08-Oct-2025 16:36:10 sphere_delaunay_test(): MATLAB/Octave version 6.4.0 Test sphere_delaunay(). sphere_delaunay_test01(): Choose random points on the unit sphere. sphere_delaunay() computes the Delaunay triangulation. triangulation_neighbor_triangles() gets triangle neighbors. stri_vertices_to_areas() gets triangle areas. Data points: Row: 1 2 3 Col 1: 0.0787683 -0.399745 0.913236 2: -0.747388 0.0191685 -0.664111 3: -0.142516 0.926992 -0.346952 4: -0.966889 -0.204627 -0.152489 5: -0.0313897 -0.255766 0.966229 6: -0.217893 0.243603 -0.945082 7: -0.286848 0.951394 -0.112102 8: -0.74948 -0.304989 0.587589 9: 0.666288 -0.337167 -0.665115 10: -0.502858 0.856506 -0.116321 Check Euler's formula on a sphere: Faces = 16 Vertices = 10 Edges = 24 F+V-E-2 = 0 Delaunay triangles Row: 1 2 3 Col 1: 1 3 5 2: 1 5 8 3: 1 8 9 4: 1 9 3 5: 2 4 10 6: 2 6 9 7: 2 9 4 8: 2 10 6 9: 3 6 10 10: 3 7 5 11: 3 9 6 12: 3 10 7 13: 4 8 10 14: 4 9 8 15: 5 7 10 16: 5 10 8 Triangle neighbors Row: 1 2 3 Col 1: 10 2 4 2: 16 3 1 3: 14 4 2 4: 11 1 3 5: 13 8 7 6: 11 7 8 7: 14 5 6 8: 9 6 5 9: 8 12 11 10: 15 1 12 11: 6 9 4 12: 15 10 9 13: 16 5 14 14: 3 13 7 15: 12 16 10 16: 13 2 15 Spherical area of triangles 1: 0.178444 2: 0.0781948 3: 1.79353 4: 4.30857 5: 0.379043 6: 0.373714 7: 0.582314 8: 0.390529 9: 0.223786 10: 0.184875 11: 0.659019 12: 0.0298596 13: 0.609219 14: 1.56853 15: 0.330997 16: 0.875749 Area sum = 12.566371 4 * PI = 12.566371 sphere_delaunay_test02() Choose random points on the unit sphere. sphere_delaunay() computes the Delaunay triangulation. Display an image of the Delaunay triangulation. Data points: Row: 1 2 3 Col 1: 0.416755 0.767492 -0.487106 2: -0.462725 0.549813 0.695407 3: -0.916617 0.354317 0.185129 4: -0.0706621 0.663134 -0.745158 5: -0.724828 -0.162786 0.669422 6: 0.825536 -0.563954 0.0211199 7: -0.531709 -0.764882 0.363649 8: -0.801806 -0.154618 -0.577235 9: 0.43195 0.879132 -0.201358 10: -0.767248 0.510155 0.38868 11: 0.589095 0.648835 -0.481643 12: 0.0702073 -0.986184 0.150038 13: -0.976292 0.214158 -0.0314526 14: 0.831599 -0.332371 -0.444941 15: 0.0626927 -0.934088 0.351497 16: -0.690096 -0.0340435 0.722917 17: -0.902448 0.38324 0.196759 18: -0.406583 -0.878882 -0.249514 19: 0.658441 -0.377711 0.650991 20: -0.412732 -0.427037 -0.804544 21: -0.87207 0.379831 -0.308582 22: 0.390105 -0.0863012 0.916717 23: -0.306845 0.846189 -0.435673 24: 0.321283 0.733925 -0.59844 25: 0.613737 0.0521795 -0.787784 26: 0.800334 0.554126 -0.22893 27: 0.495201 -0.629054 0.599222 28: -0.786586 0.488336 0.377901 29: -0.133379 -0.0906589 0.98691 30: -0.781398 -0.138776 -0.608407 31: -0.970549 0.0733549 0.229464 32: 0.132807 0.968951 0.208559 33: 0.463307 0.725731 0.508587 34: 0.174329 -0.356787 0.917776 35: 0.454817 -0.219756 -0.863046 36: -0.933685 0.0746606 -0.350226 37: 0.36887 0.927634 0.058572 38: 0.235888 0.499639 0.833497 39: 0.131635 -0.164877 -0.977491 40: 0.114849 0.651519 0.749888 41: -0.887356 0.412028 -0.20696 42: -0.932109 -0.0640112 0.356477 43: 0.425331 -0.0514315 0.903575 44: 0.859306 -0.511166 -0.0173765 45: 0.184259 0.973687 -0.1341 46: -0.620201 -0.76916 0.15409 47: 0.975198 0.147454 0.165065 48: 0.488822 -0.872043 0.0243854 49: -0.394739 0.0297487 -0.918311 50: 0.788697 0.537553 -0.298318 51: 0.367807 0.893438 0.257851 52: 0.375247 -0.715883 -0.588813 53: 0.448859 -0.188943 -0.873399 54: -0.164216 0.93597 0.311436 55: 0.435167 0.875991 0.208015 56: 0.3488 -0.872959 0.341001 57: -0.960329 -0.254239 0.114587 58: -0.815393 -0.382377 -0.434652 59: -0.559266 -0.713467 0.422122 60: 0.712737 0.155321 0.684018 61: -0.264773 -0.96431 0.0013623 62: -0.802645 -0.594326 0.0503772 63: -0.0265496 0.887072 0.460867 64: 0.470709 -0.81115 0.347087 65: -0.759729 -0.484903 0.433222 66: -0.173872 -0.0692692 -0.982329 67: 0.258541 -0.0402202 -0.965163 68: 0.823986 0.420198 0.380107 69: 0.0815193 0.695053 -0.714322 70: 0.82973 0.0229319 0.557694 71: 0.0499502 -0.566748 0.822376 72: 0.373816 0.186238 0.908613 73: -0.476323 0.293563 -0.828817 74: 0.34368 0.810462 0.474379 75: -0.533192 0.696664 -0.479964 76: 0.387524 -0.62609 0.676636 77: 0.801127 0.583494 -0.133152 78: 0.311079 -0.892996 0.32525 79: 0.369241 0.38199 0.847198 80: -0.156242 -0.278224 0.947723 81: 0.399647 0.849361 -0.344773 82: -0.907745 0.345517 -0.237943 83: -0.985306 0.0235225 -0.169171 84: -0.296625 0.0158196 0.954863 85: 0.96644 -0.0610192 0.249541 86: -0.116148 -0.944752 0.306519 87: 0.628263 -0.23916 -0.74033 88: -0.441003 0.666705 0.60085 89: 0.861265 -0.161101 -0.481943 90: -0.674344 -0.730616 0.107048 91: 0.0544137 -0.784573 -0.617645 92: 0.0451758 0.739938 0.671157 93: -0.143273 -0.980312 -0.135874 94: -0.551032 -0.242181 -0.798569 95: -0.532362 0.811265 0.241745 96: 0.691751 -0.656133 -0.301612 97: 0.596194 0.798304 0.0852266 98: -0.496046 -0.592448 -0.634779 99: -0.267983 0.428145 0.863063 100: 0.982891 -0.0158546 0.183506 Figure 1: Delaunay triangulation with TRISURF Graphics saved as "test02_plot1.png". Graphics saved as "test02_plot2.png". Figure 2: Delaunay triangulation with PATCH. sphere_delaunay_test03(): sphere_gridpoints_icos2() chooses points on the unit sphere. sphere_delaunay() computes the Delaunay triangulation. Display an image of the Delaunay triangulation. Data points: Row: 1 2 3 Col 1: 0.850651 0.525731 0 2: 0.850651 -0.525731 0 3: 0.525731 0 0.850651 4: 0.525731 0 -0.850651 5: 0 0.850651 0.525731 6: 0 0.850651 -0.525731 7: 0 -0.850651 0.525731 8: 0 -0.850651 -0.525731 9: -0.525731 0 0.850651 10: -0.525731 0 -0.850651 11: -0.850651 0.525731 0 12: -0.850651 -0.525731 0 13: 1 3.33067e-16 0 14: 0.809017 0.309017 0.5 15: 0.809017 0.309017 -0.5 16: 0.5 0.809017 0.309017 17: 0.5 0.809017 -0.309017 18: 0.809017 -0.309017 0.5 19: 0.809017 -0.309017 -0.5 20: 0.5 -0.809017 0.309017 21: 0.5 -0.809017 -0.309017 22: 0.309017 0.5 0.809017 23: 0.309017 -0.5 0.809017 24: 5.55112e-17 0 1 25: 0.309017 0.5 -0.809017 26: 0.309017 -0.5 -0.809017 27: 5.55112e-17 0 -1 28: 0 1-5.55112e-17 29: -0.309017 0.5 0.809017 30: -0.5 0.809017 0.309017 31: -0.309017 0.5 -0.809017 32: -0.5 0.809017 -0.309017 33: 0 -1-5.55112e-17 34: -0.309017 -0.5 0.809017 35: -0.5 -0.809017 0.309017 36: -0.309017 -0.5 -0.809017 37: -0.5 -0.809017 -0.309017 38: -0.809017 0.309017 0.5 39: -0.809017 -0.309017 0.5 40: -0.809017 0.309017 -0.5 41: -0.809017 -0.309017 -0.5 42: -1-5.55112e-17 0 Triangles Row: 1 2 3 Col 1: 1 13 15 2: 1 14 13 3: 1 15 17 4: 1 16 14 5: 1 17 16 6: 2 13 18 7: 2 18 20 8: 2 19 13 9: 2 20 21 10: 2 21 19 11: 3 14 22 12: 3 18 14 13: 3 22 24 14: 3 23 18 15: 3 24 23 16: 4 15 19 17: 4 19 26 18: 4 25 15 19: 4 26 27 20: 4 27 25 21: 5 16 28 22: 5 22 16 23: 5 28 30 24: 5 29 22 25: 5 30 29 26: 6 17 25 27: 6 25 31 28: 6 28 17 29: 6 31 32 30: 6 32 28 31: 7 20 23 32: 7 23 34 33: 7 33 20 34: 7 34 35 35: 7 35 33 36: 8 21 33 37: 8 26 21 38: 8 33 37 39: 8 36 26 40: 8 37 36 41: 9 24 29 42: 9 29 38 43: 9 34 24 44: 9 38 39 45: 9 39 34 46: 10 27 36 47: 10 31 27 48: 10 36 41 49: 10 40 31 50: 10 41 40 51: 11 30 32 52: 11 32 40 53: 11 38 30 54: 11 40 42 55: 11 42 38 56: 12 35 39 57: 12 37 35 58: 12 39 42 59: 12 41 37 60: 12 42 41 61: 13 14 18 62: 13 19 15 63: 14 16 22 64: 15 25 17 65: 16 17 28 66: 18 23 20 67: 19 21 26 68: 20 33 21 69: 22 29 24 70: 23 24 34 71: 25 27 31 72: 26 36 27 73: 28 32 30 74: 29 30 38 75: 31 40 32 76: 33 35 37 77: 34 39 35 78: 36 37 41 79: 38 42 39 80: 40 41 42 Figure 1: Delaunay triangulation with TRISURF Graphics saved as "test03_plot1.png". Graphics saved as "test03_plot2.png". Figure 2: Delaunay triangulation with PATCH. sphere_delaunay_test(): Normal end of execution. 08-Oct-2025 16:36:14