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============================================
== make qtest ==============================
============================================
== Tue Sep 22 22:29:50 EDT 2015
============================================
== Test non-reentrant qset.c with mem.c ====
============================================
bin/testqset 10000
Not testing qh_setduplicate and qh_setfree2.
These routines use heap-allocated set contents. See qhull tests.
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+002 average copy size
freelists(bytes->count): 16->3 24->5 32->6 40->10
testqset: OK
qh_meminitbuffers: memory initialized with alignment 8
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
============================================
== Test reentrant qset_r.c with mem_r.c ====
============================================
bin/testqset_r 10000
Not testing qh_setduplicate and qh_setfree2.
These routines use heap-allocated set contents. See qhull tests.
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+002 average copy size
freelists(bytes->count): 16->3 24->5 32->6 40->10
testqset_r: OK
qh_meminitbuffers: memory initialized with alignment 8
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
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
============================================
== 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: 712
Number of distance tests for qhull: 1433
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2.8e-015 of
all facets. Will make 13000 distance computations.
============================================
== make test ===============================
============================================
==============================
========= 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: 712
Number of distance tests for qhull: 1433
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2.8e-015 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: 27
Number of distance tests for qhull: 44
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2e-015 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: 48
Number of facets in hull: 25
Number of distance tests for qhull: 69
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 5.6e-015 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-015 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: 100
Number of distance tests for merging: 342
Number of distance tests for checking: 156
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: 48
Number of facets in hull: 25
Number of distance tests for qhull: 69
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 5.6e-015 of
all facets. Will make 150 distance computations.
==============================
========= user_eg ============
==============================
bin/user_eg
This is the output from user_eg_r.c
It shows how qhull() may be called from an application using the qhull
reentrant library. user_eg is not part of qhull itself. If it appears
accidently, please remove user_eg_r.c from your project. If it fails
immediately, user_eg_r.c was incorrectly linked to the non-reentrant library.
Also try 'user_eg T1 2>&1'
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
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: 1442975392
input
-0.483 -0.183 0.983
0.806 -0.501 0.448
0.0472 0.876 -0.00745
0.84 0.197 -0.808
-0.91 0.481 0.571
-0.759 0.159 -0.469
0.894 0.771 0.296
0.667 -0.79 0.422
8 vertices and 16 facets with normals:
-0.029 -0.14 0.0013 0.99
-0.21 0.72 -0.4 0.52
-0.33 -0.46 -0.32 0.76
-0.29 0.68 -0.5 0.46
-0.0071 -0.13 0.15 0.98
0.041 0.57 0.77 -0.29
-0.43 -0.57 -0.24 0.66
-0.39 0.16 0.35 -0.84
0.37 -0.049 0.83 0.41
0.29 0.24 0.7 -0.61
0.87 -0.19 0.023 0.46
0.66 0.17 -0.063 -0.73
-0.12 -0.41 0.18 -0.89
-0.042 -0.17 0.24 -0.95
0.2 -0.44 -0.42 -0.77
0.26 -0.17 -0.3 -0.9
find 3-d Delaunay triangle closest to [0.5, 0.5, ...]
0.81 -0.50 0.45
-0.48 -0.18 0.98
0.05 0.88 -0.01
0.89 0.77 0.30
Compute a new triangulation as a separate instance of Qhull
seed: 1442975393
input
-0.483 0.0805 0.495
-0.277 0.565 0.885
0.141 0.234 -0.649
0.709 0.964 0.231
0.752 0.55 0.678
0.3 -0.499 -0.453
-0.339 0.905 -0.87
0.0401 0.388 0.283
8 vertices and 18 facets with normals:
0.39 -0.55 0.63 -0.4
-0.79 -0.31 -0.48 -0.23
-0.39 -0.21 -0.25 -0.86
-0.64 0.43 -0.3 -0.56
0.83 0.12 -0.08 -0.53
0.07 -0.8 0.56 0.22
-0.47 -0.67 0.055 0.57
-0.098 -0.63 0.1 0.76
0.23 -0.17 0.85 -0.43
-0.58 0.73 0.055 -0.36
-0.086 -0.092 0.26 0.96
0.17 0.73 0.52 -0.41
-0.21 0.92 0.098 -0.31
0.82 0.19 -0.092 -0.53
0.13 0.84 -0.26 -0.47
0.41 -0.49 -0.23 0.74
0.87 0.12 -0.14 -0.46
0.73 -0.0072 -0.66 0.18
Free memory allocated by the new instance of Qhull, and redisplay the old results.
8 vertices and 16 facets with normals:
-0.029 -0.14 0.0013 0.99
-0.21 0.72 -0.4 0.52
-0.33 -0.46 -0.32 0.76
-0.29 0.68 -0.5 0.46
-0.0071 -0.13 0.15 0.98
0.041 0.57 0.77 -0.29
-0.43 -0.57 -0.24 0.66
-0.39 0.16 0.35 -0.84
0.37 -0.049 0.83 0.41
0.29 0.24 0.7 -0.61
0.87 -0.19 0.023 0.46
0.66 0.17 -0.063 -0.73
-0.12 -0.41 0.18 -0.89
-0.042 -0.17 0.24 -0.95
0.2 -0.44 -0.42 -0.77
0.26 -0.17 -0.3 -0.9
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
3
6
0 0 -1
0 -1 0
1 0 0
-1 0 0
0 1 0
0 0 1
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
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: 35
Number of distance tests for merging: 142
Number of distance tests for checking: 56
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: 8
Statistics for: | qhull s d Tcv
Number of points processed: 8
Number of hyperplanes created: 24
Number of facets in hull: 16
Number of distance tests for qhull: 32
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 9e-015 of
all facets. Will make 64 distance computations.
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: 26
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-014 of
all facets. Will make 96 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: 35
Number of distance tests for merging: 142
Number of distance tests for checking: 56
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.
==============================
========= user_eg2 ===========
==============================
bin/user_eg2
This is the output from user_eg2_r.c
It shows how qhull() may be called from an application using qhull's
static, reentrant library. user_eg2 is not part of qhull itself. If it
appears accidently, please remove user_eg2_r.c from your project. If it fails
immediately, user_eg2_r.c was incorrectly linked to the non-reentrant library.
Also try 'user_eg2 T1 2>&1'
compute triangulated convex hull of cube after rotating input
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
compute 2-d Delaunay triangulation
seed: 1442975392
8 vertices and 12 facets with normals:
-0.26 0.9 0.36
-0.72 -0.67 0.17
-0.21 -0.36 0.91
-0.36 -0.53 0.77
0.5 -0.05 -0.87
-0.82 0.14 -0.56
0.55 0.098 -0.83
0.26 0.28 -0.93
0.66 0.26 -0.71
0.67 0.15 -0.72
-0.42 0.9 -0.15
-0.46 0.81 -0.36
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 closest to [0.5, 0.5, ...]
0.36 0.87
0.51 -0.08
-0.01 0.84
compute halfspace intersection about the origin for a diamond
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
Output completed. Verifying that all points are below outer planes of
all facets. Will make 96 distance computations.
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_eg cube | qhull s Tcv Q11
Number of points processed: 14
Number of hyperplanes created: 23
Number of distance tests for qhull: 65
Number of distance tests for merging: 450
Number of distance tests for checking: 190
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.
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_eg Delaunay | qhull s d Tcv
Number of points processed: 8
Number of hyperplanes created: 22
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 6.7e-015 of
all facets. Will make 64 distance computations.
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_eg Delaunay | qhull s d Tcv
Number of points processed: 14
Number of hyperplanes created: 52
Number of facets in hull: 24
Number of distance tests for qhull: 74
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 6.7e-015 of
all facets. Will make 266 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: user_eg halfspaces | qhull H0 s Tcv
Number of points processed: 8
Number of hyperplanes created: 11
Number of distance tests for qhull: 35
Number of distance tests for merging: 142
Number of distance tests for checking: 56
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.
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_eg halfspaces | qhull H0 s Tcv
Number of points processed: 14
Number of hyperplanes created: 35
Number of distance tests for qhull: 59
Number of distance tests for merging: 306
Number of distance tests for checking: 214
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_eg3 ===========
==============================
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" | qhull s p
Number of points processed: 5
Number of hyperplanes created: 8
Number of distance tests for qhull: 64
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
-0.3674659290047977 0.0001301793382784133
Facets created by Qhull::runQhull()
- f1
- flags: top simplicial
- normal: 0.118775 0.992921
- offset: -0.420323
- vertices: p4(v1) p1(v0)
- neighboring facets: f6 f4
- f4
- flags: top simplicial
- normal: 0.997793 -0.0664014
- offset: -0.353096
- vertices: p8(v4) p4(v1)
- neighboring facets: f1 f5
- f5
- flags: bottom simplicial
- normal: 0.694945 -0.719063
- offset: -0.34263
- vertices: p8(v4) p0(v2)
- neighboring facets: f7 f4
- f6
- flags: bottom simplicial
- normal: -0.991816 -0.127679
- offset: -0.364442
- vertices: p10(v5) p1(v0)
- neighboring facets: f1 f7
- f7
- flags: top simplicial
- normal: -0.821881 -0.569659
- offset: -0.301939
- vertices: p10(v5) p0(v2)
- neighboring facets: f5 f6
============================================
== make testall ============================
============================================
== Tue Sep 22 22:29:52 EDT 2015
eg/q_eg
==============================
========= 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: 35
Number of distance tests for merging: 84
Number of distance tests for checking: 56
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: 45
Number of distance tests for checking: 54
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: 503
Number of distance tests for qhull: 1631
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: 891
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: 26
Number of distance tests for qhull: 40
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: 8
Number of distance tests for qhull: 12111
Number of distance tests for merging: 43
Number of distance tests for checking: 3736
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: 368
Number of distance tests for qhull: 12884
CPU seconds to compute hull (after input): 0
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: 9648
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: 409
Number of hyperplanes created: 2032
Number of distance tests for qhull: 10055
Number of distance tests for merging: 8153
Number of distance tests for checking: 10136
Number of merged facets: 1
CPU seconds to compute hull (after input): 0
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: 1642
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: 513
Number of distance tests for qhull: 1704
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: 513
Number of distance tests for qhull: 1704
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: 513
Number of distance tests for qhull: 1704
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: 1594
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: 1594
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: 1435
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 QR1442975393
Number of points processed: 71
Number of hyperplanes created: 207
Number of distance tests for qhull: 8158
Number of distance tests for merging: 1898
Number of distance tests for checking: 6765
Number of merged facets: 58
CPU seconds to compute hull (after input): 0.015
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 QR1442975393
Number of points processed: 71
Number of hyperplanes created: 207
Number of distance tests for qhull: 8158
Number of distance tests for merging: 1964
Number of distance tests for checking: 6765
Number of merged facets: 58
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: 75
Number of coplanar points: 425
Number of facets: 146
Statistics for: rbox 500 W0 | qconvex s QR0 QJ5e-2 Qc Gvp QR1442975393
Number of points processed: 88
Number of hyperplanes created: 379
Number of distance tests for qhull: 18662
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: 90
Number of facets in hull: 46
Number of distance tests for qhull: 289
Number of distance tests for merging: 492
Number of distance tests for checking: 307
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: 90
Number of facets in hull: 42
Number of distance tests for qhull: 289
Number of distance tests for merging: 482
Number of distance tests for checking: 307
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: 90
Number of facets in hull: 42
Number of distance tests for qhull: 289
Number of distance tests for merging: 482
Number of distance tests for checking: 307
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: 99
Number of facets in hull: 46
Number of distance tests for qhull: 283
CPU seconds to compute hull (after input): 0
Input joggled by: 4.2e-011
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: 90
Number of facets in hull: 42
Number of distance tests for qhull: 289
Number of distance tests for merging: 482
Number of distance tests for checking: 307
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: 46
Number of facets in hull: 24
Number of distance tests for qhull: 85
Number of distance tests for merging: 213
Number of distance tests for checking: 304
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: 46
Number of facets in hull: 24
Number of distance tests for qhull: 85
Number of distance tests for merging: 213
Number of distance tests for checking: 304
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: 46
Number of facets in hull: 24
Number of distance tests for qhull: 85
Number of distance tests for merging: 213
Number of distance tests for checking: 304
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: 44
Number of facets in hull: 27
Number of distance tests for qhull: 67
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: 18
Number of distance tests for qhull: 45
Number of distance tests for merging: 130
Number of distance tests for checking: 89
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: 115
Number of distance tests for qhull: 624
Number of distance tests for merging: 1584
Number of distance tests for checking: 721
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: 52
Number of non-simplicial facets: 43
Statistics for: rbox 200 s | qconvex s Qc R0.014 Gpav
Number of points processed: 73
Number of hyperplanes created: 291
Number of distance tests for qhull: 9744
Number of distance tests for merging: 4407
Number of distance tests for checking: 4026
Number of merged facets: 176
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.048 (0.9x)
Maximum distance of vertex below facet: -0.098 (1.7x)
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: 223
Number of coplanar points: 777
Number of facets: 117
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: 5545
Number of distance tests for qhull: 121035
Number of distance tests for merging: 79123
Number of distance tests for checking: 8141
Number of merged facets: 1879
CPU seconds to compute hull (after input): 0.015
Maximum distance of vertex below facet: -0.04 (1.3x)
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: 102
Number of coplanar points: 898
Number of facets: 103
Number of non-simplicial facets: 75
Statistics for: rbox 1000 s | qconvex s C-0.01 Qc Gcrp
Number of points processed: 108
Number of hyperplanes created: 467
Number of distance tests for qhull: 71156
Number of distance tests for merging: 6748
Number of distance tests for checking: 31209
Number of merged facets: 256
CPU seconds to compute hull (after input): 0.015
Maximum distance of point above facet: 0.031 (1.0x)
Maximum distance of vertex below facet: -0.065 (2.2x)
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: 48
Number of coplanar points: 952
Number of facets: 26
Number of non-simplicial facets: 26
Statistics for: rbox 1000 s | qconvex s C0.05 Qc Gcrpv
Number of points processed: 1000
Number of hyperplanes created: 5545
Number of distance tests for qhull: 55658
Number of distance tests for merging: 83457
Number of distance tests for checking: 7742
Number of merged facets: 1970
CPU seconds to compute hull (after input): 0.016
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: 69
Number of distance tests for qhull: 44445
Number of distance tests for merging: 1034
Number of distance tests for checking: 13690
Number of merged facets: 41
CPU seconds to compute hull (after input): 0
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: 741
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: 60073
Number of distance tests for merging: 5413
Number of distance tests for checking: 6014
Number of merged facets: 146
CPU seconds to compute hull (after input): 0
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: 30
Number of hyperplanes created: 182
Number of distance tests for qhull: 658286
Number of distance tests for merging: 4770
Number of distance tests for checking: 45000
Number of merged facets: 188
CPU seconds to compute hull (after input): 0.031
Maximum distance of point above facet: 0.14 (0.4x)
Maximum distance of vertex below facet: -0.31 (0.8x)
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: 30
Number of hyperplanes created: 182
Number of distance tests for qhull: 658286
Number of distance tests for merging: 4770
Number of distance tests for checking: 45000
Number of merged facets: 188
CPU seconds to compute hull (after input): 0.031
Maximum distance of point above facet: 0.14 (0.4x)
Maximum distance of vertex below facet: -0.31 (0.8x)
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: 302
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: 650
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: 48
Number of distance tests for qhull: 162
Number of distance tests for merging: 435
Number of distance tests for checking: 261
Number of merged facets: 18
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 f506 is flipped, distance= 0.461556194655
QH6136 qhull precision error: facet f592 is flipped, distance= 0.439612545215
QH6136 qhull precision error: facet f604 is flipped, distance= 0.465768128315
QH6136 qhull precision error: facet f506 is flipped, distance= 0.468691154013
QH6136 qhull precision error: facet f592 is flipped, distance= 0.450451888758
QH6136 qhull precision error: facet f604 is flipped, distance= 0.471152553888
QH6115 qhull precision error: f127 is concave to f267, since p65(v17) is 0.02603 above
QH6115 qhull precision error: f139 is concave to f285, since p13(v34) is 0.02883 above
QH6115 qhull precision error: f166 is concave to f316, since p189(v18) is 0.008704 above
QH6115 qhull precision error: f198 is concave to f604, since p109(v11) is 0.02657 above
QH6115 qhull precision error: f242 is concave to f527, since p65(v17) is 0.02938 above
QH6115 qhull precision error: f259 is concave to f462, since p59(v60) is 0.008633 above
QH6115 qhull precision error: f280 is concave to f286, since p22(v65) is 0.01973 above
QH6115 qhull precision error: f288 is concave to f310, since p71(v67) is 0.02406 above
QH6115 qhull precision error: f297 is concave to f487, since p180(v38) is 0.008078 above
QH6115 qhull precision error: f313 is concave to f496, since p63(v41) is 0.03309 above
QH6115 qhull precision error: f330 is concave to f331, since p10(v64) is 0.02231 above
QH6115 qhull precision error: f397 is concave to f542, since p69(v51) is 0.01923 above
QH6115 qhull precision error: f399 is concave to f543, since p155(v31) is 0.01245 above
QH6115 qhull precision error: f417 is concave to f552, since p184(v71) is 0.009005 above
QH6115 qhull precision error: f426 is concave to f477, since p135(v95) is 0.016 above
QH6115 qhull precision error: f431 is concave to f555, since p135(v95) is 0.008306 above
QH6115 qhull precision error: f442 is concave to f559, since p97(v98) is 0.04007 above
QH6115 qhull precision error: f444 is concave to f245, since p194(v99) is 0.0124 above
QH6115 qhull precision error: f457 is concave to f505, since p70(v101) is 0.05613 above
QH6115 qhull precision error: f460 is concave to f565, since p176(v61) is 0.02392 above
QH6115 qhull precision error: f469 is concave to f580, since p119(v9) is 0.07256 above
QH6115 qhull precision error: f472 is concave to f582, since p138(v63) is 0.04511 above
QH6115 qhull precision error: f481 is concave to f624, since p79(v93) is 0.0132 above
QH6115 qhull precision error: f484 is concave to f483, since p79(v93) is 0.01528 above
QH6115 qhull precision error: f492 is concave to f551, since p163(v108) is 0.05382 above
QH6115 qhull precision error: f501 is concave to f602, since p29(v10) is 0.01867 above
QH6115 qhull precision error: f505 is concave to f457, since p128(v110) is 0.008966 above
QH6113 qhull precision error: f506 is flipped(interior point is outside)
QH6115 qhull precision error: f520 is concave to f541, since p100(v114) is 0.009004 above
QH6115 qhull precision error: f521 is concave to f516, since p100(v114) is 0.01561 above
QH6115 qhull precision error: f522 is concave to f526, since p100(v114) is 0.0118 above
QH6115 qhull precision error: f534 is concave to f535, since p190(v2) is 0.01582 above
QH6115 qhull precision error: f535 is concave to f534, since p154(v47) is 0.009917 above
QH6115 qhull precision error: f544 is concave to f620, since p58(v91) is 0.01945 above
QH6115 qhull precision error: f551 is concave to f492, since p41(v120) is 0.0114 above
QH6115 qhull precision error: f559 is concave to f442, since p38(v122) is 0.01392 above
QH6115 qhull precision error: f565 is concave to f460, since p73(v123) is 0.01004 above
QH6115 qhull precision error: f566 is concave to f571, since p133(v16) is 0.01303 above
QH6115 qhull precision error: f580 is concave to f469, since p158(v127) is 0.0104 above
QH6113 qhull precision error: f592 is flipped(interior point is outside)
QH6115 qhull precision error: f595 is concave to f626, since p22(v65) is 0.008193 above
QH6115 qhull precision error: f603 is concave to f500, since p14(v132) is 0.00736 above
QH6113 qhull precision error: f604 is flipped(interior point is outside)
QH6115 qhull precision error: f619 is concave to f617, since p12(v1) is 0.007428 above
Convex hull of 200 points in 3-d:
Number of vertices: 138
Number of facets: 272
Statistics for: rbox 200 s | qhull Q0 s R0.014 Gav Po
Number of points processed: 138
Number of hyperplanes created: 629
Number of distance tests for qhull: 4659
CPU seconds to compute hull (after input): 0
precision problems (corrected unless 'Q0' or an error)
120 coplanar half ridges in output
41 concave half ridges in output
3 flipped facets
125 coplanar horizon facets for new vertices
62 coplanar points during partitioning
echo ==the preceding should report flipped and concave facets== >/dev/null
eg/q_egtest
==============================
========= 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: 11
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: 6
Number of distance tests for qhull: 4
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.3e-015 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: 11
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: 6
Number of distance tests for qhull: 4
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.3e-015 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: 26
Number of distance tests for qhull: 168
Number of distance tests for merging: 963
Number of distance tests for checking: 144
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: 11
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: 11
Number of distance tests for merging: 169
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 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: 6
Number of distance tests for qhull: 4
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: 11
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: 11
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: 11
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: 11
Number of distance tests for merging: 169
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 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: 11
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: 11
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: 26
Number of distance tests for qhull: 168
Number of distance tests for merging: 788
Number of distance tests for checking: 144
Number of merged facets: 36
CPU seconds to compute hull (after input): 0.015
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: 62
Number of distance tests for qhull: 163
Number of distance tests for merging: 1304
Number of distance tests for checking: 144
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: 26
Number of distance tests for qhull: 168
Number of distance tests for merging: 788
Number of distance tests for checking: 144
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: 3313
Number of distance tests for merging: 1030
Number of distance tests for checking: 1347
Number of merged facets: 29
CPU seconds to compute hull (after input): 0
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: 650
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: 503
Number of distance tests for qhull: 1631
CPU seconds to compute hull (after input): 0
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: 1641
CPU seconds to compute hull (after input): 0
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: 89
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-015 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: 13
Total number of nearly incident points: 91
Number of Voronoi vertices: 13
Number of non-simplicial Voronoi vertices: 5
Statistics for: rbox 100 D2 c G1.0 | qvoronoi s A-0.95 Gna Tv
Number of points processed: 13
Number of hyperplanes created: 39
Number of facets in hull: 14
Number of distance tests for qhull: 2740
Number of distance tests for merging: 464
Number of distance tests for checking: 1119
Number of merged facets: 13
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.098 (0.1x)
Maximum distance of vertex below facet: -0.082 (0.1x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 1352 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: 650
CPU seconds to compute hull (after input): 0.015
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
QH6136 qhull precision error: facet f491 is flipped, distance= 0.413460414284
QH6136 qhull precision error: facet f949 is flipped, distance= 0.558894018107
QH6107 qhull precision error: facets f977, f981 and f978 meet at a ridge with more than 2 neighbors. Can not continue.
ERRONEOUS FACET:
- f977
- flags: bottom simplicial new
- normal: -0.07131 -0.04413 0.08982 -0.9924
- offset: -0.5084414
- vertices: p108(v73) p722(v63) p713(v35) p241(v7)
- neighboring facets: f824 f968 f971 f978
ERRONEOUS OTHER FACET:
- f981
- flags: top simplicial new
- normal: -0.005308 -0.0126 0.005272 -0.9999
- offset: -0.4947257
- vertices: p108(v73) p722(v63) p713(v35) p62(v20)
- neighboring facets: f825
ERRONEOUS and NEIGHBORING FACETS to output
While executing: rbox 1000 D4 | qhull Q0 s Po R0.005 Ga Tc Tv
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554638194 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-coplanar-distance 0.0025
Width-outside 0.005 _wide-facet 0.015
Last point added to hull was p108.
Convex hull of 1000 points in 4-d:
Number of vertices: 68
Number of facets: 346
Statistics for: rbox 1000 D4 | qhull Q0 s Po R0.005 Ga Tc Tv
Number of points processed: 73
Number of hyperplanes created: 986
Number of distance tests for qhull: 28532
precision problems (corrected unless 'Q0' or an error)
2 flipped facets
42 coplanar horizon facets for new vertices
141 coplanar points during partitioning
9 degenerate hyperplanes recomputed with gaussian elimination
9 nearly singular or axis-parallel hyperplanes
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
eg/q_test
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: 35
Number of distance tests for merging: 142
Number of distance tests for checking: 56
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: 13
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: 29
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.2e-014 of
all facets. Will make 104 distance computations.
Delaunay triangulation by the convex hull of 8 points in 4-d:
Number of input sites: 8
Number of Delaunay regions: 11
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: 27
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.1e-014 of
all facets. Will make 88 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: 35
Number of distance tests for merging: 142
Number of distance tests for checking: 56
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 ======
==============================
==============================
== check user_eg, user_eg2, and user_eg3
== errors if user_eg and user_eg2 not found
==============================
user_eg "QR1 p n Qt" "v p" Fp
This is the output from user_eg_r.c
It shows how qhull() may be called from an application using the qhull
reentrant library. user_eg is not part of qhull itself. If it appears
accidently, please remove user_eg_r.c from your project. If it fails
immediately, user_eg_r.c was incorrectly linked to the non-reentrant library.
Also try 'user_eg T1 2>&1'
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
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
-0.380573002749541 0.9081645691962865 -0.1743596995716652 -1
-0.380573002749541 0.9081645691962865 -0.1743596995716652 -1
0.744442726136703 0.4127293393945193 0.5248423762474955 -1
0.744442726136703 0.4127293393945193 0.5248423762474955 -1
-0.5486066141420022 -0.06994002902120672 0.8331501516894545 -1
-0.5486066141420022 -0.06994002902120672 0.8331501516894545 -1
0.5486066141420022 0.06994002902120679 -0.8331501516894545 -1
0.5486066141420022 0.06994002902120679 -0.8331501516894545 -1
0.380573002749541 -0.9081645691962865 0.1743596995716652 -1
0.380573002749541 -0.9081645691962865 0.1743596995716652 -1
-0.7444427261367029 -0.4127293393945193 -0.5248423762474955 -0.9999999999999997
-0.7444427261367029 -0.4127293393945193 -0.5248423762474955 -0.9999999999999997
8 vertices and 12 facets with normals:
-0.38 0.91 -0.17
-0.38 0.91 -0.17
0.74 0.41 0.52
0.74 0.41 0.52
-0.55 -0.07 0.83
-0.55 -0.07 0.83
0.55 0.07 -0.83
0.55 0.07 -0.83
0.38 -0.91 0.17
0.38 -0.91 0.17
-0.74 -0.41 -0.52
-0.74 -0.41 -0.52
compute 3-d Delaunay triangulation
seed: 1442975396
input
-0.483 0.87 -0.972
0.475 -0.239 0.199
0.424 0.307 -0.573
0.317 -0.734 -0.653
-0.262 0.758 0.998
-0.522 -0.472 -0.407
-0.0387 -0.694 -0.365
0.161 -0.0778 -0.135
3
13
-0.5468778501739459 -0.3497468414641829 0.7553946850369157
-0.7593815022703543 0.5131011611254545 0.03953741577512079
0.4788709495342384 0.7572541471852259 0.3220241908835472
-0.2040500620592344 0.8526518802181451 -0.003469054687607609
0.7414838067034658 -0.266477915165952 -0.4189354523282637
-0.1914977183744108 -0.09820183919803405 -1.373858931073375
-0.3218281778232761 0.2184779660793899 -0.6305236453317936
-0.3288025693196456 -0.5264601152652346 0.4646570498148218
0.4005900990636951 -0.509020791945665 -0.2144936220758815
-0.9919406368566945 -1.675485484428414 1.997687679346762
-0.0459605746609393 -0.1557619644204564 -0.8154639986503705
-0.04578191668261705 -0.1502697818228355 -0.7886907434218087
-0.01989710335996268 -0.160940333443926 -0.7825439711007396
8 vertices and 18 facets with normals:
-0.47 -0.57 0.12 0.67
-0.49 -0.31 0.68 -0.45
-0.73 0.49 0.038 -0.48
0.45 0.7 0.3 -0.46
-0.2 0.84 -0.0034 -0.5
0.91 0.068 0.13 0.38
0.85 0.14 -0.01 0.51
0.72 -0.26 -0.41 -0.49
-0.13 -0.066 -0.93 -0.34
-0.36 0.24 -0.71 -0.56
-0.36 -0.57 0.5 -0.54
0.47 -0.6 -0.25 -0.59
-0.35 -0.59 0.7 -0.18
-0.33 -0.73 0.39 0.45
0.11 -0.74 0.62 0.24
-0.047 -0.16 -0.84 -0.52
-0.048 -0.16 -0.83 -0.53
-0.021 -0.17 -0.83 -0.53
find 3-d Delaunay triangle closest to [0.5, 0.5, ...]
0.42 0.31 -0.57
0.16 -0.08 -0.13
-0.26 0.76 1.00
0.48 -0.24 0.20
Compute a new triangulation as a separate instance of Qhull
seed: 1442975397
input
-0.483 -0.867 0.539
-0.607 0.827 0.637
0.518 -0.335 0.786
0.187 0.0325 0.386
-0.601 0.827 -0.895
0.538 0.87 -0.392
0.728 -0.561 0.47
-0.466 -0.9 -0.274
3
11
0.5595753855114969 -0.3404605131382664 -0.7667051741974538
-0.731268527113188 0.1116337965971249 -0.1294164137512704
-0.2497900705369764 0.5921698430182071 -0.1272384176286181
0.01514407430286224 -0.02568398902536651 -0.6732955724833146
1.124466173359155 1.470614139815442 1.439328714510314
1.248639284661356 0.4545647068700313 0.4007637829878587
-16.02504613428867 -1.106968174845187 -0.197252268862681
-0.7820736685904419 -0.008810164205065862 0.09102151330465119
-0.4369631431732016 -0.05498982396873331 1.328576513849616
0.084205153721854 -0.6463290812209749 0.1355152676737212
0.08845665688281146 -0.6070405235100019 0.3847361485910251
8 vertices and 17 facets with normals:
0.5 -0.3 -0.68 -0.44
0.4 0.11 0.22 0.88
0.53 -0.36 -0.66 0.39
-0.81 0.12 -0.14 -0.55
-0.3 0.72 -0.15 -0.61
0.018 -0.031 -0.8 -0.6
0.48 0.2 0.35 0.78
0.47 0.61 0.6 -0.21
0.85 0.31 0.27 -0.34
0.2 -0.1 0.24 0.94
-1 -0.069 -0.012 -0.031
0.25 -0.41 -0.16 0.86
0.2 -0.1 0.4 0.89
-0.84 -0.0094 0.098 -0.54
-0.29 -0.037 0.89 -0.34
0.1 -0.78 0.16 -0.6
0.1 -0.69 0.44 -0.57
Free memory allocated by the new instance of Qhull, and redisplay the old results.
8 vertices and 18 facets with normals:
-0.47 -0.57 0.12 0.67
-0.49 -0.31 0.68 -0.45
-0.73 0.49 0.038 -0.48
0.45 0.7 0.3 -0.46
-0.2 0.84 -0.0034 -0.5
0.91 0.068 0.13 0.38
0.85 0.14 -0.01 0.51
0.72 -0.26 -0.41 -0.49
-0.13 -0.066 -0.93 -0.34
-0.36 0.24 -0.71 -0.56
-0.36 -0.57 0.5 -0.54
0.47 -0.6 -0.25 -0.59
-0.35 -0.59 0.7 -0.18
-0.33 -0.73 0.39 0.45
0.11 -0.74 0.62 0.24
-0.047 -0.16 -0.84 -0.52
-0.048 -0.16 -0.83 -0.53
-0.021 -0.17 -0.83 -0.53
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
3
6
0 0 -1
0 -1 0
1 0 0
-1 0 0
0 1 0
0 0 1
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
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: 11
Number of distance tests for qhull: 24
Number of distance tests for merging: 186
Number of distance tests for checking: 56
Number of merged facets: 7
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below outer planes of
all facets. Will make 96 distance computations.
Voronoi diagram by the convex hull of 8 points in 4-d:
Number of Voronoi regions: 8
Number of Voronoi vertices: 13
Statistics for: | qhull s d Tcv v p
Number of points processed: 8
Number of hyperplanes created: 28
Number of facets in hull: 18
Number of distance tests for qhull: 29
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.2e-014 of
all facets. Will make 104 distance computations.
Voronoi diagram by the convex hull of 8 points in 4-d:
Number of Voronoi regions: 8
Number of Voronoi vertices: 11
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: 27
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.1e-014 of
all facets. Will make 88 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: 35
Number of distance tests for merging: 142
Number of distance tests for checking: 56
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.
user_eg2 "QR1 p" "v p" Fp
This is the output from user_eg2_r.c
It shows how qhull() may be called from an application using qhull's
static, reentrant library. user_eg2 is not part of qhull itself. If it
appears accidently, please remove user_eg2_r.c from your project. If it fails
immediately, user_eg2_r.c was incorrectly linked to the non-reentrant library.
Also try 'user_eg2 T1 2>&1'
compute triangulated convex hull of cube after rotating input
8 vertices and 12 facets with normals:
-0.38 0.91 -0.17
-0.38 0.91 -0.17
0.74 0.41 0.52
0.74 0.41 0.52
-0.55 -0.07 0.83
-0.55 -0.07 0.83
0.55 0.07 -0.83
0.55 0.07 -0.83
0.38 -0.91 0.17
0.38 -0.91 0.17
-0.74 -0.41 -0.52
-0.74 -0.41 -0.52
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 -0.66 0.37
0.63 -0.7 -0.34
-0.65 -0.65 -0.41
-0.62 -0.62 -0.49
-0.65 0.66 -0.37
-0.63 0.7 0.34
0.1 0.71 -0.7
0.65 0.65 0.41
0.62 0.62 0.49
-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
0.7 0.13 0.7
0.62 0.49 0.62
-0.11 -0.7 0.71
-0.68 -0.29 0.68
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
compute 2-d Delaunay triangulation
seed: 1442975396
8 vertices and 12 facets with normals:
-0.15 -0.21 0.97
0.17 -0.75 -0.64
0.11 0.3 0.95
-0.89 -0.1 -0.45
-0.73 -0.24 -0.65
-0.65 0.59 -0.48
0.29 -0.64 -0.71
0.64 0.73 0.24
0.076 0.7 -0.71
0.59 0.8 0.12
-0.43 0.62 -0.65
-0.53 0.64 -0.55
2
8
0.1318885744699128 -0.5866773353832734
-0.9749953925114336 -0.1143002181132337
-0.5615950129570352 -0.1831000753260824
-0.6842065237979991 0.6187537909643577
0.2078539414602336 -0.456350513575001
0.05363103945575809 0.4914762684240895
-0.3293355355261546 0.4751827730402221
-0.4878014640284577 0.5868883919416603
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
2
21
-0.6842065237979991 0.6187537909643577
0.05363103945575809 0.4914762684240895
-0.3293355355261546 0.4751827730402221
-0.4878014640284577 0.5868883919416603
1.296517073871458 0.2986988205336432
0.5322578342448032 -0.5491281889663302
0.8946798042408244 -8.949159431033582
-0.02301453748518857 -3.356589337597645
-1.878754540370903 -0.1100344656380098
-1.029568633660267 -0.1830127477892508
-0.7145624093067451 0.5422291850888282
-0.7980829882219229 -0.1437427362053064
1.978133606444146 0.7714383610897467
-0.0622147642985259 1.427609847136278
0.09469922436678835 0.5539629978421951
-0.6822000621980453 -0.163028467806336
-0.4577793158335451 0.1111402009525134
-0.3582059383636282 -0.3979819478241133
0.1161835094406034 -0.1623083804984112
0.1122190369673253 0.1314047587883284
0.1493157985893253 0.04057783177062682
find Delaunay triangle closest to [0.5, 0.5, ...]
0.36 0.87
0.42 0.31
1.00 -0.52
compute halfspace intersection about the origin for a diamond
3
6
0 0 -1
0 -1 0
1 0 0
-1 0 0
0 1 0
0 0 1
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
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 0.4226497308103742 0
-0.5773502691896257 0 0.4226497308103742
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
0.4226497308103742 -0.5773502691896257 0
0 -0.5773502691896257 0.4226497308103742
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
0.4226497308103742 0 -0.5773502691896257
0 0.4226497308103742 -0.5773502691896257
Output completed. Verifying that all points are below outer planes of
all facets. Will make 96 distance computations.
Convex hull of 14 points in 3-d:
Number of vertices: 14
Number of facets: 24
Statistics for: user_eg cube | qhull s Tcv Q11 QR1 p QR1
Number of points processed: 14
Number of hyperplanes created: 45
Number of distance tests for qhull: 68
Number of distance tests for merging: 370
Number of distance tests for checking: 214
Number of merged facets: 7
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.
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_eg Delaunay | qhull s d Tcv v p
Number of points processed: 8
Number of hyperplanes created: 19
Number of facets in hull: 12
Number of distance tests for qhull: 29
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 5.3e-015 of
all facets. Will make 64 distance computations.
Voronoi diagram by the convex hull of 14 points in 3-d:
Number of Voronoi regions: 14
Number of Voronoi vertices: 21
Statistics for: user_eg Delaunay | qhull s d Tcv v p
Number of points processed: 14
Number of hyperplanes created: 45
Number of facets in hull: 24
Number of distance tests for qhull: 63
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 5.3e-015 of
all facets. Will make 294 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: user_eg halfspaces | qhull H0 s Tcv Fp
Number of points processed: 8
Number of hyperplanes created: 11
Number of distance tests for qhull: 35
Number of distance tests for merging: 142
Number of distance tests for checking: 56
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.
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_eg halfspaces | qhull H0 s Tcv Fp
Number of points processed: 14
Number of hyperplanes created: 35
Number of distance tests for qhull: 59
Number of distance tests for merging: 306
Number of distance tests for checking: 214
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_eg3 rbox "10 D2" "2 D2" qhull "p"
rbox 10 D2
rbox 2 D2
Results of p
2
5
-0.02222276248244826 -0.4979727817680433
-0.4285431913366012 0.4745826469497594
0.3790312361708201 0.3779794437605696
0.3443122672329771 -0.1437312230875075
-0.3674659290047977 0.0001301793382784133
echo === check front ends ${d:-`date`} ==================
date
=== check front ends Tue Sep 22 22:29:56 EDT 2015 ==================
qconvex -
qconvex- compute the convex hull
http://www.qhull.org 2015.0.3 2015/09/22
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:
Qt - triangulated output
QJ - joggled input instead of merged facets
Qc - keep coplanar points with nearest facet
Qi - keep interior points with nearest facet
Qhull control options:
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
QGn - good facet if visible from point n, -n for not visible
QVn - good facet if it includes point n, -n if not
Trace options:
T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
Tc - check frequently during execution
Ts - print statistics
Tv - verify result: structure, convexity, and point inclusion
Tz - send all output to stdout
TFn - report summary when n or more facets created
TI file - input data from file, no spaces or single quotes
TO file - output results to file, may be enclosed in single quotes
TPn - turn on tracing when point n added to hull
TMn - turn on tracing at merge n
TWn - trace merge facets when width > n
TVn - stop qhull after adding point n, -n for before (see TCn)
TCn - stop qhull after building cone for point n (see TVn)
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; Voronoi regions)
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)
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,
for output: #vertices, #facets,
#coplanar points, #non-simplicial facets
#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
Gi - inner planes only
Gn - no planes
Go - outer planes only
Gc - centrums
Gh - hyperplane intersections
Gr - ridges
GDn - drop dimension n in 3-d and 4-d output
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
Pg - print good facets (needs 'QGn' or 'QVn')
PFn - keep facets whose area is at least n
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
qconvex .
Qhull 2015.0.3 2015/09/22.
Except for 'F.' and 'PG', upper-case options take an argument.
incidences mathematica normals OFF_format points
summary facet_dump
Farea FArea_total Fcoplanars FCentrums Fd_cdd_in
FD_cdd_out FFacet_xridge Finner FIDs Fmerges
Fneighbors FNeigh_vertex Fouter FOptions FPoint_near
FQhull Fsummary FSize Fvertices FVertex_ave
Fxtremes FMaple
Gvertices Gpoints Gall_points Gno_planes Ginner
Gcentrums Ghyperplanes Gridges Gouter GDrop_dim
PArea_keep Pdrop d0:0D0 PFacet_area_keep Pgood PGood_neighbors
PMerge_keep Poutput_forced Pprecision_not
QbBound 0:0.5 QbB_scale_box Qcoplanar QGood_point Qinterior
QJoggle Qrandom QRotate Qsearch_1st Qtriangulate
QVertex_good
T4_trace Tcheck_often Tstatistics Tverify Tz_stdout
TFacet_log TInput_file TPoint_trace TMerge_trace TOutput_file
TWide_trace TVertex_stop TCone_stop
Angle_max Centrum_size Random_dist Ucoplanar_max Wide_outside
qconvex
qconvex- compute the convex hull. Qhull 2015.0.3 2015/09/22
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 all options
output options (subset):
s - summary of results (default)
i - vertices incident to each facet
n - normals with offsets
p - vertex coordinates (includes coplanar points if 'Qc')
Fx - extreme points (convex hull vertices)
FA - report total area and volume
FS - compute total area and volume
o - OFF format (dim, n, points, facets)
G - Geomview output (2-d, 3-d, and 4-d)
m - Mathematica output (2-d and 3-d)
QVn - print facets that include point n, -n if not
TO file- output results to 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 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
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
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: 35
Number of distance tests for merging: 108
Number of distance tests for checking: 56
Number of merged facets: 6
CPU seconds to compute hull (after input): 0
rbox c D2 | qconvex s i
4
0 2
1 0
2 3
3 1
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: 6
CPU seconds to compute hull (after input): 0
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: 5545
Number of distance tests for qhull: 25488
CPU seconds to compute hull (after input): 0
Total facet area: 3.1201951
Total volume: 0.51650274
qhull output completed. Verifying that 1000 points are
below 2.1e-015 of the nearest facet.
rbox c d D2 | qconvex s Qc Fx
4
0
2
3
1
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: 36
CPU seconds to compute hull (after input): 0
rbox y 1000 W0 | qconvex s n
4
4
0.2135848119563837 0.1168704340428167 0.9699086708284445 -0.09806074564261891
0.08553875579270345 -0.8316435307282575 -0.5486822022403077 -0.1234144150397865
-0.749541668500822 -0.02779445272382559 -0.6613733859014792 -0.2159556159595279
0.3120013537900506 0.9498158823230658 -0.02247097950761911 -0.02453689035981485
Convex hull of 1004 points in 3-d:
Number of vertices: 4
Number of facets: 4
Statistics for: rbox y 1000 W0 | qconvex s n
Number of points processed: 4
Number of hyperplanes created: 5
Number of distance tests for qhull: 11001
CPU seconds to compute hull (after input): 0
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: 181
Number of distance tests for qhull: 6424
CPU seconds to compute hull (after input): 0
Input joggled by: 2.1e-011
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 QR1442975396
Number of points processed: 24
Number of hyperplanes created: 4108
Number of distance tests for qhull: 4216
Number of distance tests for merging: 121128
Number of distance tests for checking: 98328
Number of merged facets: 2036
CPU seconds to compute hull (after input): 0.078
Approximate facet area: 0.00035546337
Approximate volume: 8.5511197e-006
rbox c D6 | qconvex FA TF500
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 FA TF500
Number of points processed: 64
Number of hyperplanes created: 359
Number of distance tests for qhull: 2510
Number of distance tests for merging: 14115
Number of distance tests for checking: 832
Number of merged facets: 1457
CPU seconds to compute hull (after input): 0
Approximate facet area: 12
Approximate volume: 1
At 22:29:56 & 0 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 22:29:56 & 0 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 22:29:56 & 0 CPU secs, qhull has created 1575 facets and merged 1230.
The current hull contains 25 facets and 51 vertices. There are 13
outside points. Next is point p45(v52), 0.45 above f1476.
At 22:29:56 & 0 CPU secs, qhull has created 1815 facets and merged 1457.
The current hull contains 12 facets and 64 vertices. Last point was p35
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 FA TF500
Number of points processed: 64
Number of hyperplanes created: 359
Number of distance tests for qhull: 2510
Number of distance tests for merging: 13995
Number of distance tests for checking: 0
Number of merged facets: 1457
First post-merge with 'C3.5e-015' and 'A1.8e+308'
At 22:29:56 & 0 CPU secs, qhull has created 1815 facets and merged 1457.
The current hull contains 12 facets and 64 vertices. Last point was p35
Testing all coplanar points.
computing area of each facet and volume of the convex hull
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 0 2
2 2 3
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
2
0 2
1 0
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: 36
CPU seconds to compute hull (after input): 0
rbox c | qconvex Q0
QH6029 qhull error: option 'Q0' is not used with this program.
It may be used with qhull.
While executing: | qconvex Q0
Options selected for Qhull 2015.0.3 2015/09/22:
run-id 554655001
qvoronoi -
qvoronoi- compute the Voronoi diagram
http://www.qhull.org 2015.0.3 2015/09/22
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:
Qz - add point-at-infinity to Voronoi diagram
Qs - search all points for the initial simplex
QGn - Voronoi vertices if visible from point n, -n if not
QVn - Voronoi vertices for input point n, -n if not
Trace options:
T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
Tc - check frequently during execution
Ts - statistics
Tv - verify result: structure, convexity, and in-circle test
Tz - send all output to stdout
TFn - report summary when n or more facets created
TI file - input data from file, no spaces or single quotes
TO file - output results to file, may be enclosed in single quotes
TPn - turn on tracing when point n added to hull
TMn - turn on tracing at merge n
TWn - trace merge facets when width > n
TVn - stop qhull after adding point n, -n for before (see TCn)
TCn - stop qhull after building cone for point n (see TVn)
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, produces a summary to stdout):
s - summary to stderr
p - Voronoi vertices
o - OFF format (dim, Voronoi vertices, and Voronoi regions)
i - Delaunay regions (use 'Pp' to avoid warning)
f - facet dump
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 options (2-d only)
Ga - all points as dots
Gp - coplanar points and vertices as radii
Gv - vertices as spheres
Gi - inner planes only
Gn - no planes
Go - outer planes only
Gc - centrums
Gh - hyperplane intersections
Gr - ridges
GDn - drop dimension n in 3-d and 4-d output
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
Pg - print good Voronoi vertices (needs 'QGn' or 'QVn')
PFn - keep Voronoi vertices whose 'area' is at least n
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
qvoronoi .
Qhull 2015.0.3 2015/09/22.
Except for 'F.' and 'PG', upper-case options take an argument.
OFF_format p_vertices i_delaunay summary facet_dump
Fcoincident Fd_cdd_in FD_cdd_out FF-dump-xridge Fi_bounded
Fxtremes Fmerges Fneighbors FNeigh_region FOptions
Fo_unbounded FPoint_near FQvoronoi Fsummary Fvoronoi
FIDs
Gvertices Gpoints Gall_points Gno_planes Ginner
Gcentrums Ghyperplanes Gridges Gouter GDrop_dim
PArea_keep Pdrop d0:0D0 Pgood PFacet_area_keep
PGood_neighbors PMerge_keep Poutput_forced Pprecision_not
QG_vertex_good Qsearch_1st Qupper_voronoi QV_point_good Qzinfinite
T4_trace Tcheck_often Tstatistics Tverify Tz_stdout
TFacet_log TInput_file TPoint_trace TMerge_trace TOutput_file
TWide_trace TVertex_stop TCone_stop
Angle_max Centrum_size Random_dist Wide_outside
qvoronoi
qvoronoi- compute the Voronoi diagram. Qhull 2015.0.3 2015/09/22
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
output options (subset):
s - summary of results (default)
p - Voronoi vertices
o - OFF file format (dim, Voronoi vertices, and Voronoi regions)
FN - count and Voronoi vertices for each Voronoi region
Fv - Voronoi diagram as Voronoi vertices between adjacent input sites
Fi - separating hyperplanes for bounded regions, 'Fo' for unbounded
G - Geomview output (2-d only)
QVn - Voronoi vertices for input point n, -n if not
TO file- output results to 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
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
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: 7
Number of facets in hull: 5
Number of distance tests for qhull: 8
Number of distance tests for merging: 29
Number of distance tests for checking: 30
Number of merged facets: 1
CPU seconds to compute hull (after input): 0
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-016 ave. angle to ridge
2.2e-016 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
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
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 Qt Fv
4
4 1 3 0 2
4 1 2 0 1
4 2 4 0 1
4 3 4 0 2
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: 7
Number of facets in hull: 6
Number of distance tests for qhull: 8
Number of distance tests for merging: 33
Number of distance tests for checking: 30
Number of merged facets: 1
CPU seconds to compute hull (after input): 0
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
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
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: 17
Number of facets in hull: 10
Number of distance tests for qhull: 42
Number of distance tests for merging: 103
Number of distance tests for checking: 80
Number of merged facets: 3
CPU seconds to compute hull (after input): 0
rbox c G1 d D2 | qvoronoi QJ p
2
10
-2.57276422388486e-011 1.749999999802917
-2.05463598231932e-011 -1.750000000331276
0.5833333333083517 -0.5833333333052267
1.862254794815499e-011 -7.815052443180038e-011
1.750000000002628 3.498100747664324e-011
0.5833333333132078 0.5833333333796981
-0.5833333332888888 0.5833333333317835
-7.592293460589872e-011 -7.815050692933324e-011
-1.750000000049026 2.293196879294717e-011
-0.5833333333977308 -0.5833333333229861
rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN
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 1 3
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
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: 8
Number of facets in hull: 5
Number of distance tests for qhull: 33
Number of distance tests for merging: 49
Number of distance tests for checking: 43
Number of merged facets: 3
CPU seconds to compute hull (after input): 0
rbox P0 c D2 | qvoronoi s Fv QV0
4
4 0 3 1 3
4 0 1 1 2
4 0 2 2 4
4 0 4 3 4
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: 7
Number of facets in hull: 5
Number of distance tests for qhull: 8
Number of distance tests for merging: 29
Number of distance tests for checking: 30
Number of merged facets: 1
CPU seconds to compute hull (after input): 0
qdelaunay -
qdelaunay- compute the Delaunay triangulation
http://www.qhull.org 2015.0.3 2015/09/22
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 Delaunay triangulation
Qt - triangulated output
QJ - joggled input instead of merged facets
Qhull control options:
QJn - randomly joggle input in range [-n,n]
Qs - search all points for the initial simplex
Qz - add point-at-infinity to Delaunay triangulation
QGn - print Delaunay region if visible from point n, -n if not
QVn - print Delaunay regions that include point n, -n if not
Trace options:
T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
Tc - check frequently during execution
Ts - print statistics
Tv - verify result: structure, convexity, and in-circle test
Tz - send all output to stdout
TFn - report summary when n or more facets created
TI file - input data from file, no spaces or single quotes
TO file - output results to file, may be enclosed in single quotes
TPn - turn on tracing when point n added to hull
TMn - turn on tracing at merge n
TWn - trace merge facets when width > n
TVn - stop qhull after adding point n, -n for before (see TCn)
TCn - stop qhull after building cone for point n (see TVn)
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,
for 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 options (2-d and 3-d)
Ga - all points as dots
Gp - coplanar points and vertices as radii
Gv - vertices as spheres
Gi - inner planes only
Gn - no planes
Go - outer planes only
Gc - centrums
Gh - hyperplane intersections
Gr - ridges
GDn - drop dimension n in 3-d and 4-d output
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
Pg - print good Delaunay regions (needs 'QGn' or 'QVn')
PFn - keep Delaunay regions whose area is at least n
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
qdelaunay .
Qhull 2015.0.3 2015/09/22.
Except for 'F.' and 'PG', upper-case options take an argument.
incidences mathematica OFF_format points_lifted summary
facet_dump
Farea FArea_total Fcoincident Fd_cdd_in FD_cdd_out
FF_dump_xridge FIDs Fmerges Fneighbors FNeigh_vertex
FOptions FPoint_near FQdelaun Fsummary FSize
Fvertices Fxtremes FMaple
Gvertices Gpoints Gall_points Gno_planes Ginner
Gcentrums Ghyperplanes Gridges Gouter GDrop_dim
Gtransparent
PArea_keep Pdrop d0:0D0 Pgood PFacet_area_keep
PGood_neighbors PMerge_keep Poutput_forced Pprecision_not
QGood_point QJoggle Qsearch_1st Qtriangulate QupperDelaunay
QVertex_good Qzinfinite
T4_trace Tcheck_often Tstatistics Tverify Tz_stdout
TFacet_log TInput_file TPoint_trace TMerge_trace TOutput_file
TWide_trace TVertex_stop TCone_stop
Angle_max Centrum_size Random_dist Wide_outside
qdelaunay
qdelaunay- compute the Delaunay triangulation. Qhull 2015.0.3 2015/09/22
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 all options
output options (subset):
s - summary of results (default)
i - vertices incident to each Delaunay region
Fx - extreme points (vertices of the convex hull)
o - OFF format (shows the points lifted to a paraboloid)
G - Geomview output (2-d and 3-d points lifted to a paraboloid)
m - Mathematica output (2-d inputs lifted to a paraboloid)
QVn - print Delaunay regions that include point n, -n if not
TO file- output results to 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
3
5 4 6
0 0 0
-0.5 -0.5 1
-0.5 0.5 1
0.5 -0.5 1
0.5 0.5 1
3 3 0 1
3 0 2 1
3 4 0 3
3 0 4 2
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: 7
Number of facets in hull: 5
Number of distance tests for qhull: 8
Number of distance tests for merging: 29
Number of distance tests for checking: 30
Number of merged facets: 1
CPU seconds to compute hull (after input): 0
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
2
3 4 2 1
3 4 3 1
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: 7
Number of facets in hull: 6
Number of distance tests for qhull: 8
Number of distance tests for merging: 33
Number of distance tests for checking: 30
Number of merged facets: 1
CPU seconds to compute hull (after input): 0
rbox c G1 d D2 | qdelaunay s i
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
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: 17
Number of facets in hull: 10
Number of distance tests for qhull: 42
Number of distance tests for merging: 103
Number of distance tests for checking: 80
Number of merged facets: 3
CPU seconds to compute hull (after input): 0
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 4 7
3 8 7 5
rbox c G1 d D2 | qhull d Qbb QJ s Ft
2
8 10 15
-1.000000000061343 -0.999999999957446
-0.9999999999945448 0.9999999999532114
1.000000000029778 -0.9999999999701502
0.9999999999806051 1.000000000003233
-7.748592400792811e-011 -0.5000000000743411
2.849349704487493e-011 0.49999999991804
-0.5000000000721135 -1.37371989142159e-011
0.5000000000148132 7.166044474310069e-011
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
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: 20
Number of facets in hull: 12
Number of distance tests for qhull: 32
CPU seconds to compute hull (after input): 0
Input joggled by: 8.3e-011
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: 262
Number of facets in hull: 86
Number of distance tests for qhull: 1652
Number of distance tests for merging: 2778
Number of distance tests for checking: 1348
Number of merged facets: 152
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
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 1 3
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
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: 8
Number of facets in hull: 5
Number of distance tests for qhull: 33
Number of distance tests for merging: 49
Number of distance tests for checking: 42
Number of merged facets: 3
CPU seconds to compute hull (after input): 0
Approximate facet area: 1
rbox P0 P0 c D2 | qdelaunay s FP QV0
1
0 1 2 0
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: 7
Number of facets in hull: 5
Number of distance tests for qhull: 20
Number of distance tests for merging: 29
Number of distance tests for checking: 36
Number of merged facets: 1
CPU seconds to compute hull (after input): 0
qhalf -
qhalf- compute the intersection of halfspaces about a point
http://www.qhull.org 2015.0.3 2015/09/22
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
Qt - triangulated output
QJ - joggled input instead of merged facets
Qc - keep coplanar halfspaces
Qi - keep other redundant halfspaces
Qhull control options:
QJn - randomly joggle input in range [-n,n]
Qbk:0Bk:0 - remove k-th coordinate from input
Qs - search all halfspaces for the initial simplex
QGn - print intersection if visible to halfspace n, -n for not
QVn - print intersections for halfspace n, -n if not
Trace options:
T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
Tc - check frequently during execution
Ts - print statistics
Tv - verify result: structure, convexity, and redundancy
Tz - send all output to stdout
TFn - report summary when n or more facets created
TI file - input data from file, no spaces or single quotes
TO file - output results to file, may be enclosed in single quotes
TPn - turn on tracing when halfspace n added to intersection
TMn - turn on tracing at merge n
TWn - trace merge facets when width > n
TVn - stop qhull after adding halfspace n, -n for before (see TCn)
TCn - stop qhull after building cone for halfspace n (see TVn)
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 convex hull)
Fn - count plus neighboring intersections for each intersection
FN - count plus intersections for each non-redundant 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
for 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
Gi - inner planes (i.e., halfspace intersections) only
Gn - no planes
Go - outer planes only
Gc - centrums
Gh - hyperplane intersections
Gr - ridges
GDn - drop dimension n in 3-d and 4-d output
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
Pg - print good facets (needs 'QGn' or 'QVn')
PFn - keep facets whose area is at least n
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
qhalf .
Qhull 2015.0.3 2015/09/22.
Except for 'F.' and 'PG', upper_case options take an argument.
incidences Geomview mathematica OFF_format point_dual
summary facet_dump
Fc_redundant Fd_cdd_in FF_dump_xridge FIDs Fmerges
Fneighbors FN_intersect FOptions Fp_coordinates FP_nearest
FQhalf Fsummary Fv_halfspace FMaple Fx_non_redundant
Gvertices Gpoints Gall_points Gno_planes Ginner
Gcentrums Ghyperplanes Gridges Gouter GDrop_dim
PArea_keep Pdrop d0:0D0 Pgood PFacet_area_keep
PGood_neighbors PMerge_keep Poutput_forced Pprecision_not
Qbk:0Bk:0_drop Qcoplanar QG_half_good Qi_redundant QJoggle
Qsearch_1st Qtriangulate QVertex_good
T4_trace Tcheck_often Tstatistics Tverify Tz_stdout
TFacet_log TInput_file TPoint_trace TMerge_trace TOutput_file
TWide_trace TVertex_stop TCone_stop
Angle_max Centrum_size Random_dist Ucoplanar_max Wide_outside
qhalf
qhalf- halfspace intersection about a point. Qhull 2015.0.3 2015/09/22
input (stdin): [dim, 1, interior point], dim+1, n, 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 all options
output options (subset):
s - summary of results (default)
Fp - intersection coordinates
Fv - non-redundant halfspaces incident to each intersection
Fx - non-redundant halfspaces
o - OFF file format (dual convex hull)
G - Geomview output (dual convex hull)
m - Mathematica output (dual convex hull)
QVn - print intersections for halfspace n, -n if not
TO file - output results to 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
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
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: 33
Number of distance tests for merging: 119
Number of distance tests for checking: 56
Number of merged facets: 7
CPU seconds to compute hull (after input): 0
rbox c | qhull FQ FV n | qhalf s i
8
4 5 3
5 4 2
0 4 3
4 0 2
1 5 2
5 1 3
1 0 3
0 1 2
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: 11
Number of distance tests for merging: 45
Number of distance tests for checking: 54
Number of merged facets: 1
CPU seconds to compute hull (after input): 0
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 4 5 3
3 5 4 2
3 0 4 3
3 4 0 2
3 1 5 2
3 5 1 3
3 1 0 3
3 0 1 2
rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx
4
0
0
0
0
0
4
2 1 2
2 0 3
2 0 3
2 1 2
4
2 0 1
2 0 2
2 1 3
2 2 3
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
1
0
2
3
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: 6
CPU seconds to compute hull (after input): 0
echo === check quality of Qhull for ${d:-`hostname`} ${d:-`date`}
hostname
date
=== check quality of Qhull for ispy Tue Sep 22 22:29:57 EDT 2015
rbox 1000 W0 | qhull QR2 QJ s Fs Tv
10 3 1000 144 284 144 284 0 0 33 0
2 5.045982607091333e-011 -5.045982607091333e-011
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: 33562
CPU seconds to compute hull (after input): 0
After 1 retries, input joggled by: 2.9e-011
Output completed. Verifying that all points are below 2.9e-015 of
all facets. Will make 284000 distance computations.
rbox 1000 W0 | qhull QR2 s Fs Tv
10 3 1000 84 98 84 98 0 6 13 0
2 1.942124858599573e-015 -1.241679291552168e-015
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: 18051
Number of distance tests for merging: 3325
Number of distance tests for checking: 15397
Number of merged facets: 92
CPU seconds to compute hull (after input): 0
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: 114
Number of coplanar points: 886
Number of facets: 60
Number of non-simplicial facets: 60
Statistics for: rbox 1000 s | qhull C0.02 Qc Tv
Number of points processed: 1000
Number of hyperplanes created: 5545
Number of distance tests for qhull: 83858
Number of distance tests for merging: 82226
Number of distance tests for checking: 7929
Number of merged facets: 1936
CPU seconds to compute hull (after input): 0.031
Maximum distance of vertex below facet: -0.072 (1.2x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 60000 distance computations.
rbox 500 s D4 | qhull C0.01 Qc Tv
Convex hull of 500 points in 4-d:
Number of vertices: 467
Number of coplanar points: 33
Number of facets: 357
Number of non-simplicial facets: 343
Statistics for: rbox 500 s D4 | qhull C0.01 Qc Tv
Number of points processed: 500
Number of hyperplanes created: 11284
Number of distance tests for qhull: 41395
Number of distance tests for merging: 162691
Number of distance tests for checking: 20813
Number of merged facets: 2809
CPU seconds to compute hull (after input): 0.031
Maximum distance of vertex below facet: -0.073 (1.8x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 178500 distance computations.
rbox 1000 s | qhull C-0.02 Qc Tv
Convex hull of 1000 points in 3-d:
Number of vertices: 47
Number of coplanar points: 953
Number of facets: 47
Number of non-simplicial facets: 35
Statistics for: rbox 1000 s | qhull C-0.02 Qc Tv
Number of points processed: 50
Number of hyperplanes created: 199
Number of distance tests for qhull: 52519
Number of distance tests for merging: 2966
Number of distance tests for checking: 24231
Number of merged facets: 98
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.065 (1.1x)
Maximum distance of vertex below facet: -0.062 (1.0x)
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: 117
Number of coplanar points: 883
Number of facets: 232
Number of non-simplicial facets: 149
Statistics for: rbox 1000 s D4 | qhull C-0.01 Qc Tv
Number of points processed: 117
Number of hyperplanes created: 1232
Number of distance tests for qhull: 372627
Number of distance tests for merging: 31334
Number of distance tests for checking: 122166
Number of merged facets: 1167
CPU seconds to compute hull (after input): 0.031
Maximum distance of point above facet: 0.062 (1.5x)
Maximum distance of vertex below facet: -0.064 (1.6x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 232000 distance computations.
rbox 200 s D5 | qhull C-0.01 Qx Qc Tv
Convex hull of 200 points in 5-d:
Number of vertices: 160
Number of coplanar points: 40
Number of facets: 388
Number of non-simplicial facets: 342
Statistics for: rbox 200 s D5 | qhull C-0.01 Qx Qc Tv
Number of points processed: 160
Number of hyperplanes created: 4522
Number of distance tests for qhull: 235312
Number of distance tests for merging: 143140
Number of distance tests for checking: 46266
Number of merged facets: 5940
CPU seconds to compute hull (after input): 0.062
Maximum distance of point above facet: 0.059 (1.2x)
Maximum distance of vertex below facet: -0.11 (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 77600 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: 4465
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: 20175
Number of distance tests for qhull: 33383
Number of distance tests for merging: 299744
Number of distance tests for checking: 66106
Number of merged facets: 3948
CPU seconds to compute hull (after input): 0.125
Maximum distance of point above facet: 0.0029 (0.5x)
Maximum distance of vertex below facet: -0.014 (2.4x)
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 446500 distance computations.
rbox 1000 W1e-4 | qhull C-1e-6 Qc Tv
Convex hull of 1000 points in 3-d:
Number of vertices: 144
Number of coplanar points: 75
Number of facets: 243
Number of non-simplicial facets: 26
Statistics for: rbox 1000 W1e-4 | qhull C-1e-6 Qc Tv
Number of points processed: 185
Number of hyperplanes created: 939
Number of distance tests for qhull: 42000
Number of distance tests for merging: 8652
Number of distance tests for checking: 5684
Number of merged facets: 145
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 1.3e-006 (0.4x)
Maximum distance of vertex below facet: -3.2e-006 (1.1x)
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: 290
Number of coplanar points: 433
Number of facets: 1296
Number of non-simplicial facets: 154
Statistics for: rbox 1000 W5e-4 D4 | qhull C-1e-5 Qc Tv
Number of points processed: 368
Number of hyperplanes created: 6238
Number of distance tests for qhull: 182095
Number of distance tests for merging: 75580
Number of distance tests for checking: 52937
Number of merged facets: 1353
CPU seconds to compute hull (after input): 0.031
Maximum distance of point above facet: 9.1e-005 (2.3x)
Maximum distance of vertex below facet: -0.00012 (2.9x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 1296000 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: 305
Number of coplanar points: 35
Number of facets: 5552
Number of non-simplicial facets: 281
Statistics for: rbox 400 W1e-3 D5 | qhull C-1e-5 Qx Qc Tv
Number of points processed: 336
Number of hyperplanes created: 24527
Number of distance tests for qhull: 251847
Number of distance tests for merging: 277585
Number of distance tests for checking: 61531
Number of merged facets: 1482
CPU seconds to compute hull (after input): 0.093
Maximum distance of point above facet: 5.5e-005 (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 2220800 distance computations.
echo === check input format etc. ${d:-`date`}
date
=== check input format etc. Tue Sep 22 22:29:58 EDT 2015
qhull <<EOF
Convex hull of 4 points in 2-d:
Number of vertices: 3
Number of facets: 3
Statistics for: #;laskdjf | qhull
Number of points processed: 3
Number of hyperplanes created: 4
Number of distance tests for qhull: 9
CPU seconds to compute hull (after input): 0
qhull <<EOF
Convex hull of 4 points in 2-d:
Number of vertices: 3
Number of facets: 3
Statistics for: #;laskdjf | qhull
Number of points processed: 3
Number of hyperplanes created: 4
Number of distance tests for qhull: 9
CPU seconds to compute hull (after input): 0
QH7073 qhull warning: instead of 4 2-dimensional points, input contains
4 points and 1 extra coordinates. Line 2 is the first
point, line 1 is the first comment, line 2 is the first long line. Continue with 4 points.
qhull <<EOF
QH7073 qhull warning: instead of 4 2-dimensional points, input contains
3 points and 1 extra coordinates. Line 2 is the first
point, line 1 is the first comment, line 2 is the first long line. Continue with 3 points.
QH6013 qhull input error: input is less than 2-dimensional since it has the same x coordinate
While executing: #;laskdjf | qhull
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554688615 _pre-merge _zero-centrum _max-width 2
Error-roundoff 1.7e-015 _one-merge 8.6e-015 _near-inside 4.3e-014
Visible-distance 3.4e-015 U-coplanar-distance 3.4e-015
Width-outside 6.9e-015 _wide-facet 2.1e-014
qhull <<EOF
QH7073 qhull warning: instead of 4 2-dimensional points, input contains
3 points and 1 extra coordinates. Line 3 is the first
point, line 2 is the first comment, line 3 is the first short
line, line 4 is the first long line. Continue with 3 points.
QH6013 qhull input error: input is less than 2-dimensional since it has the same x coordinate
While executing: #;laskdjf | qhull
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554688615 _pre-merge _zero-centrum _max-width 2
Error-roundoff 1.7e-015 _one-merge 8.6e-015 _near-inside 4.3e-014
Visible-distance 3.4e-015 U-coplanar-distance 3.4e-015
Width-outside 6.9e-015 _wide-facet 2.1e-014
qhull <<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: 9
CPU seconds to compute hull (after input): 0
qhull d Qz <<EOF
Delaunay triangulation by the convex hull of 5 points in 3-d:
Number of input sites and at-infinity: 5
Number of Delaunay regions: 1
Number of non-simplicial Delaunay regions: 1
Statistics for: | qhull d Qz
Number of points processed: 5
Number of hyperplanes created: 7
Number of facets in hull: 5
Number of distance tests for qhull: 6
Number of distance tests for merging: 29
Number of distance tests for checking: 30
Number of merged facets: 1
CPU seconds to compute hull (after input): 0
QH7073 qhull warning: instead of 5 2-dimensional points, input contains
4 points and 1 extra coordinates. Line 1 is the first
point, line 1 is the first long line. Continue with 4 points.
qhull d Q8 Qz <<EOF
Delaunay triangulation by the convex hull of 5 points in 3-d:
Number of input sites and at-infinity: 5
Number of Delaunay regions: 1
Number of non-simplicial Delaunay regions: 1
Statistics for: | qhull d Q8 Qz
Number of points processed: 5
Number of hyperplanes created: 7
Number of facets in hull: 5
Number of distance tests for qhull: 6
Number of distance tests for merging: 29
Number of distance tests for checking: 30
Number of merged facets: 1
CPU seconds to compute hull (after input): 0
QH7073 qhull warning: instead of 5 2-dimensional points, input contains
4 points and 1 extra coordinates. Line 1 is the first
point, line 1 is the first long line. Continue with 4 points.
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-015 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: 46
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2.5e-015 of
all facets. Will make 99 distance computations.
echo === check rbox ${d:-`date`}
date
=== check rbox Tue Sep 22 22:29:59 EDT 2015
rbox 3 n D2
2
3
0.2234321234034673 0.2236923805658635
-0.4021654933711192 -0.1954478539484068
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 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 D2
2 rbox 8 L2 D2
8
-9.037112801233254e-006 -0.1339745961747267
-0.4680200990905804 0.01769241704257374
-0.05424246984329754 -0.1325023897522757
0.07519664081423347 -0.1311433207603374
0.1915694083864337 0.1154536646477271
0.4772264523261766 0.01275495170842944
-0.4048291575354194 0.04836693717712182
0.3401207718037282 -0.07435635943071228
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-017 0.5 0
1.530808498934192e-017 0.25 0.04782181019473453
1.530808498934192e-017 0.25 -0.04782181019473453
-0.5 6.123233995736766e-017 0
-0.25 3.061616997868383e-017 0.04782181019473453
-0.25 3.061616997868383e-017 -0.04782181019473453
-9.184850993605148e-017 -0.5 0
-4.592425496802574e-017 -0.25 0.04782181019473453
-4.592425496802574e-017 -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 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 L2 s D3 | qhull Tcv
Convex hull of 10 points in 3-d:
Number of vertices: 10
Number of facets: 16
Statistics for: rbox 10 L2 s D3 | qhull Tcv
Number of points processed: 10
Number of hyperplanes created: 29
Number of distance tests for qhull: 50
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.5e-015 of
all facets. Will make 160 distance computations.
rbox 10 L4 s W1e-3 D3 | qhull Tcv
Convex hull of 10 points in 3-d:
Number of vertices: 10
Number of facets: 16
Statistics for: rbox 10 L4 s W1e-3 D3 | qhull Tcv
Number of points processed: 10
Number of hyperplanes created: 27
Number of distance tests for qhull: 43
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.9e-015 of
all facets. Will make 160 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: 29
Number of distance tests for qhull: 48
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.7e-015 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: 53
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2.4e-015 of
all facets. Will make 260 distance computations.
rbox y r 100 W0 O0.5 | qhull s p Tcv
3
4
1 0.5 0.5
0.5 1 0.5
0.5 0.5 1
0 0 0
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: 1101
CPU seconds to compute hull (after input): 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: 1285
Number of distance tests for merging: 774
Number of distance tests for checking: 905
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: 91
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-015 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: 89
Number of distance tests for qhull: 47
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-015 of
all facets. Will make 840 distance computations.
rbox 1000 D4 | qhull s i A-0.97 C0.2 A0.7 Tcv
48
117 111 263 638
117 263 111 146
117 263 146 638
117 146 111 638
118 111 771 456
118 111 146 638
118 146 111 456
118 771 146 456
118 771 430 465
118 771 465 638
118 771 111 638
118 146 771 638
118 465 430 638
118 430 771 638
119 771 263 299
119 430 465 638
119 111 263 771
119 771 430 638
119 465 299 638
119 263 111 638
119 430 771 299
119 111 771 638
119 299 263 638
119 430 299 465
120 430 771 465
120 299 465 638
120 263 771 299
120 146 263 638
120 299 430 465
120 465 771 638
120 263 146 299
120 771 263 456
120 299 771 456
120 771 430 299
120 771 146 638
120 146 771 299
120 263 299 456
120 263 299 638
121 111 146 456
121 146 263 299
121 771 299 456
121 771 146 299
121 263 111 771
121 146 771 456
121 299 263 456
121 111 263 146
121 771 111 456
121 263 771 456
Convex hull of 1000 points in 4-d:
Number of vertices: 9
Number of facets: 5
Number of non-simplicial facets: 4
Statistics for: rbox 1000 D4 | qhull s i A-0.97 C0.2 A0.7 Tcv
Number of points processed: 116
Number of hyperplanes created: 2284
Number of distance tests for qhull: 518926
Number of distance tests for merging: 76090
Number of distance tests for checking: 5989
Number of merged facets: 1889
CPU seconds to compute hull (after input): 0.047
Maximum distance of point above facet: 0.07
Maximum distance of vertex below facet: -0.92 (0.6x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 5000 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 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-015 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: 48
Number of facets: 26
Number of non-simplicial facets: 26
Statistics for: rbox 1000 s | qhull C0.05 Tcv
Number of points processed: 1000
Number of hyperplanes created: 5545
Number of distance tests for qhull: 55658
Number of distance tests for merging: 100391
Number of distance tests for checking: 6790
Number of merged facets: 1970
CPU seconds to compute hull (after input): 0.016
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 26000 distance computations.
rbox 1000 s t | qhull Qm C0.05 Tcv
Convex hull of 1000 points in 3-d:
Number of vertices: 43
Number of facets: 23
Number of non-simplicial facets: 23
Statistics for: rbox 1000 s t1442975399 | qhull Qm C0.05 Tcv
Number of points processed: 1000
Number of hyperplanes created: 5564
Number of distance tests for qhull: 55123
Number of distance tests for merging: 99615
Number of distance tests for checking: 6719
Number of merged facets: 1973
CPU seconds to compute hull (after input): 0.031
Maximum distance of vertex below facet: -0.23 (1.5x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 23000 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: 294
Number of hyperplanes created: 1612
Number of distance tests for qhull: 9968
CPU seconds to compute hull (after input): 0.015
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, -0.50000000, 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}}]}
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, -0.50000000, 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]]));
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: 6
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.3e-015 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: 6
Number of distance tests for qhull: 4
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.3e-015 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: 35
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-015 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: 11
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: 62
Number of distance tests for qhull: 163
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-015 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: 24
Number of distance tests for merging: 165
Number of distance tests for checking: 136
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: 297
Number of distance tests for qhull: 856
CPU seconds to compute hull (after input): 0
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-015 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: 37
Number of distance tests for qhull: 47
Number of distance tests for merging: 510
Number of distance tests for checking: 330
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: 5986
CPU seconds to compute hull (after input): 0
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-015 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: 70
Number of distance tests for qhull: 88
Number of distance tests for merging: 1176
Number of distance tests for checking: 780
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: 163
Number of distance tests for merging: 2635
Number of distance tests for checking: 1806
Number of merged facets: 57
CPU seconds to compute hull (after input): 0.015
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: 6
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.3e-015 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: 35
Number of distance tests for merging: 142
Number of distance tests for checking: 56
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: 26
Number of distance tests for qhull: 168
Number of distance tests for merging: 788
Number of distance tests for checking: 144
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: 87
Number of distance tests for qhull: 722
Number of distance tests for merging: 4130
Number of distance tests for checking: 352
Number of merged facets: 210
CPU seconds to compute hull (after input): 0
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: 2474
Number of distance tests for merging: 22065
Number of distance tests for checking: 832
Number of merged facets: 1488
CPU seconds to compute hull (after input): 0.046
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: 1786
Number of distance tests for qhull: 9309
Number of distance tests for merging: 88772
Number of distance tests for checking: 1920
Number of merged facets: 11556
CPU seconds to compute hull (after input): 0.062
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: 63
Number of distance tests for qhull: 139
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2.1e-015 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: 898
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.3e-015 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: 1691
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2e-015 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: 1718
Number of distance tests for qhull: 4091
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2.8e-015 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: 26
Number of distance tests for qhull: 2028
Number of distance tests for merging: 788
Number of distance tests for checking: 144
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: 1457
Number of distance tests for merging: 165
Number of distance tests for checking: 136
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: 1582
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2.1e-015 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: 117
Number of distance tests for qhull: 1211
CPU seconds to compute hull (after input): 0.015
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: 298
Number of distance tests for qhull: 1753
CPU seconds to compute hull (after input): 0
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: 853
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.3e-015 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: 299
Number of distance tests for qhull: 1457
Number of distance tests for merging: 16912
Number of distance tests for checking: 2604
Number of merged facets: 97
CPU seconds to compute hull (after input): 0.016
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: 994
Number of distance tests for qhull: 6676
Number of distance tests for merging: 38219
Number of distance tests for checking: 11601
Number of merged facets: 323
CPU seconds to compute hull (after input): 0.031
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: 1622
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2.1e-015 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: 1848
Number of distance tests for merging: 2108
Number of distance tests for checking: 1274
Number of merged facets: 3
CPU seconds to compute hull (after input): 0.015
Maximum distance of vertex below facet: -1.1e-015 (0.3x)
echo === check qhull output formats ${d:-`date`}
date
=== check qhull output formats Tue Sep 22 22:30:01 EDT 2015
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: 8
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.3e-015 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: 8
CPU seconds to compute hull (after input): 0
rbox 5 r s D2 | qhull s 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-016
2 4 0
2 2 3
2 3 4
2 1 2
2 0 1
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: 8
CPU seconds to compute hull (after input): 0
rbox 5 r s D2 | qhull f
Vertices and facets:
- p0(v2): 0.15 0.48
- p4(v1): 0.5 -1.2e-016
- p3(v4): 0.15 -0.48
- p2(v0): -0.4 -0.29
- p1(v5): -0.4 0.29
- f3
- flags: bottom simplicial
- normal: 0.809 0.5878
- offset: -0.4045085
- vertices: p0(v2) p4(v1)
- neighboring facets: f5 f7
- f4
- flags: bottom simplicial
- normal: -0.309 -0.9511
- offset: -0.4045085
- vertices: p3(v4) p2(v0)
- neighboring facets: f6 f5
- f5
- flags: top simplicial
- normal: 0.809 -0.5878
- offset: -0.4045085
- vertices: p3(v4) p4(v1)
- neighboring facets: f3 f4
- f6
- flags: top simplicial
- normal: -1 9.444e-017
- offset: -0.4045085
- vertices: p1(v5) p2(v0)
- neighboring facets: f4 f7
- f7
- flags: bottom simplicial
- normal: -0.309 0.9511
- offset: -0.4045085
- vertices: p1(v5) p0(v2)
- 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 -0.5877852522924733 -0.4045084971874737
-1 9.444121133484361e-017 -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-016
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-016
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-016
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-016
3
5
0.8090169943749476 0.587785252292473 -0.4045084971874737
-0.3090169943749476 -0.9510565162951536 -0.4045084971874738
0.8090169943749472 -0.5877852522924733 -0.4045084971874737
-1 9.444121133484361e-017 -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(v2): 0.38 -0.47 -0.22
- p6(v0): -0.31 -0.011 -0.49
- p1(v3): -0.067 -0.16 0.46
- p7(v1): 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(v2) p6(v0)
- neighboring facets: f9 f6 f7
- f6
- flags: bottom simplicial
- normal: -0.9301 -0.3157 0.1877
- offset: -0.1977325
- vertices: p0(v5) p1(v3) p6(v0)
- neighboring facets: f17 f5 f8
- f7
- flags: bottom simplicial
- normal: 0.7008 -0.3956 0.5936
- offset: -0.323519
- vertices: p0(v5) p9(v2) p7(v1)
- neighboring facets: f10 f8 f5
- f8
- flags: top simplicial
- normal: 0.6544 -0.298 0.6949
- offset: -0.3219447
- vertices: p0(v5) p1(v3) p7(v1)
- neighboring facets: f13 f7 f6
- f9
- flags: bottom simplicial
- normal: 0.4866 0.2316 -0.8424
- offset: -0.2582907
- vertices: p3(v6) p9(v2) p6(v0)
- neighboring facets: f5 f16 f10
- f10
- flags: top simplicial
- normal: 0.943 0.1711 -0.2855
- offset: -0.3386013
- vertices: p3(v6) p9(v2) p7(v1)
- neighboring facets: f7 f14 f9
- f13
- flags: bottom simplicial
- normal: 0.08536 0.8035 0.5892
- offset: -0.1388354
- vertices: p4(v7) p1(v3) p7(v1)
- 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(v1)
- 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(v0)
- neighboring facets: f9 f18 f14
- f17
- flags: top simplicial
- normal: -0.6179 0.7381 0.2709
- offset: -0.04995414
- vertices: p5(v8) p1(v3) p6(v0)
- 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(v0)
- 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(v3)
- 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(v3)
- 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-015 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 -0.1360330368727754
-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 -0.1360330368727754
-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: 320
Number of distance tests for merging: 84
Number of distance tests for checking: 188
Number of merged facets: 6
CPU seconds to compute hull (after input): 0
rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 s p Tcv
3
7
0.1955434141942995 0.09315491718098735 0.4506494586374647
0.3786694231678469 0.2419725568326128 -0.2192230592287637
0.1164290160865212 0.2250749615572271 0.4310284745734756
0.3010852516984067 0.3425921496145067 0.2048860420629442
0.4995640899182717 0.005583735684776723 0.02011322848106417
0.4035338761538298 0.1419567271683243 0.2588603840063664
0.3642936952899509 -0.2163723184172344 -0.2654677445467591
Convex hull of 50 points in 3-d:
Number of vertices: 19
Number of coplanar points: 31
Number of facets: 12
Number of 'good' facets: 1
Number of 'good' non-simplicial facets: 1
Statistics for: rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 s p Tcv
Number of points processed: 50
Number of hyperplanes created: 237
Number of distance tests for qhull: 1177
Number of distance tests for merging: 3999
Number of distance tests for checking: 367
Number of merged facets: 84
CPU seconds to compute hull (after input): 0.015
Maximum distance of vertex below facet: -0.24 (0.8x)
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
1
0 1 12 1e-015
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: 111
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.
rbox 100 s | qhull C-0.003 Qc FP s
10
29 92 222 0.05221620842441997
49 2 292 0.03790045221711885
99 9 338 0.02993864679572162
54 84 341 0.06479664045626413
54 72 226 0.03827167959574595
96 6 368 0.02282529175708785
19 1 372 0.01048228658130246
69 26 409 0.04998878658421259
19 66 371 0.008281093788857875
19 45 371 0.04608027722786196
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: 400
Number of distance tests for qhull: 2016
Number of distance tests for merging: 3695
Number of distance tests for checking: 1469
Number of merged facets: 102
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)
rbox 100 s D2 | qhull C0.1 i Fx Tcv
6
4 28
70 27
77 70
68 4
27 68
28 77
6
4
28
77
70
27
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 # v2
0 0.009951 0 0
0 0 0.009951 0
-0.04234 -0.2077 -0.4529 # p3
1
0.009951 0 0 0 # v1
0 0.009951 0 0
0 0 0.009951 0
0.004313 -0.4976 0.04904 # p2
1
0.009951 0 0 0 # v0
0 0.009951 0 0
0 0 0.009951 0
-0.4876 0.03313 -0.1055 # p0
1
0.009951 0 0 0 # v3
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-015 of
all facets. Will make 16 distance computations.
rbox 6 D4 | qhull f Tcv
Vertices and facets:
- p3(v4): 0.1 -0.13 -0.17 -0.42
- p0(v3): -0.33 -0.43 -0.46 0.15
- p2(v2): 0.11 0.4 -0.063 -0.18
- p1(v0): -0.35 -0.24 0.14 -0.18
- p4(v1): 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(v4) p0(v3) p2(v2) p1(v0)
- neighboring facets: f6 f8 f10 f5
- f5
- flags: top simplicial
- normal: 0.6142 0.09488 -0.7743 0.1197
- offset: -0.1313181
- vertices: p3(v4) p0(v3) p2(v2) p4(v1)
- 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(v3) p2(v2) p1(v0)
- 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(v3) p2(v2) p4(v1)
- 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(v4) p2(v2) p1(v0)
- 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(v4) p2(v2) p4(v1)
- 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(v4) p0(v3) p1(v0)
- 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(v4) p0(v3) p4(v1)
- neighboring facets: f5 f7 f9 f10
Output completed. Verifying that all points are below 3e-015 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: 1998
Number of distance tests for qhull: 13978
CPU seconds to compute hull (after input): 0
Total facet area: 3.1415592
Total volume: 0.7853647
qhull output completed. Verifying that 1000 points are
below 1.3e-015 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: 5545
Number of distance tests for qhull: 25488
CPU seconds to compute hull (after input): 0.015
Total facet area: 3.1201951
Total volume: 0.51650274
qhull output completed. Verifying that 1000 points are
below 2.1e-015 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: 26
Number of distance tests for qhull: 168
Number of distance tests for merging: 788
Number of distance tests for checking: 144
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: 87
Number of distance tests for qhull: 722
Number of distance tests for merging: 2775
Number of distance tests for checking: 352
Number of merged facets: 210
CPU seconds to compute hull (after input): 0
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: 87
Number of distance tests for qhull: 722
Number of distance tests for merging: 3235
Number of distance tests for checking: 352
Number of merged facets: 210
CPU seconds to compute hull (after input): 0
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: 48
CPU seconds to compute hull (after input): 0
Total facet area: 0.46254269
Output completed. Verifying that all points are below 2.1e-015 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: 48
CPU seconds to compute hull (after input): 0
Total facet area: 0.46254269
Output completed. Verifying that all points are below 2.1e-015 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: 6
Number of distance tests for qhull: 52
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-015 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-015 of
all facets. Will make 56 distance computations.
rbox 1000 s | qhull FS Tcv
0
2 3.12019513507746 0.516502736886338
qhull output completed. Verifying that 1000 points are
below 2.1e-015 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 0.45089279622854
-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-018
-0.5 0.22390379870674
-0.4344308308180709 -0.25154259940753
-0.4431538257684129 0.47544639811427
-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
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
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: 6
Number of distance tests for qhull: 5
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2.6e-009 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
Vertices and facets:
- p1(v2): -0.3 0.39 -0.092
- p5(v1): 0.4 -0.22 -0.2
- p4(v0): -0.46 -0.19 -0.018
- p2(v3): 0.25 0.28 -0.33
- f1
- flags: top simplicial
- area: 0.26
- normal: 0.2054 0.06987 0.9762
- offset: 0.125398
- center: -0.1205015151724569 -0.008790385787885074 -0.1024776532548504
- vertices: p1(v2) p5(v1) p4(v0)
- neighboring facets: f2 f3 f4
- f2
- flags: bottom simplicial
- 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(v3) p5(v1) p4(v0)
- neighboring facets: f1 f3 f4
- f3
- flags: top simplicial
- area: 0.18
- normal: -0.3912 -0.01238 -0.9202
- offset: -0.1989549
- center: -0.1715856748140029 0.1590825675964338 -0.1454013928109104
- vertices: p2(v3) p1(v2) p4(v0)
- neighboring facets: f1 f2 f4
- f4
- flags: bottom simplicial
- area: 0.16
- normal: 0.4184 0.3424 0.8413
- offset: 0.07254957
- center: 0.116549362001881 0.1503252206347392 -0.2053893818610149
- vertices: p2(v3) p1(v2) p5(v1)
- 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 0.1253980026939627
-0.2031613339148238 -0.3001304507855299 -0.9320124381751694 -0.2813242952138536
-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 2015.0.3.r 2015/09/22:
run-id 554755843 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-016 _one-merge 0.3 _near-inside 1.5
Visible-distance 0.1 U-coplanar-distance 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-015
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
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554755843 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-016 _one-merge 0.3 _near-inside 1.5
Visible-distance 0.1 U-coplanar-distance 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: 5
Number of distance tests for qhull: 24
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)
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 0 2 -7 -8
1 0
5 -10 1 -6 -7 -8
4 -6 1 0 2
3 -7 2 -6
3 -10 -8 3
4 -10 1 0 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
0
QH7055 qhull warning: no facets printed
echo === test Qt ${d:-`date`}
date
=== test Qt Tue Sep 22 22:30:02 EDT 2015
rbox c | qhull Qt s o Tcv
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
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: 35
Number of distance tests for merging: 166
Number of distance tests for checking: 56
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 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(v2): -0.5 0.5 -0.5
neighbors: f17 f29 f33
- p0(v0): -0.5 -0.5 -0.5
neighbors: f17 f18 f21 f22 f29 f30
- p4(v1): 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(v3): -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 seen keepcentrum
- owner of normal & centrum is facet f17
- normal: -0 -0 -1
- offset: -0.5
- center: 0 0 -0.5
- vertices: p6(v6) p2(v2) p0(v0)
- neighboring facets: f29 f18 f33
- f18
- flags: bottom simplicial tricoplanar seen
- owner of normal & centrum is facet f17
- normal: -0 -0 -1
- offset: -0.5
- center: 0 0 -0.5
- vertices: p6(v6) p4(v1) p0(v0)
- 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(v1) p0(v0)
- neighboring facets: f18 f22 f25
- f22
- flags: bottom simplicial tricoplanar seen
- owner of normal & centrum is facet f21
- normal: 0 -1 0
- offset: -0.5
- center: 0 -0.5 0
- vertices: p5(v7) p1(v3) p0(v0)
- 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(v1)
- neighboring facets: f18 f21 f27
- f27
- flags: bottom simplicial tricoplanar seen
- 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(v2) p0(v0)
- 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(v3) p0(v0)
- 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(v2)
- 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(v3)
- 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
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
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: 35
Number of distance tests for merging: 108
Number of distance tests for checking: 56
Number of merged facets: 6
CPU seconds to compute hull (after input): 0
Approximate facet area: 6
Approximate volume: 1
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: 20
Number of facets in hull: 16
Number of distance tests for qhull: 51
Number of distance tests for merging: 257
Number of distance tests for checking: 100
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: 20
Number of facets in hull: 10
Number of distance tests for qhull: 51
Number of distance tests for merging: 239
Number of distance tests for checking: 100
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-016 -0.3453321730569308
-2.220446049250313e-016 -0.3453321730569308
1.110223024625157e-016 0.3453321730569308
1.110223024625157e-016 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
Vertices and facets:
- p6(v6): 0.5 0.5 -0.5
neighbors: f17 f18 f25 f27 f33 f34
- p2(v2): -0.5 0.5 -0.5
neighbors: f17 f29 f33
- p0(v0): -0.5 -0.5 -0.5
neighbors: f17 f18 f21 f22 f29 f30
- p4(v1): 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(v3): -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
- area: 0.5
- normal: -0 -0 -1
- offset: -0.5
- center: 0 0 -0.5
- vertices: p6(v6) p2(v2) p0(v0)
- neighboring facets: f29 f18 f33
- f18
- flags: bottom simplicial tricoplanar
- area: 0.5
- normal: -0 -0 -1
- offset: -0.5
- center: 0 0 -0.5
- vertices: p6(v6) p4(v1) p0(v0)
- neighboring facets: f21 f17 f25
- f21
- flags: top simplicial tricoplanar keepcentrum
- area: 0.5
- normal: 0 -1 0
- offset: -0.5
- center: 0 -0.5 0
- vertices: p5(v7) p4(v1) p0(v0)
- neighboring facets: f18 f22 f25
- f22
- flags: bottom simplicial tricoplanar
- area: 0.5
- normal: 0 -1 0
- offset: -0.5
- center: 0 -0.5 0
- vertices: p5(v7) p1(v3) p0(v0)
- neighboring facets: f30 f21 f37
- f25
- flags: top simplicial tricoplanar keepcentrum
- area: 0.5
- normal: 1 -0 -0
- offset: -0.5
- center: 0.5 0 0
- vertices: p5(v7) p6(v6) p4(v1)
- neighboring facets: f18 f21 f27
- f27
- flags: bottom simplicial tricoplanar
- 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 keepcentrum
- area: 0.5
- normal: -1 -0 -0
- offset: -0.5
- center: -0.5 0 0
- vertices: p3(v8) p2(v2) p0(v0)
- neighboring facets: f17 f30 f33
- f30
- flags: top simplicial tricoplanar
- area: 0.5
- normal: -1 -0 -0
- offset: -0.5
- center: -0.5 0 0
- vertices: p3(v8) p1(v3) p0(v0)
- neighboring facets: f22 f29 f37
- f33
- flags: bottom simplicial tricoplanar keepcentrum
- area: 0.5
- normal: 0 1 -0
- offset: -0.5
- center: 0 0.5 0
- vertices: p3(v8) p6(v6) p2(v2)
- neighboring facets: f17 f29 f34
- f34
- flags: top simplicial tricoplanar
- 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 keepcentrum
- area: 0.5
- normal: -0 -0 1
- offset: -0.5
- center: 0 0 0.5
- vertices: p3(v8) p5(v7) p1(v3)
- neighboring facets: f22 f30 f38
- f38
- flags: bottom simplicial tricoplanar
- 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 2015.0.3.r 2015/09/22:
run-id 554772650 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-016 _one-merge 0.3 _near-inside 1.5
Visible-distance 0.1 U-coplanar-distance 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-015 -6.936799964367356e-016
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
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554772650 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-016 _one-merge 0.3 _near-inside 1.5
Visible-distance 0.1 U-coplanar-distance 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: 35
Number of distance tests for merging: 198
Number of distance tests for checking: 56
Number of merged facets: 6
CPU seconds to compute hull (after input): 0
Approximate facet area: 6
Approximate volume: 1
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
1
0 10 36 0
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554772650 summary FPoint-nearest delaunay Qtriangulate _pre-merge
_zero-centrum Pgood Qcoplanar _max-width 1 Error-roundoff 6.9e-016
_one-merge 4.9e-015 _near-inside 2.4e-014 Visible-distance 1.4e-015
U-coplanar-distance 1.4e-015 Width-outside 2.8e-015 _wide-facet 8.3e-015
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: 20
Number of facets in hull: 16
Number of distance tests for qhull: 83
Number of distance tests for merging: 166
Number of distance tests for checking: 111
Number of merged facets: 6
CPU seconds to compute hull (after input): 0
rbox 100 W0 | qhull Tv Q11
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
Number of points processed: 52
Number of hyperplanes created: 172
Number of distance tests for qhull: 1576
Number of distance tests for merging: 1498
Number of distance tests for checking: 2172
Number of merged facets: 41
CPU seconds to compute hull (after input): 0.015
Output completed. Verifying that all points are below outer planes of
all facets. Will make 8600 distance computations.
echo === test unbounded intersection ${d:-`date`}
date
=== test unbounded intersection Tue Sep 22 22:30:03 EDT 2015
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
8
0.1446087232094601
0.1622198334884075
0.2057158590759609
0.1567143851824352
0.188985866819172
0.1580674614313253
0.1616733826473112
0.1767351337533958
0
2 5.881743214947514 0.9968516315221345
4
8
1.009144997325421e-005 0.9999999999463923 2.319049754624652e-006 -0.4999875785488853
-1.229609861584452e-005 8.587946880918045e-005 0.9999999962367613 -0.500004859549355
-1.383340239672453e-005 -0.9999999998842694 6.332306547224587e-006 -0.4999917156571327
1.802476239613105e-005 -1.901476191096464e-005 0.9999999996567733 -0.4999909156385879
0.9999999996788914 1.780140020603311e-005 -1.803683546259361e-005 -0.4999971349013697
3.470111681088057e-006 -3.668365732095583e-005 -0.9999999993211337 -0.4999893476858696
-1.633273154317779e-005 -0.9999999998072314 1.089857916466569e-005 -0.4999921708899001
-0.9999999997878146 -2.055073083002867e-005 -1.427680287414111e-006 -0.4999990322171606
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: 21470
CPU seconds to compute hull (after input): 0
Total facet area: 5.8817432
Total volume: 0.99685163
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
8
0
6
7
10
0
11
6
4
10
0.6345454980886096 0.2737427089707436 0.7227841587506171 -0.7458921924784656
-0.00253733560834815 0.666653414016696 0.7453635270845322 -0.6767722083805112
-0.0004022623770974538 0.9999997831336711 0.0005214571799133833 -0.5000167453415887
-0.5357402012449896 -0.5359428531021374 -0.6524934443952053 -0.811263040246498
-0.005480509661076106 -0.9999701072857251 0.005454223027194167 -0.4992904789191579
0.001196850675493193 0.0003334814784797861 0.9999992281689842 -0.4989807987213126
0.9999992961453315 0.00118637926097064 1.459763172590229e-005 -0.4998611663332402
-0.9129791746952519 0.1462545158779729 -0.3808919048208773 -0.6797481567213483
-0.999601787347817 0.02140818392627282 0.01838359029211947 -0.4985486000821886
-0.003237401631533091 0.002761552371517554 -0.9999909464886048 -0.4969398742962436
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
11
0.6345454980886096 0.2737427089707436 0.7227841587506171 -0.7458921924784656
0.8278306348810541 -0.3414688798813042 -0.4450791435520636 -0.7665474225756105
0.7383776593319754 -0.4655216164679658 0.4879426777814023 -0.7788991125303444
0.2008161614085187 -0.8823413491644904 0.425613219803773 -0.6982307124493008
-0.4745617604911457 -0.2935495843214587 0.8298311738084099 -0.7523676152838523
-0.8259135249806853 -0.559220008247317 0.07169261907511661 -0.6812000445406896
0.41932306725662 0.6721295192910486 -0.6102541065524131 -0.7755692997856908
-0.5357402012449896 -0.5359428531021374 -0.6524934443952053 -0.811263040246498
-0.3304054030140146 0.4364026747636864 -0.8368900615482577 -0.7495022949733237
0.6755431502353132 -0.2163920762108173 0.7048517017950092 -0.7475007704997935
-0.9129791746952519 0.1462545158779729 -0.3808919048208773 -0.6797481567213483
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 2015.0.3.r 2015/09/22:
run-id 554772650 Tz-stdout TOutput-file q_test.log.1 _pre-merge
_zero-centrum _max-width 0.92 Error-roundoff 6.8e-016 _one-merge 4.8e-015
_near-inside 2.4e-014 Visible-distance 1.4e-015
U-coplanar-distance 1.4e-015 Width-outside 2.7e-015 _wide-facet 8.2e-015
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: 27
Number of distance tests for qhull: 44
CPU seconds to compute hull (after input): 0
echo === check Delaunay/Voronoi ${d:-`date`}
date
=== check Delaunay/Voronoi Tue Sep 22 22:30:03 EDT 2015
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: 48
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2.1e-015 of
all facets. Will make 140 distance computations.
rbox 10 D2 | qhull d Tcv Qz
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 Tcv Qz
Number of points processed: 11
Number of hyperplanes created: 31
Number of facets in hull: 18
Number of distance tests for qhull: 56
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2.1e-015 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: 44
Number of facets in hull: 27
Number of distance tests for qhull: 67
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2.9e-015 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 5 7 1
4 9 7 6 2
4 9 2 6 4
4 9 6 7 4
4 9 5 1 4
4 9 7 5 4
4 9 1 3 2
4 9 3 7 2
4 9 7 3 1
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: 33
Number of facets in hull: 16
Number of distance tests for qhull: 116
Number of distance tests for merging: 395
Number of distance tests for checking: 182
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 Q8 Qz
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 Q8 Qz
Number of points processed: 11
Number of hyperplanes created: 19
Number of facets in hull: 11
Number of distance tests for qhull: 55
Number of distance tests for merging: 278
Number of distance tests for checking: 132
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 0.2323253821416526
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-015 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-015 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 0.2323253821416526
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-015 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
0.08267689532419748 -0.2397644955865706
0.1295260566906465 1.716033573116838
0.1740355150742391 0.5317519038435655
0.1851415205797575 0.3882545794457364
-0.9065939866848107 -0.2962957610652136
-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 0.211561543495592
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-015 of
all facets. Will make 140 distance computations.
rbox 10 D2 | qhull v Tcv p
2
14
-0.1294381801544404 -0.07247409101984714
0.08267689532419748 -0.2397644955865706
0.1295260566906465 1.716033573116838
0.1740355150742391 0.5317519038435655
0.1851415205797575 0.3882545794457364
-0.9065939866848107 -0.2962957610652136
-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 0.211561543495592
Output completed. Verifying that all points are below 2.1e-015 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
0.08267689532419748 -0.2397644955865706 0
# 3 f12
0.1295260566906465 1.716033573116838 0
# 4 f14
0.1740355150742391 0.5317519038435655 0
# 5 f15
0.1851415205797575 0.3882545794457364 0
# 6 f19
-0.9065939866848107 -0.2962957610652136 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 0.211561543495592 0
4 7 1 2 6 # p0(v2)
3 8 3 6 # p1(v0)
3 14 5 11 # p2(v8)
4 9 4 3 8 # p3(v7)
5 14 5 4 3 13 # p4(v1)
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(v3)
}
}
Output completed. Verifying that all points are below 2.1e-015 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-015 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 0.9533457293522945 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 0.6877523324625972 -0.7259454037269313 0.2663295190946441
5 3 5 -0.9986432053419565 0.05207445078292259 -0.1782370644858237
5 4 7 -0.9970183790688239 -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 -0.2285415587894343 -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-017 ave. distance of midpoint to ridge
1.7e-016 max. distance of midpoint to ridge
19 bounded ridges with ok normal
1.2e-017 ave. angle to ridge
1.1e-016 max. angle to ridge
Output completed. Verifying that all points are below 2.1e-015 of
all facets. Will make 140 distance computations.
rbox 10 D2 | qhull v Tcv Fo
4
5 0 1 -0.3854955578888161 0.9227096915324941 -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-015 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 0.9227096915324941 -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-016 ave. distance of midpoint to ridge
1.2e-016 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-015 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-015 of
all facets. Will make 180 distance computations.
rbox 10 D3 | qhull v Fi Tcv
13
6 0 2 0.1026012494065407 0.8309156055795224 -0.5468566905731633 0.2399036185798247
6 0 8 -0.1644981128676531 0.5492243080463513 -0.8193247404503221 0.122023739903044
6 0 5 -0.1640386761614814 0.6276090456203117 -0.7610507201092119 0.1709974344854013
6 2 3 0.8628264983391891 0.1277424492346306 -0.4890933453107607 -0.1660057988150949
6 2 9 0.514615149546644 -0.7556910962035636 -0.4050953159143434 -0.3000434746332833
6 2 7 0.9862472983740704 0.008356748990702902 0.1650649302430821 -0.2195655184060844
6 3 8 -0.9471370887617876 -0.1545163381156413 -0.281169052968456 0.0437290219976465
6 3 5 -0.9850113492204077 -0.1553182373520525 -0.07502590921037534 0.09265233510028302
6 4 8 -0.7177135399298968 -0.2457215366779669 -0.6515429387338296 -0.02974683605231299
6 5 9 0.7110332662678565 -0.6935177833709648 -0.1160378317993181 -0.270606286195582
6 5 8 -0.1310037283001487 -0.04490613421135449 -0.9903643078593113 -0.2004293237314498
6 6 8 0.5636530776159621 0.07101685912338829 0.8229531054770393 0.4221671959133706
6 8 9 0.7278413449934531 -0.6852671087526033 0.02561183671604039 -0.2412830130907243
Voronoi ridge statistics
15 non-simplicial Voronoi vertices for all ridges
4.5e-017 ave. distance to ridge
1.1e-016 max. distance to ridge
13 bounded ridges
5.1e-017 ave. distance of midpoint to ridge
1.1e-016 max. distance of midpoint to ridge
13 bounded ridges with ok normal
6e-017 ave. angle to ridge
2.2e-016 max. angle to ridge
Output completed. Verifying that all points are below 2.9e-015 of
all facets. Will make 180 distance computations.
rbox 10 D3 | qhull v Fo Tcv
19
6 0 1 -0.1769702595802887 0.8331351847724079 0.523991689932513 0.004105600879712693
6 0 9 0.5856843296472445 -0.1558732679166011 -0.7954102025713887 -0.1264594278193165
6 0 6 -0.305501768024369 0.3812318858994052 -0.8725427891556765 -0.04822326899809229
6 0 7 0.6633910639781613 0.6672883530766242 -0.3385831509130508 0.06175731395259272
6 1 7 0.7533877382120365 0.334939238848763 -0.5658821628140998 0.06152842458597928
6 1 2 0.2077539373736715 0.4344067294949107 -0.8764297432625574 0.2556318087147513
6 1 5 -0.08886729274769867 0.2768317827550707 -0.9568002760954578 0.1656561460661368
6 2 4 0.8896724708236493 0.4529391082738924 -0.05769799697211265 -0.124969949041603
6 2 5 -0.6080629223625024 -0.1069684332549472 -0.7866493734408968 -0.05602222006342443
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 -0.6546392846048743 0.1665291828386517 0.7373706247980789 0.1638426312062793
6 4 7 0.8997625993863546 -0.3161631359012113 0.3007792151107228 -0.2534488584590283
6 4 6 -0.6610636619910347 -0.1756381951302929 -0.7294834194184101 -0.1931488689248214
6 4 5 -0.8177140658972856 -0.2799433900977096 -0.5029666040348318 0.01966883326066575
6 5 6 -0.4656867325018191 -0.06587339986788444 -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
5.4e-017 ave. distance to ridge
1.2e-016 max. distance to ridge
Output completed. Verifying that all points are below 2.9e-015 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 -1.216246894786401
2.789531685277142 -5.39366622961672 -1.494034092231972
2.640156785602008 -4.796303906482421 -1.459799746992416
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 -0.5221667006142706 -0.08192192666458514 -0.8488997200501182 -0.2535440955968324
6 6 7 0.752213645322669 0.06033708575303686 0.6561509489997043 0.09003235761431797
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 -0.2436653478720987 0.147883680687048 -0.9585184480399009 -0.04663519095132841
6 1 2 0.207753937373674 0.4344067294949119 -0.8764297432625561 0.2556318087147511
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 -0.6080629223625025 -0.1069684332549475 -0.7866493734408965 -0.05602222006342417
6 2 4 0.8896724708236504 0.4529391082738911 -0.05769799697210674 -0.1249699490416038
6 3 6 -0.8429664438017096 -0.1288333013498811 -0.5223117412882751 -0.1470675860428304
6 3 7 0.3131056731324614 -0.1651787990807291 0.9352437125084115 -0.1060546443225207
6 4 6 -0.661063661991035 -0.1756381951302929 -0.7294834194184101 -0.1931488689248215
6 4 7 0.8997625993863546 -0.3161631359012115 0.3007792151107228 -0.2534488584590282
6 5 6 -0.4656867325018209 -0.06587339986788572 -0.8824945112359753 -0.3747281225645818
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
7.9e-017 ave. distance to ridge
2.2e-016 max. distance to ridge
3 bounded ridges
1.1e-016 ave. distance of midpoint to ridge
1.4e-016 max. distance of midpoint to ridge
3 bounded ridges with ok normal
7.4e-017 ave. angle to ridge
2.2e-016 max. angle to ridge
Output completed. Verifying that all points are below 2.9e-015 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(v1): 0.47 -0.11 0.24
neighbors: f1 f5 f7
- p4(v0): -0.39 0.45 0.36
neighbors: f1 f3 f5 f6
- p0(v3): -0.34 0.23 0.17
neighbors: f3 f6 f8
- p1(v2): 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(v1) p4(v0)
- 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(v3) p4(v0)
- neighboring facets: f3 f5 f8
- f7
- flags: top simplicial
- normal: 0.6288 -0.3317 -0.7033
- offset: -0.1682885
- center: 0.447029359505762 -0.2357835939937328
- vertices: p3(v5) p1(v2) p2(v1)
- 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(v3) p1(v2)
- 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
0.447029359505762 -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
echo === check Halfspace ${d:-`date`}
date
=== check Halfspace Tue Sep 22 22:30:04 EDT 2015
rbox 100 s D4 | qhull FA FV n s Tcv | qhull 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 FA FV n s Tcv
Number of points processed: 100
Number of hyperplanes created: 1718
Number of distance tests for qhull: 4091
CPU seconds to compute hull (after input): 0
Total facet area: 1.7919449
Total volume: 0.18640279
Output completed. Verifying that all points are below 2.8e-015 of
all facets. Will make 58400 distance computations.
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: | qhull FA Tcv
Number of points processed: 100
Number of hyperplanes created: 1718
Number of distance tests for qhull: 4091
CPU seconds to compute hull (after input): 0.015
Total facet area: 1.7919449
Total volume: 0.18640279
Output completed. Verifying that all points are below 2.8e-015 of
all facets. Will make 58400 distance computations.
rbox d D3 | qhull FQ n s FD Tcv | qhull Fd H0.1,0.1 Fp FQ Tcv
Convex hull of 6 points in 3-d:
Number of vertices: 6
Number of facets: 8
Statistics for: rbox d D3 | qhull FQ n s FD Tcv
Number of points processed: 6
Number of hyperplanes created: 11
Number of distance tests for qhull: 11
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.
3
6
-1.387778780781446e-017 -1.387778780781446e-017 0.5
-2.775557561562891e-017 0.5 0
-0.5 0 0
0.5 -2.775557561562891e-017 0
0 -0.5 0
-1.387778780781446e-017 1.387778780781446e-017 -0.4999999999999999
rbox d D3 | qhull FQ n s FD Tcv | qhull Fd H0.1,0.1 Fp FQ Tcv
Output completed. Verifying that all points are below outer planes of
all facets. Will make 48 distance computations.
rbox 5 r D2 | qhull s n Tcv | qhull 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 n Tcv
Number of points processed: 5
Number of hyperplanes created: 8
Number of distance tests for qhull: 8
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.3e-015 of
all facets. Will make 25 distance computations.
2
5
-0.4045084971874738 -0.2938926261462365
0.5 -1.528090898784888e-016
0.1545084971874736 -0.4755282581475768
-0.4045084971874737 0.2938926261462366
0.1545084971874737 0.4755282581475768
Output completed. Verifying that all points are below 6.4e-015 of
all facets. Will make 25 distance computations.
echo === check qhull ${d:-`date`}
date
=== check qhull Tue Sep 22 22:30:04 EDT 2015
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: 49
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2e-015 of
all facets. Will make 160 distance computations.
rbox 10 s D3 | qhull f Pd0:0.5 Pd2 Tcv
Vertices and facets:
- p7(v8): 0.2 0.093 0.45
- p9(v5): 0.29 -0.16 0.38
- p3(v1): 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(v1)
- 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(v1)
- neighboring facets: f16 f26 f28
Output completed. Verifying that all points are below 2e-015 of
all facets. Will make 20 distance computations.
rbox 10 s D3 | qhull f Tcv PD2:-0.5
Vertices and facets:
- p4(v7): 0.23 -0.32 -0.31
- p1(v3): -0.072 0.057 -0.49
- p6(v2): -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(v3) p6(v2)
- neighboring facets: f21 f11 f25
- f21
- flags: bottom simplicial
- normal: -0.8148 -0.2922 -0.5006
- offset: -0.2881945
- vertices: p0(v9) p1(v3) p6(v2)
- 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(v3)
- 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(v3)
- neighboring facets: f12 f24 f26
Output completed. Verifying that all points are below 2e-015 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-1442975404
Number of points processed: 10
Number of hyperplanes created: 29
Number of distance tests for qhull: 49
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: 49
CPU seconds to compute hull (after input): 0
rbox 1000 D3 | qhull Tcvs
qhull invoked by: rbox 1000 D3 | qhull Tcvs
2015.0.3.r 2015/09/22 with options:
run-id 554789457 Tcheck-frequently Tverify Tstatistics _pre-merge
_zero-centrum _max-width 1 Error-roundoff 6.9e-016 _one-merge 4.9e-015
_near-inside 2.4e-014 Visible-distance 1.4e-015
U-coplanar-distance 1.4e-015 Width-outside 2.8e-015 _wide-facet 8.3e-015
precision constants:
0.5 max. abs. coordinate in the (transformed) input('Qbd:n')
6.9e-016 max. roundoff error for distance computation('En')
6.7e-016 max. roundoff error for angle computations
2.8e-015 min. distance for outside points ('Wn')
1.4e-015 min. distance for visible facets ('Vn')
1.4e-015 max. distance for coplanar facets ('Un')
8.3e-015 max. facet width for recomputing centrum and area
2.4e-014 max. distance for near-inside points
1.4e-015 radius of pre-merge centrum
4.9e-015 max. distance for merging two simplicial facets
2.2e-016 max. roundoff error for arithmetic operations
1.1e-308 min. denominator for divisions
zero diagonal for Gauss: 8.88e-015 1.78e-014 2.66e-014
precision statistics
3.7e-017 ave. distance of a new vertex to a facet(!0s)
1.4e-016 max. distance of a new vertex to a facet
1.1e-016 max. distance of an output vertex to a facet
-1.4e-016 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
82 vertices created altogether
368 facets created altogether
0 maximum merges for a facet(at most 511)
0.93 average angle(cosine) of facet normals for all ridges
1 maximum angle(cosine) of facet normals across a ridge
0.21 minimum angle(cosine) of facet normals 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 number of trials
7 determinants computed(area & initial hull)
504 distance tests for facet visibility
73 points checked for facets' outer planes
12.4 ave. distance tests per check
1629 max visit_id/2
619 max vertex_visit/2
partitioning statistics(see previous for outer planes)
8 total vertices deleted
1 maximum vertices deleted per iteration
135 calls to findbest
2.59 ave. facets tested
7 max. facets tested
2045 calls to findbestnew
4.47 ave. facets tested
13 max. facets tested
36 calls due to qh_sharpnewfacets
927 calls to findhorizon
3.02 ave. facets tested
6 max. facets tested
5 horizon facets better than bestfacet
919 inside points
8 inside points that were coplanar with a facet
-3.1e-017 difference in max_outside at final check
3747 distance tests for initial partition
3132 partitions of a point
8558 distance tests for partitioning
513 distance tests for checking flipped facets
1162 distance tests for statistics
16990 total number of distance tests
8 partitions of coplanar points or deleted vertices
75 distance tests for these partitions
statistics for matching ridges
726 total lookups for matching ridges of new facets
0.574 average number of tests to match a ridge
statistics for determining merges
1089 distance tests for checking simplicial convexity
statistics for merging
1.4e-016 max distance of vertex or coplanar point above facet(w/roundoff)
-6.9e-016 max distance of merged vertex below facet(or roundoff)
memory usage statistics(in bytes)
21584 for face
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: 368
Number of distance tests for qhull: 12884
CPU seconds to compute hull (after input): 0
ts and their normals, neighbor and vertex sets
2044 for vertices and their neighbor sets
30600 for input points, outside and coplanar sets, and qhT
memory statistics:
1166 quick allocations
673 short allocations
69 long allocations
1184 short frees
68 long frees
25680 bytes of short memory in use
680 bytes of short memory in freelists
104704 bytes of dropped short memory
2948 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)
73 calls to qh_setlarger
15 average copy size
freelists(bytes->count): 16->1 24->13 32->0 88->4
size in bytes: merge 24 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.
rbox 100 D3 | qhull T8 Tz TO q_test.log.1
tail -n -10 q_test.log.1
qh_mem 00270170 n 1022 free short: 32 bytes (tot 9032 cnt 228)
qh_mem 00270190 n 1023 free short: 32 bytes (tot 9000 cnt 227)
qh_mem 002701B0 n 1024 free short: 32 bytes (tot 8968 cnt 226)
qh_mem 002701D0 n 1025 free short: 32 bytes (tot 8936 cnt 225)
qh_mem 00263408 n 30 free long: 96 bytes (tot 0 cnt 0)
qh_mem 002701F0 n 1026 free short: 16 bytes (tot 8920 cnt 224)
qh_mem 00270050 n 1027 free short: 88 bytes (tot 8832 cnt 223)
qh_mem 002700A8 n 1028 free short: 88 bytes (tot 8744 cnt 222)
qh_mem 00270100 n 1029 free short: 88 bytes (tot 8656 cnt 221)
qh_freebuffers: finished
rm q_test.log.1
rbox 100 s D3 | qhull TcvV-2
At a premature exit due to '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: 1489
CPU seconds to compute hull (after input): 0
rbox 100 s D3 | qhull TcvC2
At a premature exit due to '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: 1496
CPU seconds to compute hull (after input): 0
rbox 100 s D3 | qhull TcvV2
At a premature exit due to '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: 1496
CPU seconds to compute hull (after input): 0
rbox 100 s D3 | qhull T1cvV2P2
At a premature exit due to '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: 1496
CPU seconds to compute hull (after input): 0
qh_readpoints: read in 100 3-dimensional points
qh_initqhull_globals: for rbox 100 s D3 | qhull T1cvV2P2
Trace level 1 for rbox 100 s D3 | qhull T1cvV2P2
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554789457 Tcheck-frequently Tverify TV-stop-after-point 2
Trace-point 2 _pre-merge _zero-centrum _max-width 0.94
Error-roundoff 6.7e-016 _one-merge 4.7e-015 _near-inside 2.3e-014
Visible-distance 1.3e-015 U-coplanar-distance 1.3e-015
Width-outside 2.7e-015 _wide-facet 8.1e-015
qh_findbest: point p2 starting at f7 isnewfacets? 1, unless 0 exit if > 2.7e-015
testhorizon? 1 noupper? 0 Last point added was p41. Last merge was #0. max_outside 5.6e-017
qh_findbest: point p2 starting at f15 isnewfacets? 1, unless 0 exit if > 2.7e-015
testhorizon? 1 noupper? 0 Last point added was p52. Last merge was #0. max_outside 1.1e-016
qh_findbest: point p2 starting at f37 isnewfacets? 1, unless 0 exit if > 2.7e-015
testhorizon? 1 noupper? 0 Last point added was p73. Last merge was #0. max_outside 1.1e-016
qh_findbest: point p2 starting at f52 isnewfacets? 1, unless 0 exit if > 2.7e-015
testhorizon? 1 noupper? 0 Last point added was p87. Last merge was #0. max_outside 1.1e-016
qh_findbest: point p2 starting at f72 isnewfacets? 1, unless 0 exit if > 2.7e-015
testhorizon? 1 noupper? 0 Last point added was p76. Last merge was #0. max_outside 1.1e-016
qh_findbest: point p2 starting at f120 isnewfacets? 1, unless 0 exit if > 2.7e-015
testhorizon? 1 noupper? 0 Last point added was p84. Last merge was #0. max_outside 1.7e-016
qh_findbest: point p2 starting at f211 isnewfacets? 1, unless 0 exit if > 2.7e-015
testhorizon? 1 noupper? 0 Last point added was p10. Last merge was #0. max_outside 1.7e-016
qh_findbest: point p2 starting at f289 isnewfacets? 1, unless 0 exit if > 2.7e-015
testhorizon? 1 noupper? 0 Last point added was p6. Last merge was #0. max_outside 1.7e-016
qh_addpoint: add p2(v79) to hull of 152 facets(0.014 above f288) and 22 outside at 0 CPU secs. Previous was p56.
qh_findhorizon: find horizon for point p2 facet f288
qh_findhorizon: 5 horizon facets(good 5), 3 visible(good 3), 0 coplanar
qh_makenewfacets: created 5 new facets from point p2 to horizon
qh_matchnewfacets: match neighbors for new facets.
qh_partitionvisible: partitioned 0 points from outsidesets and 0 points from coplanarsets
qh_deletevisible: delete 3 visible facets and 0 vertices
qh_checkpolygon: check all facets from f390
qh_buildhull: completed the hull construction
Qhull: algorithm completed
qh_checkpolygon: check all facets from f62
qh_checkconvex: check all ridges are convex
qh_freeqhull: free global memory
qh_freebuild: free memory from qh_inithull and qh_buildhull
rbox 100 s D3 | qhull TcvF100
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: 1691
CPU seconds to compute hull (after input): 0
At 22:30:04 & 0 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 22:30:04 & 0 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 22:30:04 & 0 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 22:30:04 & 0 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.
Output completed. Verifying that all points are below 2e-015 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: 504
Number of distance tests for qhull: 4423
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2e-015 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: 110
Number of distance tests for qhull: 1164
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: 1176
CPU seconds to compute hull (after input): 0.015
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: 4015
Number of distance tests for qhull: 8584
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 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: 294
Number of distance tests for qhull: 2129
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: 110
Number of distance tests for qhull: 1164
CPU seconds to compute hull (after input): 0.015
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 Tcv
Vertices and facets:
- p11(v14): -0.31 0.47 0.07
- p59(v8): 0.44 0.42 -0.11
- p33(v2): -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(v2)
- 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(v2): -0.5 0.5 -0.5
neighbors: f1 f3 f10
- p4(v1): 0.5 -0.5 -0.5
neighbors: f1 f2 f9
- p0(v0): -0.5 -0.5 -0.5
neighbors: f1 f2 f3
- p5(v7): 0.5 -0.5 0.5
neighbors: f2 f9 f13
- p1(v3): -0.5 -0.5 0.5
neighbors: f2 f3 f13
- p7(v5): 0.5 0.5 0.5
neighbors: f9 f10 f13
- p3(v8): -0.5 0.5 0.5
neighbors: f3 f10 f13
- f1
- flags: bottom tested seen coplanar
- 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(v2) p4(v1) p0(v0)
- neighboring facets: f2 f3 f9 f10
- ridges:
- r4 tested
vertices: p2(v2) p0(v0)
between f1 and f3
- r3 tested
vertices: p4(v1) p0(v0)
between f2 and f1
- r1 tested
vertices: p6(v6) p4(v1)
between f9 and f1
- r2 tested
vertices: p6(v6) p2(v2)
between f1 and f10
- f2
- flags: top tested seen coplanar
- 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(v3) p4(v1) p0(v0)
- neighboring facets: f1 f3 f9 f13
- ridges:
- r3 tested
vertices: p4(v1) p0(v0)
between f2 and f1
- r8 tested
vertices: p1(v3) p0(v0)
between f3 and f2
- r7 tested
vertices: p5(v7) p1(v3)
between f13 and f2
- r6 tested
vertices: p5(v7) p4(v1)
between f2 and f9
- f9
- flags: bottom tested seen coplanar
- 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(v1)
- neighboring facets: f2 f1 f10 f13
- ridges:
- r1 tested
vertices: p6(v6) p4(v1)
between f9 and f1
- r6 tested
vertices: p5(v7) p4(v1)
between f2 and f9
- r10 tested
vertices: p5(v7) p7(v5)
between f9 and f13
- r11 tested
vertices: p6(v6) p7(v5)
between f10 and f9
- f3
- flags: bottom tested seen coplanar
- 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(v3) p2(v2) p0(v0)
- neighboring facets: f1 f2 f10 f13
- ridges:
- r4 tested
vertices: p2(v2) p0(v0)
between f1 and f3
- r13 tested
vertices: p3(v8) p2(v2)
between f10 and f3
- r14 tested
vertices: p3(v8) p1(v3)
between f3 and f13
- r8 tested
vertices: p1(v3) p0(v0)
between f3 and f2
- f10
- flags: top tested seen coplanar
- 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(v2)
- neighboring facets: f3 f1 f9 f13
- ridges:
- r2 tested
vertices: p6(v6) p2(v2)
between f1 and f10
- r11 tested
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(v2)
between f10 and f3
- f13
- flags: bottom tested seen coplanar
- 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(v3)
- neighboring facets: f10 f2 f9 f3
- ridges:
- r7 tested
vertices: p5(v7) p1(v3)
between f13 and f2
- r14 tested
vertices: p3(v8) p1(v3)
between f3 and f13
- r16 tested
vertices: p3(v8) p7(v5)
between f13 and f10
- r10 tested
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
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: 110
Number of distance tests for qhull: 1164
CPU seconds to compute hull (after input): 0
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554806264 QbBound-unit-box 0.5 Tcheck-frequently Tverify
_pre-merge _zero-centrum _max-width 1 Error-roundoff 6.9e-016
_one-merge 4.9e-015 _near-inside 2.4e-014 Visible-distance 1.4e-015
U-coplanar-distance 1.4e-015 Width-outside 2.8e-015 _wide-facet 8.3e-015
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
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: 5422
Number of facets in hull: 1996
Number of distance tests for qhull: 27767
CPU seconds to compute hull (after input): 0
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554806264 delaunay Qbbound-last Tcheck-frequently Tverify
_pre-merge _zero-centrum Pgood _max-width 2e+006 Error-roundoff 2.8e-009
_one-merge 1.9e-008 _near-inside 9.7e-008 Visible-distance 5.5e-009
U-coplanar-distance 5.5e-009 Width-outside 1.1e-008 _wide-facet 3.3e-008
qhull output completed. Verifying that 1000 points are
below 8.3e-009 of the nearest facet.
rbox 10 D3 | qhull QbB p Tcv
3
9
-0.08928142660407056 -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 -0.1289660986727641
-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-015 of
all facets. Will make 140 distance computations.
rbox 10 D3 | qhull Qbb p Tcv
3
9
-0.0222149361131852 -0.366434993563625 0.5972263834933854
-0.06676722137887703 -0.1566931052661437 0.6939998615477234
0.02820502736438535 0.04189077954915421 0.4000814320337247
0.3126723396709863 0.08400649026409401 0.2817873818077145
0.1781470954214661 0.1182274414396169 0.3929477075294902
-0.1220315663349177 0.01546165115708642 0.2574974761506134
-0.3072535691850387 -0.01073880122111998 0
0.3867462923626847 0.04492879989084675 0.4441034944549365
0.3789805913148268 -0.4732086509216658 0.1975155783347269
QH7040 qhull input warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'
Output completed. Verifying that all points are below 2.9e-015 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
-6.400761988815289 -0.1566931052661437 20
-4.97936018866004 0.04189077954915421 11.32346018178494
-0.7218812392989191 0.08400649026409401 7.831392539952951
-2.735252796494545 0.1182274414396169 11.11287098934976
-7.227875597731384 0.01546165115708642 7.114348923589699
-10 -0.01073880122111998 -0.4870359524963758
0.3867462923626847 0.04492879989084675 12.62300161615219
0.2705209571204694 -0.4732086509216658 5.343669467959106
Output completed. Verifying that all points are below 7.5e-014 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-014 of
all facets. Will make 140 distance computations.
3
9
-0.08928142660407051 -0.3194671263098747 0.3605569202297555
-0.1534778158747163 0.03516440701453921 0.5
-0.01663016790622796 0.3709299907861695 0.07648632831350066
0.3932651765570927 0.4421392241401818 -0.09396622763110274
0.1994247283046841 0.5 0.06620718432588446
-0.2331094527352668 0.3262436269787957 -0.128966098672764
-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-015 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: 32
Number of facets in hull: 16
Number of distance tests for qhull: 62
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-015 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: 32
Number of facets in hull: 16
Number of distance tests for qhull: 62
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-015 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: 44
Number of facets in hull: 27
Number of distance tests for qhull: 67
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2.9e-015 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: 49
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 1.3e-015 of
all facets. Will make 40 distance computations.
echo "== next command will error ${d:-`date`} =="
date
== next command will error Tue Sep 22 22:30:05 EDT 2015 ==
rbox 10 D2 | qhull Qb1:1B1:1 Tcv
QH6154 qhull precision error: initial facet 1 is coplanar with the interior point
ERRONEOUS FACET:
- f1
- flags: bottom simplicial flipped
- normal: 0 1
- offset: -1
- vertices: p4(v1) p1(v0)
- neighboring facets: f2 f3
While executing: rbox 10 D2 | qhull Qb1:1B1:1 Tcv
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554806264 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-016 _one-merge 4.3e-015 _near-inside 2.1e-014
Visible-distance 1.7e-015 U-coplanar-distance 1.7e-015
Width-outside 3.4e-015 _wide-facet 1e-014
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(v2): -0.022 1
- p4(v1): 0.38 1
- p1(v0): -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-016. 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-016.
- 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
Convex hull of 200 points in 2-d:
Number of vertices: 200
Number of facets: 200
Statistics for: rbox 200 L20 D2 t1442975405 | qhull FO Tcv C-0
Number of points processed: 200
Number of hyperplanes created: 398
Number of distance tests for qhull: 2135
CPU seconds to compute hull (after input): 0
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554806264 Tcheck-frequently Tverify Centrum-premerge- 0
_zero-centrum _max-width 0.99 Error-roundoff 3.4e-016 _one-merge 1.7e-015
_near-inside 8.5e-015 Visible-distance 6.8e-016
U-coplanar-distance 6.8e-016 Width-outside 1.4e-015 _wide-facet 4.1e-015
Output completed. Verifying that all points are below 1e-015 of
all facets. Will make 40000 distance computations.
rbox 1000 L20 t | qhull FO Tcv C-0
Convex hull of 1000 points in 3-d:
Number of vertices: 63
Number of facets: 122
Statistics for: rbox 1000 L20 t1442975405 | qhull FO Tcv C-0
Number of points processed: 80
Number of hyperplanes created: 368
Number of distance tests for qhull: 15279
CPU seconds to compute hull (after input): 0
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554806264 Tcheck-frequently Tverify Centrum-premerge- 0
_zero-centrum _max-width 1 Error-roundoff 6.9e-016 _one-merge 4.9e-015
_near-inside 2.4e-014 Visible-distance 1.4e-015
U-coplanar-distance 1.4e-015 Width-outside 2.8e-015 _wide-facet 8.3e-015
Output completed. Verifying that all points are below outer planes of
all facets. Will make 122000 distance computations.
rbox 200 L20 D4 t | qhull FO Tcv C-0
Convex hull of 200 points in 4-d:
Number of vertices: 62
Number of facets: 277
Statistics for: rbox 200 L20 D4 t1442975405 | qhull FO Tcv C-0
Number of points processed: 71
Number of hyperplanes created: 766
Number of distance tests for qhull: 6464
CPU seconds to compute hull (after input): 0
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554806264 Tcheck-frequently Tverify Centrum-premerge- 0
_zero-centrum _max-width 1 Error-roundoff 1e-015 _one-merge 9.1e-015
_near-inside 4.5e-014 Visible-distance 6e-015 U-coplanar-distance 6e-015
Width-outside 1.2e-014 _wide-facet 3.6e-014
Output completed. Verifying that all points are below outer planes of
all facets. Will make 55400 distance computations.
rbox 200 L20 D5 t | qhull FO Tcv Qx
Convex hull of 200 points in 5-d:
Number of vertices: 101
Number of facets: 1416
Statistics for: rbox 200 L20 D5 t1442975405 | qhull FO Tcv Qx
Number of points processed: 120
Number of hyperplanes created: 5244
Number of distance tests for qhull: 20364
CPU seconds to compute hull (after input): 0.015
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554806264 Tcheck-frequently Tverify Qxact-merge _zero-centrum
_max-width 1 Error-roundoff 1.4e-015 _one-merge 1.5e-014
_near-inside 7.5e-014 Visible-distance 8.2e-015
U-coplanar-distance 8.2e-015 Width-outside 1.6e-014 _wide-facet 4.9e-014
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 283200 distance computations.
rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu Q0
Furthest-site Delaunay triangulation by the convex hull of 1000 points in 3-d:
Number of input sites: 1000
Number of Delaunay regions: 256
Statistics for: rbox 1000 W1e-3 s D2 t1442975405 | qhull d FO Tcv Qu Q0
Number of points processed: 1000
Number of hyperplanes created: 4600
Number of facets in hull: 1996
Number of distance tests for qhull: 26593
CPU seconds to compute hull (after input): 0
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554806264 delaunay Tcheck-frequently Tverify QupperDelaunay
Q0-no-premerge Pgood _max-width 1 Error-roundoff 6.9e-016
Visible-distance 6.9e-016 U-coplanar-distance 6.9e-016
Width-outside 1.4e-015 _wide-facet 4.2e-015
Output completed. Verifying that all points are below 2.1e-015 of
all facets. Will make 256000 distance computations.
rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu C-0
Furthest-site Delaunay triangulation by the convex hull of 1000 points in 3-d:
Number of input sites: 1000
Number of Delaunay regions: 256
Statistics for: rbox 1000 W1e-3 s D2 t1442975405 | qhull d FO Tcv Qu C-0
Number of points processed: 1000
Number of hyperplanes created: 4600
Number of facets in hull: 1996
Number of distance tests for qhull: 26593
CPU seconds to compute hull (after input): 0
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554806264 delaunay Tcheck-frequently Tverify QupperDelaunay
Centrum-premerge- 0 _zero-centrum Pgood _max-width 1
Error-roundoff 6.9e-016 _one-merge 4.9e-015 _near-inside 2.4e-014
Visible-distance 1.4e-015 U-coplanar-distance 1.4e-015
Width-outside 2.8e-015 _wide-facet 8.3e-015
Output completed. Verifying that all points are below 2.1e-015 of
all facets. Will make 256000 distance computations.
echo === check joggle and TRn ${d:-`date`}
date
=== check joggle and TRn Tue Sep 22 22:30:05 EDT 2015
rbox 100 W0 | qhull QJ1e-14 Qc TR100 Tv
At a premature exit due to '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: 11270
Number of distance tests for qhull: 120689
CPU seconds to compute hull (after input): 0.015
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
At a premature exit due to '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: 24800
Number of distance tests for qhull: 197857
CPU seconds to compute hull (after input): 0.031
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
At a premature exit due to '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: 29205
Number of distance tests for qhull: 217398
CPU seconds to compute hull (after input): 0.031
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: 29630
Number of distance tests for qhull: 219104
CPU seconds to compute hull (after input): 0.046
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-015 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: 29636
Number of distance tests for qhull: 218960
CPU seconds to compute hull (after input): 0.031
Percentage of runs with precision errors: 0.0
Output completed. Verifying that all points are below 2.1e-015 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
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: 1578
Number of facets in hull: 560
Number of distance tests for qhull: 3924
CPU seconds to compute hull (after input): 0
Input joggled by: 6.7e+003
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554823071 delaunay Qbound-dim-low 0 1e+004 QBound-dim-high 0 1e+005
Qbound-dim-low 1 1e+004 QBound-dim-high 1 1e+006 Qbound-dim-low 2 1e+005
QBound-dim-high 2 1e+007 Tverify Pgood _run 1 QJoggle 6.7e+003
_joggle-seed 16807 _max-width 1e+014 Error-roundoff 0.11
Visible-distance 0.11 U-coplanar-distance 0.11 Width-outside 0.23
_wide-facet 0.68
Output completed. Verifying that all points are below 0.34 of
all facets. Will make 48800 distance computations.
echo === check precision options ${d:-`date`}
date
=== check precision options Tue Sep 22 22:30:06 EDT 2015
rbox 100 D3 s | qhull E0.01 Qx Tcv FO
Convex hull of 100 points in 3-d:
Number of vertices: 45
Number of facets: 42
Number of non-simplicial facets: 28
Statistics for: rbox 100 D3 s | qhull E0.01 Qx Tcv FO
Number of points processed: 45
Number of hyperplanes created: 160
Number of distance tests for qhull: 3992
Number of distance tests for merging: 2006
Number of distance tests for checking: 1937
Number of merged facets: 57
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.048 (0.6x)
Maximum distance of vertex below facet: -0.072 (0.9x)
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554823071 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-coplanar-distance 0.02 Width-outside 0.04
_wide-facet 0.12
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 4200 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: 170
Number of distance tests for qhull: 1580
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: 128
Number of distance tests for qhull: 1442
CPU seconds to compute hull (after input): 0
precision problems (corrected unless 'Q0' or an error)
22 coplanar points during partitioning
Output completed. Verifying that all points are below 0.0097 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: 132
Number of distance tests for qhull: 1768
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: 46
Number of distance tests for qhull: 2521
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: 64
Number of facets in hull: 28
Number of distance tests for qhull: 142
Number of distance tests for merging: 527
Number of distance tests for checking: 194
Number of merged facets: 7
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 1.6e-015 (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: 124
Number of facets in hull: 60
Number of distance tests for qhull: 225
CPU seconds to compute hull (after input): 0
Output completed. Verifying that all points are below 2.8e-015 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: 107
Number of coplanar points: 893
Number of facets: 96
Number of non-simplicial facets: 77
Statistics for: rbox 1000 s D3 | qhull C-0.01 Tcv Qc
Number of points processed: 112
Number of hyperplanes created: 449
Number of distance tests for qhull: 64526
Number of distance tests for merging: 8425
Number of distance tests for checking: 23411
Number of merged facets: 256
CPU seconds to compute hull (after input): 0.015
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 96000 distance computations.
rbox 1000 s D3 | qhull C-0.01 V0 Qc Tcv
Convex hull of 1000 points in 3-d:
Number of vertices: 120
Number of coplanar points: 880
Number of facets: 82
Number of non-simplicial facets: 71
Statistics for: rbox 1000 s D3 | qhull C-0.01 V0 Qc Tcv
Number of points processed: 445
Number of hyperplanes created: 2451
Number of distance tests for qhull: 172077
Number of distance tests for merging: 52430
Number of distance tests for checking: 19885
Number of merged facets: 1741
CPU seconds to compute hull (after input): 0.031
Maximum distance of point above facet: 0.032 (1.1x)
Maximum distance of vertex below facet: -0.064 (2.1x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 82000 distance computations.
rbox 1000 s D3 | qhull C-0.01 U0 Qc Tcv
Convex hull of 1000 points in 3-d:
Number of vertices: 107
Number of coplanar points: 893
Number of facets: 98
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: 497
Number of distance tests for qhull: 64717
Number of distance tests for merging: 9106
Number of distance tests for checking: 23621
Number of merged facets: 254
CPU seconds to compute hull (after input): 0.015
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 98000 distance computations.
rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv
Convex hull of 1000 points in 3-d:
Number of vertices: 106
Number of coplanar points: 894
Number of facets: 94
Number of non-simplicial facets: 71
Statistics for: rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv
Number of points processed: 114
Number of hyperplanes created: 597
Number of distance tests for qhull: 54389
Number of distance tests for merging: 10179
Number of distance tests for checking: 18597
Number of merged facets: 288
CPU seconds to compute hull (after input): 0.015
Maximum distance of point above facet: 0.025 (0.8x)
Maximum distance of vertex below facet: -0.07 (2.3x)
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 Qcm Tcv
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: 69
Statistics for: rbox 1000 s D3 | qhull C-0.01 Qcm Tcv
Number of points processed: 106
Number of hyperplanes created: 434
Number of distance tests for qhull: 64355
Number of distance tests for merging: 7947
Number of distance tests for checking: 23460
Number of merged facets: 234
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.022 (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 96000 distance computations.
rbox 1000 s D3 | qhull C-0.01 Q1 FO Tcv Qc
Convex hull of 1000 points in 3-d:
Number of vertices: 105
Number of coplanar points: 895
Number of facets: 94
Number of non-simplicial facets: 70
Statistics for: rbox 1000 s D3 | qhull C-0.01 Q1 FO Tcv Qc
Number of points processed: 110
Number of hyperplanes created: 457
Number of distance tests for qhull: 66717
Number of distance tests for merging: 8730
Number of distance tests for checking: 23168
Number of merged facets: 258
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.02 (0.7x)
Maximum distance of vertex below facet: -0.035 (1.2x)
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554823071 Centrum-premerge- 0.01 Q1-no-angle-sort Tcheck-frequently
Tverify Qcoplanar-keep _max-width 1 Error-roundoff 6.9e-016
_one-merge 0.03 _near-inside 0.15 Visible-distance 0.01
U-coplanar-distance 0.01 Width-outside 0.02 _wide-facet 0.06
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 Q2 FO Tcv Qc
Convex hull of 1000 points in 3-d:
Number of vertices: 106
Number of coplanar points: 894
Number of facets: 91
Number of non-simplicial facets: 74
Statistics for: rbox 1000 s D3 | qhull C-0.01 Q2 FO Tcv Qc
Number of points processed: 112
Number of hyperplanes created: 454
Number of distance tests for qhull: 64909
Number of distance tests for merging: 8602
Number of distance tests for checking: 22777
Number of merged facets: 267
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.02 (0.7x)
Maximum distance of vertex below facet: -0.049 (1.6x)
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554823071 Centrum-premerge- 0.01 Q2-no-merge-independent
Tcheck-frequently Tverify Qcoplanar-keep _max-width 1
Error-roundoff 6.9e-016 _one-merge 0.03 _near-inside 0.15
Visible-distance 0.01 U-coplanar-distance 0.01 Width-outside 0.02
_wide-facet 0.06
Output completed. Verifying that all points are below outer planes of
all facets. Will make 91000 distance computations.
rbox 1000 s D3 | qhull C-0.01 Q3 FO Tcv Qc
Convex hull of 1000 points in 3-d:
Number of vertices: 112
Number of coplanar points: 888
Number of facets: 95
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: 453
Number of distance tests for qhull: 64248
Number of distance tests for merging: 8529
Number of distance tests for checking: 23283
Number of merged facets: 260
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.02 (0.7x)
Maximum distance of vertex below facet: -0.035 (1.2x)
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554823071 Centrum-premerge- 0.01 Q3-no-merge-vertices
Tcheck-frequently Tverify Qcoplanar-keep _max-width 1
Error-roundoff 6.9e-016 _one-merge 0.03 _near-inside 0.15
Visible-distance 0.01 U-coplanar-distance 0.01 Width-outside 0.02
_wide-facet 0.06
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 Q4 FO Tcv Qc
Convex hull of 1000 points in 3-d:
Number of vertices: 107
Number of coplanar points: 893
Number of facets: 96
Number of non-simplicial facets: 77
Statistics for: rbox 1000 s D3 | qhull C-0.01 Q4 FO Tcv Qc
Number of points processed: 112
Number of hyperplanes created: 449
Number of distance tests for qhull: 64526
Number of distance tests for merging: 8425
Number of distance tests for checking: 23411
Number of merged facets: 256
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.02 (0.7x)
Maximum distance of vertex below facet: -0.035 (1.2x)
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554823071 Centrum-premerge- 0.01 Q4-avoid-old-into-new
Tcheck-frequently Tverify Qcoplanar-keep _max-width 1
Error-roundoff 6.9e-016 _one-merge 0.03 _near-inside 0.15
Visible-distance 0.01 U-coplanar-distance 0.01 Width-outside 0.02
_wide-facet 0.06
Output completed. Verifying that all points are below outer planes of
all facets. Will make 96000 distance computations.
echo === this may generate an error ${d:-`date`}
date
=== this may generate an error Tue Sep 22 22:30:07 EDT 2015
rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv
Convex hull of 1000 points in 3-d:
Number of vertices: 107
Number of facets: 96
Number of non-simplicial facets: 77
Statistics for: rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv
Number of points processed: 112
Number of hyperplanes created: 449
Number of distance tests for qhull: 38064
Number of distance tests for merging: 8425
Number of distance tests for checking: 0
Number of merged facets: 256
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.022 (0.7x)
Maximum distance of vertex below facet: -0.035 (1.2x)
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554839878 Centrum-premerge- 0.01 Q5-no-check-outer
Tcheck-frequently Tverify _max-width 1 Error-roundoff 6.9e-016
_one-merge 0.03 Visible-distance 0.01 U-coplanar-distance 0.01
Width-outside 0.02 _wide-facet 0.06
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 96000 distance computations.
echo === this should generate an error ${d:-`date`}
date
=== this should generate an error Tue Sep 22 22:30:07 EDT 2015
rbox 1000 s D3 | qhull C-0.01 Q6 FO Po Tcv Qc
Convex hull of 1000 points in 3-d:
Number of vertices: 114
Number of coplanar points: 886
Number of facets: 182
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: 114
Number of hyperplanes created: 447
Number of distance tests for qhull: 53157
Number of distance tests for merging: 3458
Number of distance tests for checking: 27470
Number of merged facets: 88
CPU seconds to compute hull (after input): 0.015
Maximum distance of point above facet: 0.02 (0.7x)
Maximum distance of vertex below facet: -0.009 (0.3x)
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554839878 Centrum-premerge- 0.01 Q6-no-concave-merge Poutput-forced
Tcheck-frequently Tverify Qcoplanar-keep _max-width 1
Error-roundoff 6.9e-016 _one-merge 0.03 _near-inside 0.15
Visible-distance 0.01 U-coplanar-distance 0.01 Width-outside 0.02
_wide-facet 0.06
QH6117 qhull precision error: f324 is concave to f325. Centrum of f324 is 0.004134 above f325
QH6117 qhull precision error: f325 is concave to f324. Centrum of f325 is 0.001027 above f324
rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc
Convex hull of 1000 points in 3-d:
Number of vertices: 100
Number of coplanar points: 900
Number of facets: 94
Number of non-simplicial facets: 73
Statistics for: rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc
Number of points processed: 103
Number of hyperplanes created: 448
Number of distance tests for qhull: 70481
Number of distance tests for merging: 8005
Number of distance tests for checking: 21158
Number of merged facets: 233
CPU seconds to compute hull (after input): 0.015
Maximum distance of point above facet: 0.02 (0.7x)
Maximum distance of vertex below facet: -0.042 (1.4x)
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554839878 Centrum-premerge- 0.01 Q7-no-breadth-first
Tcheck-frequently Tverify Qcoplanar-keep _max-width 1
Error-roundoff 6.9e-016 _one-merge 0.03 _near-inside 0.15
Visible-distance 0.01 U-coplanar-distance 0.01 Width-outside 0.02
_wide-facet 0.06
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 Qx Tcv Qc
Convex hull of 1000 points in 3-d:
Number of vertices: 114
Number of coplanar points: 886
Number of facets: 103
Number of non-simplicial facets: 77
Statistics for: rbox 1000 s D3 | qhull C-0.01 Qx Tcv Qc
Number of points processed: 114
Number of hyperplanes created: 447
Number of distance tests for qhull: 90887
Number of distance tests for merging: 5483
Number of distance tests for checking: 20583
Number of merged facets: 167
CPU seconds to compute hull (after input): 0
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 103000 distance computations.
echo === this may generate an error e.g., t1263080158 ${d:-`date`}
date
=== this may generate an error e.g., t1263080158 Tue Sep 22 22:30:07 EDT 2015
rbox 100 s D3 t | qhull R1e-3 Tcv Qc
Convex hull of 100 points in 3-d:
Number of vertices: 96
Number of coplanar points: 4
Number of facets: 173
Number of non-simplicial facets: 15
Statistics for: rbox 100 s D3 t1442975407 | qhull R1e-3 Tcv Qc
Number of points processed: 96
Number of hyperplanes created: 459
Number of distance tests for qhull: 1673
Number of distance tests for merging: 2955
Number of distance tests for checking: 1311
Number of merged facets: 30
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.0023 (0.6x)
Maximum distance of vertex below facet: -0.0044 (1.1x)
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: 65
Number of coplanar points: 35
Number of facets: 58
Number of non-simplicial facets: 44
Statistics for: rbox 100 s D3 t1442975407 | qhull R1e-2 Tcv Qc
Number of points processed: 71
Number of hyperplanes created: 325
Number of distance tests for qhull: 4291
Number of distance tests for merging: 5827
Number of distance tests for checking: 2083
Number of merged facets: 176
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.033 (0.8x)
Maximum distance of vertex below facet: -0.086 (2.2x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 5800 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: 16
Number of non-simplicial facets: 11
Statistics for: rbox 500 s D3 t1442975407 | qhull R0.05 A-1 Tcv Qc
Number of points processed: 26
Number of hyperplanes created: 85
Number of distance tests for qhull: 24197
Number of distance tests for merging: 1825
Number of distance tests for checking: 8881
Number of merged facets: 59
CPU seconds to compute hull (after input): 0.015
Maximum distance of point above facet: 0.14 (0.2x)
Maximum distance of vertex below facet: -0.3 (0.5x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 8000 distance computations.
rbox 100 W0 D3 t | qhull R1e-3 Tcv Qc
Convex hull of 100 points in 3-d:
Number of vertices: 43
Number of coplanar points: 57
Number of facets: 54
Number of non-simplicial facets: 8
Statistics for: rbox 100 W0 D3 t1442975407 | qhull R1e-3 Tcv Qc
Number of points processed: 44
Number of hyperplanes created: 154
Number of distance tests for qhull: 2135
Number of distance tests for merging: 1725
Number of distance tests for checking: 1174
Number of merged facets: 35
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.0019 (0.5x)
Maximum distance of vertex below facet: -0.0029 (0.7x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 5400 distance computations.
rbox 100 W0 D3 t | qhull R1e-3 Qx Tcv Qc
Convex hull of 100 points in 3-d:
Number of vertices: 43
Number of coplanar points: 57
Number of facets: 53
Number of non-simplicial facets: 10
Statistics for: rbox 100 W0 D3 t1442975407 | qhull R1e-3 Qx Tcv Qc
Number of points processed: 45
Number of hyperplanes created: 154
Number of distance tests for qhull: 2419
Number of distance tests for merging: 1519
Number of distance tests for checking: 1186
Number of merged facets: 34
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.0018 (0.5x)
Maximum distance of vertex below facet: -0.0037 (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 5300 distance computations.
rbox 100 W0 D3 t | qhull R1e-2 Tcv Qc
Convex hull of 100 points in 3-d:
Number of vertices: 26
Number of coplanar points: 74
Number of facets: 28
Number of non-simplicial facets: 9
Statistics for: rbox 100 W0 D3 t1442975407 | qhull R1e-2 Tcv Qc
Number of points processed: 32
Number of hyperplanes created: 102
Number of distance tests for qhull: 2502
Number of distance tests for merging: 1391
Number of distance tests for checking: 1183
Number of merged facets: 42
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.023 (0.6x)
Maximum distance of vertex below facet: -0.046 (1.1x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 2800 distance computations.
rbox 100 W0 D3 t | qhull R1e-2 Qx Tcv Qc
Convex hull of 100 points in 3-d:
Number of vertices: 26
Number of coplanar points: 74
Number of facets: 25
Number of non-simplicial facets: 10
Statistics for: rbox 100 W0 D3 t1442975407 | qhull R1e-2 Qx Tcv Qc
Number of points processed: 33
Number of hyperplanes created: 105
Number of distance tests for qhull: 3188
Number of distance tests for merging: 1305
Number of distance tests for checking: 1032
Number of merged facets: 40
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.022 (0.6x)
Maximum distance of vertex below facet: -0.06 (1.5x)
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 2500 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 t1442975407 | qhull R0.05 A-1 Tcv Qc
Number of points processed: 14
Number of hyperplanes created: 37
Number of distance tests for qhull: 16109
Number of distance tests for merging: 639
Number of distance tests for checking: 3990
Number of merged facets: 22
CPU seconds to compute hull (after input): 0.015
Maximum distance of point above facet: 0.11 (0.2x)
Maximum distance of vertex below facet: -0.19 (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: 9
Number of coplanar points: 491
Number of facets: 7
Number of non-simplicial facets: 6
Statistics for: rbox 500 W0 D3 t1442975407 | qhull R0.05 Qx Tcv Qc
Number of points processed: 16
Number of hyperplanes created: 40
Number of distance tests for qhull: 20408
Number of distance tests for merging: 525
Number of distance tests for checking: 4410
Number of merged facets: 23
CPU seconds to compute hull (after input): 0
Maximum distance of point above facet: 0.11 (0.6x)
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 3500 distance computations.
rbox 1000 W1e-20 t | qhull Tcv Qc
Convex hull of 1000 points in 3-d:
Number of vertices: 74
Number of coplanar points: 926
Number of facets: 88
Number of non-simplicial facets: 6
Statistics for: rbox 1000 W1e-20 t1442975407 | qhull Tcv Qc
Number of points processed: 95
Number of hyperplanes created: 319
Number of distance tests for qhull: 21849
Number of distance tests for merging: 4103
Number of distance tests for checking: 28284
Number of merged facets: 98
CPU seconds to compute hull (after input): 0.015
Output completed. Verifying that all points are below outer planes of
all facets. Will make 88000 distance computations.
rbox 1000 W1e-20 D4 t | qhull Tcv Qc
Convex hull of 1000 points in 4-d:
Number of vertices: 266
Number of coplanar points: 734
Number of facets: 978
Number of non-simplicial facets: 8
Statistics for: rbox 1000 W1e-20 D4 t1442975407 | qhull Tcv Qc
Number of points processed: 348
Number of hyperplanes created: 4399
Number of distance tests for qhull: 73412
Number of distance tests for merging: 67272
Number of distance tests for checking: 139166
Number of merged facets: 1083
CPU seconds to compute hull (after input): 0.078
Output completed. Verifying that all points are below outer planes of
all facets. Will make 978000 distance computations.
rbox 500 W1e-20 D5 t | qhull Tv Qc
Convex hull of 500 points in 5-d:
Number of vertices: 342
Number of coplanar points: 158
Number of facets: 5792
Number of non-simplicial facets: 10
Statistics for: rbox 500 W1e-20 D5 t1442975407 | qhull Tv Qc
Number of points processed: 399
Number of hyperplanes created: 26992
Number of distance tests for qhull: 125820
Number of distance tests for merging: 302414
Number of distance tests for checking: 239686
Number of merged facets: 3340
CPU seconds to compute hull (after input): 0.109
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 2896000 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: 5929
Number of non-simplicial facets: 10
Statistics for: rbox 100 W1e-20 D6 t1442975408 | qhull Tv Qc
Number of points processed: 100
Number of hyperplanes created: 19239
Number of distance tests for qhull: 30187
Number of distance tests for merging: 180189
Number of distance tests for checking: 122402
Number of merged facets: 189
CPU seconds to compute hull (after input): 0.062
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 592900 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: 2069
Statistics for: rbox 50 W1e-20 D6 t1442975408 | qhull Qv Tv Qc
Number of points processed: 50
Number of hyperplanes created: 5634
Number of distance tests for qhull: 8055
CPU seconds to compute hull (after input): 0.14
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 103450 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: 8570
Number of facets: 8
Number of non-simplicial facets: 8
Statistics for: rbox 10000 D4 t1442975408 | qhull QR0 Qc C-0.01 A0.3 Tv QR1442975408
Number of points processed: 51
Number of hyperplanes created: 331
Number of distance tests for qhull: 1654817
Number of distance tests for merging: 11223
Number of distance tests for checking: 99774
Number of merged facets: 366
CPU seconds to compute hull (after input): 0.062
Maximum distance of point above facet: 0.043
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 t1442975408 | qhull d QR0 Qc C-1e-8 Qu Tv QR1442975408
Number of points processed: 1000
Number of hyperplanes created: 5514
Number of facets in hull: 1996
Number of distance tests for qhull: 31183
CPU seconds to compute hull (after input): 0
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: 145
Number of coplanar points: 37
Number of facets: 1591
Number of non-simplicial facets: 399
Statistics for: rbox 300 D5 t1442975408 | qhull A-0.999 Qx Qc Tcv
Number of points processed: 182
Number of hyperplanes created: 10243
Number of distance tests for qhull: 170694
Number of distance tests for merging: 50845
Number of distance tests for checking: 19040
Number of merged facets: 1005
CPU seconds to compute hull (after input): 0.031
Maximum distance of vertex below facet: -0.025 (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 477300 distance computations.
rbox 100 D6 t |qhull A-0.9999 Qx Qc Tcv
Convex hull of 100 points in 6-d:
Number of vertices: 83
Number of coplanar points: 3
Number of facets: 3170
Number of non-simplicial facets: 214
Statistics for: rbox 100 D6 t1442975408 | qhull A-0.9999 Qx Qc Tcv
Number of points processed: 87
Number of hyperplanes created: 12742
Number of distance tests for qhull: 33407
Number of distance tests for merging: 68429
Number of distance tests for checking: 68286
Number of merged facets: 516
CPU seconds to compute hull (after input): 0.047
Maximum distance of vertex below facet: -0.007 (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 317000 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: 44
Number of coplanar points: 6
Number of facets: 4077
Number of non-simplicial facets: 63
Statistics for: rbox 50 D7 t1442975408 | qhull A-0.99999 Qx Qc Tcv W0.1
Number of points processed: 44
Number of hyperplanes created: 11162
Number of distance tests for qhull: 26970
Number of distance tests for merging: 80889
Number of distance tests for checking: 129530
Number of merged facets: 177
CPU seconds to compute hull (after input): 0.047
Maximum distance of point above facet: 0.15
Maximum distance of vertex below facet: -0.0018 (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 203850 distance computations.
echo === check bad cases for Qhull. May cause errors ${d:-`date`}
date
=== check bad cases for Qhull. May cause errors Tue Sep 22 22:30:08 EDT 2015
rbox 1000 L100000 s G1e-6 t | qhull Tv
Convex hull of 1000 points in 3-d:
Number of vertices: 988
Number of facets: 1497
Number of non-simplicial facets: 7
Statistics for: rbox 1000 L100000 s G1e-6 t1442975408 | qhull Tv
Number of points processed: 989
Number of hyperplanes created: 3875
Number of distance tests for qhull: 31438
Number of distance tests for merging: 137112
Number of distance tests for checking: 123050
Number of merged facets: 478
CPU seconds to compute hull (after input): 0.016
Maximum distance of point above facet: 1.9e-015 (0.3x)
Maximum distance of vertex below facet: -3.9e-015 (0.7x)
qhull precision warning:
The initial hull is narrow (cosine of min. angle is 1.0000000000000000).
Is the input lower dimensional (e.g., on a plane in 3-d)? Qhull may
produce a wide facet. Options 'QbB' (scale to unit box) or 'Qbb' (scale
last coordinate) may remove this warning. Use 'Pp' to skip this warning.
See 'Limitations' in qh-impre.htm.
Output completed. Verifying that all points are below outer planes of
all facets. Will make 1497000 distance computations.
rbox 1000 L100000 s G1e-6 t | qhull Tv Q10
Convex hull of 1000 points in 3-d:
Number of vertices: 989
Number of facets: 1494
Number of non-simplicial facets: 9
Statistics for: rbox 1000 L100000 s G1e-6 t1442975409 | qhull Tv Q10
Number of points processed: 991
Number of hyperplanes created: 3826
Number of distance tests for qhull: 32118
Number of distance tests for merging: 138324
Number of distance tests for checking: 124611
Number of merged facets: 482
CPU seconds to compute hull (after input): 0.015
Maximum distance of point above facet: 1.6e-015 (0.3x)
Maximum distance of vertex below facet: -4.4e-015 (0.8x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 1494000 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: 1487
Number of non-simplicial facets: 156
Statistics for: rbox 1000 s Z1 G1e-13 t1442975409 | qhull Tv
Number of points processed: 1001
Number of hyperplanes created: 4088
Number of distance tests for qhull: 26418
Number of distance tests for merging: 75425
Number of distance tests for checking: 230009
Number of merged facets: 1270
CPU seconds to compute hull (after input): 0.015
Maximum distance of point above facet: 7.4e-015 (1.3x)
Maximum distance of vertex below facet: -1e-014 (1.8x)
Output completed. Verifying that all points are below outer planes of
all facets. Will make 1488487 distance computations.
rbox 1000 s W1e-13 P0 t | qhull d Qbb Qc 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 t1442975409 | qhull d Qbb Qc Tv
Number of points processed: 1001
Number of hyperplanes created: 13874
Number of facets in hull: 3743
Number of distance tests for qhull: 56443
Number of distance tests for merging: 203311
Number of distance tests for checking: 218553
Number of merged facets: 4693
CPU seconds to compute hull (after input): 0.078
Maximum distance of point above facet: 6.2e-014 (3.1x)
Maximum distance of vertex below facet: -6.9e-014 (3.4x)
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 Tv
Delaunay triangulation by the convex hull of 1000 points in 4-d:
Number of input sites: 10
Total number of deleted points due to merging: 967
Total number of nearly incident points: 23
Number of Delaunay regions: 5
Number of non-simplicial Delaunay regions: 1
Statistics for: rbox 1000 s W1e-13 t1442975409 | qhull d Tv
Number of points processed: 977
Number of hyperplanes created: 12910
Number of facets in hull: 11
Number of distance tests for qhull: 4975969
Number of distance tests for merging: 553763
Number of distance tests for checking: 12000
Number of merged facets: 11701
CPU seconds to compute hull (after input): 0.453
Maximum distance of point above facet: 4.2e-014 (4.2x)
Maximum distance of vertex below facet: -4.3e-014 (4.2x)
qhull precision warning:
The initial hull is narrow (cosine of min. angle is 1.0000000000000000).
Is the input lower dimensional (e.g., on a plane in 3-d)? Qhull may
produce a wide facet. Options 'QbB' (scale to unit box) or 'Qbb' (scale
last coordinate) may remove this warning. Use 'Pp' to skip this warning.
See 'Limitations' in qh-impre.htm.
Output completed. Verifying that all points are below outer planes of
all facets. Will make 5000 distance computations.
rbox 1000 s W1e-13 t D2 | qhull d Tv
Delaunay triangulation by the convex hull of 1000 points in 3-d:
Number of input sites: 980
Total number of deleted points due to merging: 5
Total number of nearly incident points: 15
Number of Delaunay regions: 723
Number of non-simplicial Delaunay regions: 134
Statistics for: rbox 1000 s W1e-13 D2 t1442975409 | qhull d Tv
Number of points processed: 985
Number of hyperplanes created: 3790
Number of facets in hull: 1431
Number of distance tests for qhull: 119201
Number of distance tests for merging: 43040
Number of distance tests for checking: 349672
Number of merged facets: 828
CPU seconds to compute hull (after input): 0.015
Maximum distance of point above facet: 1.1e-013 (20.7x)
Maximum distance of vertex below facet: -1.5e-014 (2.7x)
qhull precision warning:
The initial hull is narrow (cosine of min. angle is 1.0000000000000000).
Is the input lower dimensional (e.g., on a plane in 3-d)? Qhull may
produce a wide facet. Options 'QbB' (scale to unit box) or 'Qbb' (scale
last coordinate) may remove this warning. Use 'Pp' to skip this warning.
See 'Limitations' in qh-impre.htm.
Output completed. Verifying that all points are below outer planes of
all facets. Will make 723000 distance computations.
echo =======================================================
=======================================================
echo =======================================================
=======================================================
echo === The following commands may cause errors ${d:-`date`}
date
=== The following commands may cause errors Tue Sep 22 22:30:09 EDT 2015
echo =======================================================
=======================================================
echo =======================================================
=======================================================
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: 32936
CPU seconds to compute hull (after input): 0.031
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-015 of the nearest facet.
rbox 100 s D3 | qhull Q0 E1e-3 Tc Po
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: 1728
CPU seconds to compute hull (after input): 0
QH6115 qhull precision error: f100 is concave to f247, since p44(v13) is 0.002232 above
QH6115 qhull precision error: f139 is concave to f274, since p90(v32) is 0.007128 above
QH6115 qhull precision error: f163 is concave to f232, since p5(v6) is 0.001226 above
QH6115 qhull precision error: f293 is concave to f389, since p11(v61) is 0.002161 above
QH6115 qhull precision error: f307 is concave to f459, since p75(v21) is 0.01537 above
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
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: 1693
CPU seconds to compute hull (after input): 0
QH6115 qhull precision error: f123 is concave to f235, since p85(v8) is 0.06092 above
QH6115 qhull precision error: f177 is concave to f272, since p98(v20) is 0.03571 above
QH6115 qhull precision error: f246 is concave to f252, since p7(v57) is 0.02104 above
QH6115 qhull precision error: f261 is concave to f305, since p82(v60) is 0.01847 above
QH6115 qhull precision error: f266 is concave to f317, since p82(v60) is 0.02592 above
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: 977
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
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: 513
Number of distance tests for qhull: 1693
CPU seconds to compute hull (after input): 0.015
QH6115 qhull precision error: f229 is concave to f300, since p90(v34) is 0.007895 above
QH6115 qhull precision error: f323 is concave to f421, since p11(v67) is 0.001894 above
QH6115 qhull precision error: f343 is concave to f493, since p75(v21) is 0.011 above
QH6115 qhull precision error: f493 is concave to f343, since p25(v97) is 0.000937 above
precision problems (corrected unless 'Q0' or an error)
14 coplanar half ridges in output
4 concave half ridges in output
9 coplanar horizon facets for new vertices
rbox 100 s D3 | qhull Q0 R1e-2 Tc Po
Convex hull of 100 points in 3-d:
Number of vertices: 87
Number of facets: 170
Statistics for: rbox 100 s D3 | qhull Q0 R1e-2 Tc Po
Number of points processed: 87
Number of hyperplanes created: 405
Number of distance tests for qhull: 1734
CPU seconds to compute hull (after input): 0
QH6136 qhull precision error: facet f326 is flipped, distance= 0.51437088552
QH6136 qhull precision error: facet f326 is flipped, distance= 0.511098236347
QH6115 qhull precision error: f76 is concave to f201, since p76(v21) is 0.0101 above
QH6115 qhull precision error: f96 is concave to f279, since p38(v22) is 0.008383 above
QH6115 qhull precision error: f132 is concave to f140, since p57(v0) is 0.02117 above
QH6115 qhull precision error: f140 is concave to f132, since p96(v34) is 0.00703 above
QH6115 qhull precision error: f150 is concave to f230, since p11(v37) is 0.04121 above
QH6115 qhull precision error: f161 is concave to f326, since p26(v32) is 0.01279 above
QH6115 qhull precision error: f194 is concave to f281, since p73(v12) is 0.03149 above
QH6115 qhull precision error: f230 is concave to f150, since p47(v52) is 0.008464 above
QH6115 qhull precision error: f263 is concave to f156, since p15(v60) is 0.01055 above
QH6115 qhull precision error: f277 is concave to f353, since p89(v36) is 0.005387 above
QH6115 qhull precision error: f281 is concave to f194, since p66(v63) is 0.005996 above
QH6115 qhull precision error: f319 is concave to f341, since p82(v70) is 0.07818 above
QH6115 qhull precision error: f324 is concave to f368, since p41(v5) is 0.01436 above
QH6113 qhull precision error: f326 is flipped(interior point is outside)
QH6115 qhull precision error: f344 is concave to f352, since p29(v75) is 0.009226 above
QH6115 qhull precision error: f348 is concave to f351, since p27(v76) is 0.008815 above
QH6115 qhull precision error: f349 is concave to f350, since p15(v60) is 0.01089 above
QH6115 qhull precision error: f352 is concave to f344, since p69(v77) is 0.008279 above
QH6115 qhull precision error: f353 is concave to f277, since p69(v77) is 0.006627 above
QH6115 qhull precision error: f385 is concave to f404, since p18(v73) is 0.007494 above
QH6115 qhull precision error: f404 is concave to f385, since p13(v87) is 0.005049 above
precision problems (corrected unless 'Q0' or an error)
45 coplanar half ridges in output
20 concave half ridges in output
1 flipped facets
47 coplanar horizon facets for new vertices
13 coplanar points during partitioning
rbox 100 s D3 | qhull Q0 R0.05 Tc
QH6136 qhull precision error: facet f160 is flipped, distance= 0.41168102504
ERRONEOUS FACET:
- f160
- flags: bottom simplicial flipped
- normal: -0.3615 -0.1924 0.9123
- offset: 0.4644952
- vertices: p94(v40) p19(v28) p56(v27)
- neighboring facets: f107 f158 f202
QH6136 qhull precision error: facet f203 is flipped, distance= 0.448767103644
ERRONEOUS FACET:
- f203
- flags: top simplicial flipped
- normal: -0.2281 0.05702 -0.972
- offset: 0.4136177
- vertices: p40(v51) p83(v19) p48(v6)
- neighboring facets: f123 f204 f205
A flipped facet occurs when its distance to the interior point is
greater than -0.024, the maximum roundoff error.
While executing: rbox 100 s D3 | qhull Q0 R0.05 Tc
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554890299 Q0-no-premerge Random_perturb 0.05 Tcheck-frequently
_max-width 0.94 Error-roundoff 0.024 Visible-distance 0.024
U-coplanar-distance 0.024 Width-outside 0.048 _wide-facet 0.15
Last point added to hull was p40.
Qhull has finished constructing the hull.
At error exit:
Convex hull of 100 points in 3-d:
Number of vertices: 51
Number of facets: 98
Statistics for: rbox 100 s D3 | qhull Q0 R0.05 Tc
Number of points processed: 51
Number of hyperplanes created: 206
Number of distance tests for qhull: 2041
CPU seconds to compute hull (after input): 0
precision problems (corrected unless 'Q0' or an error)
50 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 0.024.
- 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
Convex hull of 100 points in 3-d:
Number of vertices: 51
Number of facets: 98
Statistics for: rbox 100 s D3 | qhull Q0 R0.05 Tc Po
Number of points processed: 51
Number of hyperplanes created: 209
Number of distance tests for qhull: 2072
CPU seconds to compute hull (after input): 0
QH6136 qhull precision error: facet f105 is flipped, distance= 0.531034433025
QH6136 qhull precision error: facet f172 is flipped, distance= 0.351989788321
QH6136 qhull precision error: facet f105 is flipped, distance= 0.524438872687
QH6136 qhull precision error: facet f172 is flipped, distance= 0.311891927779
QH6115 qhull precision error: f30 is concave to f172, since p90(v11) is 0.05852 above
QH6115 qhull precision error: f41 is concave to f70, since p28(v14) is 0.03835 above
QH6115 qhull precision error: f65 is concave to f128, since p18(v19) is 0.03961 above
QH6115 qhull precision error: f77 is concave to f201, since p89(v21) is 0.03681 above
QH6115 qhull precision error: f99 is concave to f192, since p85(v8) is 0.1891 above
QH6113 qhull precision error: f105 is flipped(interior point is outside)
QH6115 qhull precision error: f143 is concave to f179, since p3(v2) is 0.0956 above
QH6115 qhull precision error: f150 is concave to f185, since p70(v13) is 0.03157 above
QH6115 qhull precision error: f161 is concave to f171, since p41(v5) is 0.07964 above
QH6115 qhull precision error: f166 is concave to f108, since p96(v41) is 0.02537 above
QH6115 qhull precision error: f169 is concave to f129, since p60(v42) is 0.02492 above
QH6113 qhull precision error: f172 is flipped(interior point is outside)
QH6115 qhull precision error: f183 is concave to f205, since p44(v37) is 0.1309 above
QH6115 qhull precision error: f186 is concave to f207, since p5(v25) is 0.1066 above
QH6115 qhull precision error: f187 is concave to f151, since p75(v47) is 0.04347 above
QH6115 qhull precision error: f199 is concave to f200, since p12(v3) is 0.08495 above
QH6115 qhull precision error: f201 is concave to f77, since p35(v50) is 0.02603 above
precision problems (corrected unless 'Q0' or an error)
61 coplanar half ridges in output
15 concave half ridges in output
2 flipped facets
44 coplanar horizon facets for new vertices
46 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: 22647
CPU seconds to compute hull (after input): 0
rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po
QH6136 qhull precision error: facet f105 is flipped, distance= 0.328228630954
QH6136 qhull precision error: facet f125 is flipped, distance= 0.389476173148
QH6136 qhull precision error: facet f152 is flipped, distance= 0.420187947128
QH6136 qhull precision error: facet f155 is flipped, distance= 0.396217639489
QH6136 qhull precision error: facet f161 is flipped, distance= 0.0543980568868
QH6136 qhull precision error: facet f164 is flipped, distance= 0.448464152152
QH6136 qhull precision error: facet f170 is flipped, distance= 0.430073300444
QH6136 qhull precision error: facet f105 is flipped, distance= 0.328228630954
QH6136 qhull precision error: facet f125 is flipped, distance= 0.389476173148
QH6136 qhull precision error: facet f152 is flipped, distance= 0.420187947128
QH6136 qhull precision error: facet f155 is flipped, distance= 0.396217639489
QH6136 qhull precision error: facet f161 is flipped, distance= 0.0543980568868
QH6136 qhull precision error: facet f164 is flipped, distance= 0.448464152152
QH6136 qhull precision error: facet f170 is flipped, distance= 0.430073300444
QH6115 qhull precision error: f25 is concave to f60, since p41(v8) is 0.1672 above
QH6115 qhull precision error: f25 is concave to f155, since p19(v2) is 0.01771 above
QH6115 qhull precision error: f38 is concave to f70, since p0(v13) is 0.06094 above
QH6115 qhull precision error: f39 is concave to f145, since p8(v11) is 0.2589 above
QH6115 qhull precision error: f45 is concave to f72, since p5(v15) is 0.02091 above
QH6115 qhull precision error: f47 is concave to f98, since p5(v15) is 0.05573 above
QH6115 qhull precision error: f47 is concave to f96, since p42(v7) is 0.05284 above
QH6115 qhull precision error: f50 is concave to f59, since p49(v16) is 0.01059 above
QH6115 qhull precision error: f54 is concave to f84, since p28(v17) is 0.03013 above
QH6115 qhull precision error: f54 is concave to f152, since p29(v1) is 0.2143 above
QH6115 qhull precision error: f59 is concave to f50, since p1(v19) is 0.01736 above
QH6115 qhull precision error: f60 is concave to f25, since p1(v19) is 0.02263 above
QH6115 qhull precision error: f62 is concave to f119, since p14(v5) is 0.02783 above
QH6115 qhull precision error: f65 is concave to f120, since p16(v10) is 0.003387 above
QH6115 qhull precision error: f70 is concave to f38, since p9(v22) is 0.04722 above
QH6115 qhull precision error: f71 is concave to f73, since p9(v22) is 0.04568 above
QH6115 qhull precision error: f72 is concave to f45, since p31(v23) is 0.02334 above
QH6115 qhull precision error: f73 is concave to f71, since p31(v23) is 0.04141 above
QH6115 qhull precision error: f78 is concave to f125, since p38(v24) is 0.01386 above
QH6115 qhull precision error: f84 is concave to f54, since p25(v26) is 0.01696 above
QH6115 qhull precision error: f87 is concave to f93, since p14(v5) is 0.01836 above
QH6115 qhull precision error: f88 is concave to f112, since p4(v27) is 0.04742 above
QH6115 qhull precision error: f91 is concave to f161, since p26(v28) is 0.3121 above
QH6115 qhull precision error: f93 is concave to f87, since p26(v28) is 0.01572 above
QH6115 qhull precision error: f96 is concave to f47, since p21(v29) is 0.02763 above
QH6115 qhull precision error: f98 is concave to f47, since p20(v30) is 0.03086 above
QH6113 qhull precision error: f105 is flipped(interior point is outside)
QH6115 qhull precision error: f106 is concave to f149, since p29(v1) is 0.0618 above
QH6115 qhull precision error: f112 is concave to f88, since p6(v34) is 0.02917 above
QH6115 qhull precision error: f119 is concave to f62, since p39(v36) is 0.006072 above
QH6115 qhull precision error: f120 is concave to f65, since p39(v36) is 0.001213 above
QH6113 qhull precision error: f125 is flipped(interior point is outside)
QH6115 qhull precision error: f134 is concave to f139, since p46(v40) is 0.07699 above
QH6115 qhull precision error: f139 is concave to f134, since p47(v41) is 0.01871 above
QH6115 qhull precision error: f141 is concave to f144, since p47(v41) is 0.1017 above
QH6115 qhull precision error: f144 is concave to f14
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: 552
CPU seconds to compute hull (after input): 0
1, since p35(v42) is 0.03263 above
QH6115 qhull precision error: f145 is concave to f39, since p2(v43) is 0.04048 above
QH6115 qhull precision error: f149 is concave to f106, since p18(v44) is 0.009672 above
QH6113 qhull precision error: f152 is flipped(interior point is outside)
QH6113 qhull precision error: f155 is flipped(interior point is outside)
QH6113 qhull precision error: f161 is flipped(interior point is outside)
QH6113 qhull precision error: f164 is flipped(interior point is outside)
QH6115 qhull precision error: f166 is concave to f170, since p16(v10) is 0.04552 above
QH6113 qhull precision error: f170 is flipped(interior point is outside)
precision problems (corrected unless 'Q0' or an error)
37 concave half ridges in output
7 flipped facets
82 coplanar horizon facets for new vertices
rbox 100 s D5 | qhull Q0 R1e-2 Tc Po
Convex hull of 100 points in 5-d:
Number of vertices: 37
Number of facets: 500
Statistics for: rbox 100 s D5 | qhull Q0 R1e-2 Tc Po
Number of points processed: 37
Number of hyperplanes created: 1198
Number of distance tests for qhull: 2764
QH6107 qhull precision error: facets f1150, f1191 and f1152 meet at a ridge with more than 2 neighbors. Can not continue.
ERRONEOUS FACET:
- f1150
- flags: top simplicial new
- normal: -0.7563 0.3207 -0.3738 0.2956 0.3133
- offset: -0.2362615
- vertices: p70(v37) p59(v25) p47(v17) p33(v15) p6(v9)
- neighboring facets: f519 f1148 f1151 f1152 f1153
ERRONEOUS OTHER FACET:
- f1191
- flags: top simplicial new
- normal: 0.7615 -0.2592 0.3014 -0.3662 -0.3577
- offset: 0.27682
- vertices: p70(v37) p59(v25) p47(v17) p6(v9) p54(v0)
- neighboring facets: f519 f1148
ERRONEOUS and NEIGHBORING FACETS to output
While executing: rbox 100 s D5 | qhull Q0 R1e-2 Tc Po
Options selected for Qhull 2015.0.3.r 2015/09/22:
run-id 554890299 Q0-no-premerge Random_perturb 0.01 Tcheck-frequently
Poutput-forced _max-width 0.88 Error-roundoff 0.0045
Visible-distance 0.0045 U-coplanar-distance 0.0045 Width-outside 0.009
_wide-facet 0.027
Last point added to hull was p70.
precision problems (corrected unless 'Q0' or an error)
50 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)
qhull
qhull- compute convex hulls and related structures. Qhull 2015.0.3.r 2015/09/22
input (stdin): dimension, n, 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
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
Fp - halfspace intersections
Fx - extreme points (convex hull vertices)
FA - compute total area and volume
o - OFF format (if 'v', outputs Voronoi regions)
G - Geomview output (2-d, 3-d and 4-d)
m - Mathematica output (2-d and 3-d)
QVn - print facets that include point n, -n if not
TO file- output results to 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 rbox c | qhull n
qhull .
Qhull 2015.0.3.r 2015/09/22.
Except for 'F.' and 'PG', upper-case options take an argument.
delaunay voronoi Geomview Halfspace facet_dump
incidences mathematica normals OFF_format points
summary
Farea FArea-total Fcoplanars FCentrums Fd-cdd-in
FD-cdd-out FF-dump-xridge Finner FIDs Fmerges
Fneighbors FNeigh-vertex Fouter FOptions Fpoint-intersect
FPoint_near FQhull Fsummary FSize Ftriangles
Fvertices Fvoronoi FVertex-ave Fxtremes FMaple
Gvertices Gpoints Gall_points Gno_planes Ginner
Gcentrums Ghyperplanes Gridges Gouter GDrop_dim
Gtransparent
PArea-keep Pdrop d0:0D0 Pgood PFacet_area_keep
PGood_neighbors PMerge-keep Poutput_forced Pprecision_not
QbBound 0:0.5 Qbk:0Bk:0_drop QbB-scale-box Qbb-scale-last Qcoplanar
Qfurthest Qgood_only QGood_point Qinterior Qmax_out
QJoggle Qrandom QRotate Qsearch_1st Qtriangulate
QupperDelaunay QVertex_good Qvneighbors Qxact_merge Qzinfinite
Q0_no_premerge Q1_no_angle 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
T4_trace Tannotate Tcheck_often Tstatistics Tverify
Tz_stdout TFacet_log TInput_file TPoint_trace TMerge_trace
TOutput_file TRerun TWide_trace TVertex_stop TCone_stop
Angle_max Centrum_size Error_round Random_dist Visible_min
Ucoplanar_max Wide_outside
qhull -
qhull- compute convex hulls and related structures.
http://www.qhull.org 2015.0.3.r 2015/09/22
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)
v - Voronoi diagram (dual of the Delaunay triangulation)
v Qu - furthest-site Voronoi diagram
Hn,n,... - halfspace intersection about point [n,n,0,...]
Qt - triangulated output
QJ - joggled input instead of merged facets
Qc - keep coplanar points with nearest facet
Qi - keep interior points with nearest facet
Qhull control options:
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)
Qf - partition point to furthest outside facet
Qg - only build good facets (needs 'QGn', 'QVn', or 'PdD')
Qm - only process points that would increase max_outside
Qr - process random outside points instead of furthest ones
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
Qv - test vertex neighbors for convexity
Qx - exact pre-merges (skips coplanar and angle-coplanar facets)
Qz - add point-at-infinity to Delaunay triangulation
QGn - good facet if visible from point n, -n for not visible
QVn - good facet if it includes point n, -n if not
Q0 - turn off default premerge with 'C-0'/'Qx'
Q1 - sort merges by type instead of angle
Q2 - merge all non-convex at once instead of 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
Topts- Trace options:
T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
Ta - annotate output with message codes
Tc - check frequently during execution
Ts - print statistics
Tv - verify result: structure, convexity, and point inclusion
Tz - send all output to stdout
TFn - report summary when n or more facets created
TI file - input data from file, no spaces or single quotes
TO file - output results to file, may be enclosed in single quotes
TPn - turn on tracing when point n added to hull
TMn - turn on tracing at merge n
TWn - trace merge facets when width > n
TRn - rerun qhull n times. Use with 'QJn'
TVn - stop qhull after adding point n, -n for before (see TCn)
TCn - stop qhull after building cone for point n (see TVn)
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)
o - OFF format (dim, points and facets; Voronoi regions)
n - normals with offsets
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 options (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
Gi - inner planes only
Gn - no planes
Go - outer planes only
Gc - centrums
Gh - hyperplane intersections
Gr - ridges
GDn - drop dimension n in 3-d and 4-d output
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
Pg - print good facets (needs 'QGn' or 'QVn')
PFn - keep facets whose area is at least n
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
rbox
-rbox- generate various point distributions. Default is random in cube.
args (any order, space separated): Version: 2015/08/30
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
Pn,m,r add point [n,m,r] first, pads with 0
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+006
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
v - Voronoi diagram via the Delaunay triangulation
H1,1 - Halfspace intersection about [1,1,0,...]
d Qu - Furthest-site Delaunay triangulation (upper convex hull)
v Qu - Furthest-site Voronoi diagram
QJ - Joggle the input to avoid precision problems
. - concise list of all options
- - one-line description of all options
Output options (subset):
FA - compute total area and volume
Fx - extreme points (convex hull vertices)
G - Geomview output (2-d, 3-d and 4-d)
Fp - halfspace intersection coordinates
m - Mathematica output (2-d and 3-d)
n - normals with offsets
o - OFF file format (if Voronoi, outputs regions)
TO file- output results to file, may be enclosed in single quotes
f - print all fields of all facets
s - summary of results (default)
Tv - verify result: structure, convexity, and point inclusion
p - vertex coordinates
i - vertices incident to each facet
example:
rbox 1000 s | qhull Tv s FA
- html manual: 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>
- mirror: <http://www6.uniovi.es/ftp/pub/mirrors/geom.umn.edu/software/ghindex.html>
- news: <http://www.qhull.org/news>
- Geomview: <http://www.geomview.org>
- news group: <news:comp.graphics.algorithms>
- FAQ: <http://exaflop.org/docs/cgafaq/cga6.html>
- 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 (qh-
man.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' by itself. 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 for other output for-
mats ('F'), Geomview output ('G'), printing ('P'), Qhull
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qhull(1) qhull(1)
control ('Q'), 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
Geometry Center 2003/12/30 4
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 out 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'.
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
Geometry Center 2003/12/30 5
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 at all, 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
Geometry Center 2003/12/30 6
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.
Geometry Center 2003/12/30 7
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
Geometry Center 2003/12/30 8
qhull(1) qhull(1)
last float is the offset. The hyperplane is ori-
ented toward verify that the hyperplanes are per-
pendicular 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 verify that the hyperplanes are per-
pendicular 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
Geometry Center 2003/12/30 9
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
Geometry Center 2003/12/30 10
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
Geometry Center 2003/12/30 11
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 'PAn' and
'PFn'.
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
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.
Geometry Center 2003/12/30 13
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.
Geometry Center 2003/12/30 14
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.
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 sorts merges by type (coplanar,
angle coplanar, concave) instead of by angle.
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.
Geometry Center 2003/12/30 15
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.
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.
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'.
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.
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.
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
Geometry Center 2003/12/30 16
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'
TMn Turn on tracing at n'th merge.
TWn Trace merge facets when the width is greater than
n.
Tz Redirect stderr to stdout.
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 2003/12/30 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
Geometry Center 2003/12/30 18
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 2003/12/30 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
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
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