29-Jul-2021 15:47:13 sphere_delaunay_test(): MATLAB/Octave version 9.9.0.1467703 (R2020b) Test sphere_delaunay(). SPHERE_DELAUNAY_TEST01 Choose random points on the unit sphere. Call SPHERE_DELAUNAY to compute the Delaunay triangulation. Call TRIANGULATION_NEIGHBOR_TRIANGLES to get triangle neighbors. Call STRI_VERTICES_TO_AREAS to get triangle areas. Data 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 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 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 Triangle 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 Spherical area of triangles 1: 0.181234 2: 0.42219 3: 1.12477 4: 0.282432 5: 0.965173 6: 0.0174488 7: 0.314607 8: 0.725714 9: 0.440178 10: 0.0885446 11: 0.0474998 12: 0.304738 13: 0.124732 14: 5.44366 15: 0.180141 16: 0.224261 Area sum = 10.887320 4 * PI = 12.566371 SPHERE_DELAUNAY_TEST02 Choose random points on the unit sphere. Call SPHERE_DELAUNAY to compute the Delaunay triangulation. Display an image of the Delaunay triangulation. Data 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 51: -0.816459 0.272831 -0.508878 52: -0.273669 0.451733 0.849142 53: -0.617662 0.696702 0.364828 54: -0.226131 -0.650486 -0.725074 55: -0.983225 0.0747557 0.166376 56: 0.459488 0.849364 0.259716 57: -0.306415 0.913476 0.267716 58: -0.718218 0.662041 0.214162 59: 0.22781 0.868344 0.440548 60: -0.97414 -0.167968 -0.15112 61: -0.270108 0.854024 -0.444618 62: -0.332301 -0.48903 -0.80649 63: -0.122737 -0.174983 0.976891 64: -0.128329 -0.548415 0.826301 65: 0.629604 -0.117094 -0.768041 66: -0.814188 -0.285554 0.505527 67: -0.403749 0.685513 0.605853 68: -0.720632 -0.546208 -0.42702 69: -0.84542 -0.533698 0.0207586 70: -0.916316 -0.138245 0.375837 71: -0.730476 0.639416 0.239899 72: -0.0184056 0.115775 -0.993105 73: -0.0525357 0.996747 0.0611167 74: 0.0562157 -0.99754 -0.0418677 75: 0.379534 0.696494 -0.608975 76: -0.0777399 0.665335 -0.742486 77: 0.903825 0.13685 0.405428 78: -0.931038 -0.330102 -0.155567 79: 0.236649 -0.935031 0.264036 80: -0.879672 0.0480073 0.473151 81: 0.216068 0.715228 0.664652 82: -0.553767 0.218693 -0.80344 83: -0.819356 0.573285 3.09007e-05 84: -0.0504141 0.83639 0.545812 85: 0.219293 0.782895 0.582225 86: 0.244885 -0.705109 -0.665472 87: 0.594588 -0.803938 -0.012201 88: -0.824867 0.431935 0.364729 89: 0.000467208 -0.0284796 -0.999594 90: 0.179153 -0.675841 -0.714943 91: 0.0770831 -0.914656 0.396816 92: 0.523594 0.663395 -0.534562 93: 0.475151 0.106405 0.873447 94: 0.508651 0.851825 -0.125169 95: -0.0624994 0.427884 -0.90167 96: -0.355432 -0.895009 -0.269493 97: 0.444184 0.565418 -0.694984 98: -0.825211 0.240038 -0.511281 99: 0.285719 0.378598 -0.880357 100: -0.0728681 -0.878593 0.47198 Figure 1: Delaunay triangulation with TRISURF Plot saved as "test02_plot1.png". Plot saved as "test02_plot2.png". Figure 2: Delaunay triangulation with PATCH. SPHERE_DELAUNAY_TEST03 Choose SPHERE_GRIDPOINTS_ICOS2 points on the unit sphere. Call SPHERE_DELAUNAY to compute 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 3.88578e-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:-1.66533e-16 0 1 25: 0.309017 0.5 -0.809017 26: 0.309017 -0.5 -0.809017 27:-1.66533e-16 0 -1 28: 0 1 0 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 0 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 0 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 Plot saved as "test03_plot1.png". Plot saved as "test03_plot2.png". Figure 2: Delaunay triangulation with PATCH. sphere_delaunay_test(): Normal end of execution. 29-Jul-2021 15:47:20