4z QR123456
4:[QH2005]qh_initqhull_globals: initialize globals.  input_dim 3, numpoints 10, malloc? 1, projected 0 to hull_dim 3
5:[QH3024]qh_initqhull_outputflags: qhull T4z QR123456
7:[QH3078]qh_memsize: quick memory of 32 bytes
8:[QH3078]qh_memsize: quick memory of 24 bytes
9:[QH3078]qh_memsize: quick memory of 48 bytes
10:[QH3078]qh_memsize: quick memory of 88 bytes
11:[QH3078]qh_memsize: quick memory of 16 bytes
== qtest.sh grep 'qh_addpoint|QH1' >qhull-grep.log
qtest.sh: grep from 'qhull.log' to stdout
2:[QH1008]qh_readpoints: read in 10 3-dimensional points
32:[QH1002]qh_maxsimplex: selected point p9 for 3`th initial vertex, det=0.3388, targetdet=0.6029, mindet=0.006029
36:[QH1002]qh_maxsimplex: selected point p7 for 4`th initial vertex, det=0.253, targetdet=0.3628, mindet=0.003628
53:[QH1028]qh_createsimplex: created simplex
93:[QH1027]qh_checkpolygon: check all facets from f1, qh.NEWtentative? 0
99:[QH1064]qh_checkconvex: check that facets are not-flipped and for qh.ZEROcentrum that simplicial vertices are below their neighbor (dist<0.0)
113:[QH1042]qh_partitionall: partition all points into outside sets
177:[QH1029]qh_furthestnext: made f1 next facet(dist 0.53)
178:[QH1030]qh_initbuild: initial hull created and points partitioned
qhull-grep.log
1706:  qh.visible_list f24, newfacet_list f24, facet_next f14 for qh_addpoint
1742:[QH1027]qh_checkpolygon: check all facets from f5, qh.NEWtentative? 0
1761:[QH2056]qh_addpoint: added p4 to convex hull with point balance  0
1762:[QH1039]qh_buildhull: completed the hull construction
1764:[QH1036]Qhull: algorithm completed
1765:[QH1027]qh_checkpolygon: check all facets from f5, qh.NEWtentative? 0
1799:[QH1064]qh_checkconvex: check that facets are not-flipped and for qh.ZEROcentrum that simplicial vertices are below their neighbor (dist<0.0)
1863:[QH1006]qh_freeqhull: free global memory
1864:[QH1005]qh_freebuild: free memory from qh_inithull and qh_buildhull
1865:[QH1061]qh_freeqhull: clear qhT except for qh.qhmem and qh.qhstat
== qtest.sh grep 'qh_addpoint' 'added| qh_addpoint' >qhull-grep.log
qtest.sh: grep from 'qhull.log' to stdout
182:[QH1049]qh_addpoint: add p1(v5) 0.53 above f1 to hull of 4 facets, 0 merges, 6 outside at 0.001 CPU secs.  Previous p-1(v4) delta 0.001 CPU, 4 facets, 0 merges, 4 hyperplanes, 44 distplanes, 0 retries
453:[QH1049]qh_addpoint: add p3(v6) 0.18 above f3 to hull of 6 facets, 0 merges, 5 outside at 0.001 CPU secs.  Previous p1(v5) delta    0 CPU, 2 facets, 0 merges, 4 hyperplanes, 32 distplanes, 0 retries
734:[QH1049]qh_addpoint: add p5(v7) 0.15 above f6 to hull of 8 facets, 0 merges, 4 outside at 0.002 CPU secs.  Previous p3(v6) delta 0.001 CPU, 2 facets, 0 merges, 4 hyperplanes, 33 distplanes, 0 retries
954:[QH1049]qh_addpoint: add p2(v8) 0.24 above f8 to hull of 10 facets, 0 merges, 3 outside at 0.002 CPU secs.  Previous p5(v7) delta    0 CPU, 2 facets, 0 merges, 3 hyperplanes, 24 distplanes, 0 retries
1223:[QH1049]qh_addpoint: add p8(v9) 0.18 above f12 to hull of 12 facets, 0 merges, 2 outside at 0.003 CPU secs.  Previous p2(v8) delta 0.001 CPU, 2 facets, 0 merges, 4 hyperplanes, 30 distplanes, 0 retries
1494:[QH1049]qh_addpoint: add p4(v10) 0.073 above f13 to hull of 14 facets, 0 merges, 1 outside at 0.003 CPU secs.  Previous p8(v9) delta    0 CPU, 2 facets, 0 merges, 4 hyperplanes, 30 distplanes, 0 retries
qhull-grep.log
qtest.sh: grep from 'qhull.log' to stdout
182:[QH1049]qh_addpoint: add p1(v5) 0.53 above f1 to hull of 4 facets, 0 merges, 6 outside at 0.001 CPU secs.  Previous p-1(v4) delta 0.001 CPU, 4 facets, 0 merges, 4 hyperplanes, 44 distplanes, 0 retries
453:[QH1049]qh_addpoint: add p3(v6) 0.18 above f3 to hull of 6 facets, 0 merges, 5 outside at 0.001 CPU secs.  Previous p1(v5) delta    0 CPU, 2 facets, 0 merges, 4 hyperplanes, 32 distplanes, 0 retries
734:[QH1049]qh_addpoint: add p5(v7) 0.15 above f6 to hull of 8 facets, 0 merges, 4 outside at 0.002 CPU secs.  Previous p3(v6) delta 0.001 CPU, 2 facets, 0 merges, 4 hyperplanes, 33 distplanes, 0 retries
954:[QH1049]qh_addpoint: add p2(v8) 0.24 above f8 to hull of 10 facets, 0 merges, 3 outside at 0.002 CPU secs.  Previous p5(v7) delta    0 CPU, 2 facets, 0 merges, 3 hyperplanes, 24 distplanes, 0 retries
1223:[QH1049]qh_addpoint: add p8(v9) 0.18 above f12 to hull of 12 facets, 0 merges, 2 outside at 0.003 CPU secs.  Previous p2(v8) delta 0.001 CPU, 2 facets, 0 merges, 4 hyperplanes, 30 distplanes, 0 retries
1494:[QH1049]qh_addpoint: add p4(v10) 0.073 above f13 to hull of 14 facets, 0 merges, 1 outside at 0.003 CPU secs.  Previous p8(v9) delta    0 CPU, 2 facets, 0 merges, 4 hyperplanes, 30 distplanes, 0 retries
== qtest.sh grep-merge 'qhull.log' >qhull-grep.log
qtest.sh: grep merges from 'qhull.log' to stdout
qtest.sh: log 'rbox 10 | qhull T4z QR123456' to 'qhull.log' and 'qhull-step.log'
182:[QH1049]qh_addpoint: add p1(v5) 0.53 above f1 to hull of 4 facets, 0 merges, 6 outside at 0.001 CPU secs.  Previous p-1(v4) delta 0.001 CPU, 4 facets, 0 merges, 4 hyperplanes, 44 distplanes, 0 retries
183:[QH1040]qh_findhorizon: find horizon for point
450:[QH2056]qh_addpoint: added p1 to convex hull with point balance  0
453:[QH1049]qh_addpoint: add p3(v6) 0.18 above f3 to hull of 6 facets, 0 merges, 5 outside at 0.001 CPU secs.  Previous p1(v5) delta    0 CPU, 2 facets, 0 merges, 4 hyperplanes, 32 distplanes, 0 retries
454:[QH1040]qh_findhorizon: find horizon for point
731:[QH2056]qh_addpoint: added p3 to convex hull with point balance -1
734:[QH1049]qh_addpoint: add p5(v7) 0.15 above f6 to hull of 8 facets, 0 merges, 4 outside at 0.002 CPU secs.  Previous p3(v6) delta 0.001 CPU, 2 facets, 0 merges, 4 hyperplanes, 33 distplanes, 0 retries
735:[QH1040]qh_findhorizon: find horizon for point
951:[QH2056]qh_addpoint: added p5 to convex hull with point balance -0.29
qhull-grep.log
954:[QH1049]qh_addpoint: add p2(v8) 0.24 above f8 to hull of 10 facets, 0 merges, 3 outside at 0.002 CPU secs.  Previous p5(v7) delta    0 CPU, 2 facets, 0 merges, 3 hyperplanes, 24 distplanes, 0 retries
955:[QH1040]qh_findhorizon: find horizon for point
1220:[QH2056]qh_addpoint: added p2 to convex hull with point balance -0.75
1223:[QH1049]qh_addpoint: add p8(v9) 0.18 above f12 to hull of 12 facets, 0 merges, 2 outside at 0.003 CPU secs.  Previous p2(v8) delta 0.001 CPU, 2 facets, 0 merges, 4 hyperplanes, 30 distplanes, 0 retries
1224:[QH1040]qh_findhorizon: find horizon for point
1491:[QH2056]qh_addpoint: added p8 to convex hull with point balance -0.33
1494:[QH1049]qh_addpoint: add p4(v10) 0.073 above f13 to hull of 14 facets, 0 merges, 1 outside at 0.003 CPU secs.  Previous p8(v9) delta    0 CPU, 2 facets, 0 merges, 4 hyperplanes, 30 distplanes, 0 retries
1495:[QH1040]qh_findhorizon: find horizon for point
1761:[QH2056]qh_addpoint: added p4 to convex hull with point balance  0
1861:qh_maxouter: max distance from facet to outer plane is 1.571e-15, qh.max_outside is 9.714e-17
== qtest.sh grep-step 'qhull.log' >qhull-step.log
qtest.sh: grep step log from 'qhull.log' to stdout
2:[QH1008]qh_readpoints: read in 10 3-dimensional points
3:[QH0013]qh_initqhull_globals: for rbox 10 | qhull T4z QR123456
4:[QH2005]qh_initqhull_globals: initialize globals.  input_dim 3, numpoints 10, malloc? 1, projected 0 to hull_dim 3
5:[QH3024]qh_initqhull_outputflags: qhull T4z QR123456
7:[QH3078]qh_memsize: quick memory of 32 bytes
8:[QH3078]qh_memsize: quick memory of 24 bytes
9:[QH3078]qh_memsize: quick memory of 48 bytes
10:[QH3078]qh_memsize: quick memory of 88 bytes
11:[QH3078]qh_memsize: quick memory of 16 bytes
12:[QH3078]qh_memsize: quick memory of 24 bytes
qhull-step.log
1851:
1852:  Number of vertices: 10
1853:  Number of facets: 16
1854:
1855:Statistics for: rbox 10 | qhull T4z QR123456 QR123456
1856:
1857:  Number of points processed: 10
1858:  Number of hyperplanes created: 27
1859:  Number of distance tests for qhull: 45
1860:  CPU seconds to compute hull (after input): 0.004
== qtest.sh -v -3 'rbox 10 | qhull'
Testing -- rbox 10 | qhull >/d/bash/var/tmp/qtest-2020-07-24/qhull-198775.log
qtest.sh: rbox 10 | qhull QR1 Tsz | grep -E 'QH[67]| Statis|[0-9][0-9][.][0-9]x|CPU|FIXUP|retries, input joggled|initial hull is narrow' | grep -Ev 'keep 239874664' | tee -a '/d/bash/var/tmp/qtest-2020-07-24/qhull-198775.log' | grep -E '.' | grep -Ev 'QH7[0-9][^8]|Stati' | tee -a '/d/bash/var/tmp/qtest-2020-07-24/qhull-198775-show.log' 
  QH_TEST_DEST='/d/bash/var/tmp/qtest-2020-07-24/qhull-198775.log'
  QH_SHOW_DEST='/d/bash/var/tmp/qtest-2020-07-24/qhull-198775-show.log'
  QH_TEST_GREP='QH[67]| Statis|[0-9][0-9][.][0-9]x|CPU|FIXUP|retries, input joggled|initial hull is narrow'
  QH_SHOW_GREPX='QH7[0-9][^8]|Stati'
  QH_TEST=''
  QH_TESTX=''
  QH_SHOW=''
  QH_SHOWX=''
Test -- QR1
  CPU seconds to compute hull (after input):  0
Test -- QR2
  CPU seconds to compute hull (after input):  0
Test -- QR3
  CPU seconds to compute hull (after input):  0
1595644076 Test 3 runs in 0 seconds (average 0 msec) -- rbox 10 | qhull

============================
=== test qtest.sh errors ===
============================
== qtest.sh run -3 'rbox 10 | qhull'
QH7094 qhull option warning: unknown option 'r'(72)
QH7036 qhull option warning: missing space after option 'r'(72), reserved for sub-options, ignoring 'r' options to next space
QH7094 qhull option warning: unknown option '1'(31)
QH7036 qhull option warning: missing space after option '1'(31), reserved for sub-options, ignoring '1' options to next space
QH7094 qhull option warning: unknown option '|'(7c)
QH7094 qhull option warning: unknown option 'q'(71)
QH7036 qhull option warning: missing space after option 'q'(71), reserved for sub-options, ignoring 'q' options to next space
QH6035 qhull option error: see previous warnings, use 'Qw' to override: 'qhull rbox 10 | qhull' (last offset 16)

While executing:  | qhull rbox 10 | qhull
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 214218403  _maxoutside  0
== qtest.sh run 3 '10' ''
qtest.sh: Expecting 'run' followed by 'tNNN rbox-args qhull-args'. See 'qtest.sh help'
== qtest.sh run '10' ''

Convex hull of 10 points in 3-d:

  Number of vertices: 10
  Number of facets: 16

Statistics for: rbox 10 | qhull

  Number of points processed: 10
  Number of hyperplanes created: 26
  Number of distance tests for qhull: 43
  CPU seconds to compute hull (after input):  0

== qtest.sh run
qtest.sh: Expecting 'run' followed by 1 to 3 arguments. Got total of 1 arguments. See 'qtest.sh help'
== qtest.sh 3 '10' d T4
qtest.sh: Expecting 1 to 3 arguments. Got 4 arguments. See 'qtest.sh help'
== qtest.sh 3 '10' 'd H'

Testing -- rbox 10 t332683 | qhull d H >/d/bash/var/tmp/qtest-2020-07-24/qhull-332683.log
QH6037 qhull option error (qh_readpoints): can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H')

While executing: rbox 20
 | qhull d H TA1
Options selected for Qhull 2020.2.r 2020/07/24:
  run-id 214252017  delaunay  Halfspace  TA-stop-add 1  _maxoutside  0

qtest.sh error: 'rbox 20 | qhull d H TA1' failed
== qtest.sh 3
qtest.sh: Expecting run count followed by rbox and qhull options.  Only run count provided (3).
== qtest.sh grep
qtest.sh: Expecting 'grep' followed by include and exclude regexps or $QH_GREP or $QH_GREPX.  None defined.
== qtest.sh grep-merge '10' 'v'
qtest.sh: Expecting 'grep-merge' followed by log file. Got 'grep-merge 10 v ...'
== qtest.sh grep-merge
qtest.sh: Expecting 'grep-merge' followed by log file. Got 'grep-merge   ...'
== qtest.sh grep-merge not-a-file
qtest.sh: Expecting 'grep-merge' followed by log file. Got 'grep-merge not-a-file  ...'
== qtest.sh grep-step '10' 'v'
qtest.sh: Expecting 'grep-step' followed by log file. Got 'grep-step 10 v ...'
== qtest.sh grep-step
qtest.sh: Expecting 'grep-step' followed by log file. Got 'grep-step   ...'
== qtest.sh grep-step not-a-file
qtest.sh: Expecting 'grep-step' followed by log file. Got 'grep-step not-a-file  ...'
== qtest.sh log '10' 'd'
qtest.sh: Expecting 'log' followed by a qhull command line in quotes.  Got 3 arguments
== qtest.sh t34
qtest.sh: Expecting txxxxxx followed by rbox and qhull options.  Got tag 't34' only
== qtest.sh t34 'rbox 10 | qhull'
qtest.sh: Expecting txxxxxx followed by rbox and qhull options.  Tag 't34' was followed by a qhull command -- rbox 10 | qhull
== qtest.sh QR34
qtest.sh: Expecting QRxxxxxx followed by a qhull command.  Got tag 'QR34' only
== qtest.sh QR34 '10' 'v'
qtest.sh: Expecting QRxxxxxx followed by a qhull command.  Got rbox options '10' and qhull options 'v'
== qtest.sh t34 '10  ZERROR' 'v'
qtest.sh: logging 'rbox 10 ZERROR t34 | qhull T4sz v' to 'qhull.log' and 'qhull-step.log'
QH6353 rbox error: missing space between flags at ERROR t34 1000.

qtest.sh error: 'rbox 10 ZERROR t34' failed
== Delete temporary log files ghull.log, qhull-grep.log, and qhull-step.log

==============================
=== N_PRECISION test cases ===
==============================
== difficult cases for qhull Fri, Jul 24, 2020 10:28:05 PM

====================
== Convex hull of fuzzy cube (large flat facets)
====================

Testing -- rbox 1000000 W1e-13 D2 t67022 | qhull Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-67022.log
Test -- t67022
  CPU seconds to compute hull (after input): 0.261

Testing -- rbox 500000 W1e-13 D3 t200930 | qhull Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-200930.log
Test -- t200930
  CPU seconds to compute hull (after input): 0.659

Testing -- rbox 10000 W1e-13 D4 t935269 | qhull Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-935269.log
Test -- t935269
  CPU seconds to compute hull (after input): 0.104

Testing -- rbox 2000 W1e-13 D5 t2223 | qhull Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-2223.log
Test -- t2223
  CPU seconds to compute hull (after input): 0.584

Testing -- rbox 1000 W1e-13 D6 t69177 | qhull Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-69177.log
Test -- t69177
  CPU seconds to compute hull (after input): 2.013

====================
== narrow lense
====================

Testing -- rbox 1000000 L100000 s G1e-6 D2 t203085 | qhull Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-203085.log
Test -- t203085
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
  CPU seconds to compute hull (after input): 0.188

Testing -- rbox 10000 L100000 s G1e-6 D3 t336993 | qhull Q12 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-336993.log
Test -- t336993
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
  CPU seconds to compute hull (after input): 0.689

Testing -- rbox 5000 L100000 s G1e-6 D4 t937424 | qhull Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-937424.log
Test -- t937424
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
  CPU seconds to compute hull (after input): 0.599

Testing -- rbox 1000 L100000 s G1e-6 D5 t537855 | qhull Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-537855.log
Test -- t537855
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
  CPU seconds to compute hull (after input): 0.216

Testing -- rbox 400 L100000 s G1e-6 D6 t604809 | qhull Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-604809.log
Test -- t604809
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
  CPU seconds to compute hull (after input): 0.494

====================
== cone
====================

Testing -- rbox 100000 s Z1 G1e-13 D2 t671763 | qhull Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-671763.log
Test -- t671763
  CPU seconds to compute hull (after input): 0.02

Testing -- rbox 10000 s Z1 G1e-13 D3 t205240 | qhull Q12 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-205240.log
Test -- t205240
  CPU seconds to compute hull (after input): 0.603

Testing -- rbox 2000 s Z1 G1e-13 D4 t339148 | qhull Q12 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-339148.log
Test -- t339148
  CPU seconds to compute hull (after input): 3.031

Testing -- rbox 1000 s Z1 G1e-13 D5 t473056 | qhull Q12 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-473056.log
Test -- t473056
  CPU seconds to compute hull (after input): 0.599

Testing -- rbox 400 s Z1 G1e-13 D6 t540010 | qhull Q12 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-540010.log
Test -- t540010
QH6271 qhull topology error (qh_check_dupridge): wide merge (1662534044043.3x wider) due to dupridge between f3740 and f124 (vertex dist 0.11), merge dist 0.48, while processing p68
QH6227 qhull topology error: Only 7 facets remain.  The input is too degenerate or the convexity constraints are too strong.
  Maximum distance of point above facet: 0.26 (10708130307576.8x)
  Maximum distance of vertex below facet: -0.54 (22117535651526.7x)

==========================
=== N_OTHER test cases ===
==========================

====================
== Delaunay triangulation of fuzzy circle (large, narrow disk)
== No Qbb, highly degenerate due to narrow disk of two cospherical sets of points
====================

Testing -- rbox 10000 s W1e-13 D2 t606964 | qhull d Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-606964.log
Test -- t606964
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
  CPU seconds to compute hull (after input): 0.527
  Maximum distance of point above facet: 1.1e-12 (191.6x)

Testing -- rbox 2000 s W1e-13 D3 t207395 | qhull d Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-207395.log
Test -- t207395
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
QH6347 qhull precision error (qh_mergefacet): wide merge for facet f8586 into f5812 for mergetype 6 (flip).  maxdist  0 (0.0x) mindist -1.8e-12 (178.9x) vertexdist 0.054  Allow with 'Q12' (allow-wide)
  Maximum distance of point above facet: 3.2e-13 (31.3x)
  Maximum distance of vertex below facet: -1.3e-13 (12.7x)

Testing -- rbox 1000 s W1e-13 D4 t274349 | qhull d Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-274349.log
Test -- t274349
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
QH7086 Qhull precision warning: repartition coplanar point p819 from f106 as an outside point above hidden facet f64145 dist 7e-12 nearest vertices 0.11
  CPU seconds to compute hull (after input): 0.994
  Maximum distance of point above facet: 1.9e-12 (114.1x)

Testing -- rbox 200 s W1e-13  D5 t341303 | qhull d Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-341303.log
Test -- t341303
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
  CPU seconds to compute hull (after input): 0.304
  Maximum distance of point above facet: 2.8e-13 (12.0x)

Testing -- rbox 100 s W1e-13  D6 t408257 | qhull d Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-408257.log
Test -- t408257
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
QH6227 qhull topology error: Only 8 facets remain.  The input is too degenerate or the convexity constraints are too strong.

===========================================================
=== N_PINCHED test cases for Q14-merge-pinched-vertices ===
===========================================================

====================
== Convex hull of fuzzy cube with point pairs (large flat facets)
====================

Testing -- rbox 1000000 W1e-13 C1,2e-13 D2 t475211 | qhull Q14 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-475211.log
Test -- t475211
  CPU seconds to compute hull (after input): 0.355

Testing -- rbox 500000 W1e-13 C1,2e-13 D3 t209550 | qhull Q14 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-209550.log
Test -- t209550
  CPU seconds to compute hull (after input): 0.645

Testing -- rbox 20000 W1e-13 C1,2e-13 D4 t745182 | qhull Q14 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-745182.log
Test -- t745182
  CPU seconds to compute hull (after input): 0.205

Testing -- rbox 2000 W1e-13 C1,2e-13 D5 t879090 | qhull Q14 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-879090.log
Test -- t879090
QH6271 qhull topology error (qh_check_dupridge): wide merge (114884573208.0x wider) due to dupridge between f95160 and f95159 (vertex dist 2.4e-13), merge dist 0.008, while processing p2645

Testing -- rbox 500 W1e-13 C1,2e-13 D6 t946044 | qhull Q14 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-946044.log
Test -- t946044
QH6347 qhull precision error (qh_mergefacet): wide merge for facet f253245 into f252997 for mergetype 7 (dupridge).  maxdist  0 (0.0x) mindist -5.7e-12 (231.7x) vertexdist 0.44  Allow with 'Q12' (allow-wide)
  Maximum distance of point above facet: 3.3e-13 (13.4x)

====================
== Convex hull of cube with point pairs (large flat facets)
====================

Testing -- rbox 1000000 W0 C1,2e-13 D2 t12998 | qhull Q14 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-12998.log
Test -- t12998
  CPU seconds to compute hull (after input): 0.345

Testing -- rbox 100000 W0 C1,2e-13 D3 t747337 | qhull Q14 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-747337.log
Test -- t747337
  CPU seconds to compute hull (after input): 0.092

Testing -- rbox 5000  W0 C1,2e-13 D4 t347768 | qhull Q14 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-347768.log
Test -- t347768
  CPU seconds to compute hull (after input): 0.051

Testing -- rbox 1000 W0 C1,2e-13 D5 t881245 | qhull Q14 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-881245.log
Test -- t881245
  CPU seconds to compute hull (after input): 0.189

Testing -- rbox 500 W0 C1,2e-13 D6 t948199 | qhull Q14 Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-948199.log
Test -- t948199
QH6271 qhull topology error (qh_check_dupridge): wide merge (382263037091.0x wider) due to dupridge between f319376 and f320185 (vertex dist 2.4e-13), merge dist 0.21, while processing p208
  Maximum distance of point above facet: 5.4e-13 (22.1x)
  Maximum distance of vertex below facet: -7.3e-13 (29.5x)

====================
== Delaunay triangulation of point pairs (large upper facet)
== Difficult case due to large upper facet with nearly adjacent vertices
== A bounding box helps avoid this case, see TIME_DELAUNAY_PAIRS
====================

Testing -- rbox 100000 C1,2e-13 D2 t548630 | qhull Q14 d Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-548630.log
Test -- t548630
  CPU seconds to compute hull (after input): 1.306

Testing -- rbox 10000 C1,2e-13 D3 t149061 | qhull Q14 d Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-149061.log
Test -- t149061
  CPU seconds to compute hull (after input): 0.657

Testing -- rbox 500 C1,2e-13 D4 t684693 | qhull Q14 d Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-684693.log
Test -- t684693
QH6271 qhull topology error (qh_check_dupridge): wide merge (37732005938.4x wider) due to dupridge between f52566 and f52538 (vertex dist 2.3e-13), merge dist 0.0032, while processing p553

Testing -- rbox 200 C1,2e-13 D5 t751647 | qhull Q14 d Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-751647.log
Test -- t751647
QH6381 qhull topology error (qh_next_vertexmerge): no nearly adjacent vertices to resolve duplicate ridges r108296 and r108302.  Nearest v293 and v387 dist 0.16 (7021422850377.3x)

Testing -- rbox 100 C1,2e-13 D6 t285124 | qhull Q14 d Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-285124.log
Test -- t285124
  CPU seconds to compute hull (after input): 1.292

====================
== Delaunay triangulation of point quads (2e-13, large upper facet)
== Difficult case due to large upper facet with many nearly adjacent vertices
====================

Testing -- rbox 50000 C3,2e-13 D2 t885555 | qhull Q14 d Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-885555.log
Test -- t885555
  CPU seconds to compute hull (after input): 0.846

Testing -- rbox 10000 C3,2e-13 D3 t485986 | qhull Q14 d Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-485986.log
Test -- t485986
QH6348 qhull precision error (qh_mergefacet): wide merge for pinched facet f179300 into f83347 for mergetype 3 (concave).  maxdist  0 (0x) mindist -0.00015 (15229327719.9x) vertexdist 1.1e-13  Allow with 'Q12' (allow-wide)

Testing -- rbox 200 C3,2e-13 D4 t552940 | qhull Q14 d Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-552940.log
Test -- t552940
QH6348 qhull precision error (qh_mergefacet): wide merge for pinched facet f17712 into f17726 for mergetype 10 (degen).  maxdist  0 (0x) mindist -0.0021 (128521499042.8x) vertexdist 3e-13  Allow with 'Q12' (allow-wide)

Testing -- rbox 100 C3,2e-13 D5 t86417 | qhull Q14 d Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-86417.log
Test -- t86417
QH7084 qhull topology warning (qh_matchneighbor): will merge vertices to undo new facets -- f66306 and f66308 have the same vertices (skip 1, skip 1) and same horizon ridges to f52073 and f55106
QH7084 qhull topology warning (qh_matchneighbor): will merge vertices to undo new facets -- f66306 and f66308 have the same vertices (skip 2, skip 2) and same horizon ridges to f52073 and f55106
QH7084 qhull topology warning (qh_matchneighbor): will merge vertices to undo new facets -- f66306 and f66308 have the same vertices (skip 4, skip 4) and same horizon ridges to f52073 and f55106
QH7084 qhull topology warning (qh_matchneighbor): will merge vertices to undo new facets -- f66306 and f66308 have the same vertices (skip 5, skip 5) and same horizon ridges to f52073 and f55106
QH6155 qhull topology error (qh_matchdupridge): missing qh_DUPLICATEridge at f66308 skip 4 for new f66306 skip 4 hash 3265 ismatch 1.  Set by qh_matchneighbor
  Maximum distance of point above facet: 3.7e-13 (15.0x)

Testing -- rbox 100 C3,2e-13 D6 t619894 | qhull Q14 d Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-619894.log
Test -- t619894
QH6425 Qhull topology error (qh_partitioncoplanar): can not repartition coplanar point p360 from f389002 as outside point above f503604.  It previously failed to form a cone of facets, dist 0.00014, nearest vertices 3.3e-13
  Maximum distance of point above facet: 5.3e-13 (15.3x)

====================
== Delaunay triangulation of fuzzy circle with pairs (large, narrow disk)
== Highly degenerate due to narrow disk of two cospherical sets of point pairs
== Worse with Qbb since it stretches out the paraboloid, doubling _one-merge
====================

Testing -- rbox 10000 s W1e-13 C1,1e-13 D2 t753802 | qhull Q14 d Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-753802.log
Test -- t753802
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
QH7085 Qhull precision warning: repartition coplanar point p13605 from f33398 as an outside point above twisted facet f33398 dist 1.5e-08 nearest vertices 8.5e-14
QH7085 Qhull precision warning: repartition coplanar point p3161 from f46136 as an outside point above twisted facet f46131 dist 1.7e-09 nearest vertices 1.5e-13
QH7085 Qhull precision warning: repartition coplanar point p13717 from f34469 as an outside point above twisted facet f59096 dist 1.9e-09 nearest vertices 5.3e-14
  CPU seconds to compute hull (after input): 0.161
  Maximum distance of point above facet: 5.8e-14 (10.4x)

Testing -- rbox 5000 s W1e-13 C1,1e-13 D3 t488141 | qhull Q14 d Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-488141.log
Test -- t488141
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
  CPU seconds to compute hull (after input): 0.606

Testing -- rbox 500 s W1e-13  C1,1e-13 D4 t155526 | qhull Q14 d Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-155526.log
Test -- t155526
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
  CPU seconds to compute hull (after input): 0.318

Testing -- rbox 200 s W1e-13  C1,1e-13 D5 t222480 | qhull Q14 d Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-222480.log
Test -- t222480
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
QH6381 qhull topology error (qh_next_vertexmerge): no nearly adjacent vertices to resolve duplicate ridges r81322 and r81457.  Nearest v137 and v201 dist 0.21 (9398058245899.0x)

Testing -- rbox 100 s W1e-13  C1,1e-13 D6 t289434 | qhull Q14 d Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-289434.log
Test -- t289434
QH7089 qhull precision warning: The initial hull is narrow.  Is the input lower
QH6381 qhull topology error (qh_next_vertexmerge): no nearly adjacent vertices to resolve duplicate ridges r41099 and r40865.  Nearest v8 and v45 dist 0.22 (7248633393770.0x)

====================
== Voronoi diagram of rotated mesh with wide, 1e-8 pairs
== All fail at C1,1e-12
====================

Testing -- rbox 10000 M3,4 C1,1e-8 D2 t822911 | qhull QR3 Q14 v Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-822911.log
Test -- t822911
  CPU seconds to compute hull (after input): 0.152

Testing -- rbox 2000 M3,4,5 C1,1e-8 D3 t157681 | qhull QR3 Q14 v Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-157681.log
Test -- t157681
QH7081 qhull precision warning (qh_getpinchedmerges): pinched vertices v910 and v456 (dist 8.1e-09, 3294x) would produce a wide merge for f40800 and f40814.  Will merge dupridge instead
QH6271 qhull topology error (qh_check_dupridge): wide merge (417465268.1x wider) due to dupridge between f40800 and f40814 (vertex dist 8.1e-09), merge dist 0.001, while processing p3608

Testing -- rbox 600 M3,4,5 C1,1e-8 D4 t691158 | qhull QR3 Q14 v Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-691158.log
Test -- t691158
  CPU seconds to compute hull (after input): 0.258

Testing -- rbox 300 M3,4,5 C1,1e-8 D5 t758112 | qhull QR3 Q14 v Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-758112.log
Test -- t758112
  CPU seconds to compute hull (after input): 0.902
skip D6, millions of vertices

============================
== Delaunay triangulation of nearly cospherical point pairs with Qbb drum
== Qbb makes this the most difficult distribution for Qhull, only 100 points
============================

Testing -- rbox 1000 s C1,1e-13 D3 t358543 | qhull Q14 d Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-358543.log
Test -- t358543
  CPU seconds to compute hull (after input): 0.052

Testing -- rbox 100 s C1,1e-13 D4 t425497 | qhull Q14 d Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-425497.log
Test -- t425497
  CPU seconds to compute hull (after input): 0.023

Testing -- rbox 50 s C1,1e-13 D5 t958974 | qhull Q14 d Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-958974.log
Test -- t958974
QH7081 qhull precision warning (qh_getpinchedmerges): pinched vertices v65 and v49 (dist 0.0034, 139424997685x) would produce a wide merge for f11052 and f11054.  Will merge dupridge instead
QH6271 qhull topology error (qh_check_dupridge): wide merge (322371235117.8x wider) due to dupridge between f11052 and f11054 (vertex dist 0.0034), merge dist 0.0078, while processing p50

Testing -- rbox 50 s C1,1e-13 D6 t492451 | qhull Q14 d Qbb Tv >/d/bash/var/tmp/qtest-2020-07-24/qhull-492451.log
Test -- t492451
QH6271 qhull topology error (qh_check_dupridge): wide merge (33307682655.3x wider) due to dupridge between f19365 and f19401 (vertex dist 0.011), merge dist 0.001, while processing p18

============================
== Time for pinched Delaunay triangulation of random point pairs (Q14) with bounding box
============================

Testing -- rbox 50000 C1,2e-13 c G2.0 D2 t559405 | qhull Q14 d Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-559405.log
Test -- t559405
  CPU seconds to compute hull (after input): 0.641

Testing -- rbox 10000 C1,2e-13 c G2.0 D3 t626359 | qhull Q14 d Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-626359.log
Test -- t626359
  CPU seconds to compute hull (after input): 0.456

Testing -- rbox 3000 C1,2e-13 c G2.0 D4 t693313 | qhull Q14 d Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-693313.log
Test -- t693313
QH7085 Qhull precision warning: repartition coplanar point p5346 from f250733 as an outside point above twisted facet f250738 dist 0.00038 nearest vertices 2.5e-13
  CPU seconds to compute hull (after input): 1.179

Testing -- rbox 500 C1,2e-13 c G2.0 D5 t760267 | qhull Q14 d Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-760267.log
Test -- t760267
  CPU seconds to compute hull (after input): 1.176

Testing -- rbox 100 C1,2e-13 c G2.0 D6 t360698 | qhull Q14 d Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-360698.log
Test -- t360698
QH6381 qhull topology error (qh_next_vertexmerge): no nearly adjacent vertices to resolve duplicate ridges r88304 and r87884.  Nearest v82 and v86 dist 0.61 (4668353828614.3x)

============================
== Time for pinched Delaunay triangulation of random point pairs (Q14, Q12)
== qh_next_facetmerge, qh_findbesthorizon (qh_distplane)
============================

Testing -- rbox 50000 C1,2e-13 D2 t427652 | qhull Q14 d Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-427652.log
Test -- t427652
  CPU seconds to compute hull (after input): 0.548

Testing -- rbox 5000 C1,2e-13 D3 t494606 | qhull Q14 d Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-494606.log
Test -- t494606
  CPU seconds to compute hull (after input): 0.461
  Maximum distance of point above facet: 1.6e-13 (15.6x)
  Maximum distance of vertex below facet: -1.3e-13 (13.2x)

Testing -- rbox 500 C1,2e-13 D4 t561560 | qhull Q12 Q14 d Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-561560.log
Test -- t561560
QH6271 qhull topology error (qh_check_dupridge): wide merge (231733071381.3x wider) due to dupridge between f76307 and f76302 (vertex dist 2.4e-13), merge dist 0.02, while processing p507
  CPU seconds to compute hull (after input): 0.345
  Maximum distance of point above facet: 2e-13 (12.3x)
  Maximum distance of vertex below facet: -2.1e-13 (12.9x)

Testing -- rbox 300 C1,2e-13 D5 t95037 | qhull Q12 Q14 d Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-95037.log
Test -- t95037
QH6271 qhull topology error (qh_check_dupridge): wide merge (80235921958.0x wider) due to dupridge between f243374 and f243379 (vertex dist 2.1e-13), merge dist 0.018, while processing p428
  CPU seconds to compute hull (after input): 1.498
  Maximum distance of point above facet: 3.3e-13 (13.3x)
  Maximum distance of vertex below facet: -3.3e-13 (13.5x)

Testing -- rbox 100 C1,2e-13 D6 t695468 | qhull Q14 d Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-695468.log
Test -- t695468
  CPU seconds to compute hull (after input): 1.234

===========================
=== N_TIMING test cases ===
===========================

============================
== Time for random points in a cube
============================

Testing -- rbox 1000000 D2 t295899 | qhull  >/d/bash/var/tmp/qtest-2020-07-24/qhull-295899.log
Test -- t295899
  CPU seconds to compute hull (after input): 0.114

Testing -- rbox 500000 D3 t429807 | qhull  >/d/bash/var/tmp/qtest-2020-07-24/qhull-429807.log
Test -- t429807
  CPU seconds to compute hull (after input): 0.14

Testing -- rbox 200000 D4 t563715 | qhull  >/d/bash/var/tmp/qtest-2020-07-24/qhull-563715.log
Test -- t563715
  CPU seconds to compute hull (after input): 0.192

Testing -- rbox 100000 D5 t630669 | qhull Q12 >/d/bash/var/tmp/qtest-2020-07-24/qhull-630669.log
Test -- t630669
  CPU seconds to compute hull (after input): 0.774

Testing -- rbox 3000 D6 t231100 | qhull  >/d/bash/var/tmp/qtest-2020-07-24/qhull-231100.log
Test -- t231100
  CPU seconds to compute hull (after input): 1.059

============================
== Time for random cospherical points
============================

Testing -- rbox 100000 s D2 t298054 | qhull  >/d/bash/var/tmp/qtest-2020-07-24/qhull-298054.log
Test -- t298054
  CPU seconds to compute hull (after input): 0.287

Testing -- rbox 100000 s D3 t365008 | qhull  >/d/bash/var/tmp/qtest-2020-07-24/qhull-365008.log
Test -- t365008
  CPU seconds to compute hull (after input): 0.521

Testing -- rbox 50000 s D4 t431962 | qhull  >/d/bash/var/tmp/qtest-2020-07-24/qhull-431962.log
Test -- t431962
  CPU seconds to compute hull (after input): 1.199

== Repeat with qconvex, bin/qconvex is built with libqhull instead of libqhull_r

Testing -- rbox 50000 s D4 t32393 | qconvex  >/d/bash/var/tmp/qtest-2020-07-24/qhull-32393.log
Test -- t32393
  CPU seconds to compute hull (after input): 1.251

Testing -- rbox 10000 s D5 t632824 | qhull  >/d/bash/var/tmp/qtest-2020-07-24/qhull-632824.log
Test -- t632824
  CPU seconds to compute hull (after input): 1.498

Testing -- rbox 1000 s D6 t233255 | qhull  >/d/bash/var/tmp/qtest-2020-07-24/qhull-233255.log
Test -- t233255
  CPU seconds to compute hull (after input): 0.747

============================
== Time for extreme post-merge of random cospherical points
============================

Testing -- rbox 100000 s D2 t833686 | qhull C0.01 >/d/bash/var/tmp/qtest-2020-07-24/qhull-833686.log
Test -- t833686
  CPU seconds to compute hull (after input): 0.657

Testing -- rbox 10000 s D3 t900640 | qhull C0.01 >/d/bash/var/tmp/qtest-2020-07-24/qhull-900640.log
Test -- t900640
  CPU seconds to compute hull (after input): 0.185

Testing -- rbox 5000 s D4 t967594 | qhull C0.01 >/d/bash/var/tmp/qtest-2020-07-24/qhull-967594.log
Test -- t967594
  CPU seconds to compute hull (after input): 0.422

== Repeat with qconvex, bin/qconvex is built with libqhull instead of libqhull_r

Testing -- rbox 5000 s D4 t34548 | qconvex C0.01 >/d/bash/var/tmp/qtest-2020-07-24/qhull-34548.log
Test -- t34548
  CPU seconds to compute hull (after input): 0.438

Testing -- rbox 2000 s D5 t568025 | qhull C0.01 >/d/bash/var/tmp/qtest-2020-07-24/qhull-568025.log
Test -- t568025
  CPU seconds to compute hull (after input): 0.989

Testing -- rbox 500 s D6 t168456 | qhull C0.01 >/d/bash/var/tmp/qtest-2020-07-24/qhull-168456.log
Test -- t168456
  CPU seconds to compute hull (after input): 1.015

============================
== Time for rotated cubical points with large merged facets
============================

Testing -- rbox 5000000 W0 D2 t235410 | qhull QR3 >/d/bash/var/tmp/qtest-2020-07-24/qhull-235410.log
Test -- t235410
  CPU seconds to compute hull (after input): 0.879

Testing -- rbox 1000000 W0 D3 t103657 | qhull QR3 >/d/bash/var/tmp/qtest-2020-07-24/qhull-103657.log
Test -- t103657
  CPU seconds to compute hull (after input): 0.686

Testing -- rbox 100000 W0 D4 t771042 | qhull QR3 >/d/bash/var/tmp/qtest-2020-07-24/qhull-771042.log
Test -- t771042
  CPU seconds to compute hull (after input): 0.477

Testing -- rbox 10000 W0 D5 t837996 | qhull QR3 >/d/bash/var/tmp/qtest-2020-07-24/qhull-837996.log
Test -- t837996
  CPU seconds to compute hull (after input): 0.742

Testing -- rbox 1000 W0 D6 t371473 | qhull QR3 >/d/bash/var/tmp/qtest-2020-07-24/qhull-371473.log
Test -- t371473
  CPU seconds to compute hull (after input): 0.941

============================
== Time for joggled, rotated cubical points with multiple retries
============================

Testing -- rbox 5000000 W0 D2 t971904 | qhull QR3 QJ >/d/bash/var/tmp/qtest-2020-07-24/qhull-971904.log
Test -- t971904
  CPU seconds to compute hull (after input): 0.808

Testing -- rbox 1000000 W0 D3 t840151 | qhull QR3 QJ >/d/bash/var/tmp/qtest-2020-07-24/qhull-840151.log
Test -- t840151
  CPU seconds to compute hull (after input): 1.002
  After 1 retries, input joggled by: 3.5e-11

Testing -- rbox 100000 W0 D4 t507536 | qhull QR3 QJ >/d/bash/var/tmp/qtest-2020-07-24/qhull-507536.log
Test -- t507536
  CPU seconds to compute hull (after input): 0.458
  After 3 retries, input joggled by: 5.7e-09

Testing -- rbox 10000 W0 D5 t574490 | qhull QR3 QJ >/d/bash/var/tmp/qtest-2020-07-24/qhull-574490.log
Test -- t574490
  CPU seconds to compute hull (after input): 0.651
  After 3 retries, input joggled by: 8.2e-09

Testing -- rbox 1000 W0 D6 t641444 | qhull QR3 QJ >/d/bash/var/tmp/qtest-2020-07-24/qhull-641444.log
Test -- t641444
  CPU seconds to compute hull (after input): 1.17
  After 2 retries, input joggled by: 1.1e-09

============================
== Time for joggled, nearly cubical points
============================

Testing -- rbox 1000000 W1e-13 D2 t708398 | qhull QJ >/d/bash/var/tmp/qtest-2020-07-24/qhull-708398.log
Test -- t708398
  CPU seconds to compute hull (after input): 0.166

Testing -- rbox 500000 W1e-13 D3 t308829 | qhull QJ >/d/bash/var/tmp/qtest-2020-07-24/qhull-308829.log
Test -- t308829
  CPU seconds to compute hull (after input): 1.447
  After 4 retries, input joggled by: 2.1e-08

Testing -- rbox 100000 W1e-13 D4 t976214 | qhull QJ >/d/bash/var/tmp/qtest-2020-07-24/qhull-976214.log
Test -- t976214
  CPU seconds to compute hull (after input): 0.483
  After 3 retries, input joggled by: 3e-09

Testing -- rbox 10000 W1e-13 D5 t43168 | qhull QJ >/d/bash/var/tmp/qtest-2020-07-24/qhull-43168.log
Test -- t43168
  CPU seconds to compute hull (after input): 0.635
  After 3 retries, input joggled by: 4.1e-09

Testing -- rbox 1000 W1e-13 D6 t576645 | qhull QJ >/d/bash/var/tmp/qtest-2020-07-24/qhull-576645.log
Test -- t576645
  CPU seconds to compute hull (after input): 1.025
  After 3 retries, input joggled by: 5.3e-09

============================
== Time for merging nearly cubical points
============================

Testing -- rbox 1000000 W1e-13 D2 t177076 | qhull  >/d/bash/var/tmp/qtest-2020-07-24/qhull-177076.log
Test -- t177076
  CPU seconds to compute hull (after input): 0.21

Testing -- rbox 1000000 W1e-13 D3 t310984 | qhull  >/d/bash/var/tmp/qtest-2020-07-24/qhull-310984.log
Test -- t310984
  CPU seconds to compute hull (after input): 1.573

Testing -- rbox 100000 W1e-13 D4 t511846 | qhull Q12 >/d/bash/var/tmp/qtest-2020-07-24/qhull-511846.log
Test -- t511846
  CPU seconds to compute hull (after input): 1.446

Testing -- rbox 2000 W1e-13 D5 t112277 | qhull Q12 >/d/bash/var/tmp/qtest-2020-07-24/qhull-112277.log
Test -- t112277
  CPU seconds to compute hull (after input): 0.652

Testing -- rbox 500 W1e-13 D6 t179231 | qhull  >/d/bash/var/tmp/qtest-2020-07-24/qhull-179231.log
Test -- t179231
  CPU seconds to compute hull (after input): 0.52

============================
== Time for Delaunay triangulation of random points
== qh_findbesthorizon, qh_distplane, qh_update_vertexneighbors_cone, qh_makenew_simplicial
============================

Testing -- rbox 100000 D2 t246185 | qhull d Qbb Qz >/d/bash/var/tmp/qtest-2020-07-24/qhull-246185.log
Test -- t246185
  CPU seconds to compute hull (after input): 0.791

Testing -- rbox 50000 D3 t846616 | qhull d Qbb Qz >/d/bash/var/tmp/qtest-2020-07-24/qhull-846616.log
Test -- t846616
  CPU seconds to compute hull (after input): 1.818

Testing -- rbox 10000 D4 t447047 | qhull d Qbb Qz >/d/bash/var/tmp/qtest-2020-07-24/qhull-447047.log
Test -- t447047
  CPU seconds to compute hull (after input): 1.502

Testing -- rbox 1000 D5 t580955 | qhull d Qbb Qz >/d/bash/var/tmp/qtest-2020-07-24/qhull-580955.log
Test -- t580955
  CPU seconds to compute hull (after input): 0.68

Testing -- rbox 200 D6 t647909 | qhull d Qbb Qz >/d/bash/var/tmp/qtest-2020-07-24/qhull-647909.log
Test -- t647909
  CPU seconds to compute hull (after input): 0.471

====================
== Time for Delaunay triangulation of regular mesh, integer coordinates
====================

Testing -- rbox 100000 M3,4 z D2 t714863 | qhull QR3 d Qt Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-714863.log
Test -- t714863
  CPU seconds to compute hull (after input): 0.937

Testing -- rbox 20000 M3,4,5 z D3 t315294 | qhull QR3 d Qt Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-315294.log
Test -- t315294
  CPU seconds to compute hull (after input): 1.055

Testing -- rbox 5000 M3,4,5 z D4 t382248 | qhull QR3 d Qt Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-382248.log
Test -- t382248
  CPU seconds to compute hull (after input): 1.095

Testing -- rbox 1500 M3,4,5 z D5 t982679 | qhull QR3 d Qt Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-982679.log
Test -- t982679
  CPU seconds to compute hull (after input): 1.073

Testing -- rbox 500 M3,4,5 z D6 t49633 | qhull QR3 d Qt Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-49633.log
Test -- t49633
  CPU seconds to compute hull (after input): 0.857

====================
== Time for Voronoi diagram of regular mesh
====================
Testing -- rbox 100000 M3,4 z D2 | qhull v Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-650064.log
Test -- QR650064
  CPU seconds to compute hull (after input): 0.942
Testing -- rbox 20000 M3,4,5 z | qhull v Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-250495.log
Test -- QR250495
  CPU seconds to compute hull (after input): 0.9
Testing -- rbox 5000 M3,4,5 z D4 | qhull v Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-317449.log
Test -- QR317449
  CPU seconds to compute hull (after input): 1.037
Testing -- rbox 1500 M3,4,5 z D5 | qhull v Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-384403.log
Test -- QR384403
  CPU seconds to compute hull (after input): 1.256
Testing -- rbox 500 M3,4,5 z D6 | qhull v Qbb >/d/bash/var/tmp/qtest-2020-07-24/qhull-451357.log
Test -- QR451357
  CPU seconds to compute hull (after input): 0.955
