10-May-2023 13:41:16 sphere_voronoi_test(): MATLAB/Octave version 5.2.0 Test sphere_voronoi(). sphere_voronoi_test01(): Demonstrate the computation of a Voronoi diagram on a sphere. Delaunay points: Row: 1 2 3 Col 1: 0.743604 0.369576 -0.557195 2: -0.910994 0.400919 0.0967152 3: -0.0992306 -0.992514 0.0712027 4: -0.866583 -0.351559 -0.354176 5: -0.405469 -0.895463 -0.183687 6: 0.221787 0.975091 -0.00290325 7: 0.951083 -0.241821 -0.192259 8: -0.832756 0.417081 0.364089 9: -0.555997 -0.0276888 -0.830723 10: 0.314512 0.637293 -0.70352 Delaunay vertices: Row: 1 2 3 Col 1: 1 6 7 2: 1 7 9 3: 1 9 10 4: 1 10 6 5: 2 4 8 6: 2 6 10 7: 2 8 6 8: 2 9 4 9: 2 10 9 10: 3 5 7 11: 3 7 8 12: 3 8 5 13: 4 5 8 14: 4 9 5 15: 5 9 7 16: 6 8 7 Delaunay neighbors: Row: 1 2 3 Col 1: 16 2 4 2: 15 3 1 3: 9 4 2 4: 6 1 3 5: 13 7 8 6: 4 9 7 7: 16 6 5 8: 14 5 9 9: 3 8 6 10: 15 11 12 11: 16 12 10 12: 13 10 11 13: 12 5 14 14: 15 13 8 15: 2 10 14 16: 11 1 7 Voronoi vertices Row: 1 2 3 Col 1: 0.840082 0.458305 0.290206 2: 0.306012 -0.409231 -0.859585 3: 0.243389 -0.13488 -0.960505 4: 0.575957 0.763578 -0.291928 5: -0.93106 -0.226401 0.286128 6: -0.436947 0.786247 -0.436913 7: -0.445431 0.892049 0.0764201 8: -0.878002 0.206836 -0.431662 9: -0.472807 0.716937 -0.512304 10: 0.325758 -0.68462 -0.652056 11: 0.279077 -0.0539836 0.95875 12: -0.649072 -0.463157 0.603482 13: -0.725515 -0.452564 0.518472 14: -0.437614 -0.585033 -0.682811 15: 0.259055 -0.548066 -0.795307 16: 0.31035 0.0381927 0.949855 Voronoi orders: 1: 4 2: 5 3: 3 4: 4 5: 5 6: 5 7: 6 8: 6 9: 6 10: 4 Voronoi polygons: 1: 1 2 3 4 2: 5 7 6 9 8 3: 10 11 12 4: 5 8 14 13 5: 10 12 13 14 15 6: 1 4 6 7 16 7: 1 16 11 10 15 2 8: 5 13 12 11 16 7 9: 2 15 14 8 9 3 10: 3 9 6 4 Voronoi areas: 1: 0.859905 2: 0.746465 3: 1.77463 4: 0.758168 5: 0.860575 6: 1.7809 7: 2.03345 8: 1.68732 9: 1.21603 10: 0.848917 Voronoi centroids Row: 1 2 3 Col 1: 0.771726 0.296987 -0.562349 2: -0.865093 0.488067 -0.115779 3: 0.0394756 -0.91119 0.410091 4: -0.904122 -0.363722 -0.224207 5: -0.395094 -0.865919 -0.306731 6: 0.26678 0.913844 0.306133 7: 0.94966 -0.307918 0.0577287 8: -0.580028 0.267101 0.769562 9: -0.398334 -0.0259255 -0.916874 10: 0.144899 0.617924 -0.77277 sphere_voronoi_test02(): Choose random points on the unit sphere. sphere_delaunay() computes the Delaunay triangulation. Display an image of the Delaunay triangulation. Delaunay points: Row: 1 2 3 Col 1: -0.891045 -0.273127 0.362547 2: -0.0176158 0.453007 0.891333 3: 0.142496 0.338918 -0.929962 4: -0.175716 -0.0892719 -0.980385 5: -0.621644 0.782308 0.0394075 6: -0.0156532 -0.568152 -0.822775 7: -0.144548 0.989199 0.024327 8: -0.265058 0.153323 -0.951965 9: -0.891443 -0.157533 -0.424867 10: 0.249941 0.730979 -0.634979 11: -0.642245 -0.75237 0.146493 12: 0.730948 0.587209 0.347707 13: 0.863996 -0.500831 -0.0517557 14: -0.450734 -0.186077 -0.873049 15: 0.735987 -0.303123 -0.605342 16: -0.440315 -0.569349 -0.694237 17: 0.494531 0.340126 -0.799846 18: 0.835735 0.302188 -0.458507 19: 0.38643 -0.921108 -0.047239 20: -0.994685 0.0329508 -0.0975513 21: 0.00877262 0.999928 0.00816156 22: -0.762822 -0.373109 -0.528102 23: 0.824692 0.483384 0.293637 24: 0.0486099 -0.952381 -0.30101 25: 0.419384 0.497143 -0.759582 26: 0.575584 -0.785614 0.226968 27: 0.152615 -0.264749 0.952164 28: 0.507314 -0.0947638 -0.856535 29: -0.387147 0.432792 0.814131 30: 0.679022 -0.685472 0.262788 31: 0.899653 -0.208397 0.383659 32: 0.701113 0.590858 0.399159 33: -0.991861 0.0533044 0.115633 34: -0.582901 0.412886 -0.699823 35: -0.850158 0.251434 0.462615 36: 0.120724 -0.709356 -0.694435 37: 0.684612 0.0860418 0.723811 38: 0.829264 0.558344 -0.0239624 39: -0.662693 0.0620189 0.746319 40: -0.342585 0.182882 0.921515 41: 0.97727 -0.207558 -0.0431521 42: 0.736968 0.281724 -0.614418 43: 0.501132 0.494372 -0.710256 44: -0.836924 0.398905 0.374744 45: 0.711717 0.216456 -0.668285 46: 0.321811 0.799863 0.506613 47: 0.054696 -0.941602 -0.332255 48: 0.9469 -0.30366 0.105688 49: -0.199639 -0.794055 0.574127 50: -0.54993 0.67258 0.49519 Figure 1: Voronoi polygons using PATCH. sphere_voronoi_test03(): For a Voronoi diagram on a sphere, compute the area of each Voronoi polygon two ways and compare the results: 1: by building the polygons from triangles, the computing areas; 2: by dividing each triangle among the Voronoi centers. Voronoi vertices Row: 1 2 3 Col 1: -0.155295 0.535026 0.83044 2: 0.0434185 -0.00441397 0.999047 3: 0.752371 -0.111988 0.649151 4: 0.988291 0.102695 0.112849 5: 0.232824 -0.150337 0.960829 6: 0.721534 0.656644 -0.219561 7: -0.191589 0.580959 0.791063 8: 0.994481 0.104625 -0.00776241 9: -0.575119 -0.746815 0.333926 10: -0.816988 0.2143 -0.535356 11: -0.658007 0.20718 -0.72395 12: 0.606068 -0.690523 -0.394791 13: 0.998581 0.0135285 -0.0515 14: 0.338399 -0.91742 0.209351 15: 0.709455 -0.488086 0.508376 16: 0.350852 -0.899769 0.259458 Voronoi polygons: 1: 1 2 5 3 4 2: 1 4 8 6 7 3: 1 7 10 9 2 4: 6 8 13 12 11 5: 9 10 11 12 14 6: 3 5 16 15 7: 6 11 10 7 8: 12 13 15 16 14 9: 3 15 13 8 4 10: 2 9 14 16 5 Voronoi areas, method 1: 1: 0.729672 2: 0.79669 3: 2.12427 4: 2.28564 5: 2.31224 6: 0.376363 7: 2.25484 8: 0.651242 9: 0.217982 10: 0.817429 Voronoi areas, method 2: 1: 0.729672 2: 0.79669 3: 2.12427 4: 2.28564 5: 2.31224 6: 0.376363 7: 2.25484 8: 0.651242 9: 0.217982 10: 0.817429 Voronoi centroids, method 1 Row: 1 2 3 Col 1: 0.510392 0.206329 0.834822 2: 0.673192 0.626413 0.392961 3: -0.811003 0.00624772 0.585008 4: 0.552161 0.0929939 -0.828535 5: -0.351657 -0.826869 -0.438891 6: 0.533456 -0.474969 0.699878 7: -0.189697 0.976527 -0.102032 8: 0.798132 -0.598528 0.0689129 9: 0.920372 -0.158258 0.357588 10: -0.033568 -0.693938 0.719252 Voronoi centroids, method 2 Row: 1 2 3 Col 1: 0.507704 0.207622 0.83614 2: 0.668588 0.630413 0.394423 3: -0.817824 0.0151207 0.57527 4: 0.52483 0.0921313 -0.846206 5: -0.357346 -0.815374 -0.455488 6: 0.530359 -0.475638 0.701774 7: -0.214703 0.96965 -0.11697 8: 0.797612 -0.599719 0.0644342 9: 0.919429 -0.159485 0.359464 10: -0.0337003 -0.693615 0.719558 sphere_voronoi_test04(): Compute the area of each Voronoi polygon on a sphere. Number of faces = 64 Faces: Row: 1 2 3 Col 1: 1 2 3 2: 1 3 4 3: 1 4 5 4: 1 5 6 5: 1 6 7 6: 1 7 2 7: 2 7 8 8: 2 8 9 9: 2 9 3 10: 3 9 10 11: 3 10 11 12: 3 11 4 13: 4 11 12 14: 4 12 13 15: 4 13 5 16: 5 13 14 17: 5 14 15 18: 5 15 6 19: 6 15 16 20: 6 16 7 21: 7 16 17 22: 7 17 8 23: 8 17 27 24: 8 18 9 25: 8 27 18 26: 9 18 19 27: 9 19 10 28: 10 19 20 29: 10 20 11 30: 11 20 21 31: 11 21 12 32: 12 21 22 33: 12 22 13 34: 13 22 23 35: 13 23 14 36: 14 23 24 37: 14 24 15 38: 15 24 25 39: 15 25 16 40: 16 25 26 41: 16 26 17 42: 17 26 27 43: 18 27 33 44: 18 28 19 45: 18 33 28 46: 19 28 20 47: 20 28 29 48: 20 29 21 49: 21 29 30 50: 21 30 22 51: 22 30 23 52: 23 30 31 53: 23 31 24 54: 24 31 25 55: 25 31 32 56: 25 32 26 57: 26 32 27 58: 27 32 33 59: 28 33 34 60: 28 34 29 61: 29 34 30 62: 30 34 31 63: 31 34 32 64: 32 34 33 Voronoi vertices: Row: 1 2 3 Col 1: 0 0.351275 0.936272 2: -0.304213 0.175638 0.936272 3: -0.304213 -0.175638 0.936272 4: 0 -0.351275 0.936272 5: 0.304213 -0.175638 0.936272 6: 0.304213 0.175638 0.936272 7: 0.652197 0.376546 0.657915 8: 0.4951 0.681447 0.538986 9: 0 0.784322 0.620354 10: 0 0.784322 0.620354 11: -0.4951 0.681447 0.538986 12: -0.652197 0.376546 0.657915 13: -0.782436 0.254229 0.568473 14: -0.782436 -0.254229 0.568473 15: -0.652197 -0.376546 0.657915 16: -0.4951 -0.681447 0.538986 17: 0 -0.784322 0.620354 18: 0 -0.784322 0.620354 19: 0.4951 -0.681447 0.538986 20: 0.652197 -0.376546 0.657915 21: 0.782436 -0.254229 0.568473 22: 0.782436 0.254229 0.568473 23: 0.94837 0.308144 0.0751036 24: 0.586125 0.806732 0.0751036 25: 0.806732 0.586125 -0.0751036 26: 0.308144 0.94837 -0.0751036 27: 0 0.997176 0.0751036 28: -0.308144 0.94837 -0.0751036 29: -0.586125 0.806732 0.0751036 30: -0.806732 0.586125 -0.0751036 31: -0.94837 0.308144 0.0751036 32: -0.997176 0 -0.0751036 33: -0.94837 -0.308144 0.0751036 34: -0.806732 -0.586125 -0.0751036 Voronoi polygons: 1: 1 2 3 4 5 6 2: 1 6 7 8 9 3: 1 9 10 11 12 2 4: 2 12 13 14 15 3 5: 3 15 16 17 18 4 6: 4 18 19 20 5 7: 5 20 21 22 7 6 8: 7 22 23 25 24 8 9: 8 24 26 27 10 9 10: 10 27 28 29 11 11: 11 29 30 31 13 12 12: 13 31 32 33 14 13: 14 33 34 35 16 15 14: 16 35 36 37 17 15: 17 37 38 39 19 18 16: 19 39 40 41 21 20 17: 21 41 42 23 22 18: 24 25 43 45 44 26 19: 26 44 46 28 27 20: 28 46 47 48 30 29 21: 30 48 49 50 32 31 22: 32 50 51 34 33 23: 34 51 52 53 36 35 24: 36 53 54 38 37 25: 38 54 55 56 40 39 26: 40 56 57 42 41 27: 23 42 57 58 43 25 28: 44 45 59 60 47 46 29: 47 60 61 49 48 30: 49 61 62 52 51 50 31: 52 62 63 55 54 53 32: 55 63 64 58 57 56 33: 43 58 64 59 45 34: 59 64 63 62 61 60 Voronoi areas: 1: 0.336412 2: 0.363447 3: 0.363447 4: 0.367562 5: 0.363447 6: 0.363447 7: 0.367562 8: 0.383575 9: 0.373241 10: 0.373241 11: 0.383575 12: 0.365299 13: 0.383575 14: 0.373241 15: 0.373241 16: 0.383575 17: 0.365299 18: 0.383575 19: 0.365299 20: 0.383575 21: 0.373241 22: 0.373241 23: 0.383575 24: 0.365299 25: 0.383575 26: 0.373241 27: 0.373241 28: 0.367562 29: 0.363447 30: 0.363447 31: 0.367562 32: 0.363447 33: 0.363447 34: 0.336412 sphere_voronoi_test(): Normal end of execution. 10-May-2023 13:41:17