08-Jan-2022 09:49:30 sphere_voronoi_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test sphere_voronoi(). SPHERE_VORONOI_TEST01 Demonstrate the computation of a Voronoi diagram on a sphere. Delaunay points: Row: 1 2 3 Col 1: 0.181717 0.619803 -0.763429 2: 0.539385 0.199423 -0.818104 3: -0.11975 0.0946263 0.988284 4: 0.640382 -0.312137 0.701771 5: 0.71096 -0.0617994 0.700511 6: -0.135843 -0.0822776 0.987308 7: 0.668343 0.672212 0.318509 8: -0.561159 0.333325 0.757625 9: 0.360616 0.763207 0.536163 10: -0.339629 0.328918 -0.881173 Delaunay vertices: Row: 1 2 3 Col 1: 1 2 10 2: 1 7 2 3: 1 8 9 4: 1 9 7 5: 1 10 8 6: 2 4 10 7: 2 5 4 8: 2 7 5 9: 3 5 9 10: 3 6 5 11: 3 8 6 12: 3 9 8 13: 4 5 6 14: 4 6 10 15: 5 7 9 16: 6 8 10 Delaunay neighbors: Row: 1 2 3 Col 1: 6 5 2 2: 8 1 4 3: 12 4 5 4: 15 2 3 5: 16 3 1 6: 14 1 7 7: 13 6 8 8: 15 7 2 9: 15 12 10 10: 13 9 11 11: 16 10 12 12: 3 11 9 13: 10 14 7 14: 16 6 13 15: 4 9 8 16: 5 14 11 Voronoi vertices Row: 1 2 3 Col 1: 0.101023 0.212366 -0.971954 2: 0.693123 0.634266 -0.342472 3: -0.43025 0.901811 -0.0402833 4: 0.192802 0.972072 -0.133805 5: -0.474662 0.877651 -0.0665241 6: -0.116778 -0.943592 -0.309834 7: 0.950844 -0.268849 -0.153673 8: 0.993662-0.000805457 -0.112404 9: 0.363787 0.328148 0.871767 10: 0.32134 -0.0344549 0.946337 11: -0.447568 0.0357843 0.893534 12: -0.089694 0.60134 0.793943 13: 0.321461 -0.0858872 0.94302 14: -0.336022 -0.926872 -0.167328 15: 0.605498 0.394787 0.691025 16: -0.671203 -0.735941 -0.0887535 Voronoi orders: 1: 5 2: 5 3: 4 4: 4 5: 6 6: 5 7: 4 8: 5 9: 5 10: 5 Voronoi polygons: 1: 1 5 3 4 2 2: 1 2 8 7 6 3: 9 12 11 10 4: 6 7 13 14 5: 7 8 15 9 10 13 6: 10 11 16 14 13 7: 2 4 15 8 8: 3 5 16 11 12 9: 3 12 9 15 4 10: 1 6 14 16 5 Voronoi areas: 1: 0.880247 2: 1.82296 3: 0.359304 4: 1.6915 5: 0.636028 6: 1.20421 7: 0.83291 8: 1.82831 9: 0.882838 10: 2.42806 Voronoi centroids Row: 1 2 3 Col 1: 0.12417 0.813877 -0.567615 2: 0.641061 -0.222017 -0.734676 3: -0.00302147 0.24791 0.968778 4: 0.530957 -0.775302 0.342041 5: 0.828459 0.0337872 0.559029 6: -0.346153 -0.590196 0.729278 7: 0.778243 0.617594 0.113645 8: -0.825555 0.298393 0.478979 9: 0.131765 0.873699 0.468282 10: -0.648783 -0.0390903 -0.759969 SPHERE_VORONOI_TEST02 Choose random points on the unit sphere. Call SPHERE_DELAUNAY to compute the Delaunay triangulation. Display an image of the Delaunay triangulation. Delaunay points: Row: 1 2 3 Col 1: 0.492983 -0.636525 -0.593131 2: -0.239826 -0.872288 0.426142 3: 0.203507 -0.472441 0.857545 4: -0.988468 -0.059049 -0.139445 5: 0.327881 0.32136 -0.888382 6: -0.0462544 -0.253779 0.966156 7: 0.613883 0.622871 -0.484952 8: 0.0469063 -0.736174 -0.675165 9: -0.00399367 0.893637 -0.448772 10: 0.309773 -0.188164 0.932006 11: -0.891476 0.0266506 0.452283 12: 0.579805 0.813496 0.0452688 13: -0.755024 -0.375744 -0.537359 14: 0.924544 -0.242145 0.294253 15: -0.161951 0.747908 -0.643743 16: -0.68198 -0.691759 0.237428 17: -0.122859 -0.135797 0.983089 18: 0.17929 0.121631 0.976248 19: -0.594707 0.514984 0.617345 20: -0.201349 0.178179 -0.963178 21: -0.84389 0.0770961 0.530948 22: 0.965933 -0.249149 0.0699864 23: -0.0415808 -0.974328 -0.221258 24: -0.826444 0.38699 -0.408936 25: 0.158527 -0.862427 0.480717 26: -0.560511 0.457469 0.690326 27: 0.623399 -0.0706918 -0.778701 28: -0.437111 0.705236 -0.558191 29: 0.554537 0.0715854 0.829074 30: -0.848318 -0.0855275 -0.522534 31: 0.875245 0.248372 0.415039 32: -0.890018 -0.394145 -0.229169 33: 0.824252 -0.208514 0.526433 34: -0.916368 -0.158034 -0.367825 35: -0.938348 0.302245 0.16778 36: 0.0191672 -0.76353 0.645488 37: 0.759485 -0.648628 0.0496444 38: -0.146152 -0.976344 -0.159348 39: -0.481011 -0.566547 -0.669069 40: -0.23342 -0.876113 0.421831 41: 0.997037 -0.0383965 -0.0666616 42: -0.613513 0.783018 -0.102398 43: -0.462451 0.87463 -0.145474 44: -0.548742 -0.273662 -0.789931 45: -0.347738 0.784183 0.513941 46: 0.19753 -0.807446 -0.555889 47: -0.113206 0.507512 -0.854176 48: -0.84295 -0.524286 0.120665 49: 0.639807 0.738431 -0.212997 50: 0.183364 -0.475311 0.860498 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: -0.69301 -0.288366 -0.660743 2: -0.903711 0.416022 -0.101153 3: 0.328048 0.409114 -0.851476 4: 0.0560681 0.751795 -0.657009 5: -0.446687 0.811728 -0.376256 6: -0.963429 0.198869 -0.179599 7: -0.735347 0.228658 0.63795 8: 0.674256 -0.595232 0.437125 9: -0.15647 -0.786809 0.597033 10: 0.616525 0.029525 0.786781 11: -0.322862 0.732219 0.599679 12: -0.135618 0.772128 0.620827 13: -0.0901925 -0.817105 0.569389 14: -0.529491 0.832741 0.161809 15: -0.818271 0.330996 0.469973 16: 0.0834397 0.99651 0.00230801 Voronoi polygons: 1: 1 6 2 5 4 3 2: 7 9 13 8 10 12 11 3: 7 11 14 15 4: 1 3 8 13 5: 2 6 9 7 15 6: 3 4 16 10 8 7: 4 5 14 11 12 16 8: 2 15 14 5 9: 10 16 12 10: 1 13 9 6 Voronoi areas, method 1: 1: 1.25065 2: 1.94552 3: 0.234595 4: 3.45477 5: 0.801443 6: 2.5382 7: 0.622802 8: 0.350457 9: 0.463612 10: 0.90433 Voronoi areas, method 2: 1: 1.25065 2: 1.94552 3: 0.234595 4: 3.45477 5: 0.801443 6: 2.5382 7: 0.622802 8: 0.350457 9: 0.463612 10: 0.90433 Voronoi centroids, method 1 Row: 1 2 3 Col 1: -0.540311 0.408805 -0.735488 2: -0.00230367 -0.12518 0.992131 3: -0.619318 0.611673 0.492242 4: 0.201042 -0.768248 -0.607764 5: -0.895274 -0.10625 0.432661 6: 0.850705 0.524732 -0.0309331 7: -0.22948 0.97315 -0.0178223 8: -0.752106 0.657546 0.044388 9: 0.259683 0.757987 0.598348 10: -0.867097 -0.493599 -0.0671042 Voronoi centroids, method 2 Row: 1 2 3 Col 1: -0.550061 0.410096 -0.727499 2: -0.0935589 0.000882739 0.995613 3: -0.619577 0.61108 0.492651 4: 0.167847 -0.758791 -0.629335 5: -0.894407 -0.108331 0.433936 6: 0.842301 0.538121 -0.0308847 7: -0.234515 0.972097 -0.00542371 8: -0.752126 0.657565 0.0437708 9: 0.264175 0.75198 0.603935 10: -0.861941 -0.503863 -0.0563925 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. 08-Jan-2022 09:49:33