27-Mar-2019 09:39:36 sphere_voronoi_test MATLAB version: Test sphere_voronoi. SPHERE_VORONOI_TEST01 Demonstrate the computation of a Voronoi diagram on a sphere. Delaunay points: Row: 1 2 3 Col 1: 0.915568 -0.257797 -0.308668 2: -0.171751 0.901345 0.397592 3: 0.541822 0.447986 -0.711152 4: -0.620052 -0.745456 0.244603 5: 0.026281 -0.894727 0.445840 6: 0.016716 -0.591520 0.806117 7: 0.987108 0.084661 0.135834 8: -0.220974 0.974193 0.046018 9: 0.679580 -0.416543 -0.603873 10: 0.936980 -0.037537 0.347361 Delaunay vertices: Row: 1 2 3 Col 1: 1 3 7 2: 1 5 9 3: 1 7 10 4: 1 9 3 5: 1 10 5 6: 2 4 6 7: 2 6 10 8: 2 7 8 9: 2 8 4 10: 2 10 7 11: 3 4 8 12: 3 8 7 13: 3 9 4 14: 4 5 6 15: 4 9 5 16: 5 10 6 Delaunay neighbors: Row: 1 2 3 Col 1: 12 3 4 2: 15 4 5 3: 10 5 1 4: 13 1 2 5: 16 2 3 6: 14 7 9 7: 16 10 6 8: 12 9 10 9: 11 6 8 10: 3 8 7 11: 9 12 13 12: 8 1 11 13: 15 11 4 14: 16 6 15 15: 2 14 13 16: 7 14 5 Voronoi vertices Row: 1 2 3 Col 1: 0.894880 0.272171 -0.353714 2: 0.572625 -0.819641 -0.016998 3: 0.957150 -0.282520 0.063615 4: 0.768862 0.043352 -0.637943 5: 0.681801 -0.699920 0.212744 6: -0.672512 0.115158 0.731072 7: 0.283872 0.286265 0.915133 8: 0.586700 0.805359 0.084733 9: -0.952677 0.242288 0.183586 10: 0.569882 0.645792 0.508122 11: -0.676982 0.072527 -0.732417 12: 0.590866 0.806005 0.035111 13: -0.503978 -0.184997 -0.843672 14: -0.352343 -0.720626 0.597120 15: -0.066570 -0.891729 -0.447646 16: 0.615704 -0.594756 0.516889 Voronoi orders: 1: 5 2: 5 3: 5 4: 6 5: 5 6: 4 7: 5 8: 4 9: 4 10: 5 Voronoi polygons: 1: 1 3 5 2 4 2: 6 7 10 8 9 3: 1 4 13 11 12 4: 6 9 11 13 15 14 5: 2 5 16 14 15 6: 6 14 16 7 7: 1 12 8 10 3 8: 8 12 11 9 9: 2 15 13 4 10: 3 10 7 16 5 Voronoi areas: 1: 0.524598 2: 1.532651 3: 1.666072 4: 2.269122 5: 0.877697 6: 1.220752 7: 0.610702 8: 1.604935 9: 1.334342 10: 0.925501 Voronoi centroids Row: 1 2 3 Col 1: 0.915797 -0.332282 -0.225619 2: -0.203119 0.712487 0.671643 3: 0.301128 0.471796 -0.828692 4: -0.857935 -0.509699 -0.064451 5: 0.175448 -0.956881 0.231510 6: -0.020341 -0.311993 0.949867 7: 0.916114 0.390013 0.092875 8: -0.470777 0.849122 -0.239502 9: 0.327245 -0.576910 -0.748389 10: 0.797686 -0.043407 0.601509 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: 0.915568 -0.257797 -0.308668 2: -0.171751 0.901345 0.397592 3: 0.541822 0.447986 -0.711152 4: -0.620052 -0.745456 0.244603 5: 0.026281 -0.894727 0.445840 6: 0.016716 -0.591520 0.806117 7: 0.987108 0.084661 0.135834 8: -0.220974 0.974193 0.046018 9: 0.679580 -0.416543 -0.603873 10: 0.936980 -0.037537 0.347361 11: -0.790266 -0.322477 -0.521045 12: 0.342480 -0.767254 -0.542243 13: 0.069208 -0.956800 0.282391 14: 0.764412 -0.432490 0.478150 15: -0.599427 0.710574 -0.368472 16: -0.638289 -0.234792 0.733116 17: 0.331413 -0.653883 -0.680148 18: -0.720304 0.121381 -0.682956 19: -0.359903 0.931597 0.050960 20: -0.528160 -0.708164 0.468562 21: -0.114968 -0.047273 -0.992244 22: -0.007810 -0.679244 0.733871 23: 0.328497 -0.404415 0.853545 24: 0.148354 0.744604 0.650812 25: 0.704016 0.655377 0.273573 26: 0.867790 0.181536 -0.462585 27: 0.213656 0.969908 -0.116747 28: -0.492074 0.534329 -0.687281 29: 0.241202 -0.155084 0.958003 30: 0.175574 -0.258658 0.949879 31: -0.258893 -0.456159 0.851407 32: 0.878409 0.466006 -0.105998 33: -0.682985 0.193322 -0.704385 34: 0.417484 0.449129 -0.789931 35: -0.199614 -0.952691 -0.229202 36: 0.434509 -0.656468 0.616645 37: 0.668596 -0.648584 0.363757 38: -0.187404 -0.251422 0.949561 39: 0.120848 -0.877533 0.464038 40: -0.766804 0.609429 -0.201512 41: 0.301255 0.040688 0.952675 42: -0.106947 -0.280224 -0.953958 43: -0.037400 -0.028761 -0.998886 44: -0.321987 -0.732749 -0.599503 45: -0.007006 -0.699781 0.714323 46: 0.458877 0.566868 -0.684173 47: 0.128447 -0.846309 0.516975 48: -0.699698 0.424710 0.574495 49: -0.905411 0.324636 0.273574 50: 0.688430 -0.463664 -0.557745 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: 0.894880 0.272171 -0.353714 2: 0.572625 -0.819641 -0.016998 3: 0.957150 -0.282520 0.063615 4: 0.768862 0.043352 -0.637943 5: 0.681801 -0.699920 0.212744 6: -0.672512 0.115158 0.731072 7: 0.283872 0.286265 0.915133 8: 0.586700 0.805359 0.084733 9: -0.952677 0.242288 0.183586 10: 0.569882 0.645792 0.508122 11: -0.676982 0.072527 -0.732417 12: 0.590866 0.806005 0.035111 13: -0.503978 -0.184997 -0.843672 14: -0.352343 -0.720626 0.597120 15: -0.066570 -0.891729 -0.447646 16: 0.615704 -0.594756 0.516889 Voronoi polygons: 1: 1 3 5 2 4 2: 6 7 10 8 9 3: 1 4 13 11 12 4: 6 9 11 13 15 14 5: 2 5 16 14 15 6: 6 14 16 7 7: 1 12 8 10 3 8: 8 12 11 9 9: 2 15 13 4 10: 3 10 7 16 5 Voronoi areas, method 1: 1: 0.524598 2: 1.532651 3: 1.666072 4: 2.269122 5: 0.877697 6: 1.220752 7: 0.610702 8: 1.604935 9: 1.334342 10: 0.925501 Voronoi areas, method 2: 1: 0.524598 2: 1.532651 3: 1.666072 4: 2.269122 5: 0.877697 6: 1.220752 7: 0.610702 8: 1.604935 9: 1.334342 10: 0.925501 Voronoi centroids, method 1 Row: 1 2 3 Col 1: 0.915797 -0.332282 -0.225619 2: -0.203119 0.712487 0.671643 3: 0.301128 0.471796 -0.828692 4: -0.857935 -0.509699 -0.064451 5: 0.175448 -0.956881 0.231510 6: -0.020341 -0.311993 0.949867 7: 0.916114 0.390013 0.092875 8: -0.470777 0.849122 -0.239502 9: 0.327245 -0.576910 -0.748389 10: 0.797686 -0.043407 0.601509 Voronoi centroids, method 2 Row: 1 2 3 Col 1: 0.915667 -0.332881 -0.225264 2: -0.206579 0.707577 0.675766 3: 0.274962 0.473958 -0.836517 4: -0.853724 -0.517634 -0.056660 5: 0.176640 -0.957729 0.227054 6: -0.020995 -0.304767 0.952196 7: 0.915001 0.392609 0.092910 8: -0.480777 0.836852 -0.261788 9: 0.328487 -0.578669 -0.746484 10: 0.794903 -0.041495 0.605316 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: 0.000000 0.351275 0.936272 2: -0.304213 0.175638 0.936272 3: -0.304213 -0.175638 0.936272 4: 0.000000 -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: 0.495100 0.681447 0.538986 9: 0.000000 0.784322 0.620354 10: 0.000000 0.784322 0.620354 11: -0.495100 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: -0.495100 -0.681447 0.538986 17: 0.000000 -0.784322 0.620354 18: 0.000000 -0.784322 0.620354 19: 0.495100 -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: 0.948370 0.308144 0.075104 24: 0.586125 0.806732 0.075104 25: 0.806732 0.586125 -0.075104 26: 0.308144 0.948370 -0.075104 27: 0.000000 0.997176 0.075104 28: -0.308144 0.948370 -0.075104 29: -0.586125 0.806732 0.075104 30: -0.806732 0.586125 -0.075104 31: -0.948370 0.308144 0.075104 32: -0.997176 0.000000 -0.075104 33: -0.948370 -0.308144 0.075104 34: -0.806732 -0.586125 -0.075104 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. 27-Mar-2019 09:39:37