07-Jun-2023 08:04:29 test_triangulation_test(): MATLAB/Octave version 5.2.0 Test test_triangulation(). test_triangulation_test01(): p00_test_num() reports the number of problems. p00_title() returns a title for each problem. p00_header() prints some information about each problem. The number of tests available = 15 Test number: 1 Title: "#1: The unit circle." P01: Strang and Persson example #1 The unit circle. Radius = 1.000000 Center = (0.000000, 0.000000) A uniform mesh density is requested. Element sizes tried were 0.4, 0.2, 0.1. Number of boundary segments = 1 Number of fixed points = 0 Number of holes = 0 Test number: 2 Title: "#2: The circle with concentric circular hole." P02: Strang and Persson example #2 The unit circle, with a concentric hole. Radius1 = 1.000000 Center = (0.000000, 0.000000) A uniform mesh density is requested. Element sizes tried were 0.4, 0.2, 0.1. Number of boundary segments = 2 Number of fixed points = 0 Number of holes = 1 Test number: 3 Title: "#3: The unit square with circular hole." P03: Strang and Persson example #3 The unit square, with a hole. The hole is a concentric circle of radius 0.4. A uniform mesh density is requested. Element sizes tried were 0.4, 0.2, 0.1. Number of boundary segments = 2 Number of fixed points = 4 Number of holes = 1 Test number: 4 Title: "#4: The unit hexagon with hexagonal hole." P04: Strang and Persson example #4 The hexagon with hexagonal hole. Radius of outer hexagon R1 = 1.000000 Radius of outer hexagon R2 = 0.500000 A uniform mesh density is requested. Element sizes tried were ? Number of boundary segments = 2 Number of fixed points = 12 Number of holes = 1 Test number: 5 Title: "#5: The horn." P05: Strang and Persson example #5 The horn. Circle C1 has center = (0,0) Radius R1 = 1.000000 Circle C2 has center = (-0.4,0) Radius R2 = 0.550000 Points in the region are: in C1 and not in C2 and have 0 <= Y. A uniform mesh density is requested. Element sizes tried were 0.4, 0.2, 0.1. Number of boundary segments = 1 Number of fixed points = 4 Number of holes = 0 Test number: 6 Title: "#6: The superellipse with superelliptical hole." P06: Strang and Persson example #6 Superellipse with superelliptical hole. Radius R1 = 1.000000 Radius R2 = 0.500000 A uniform mesh density is requested. Element sizes tried were 0.4, 0.2, 0.1. Number of boundary segments = 2 Number of fixed points = 0 Number of holes = 1 Test number: 7 Title: "#7: Bicycle seat (implicit)." P07: Strang and Persson example #7 Bicycle seat (implicit). A uniform mesh density is requested. The boundary is formed by two algebraic expressions. Number of boundary segments = 1 Number of fixed points = 2 Number of holes = 0 Test number: 8 Title: "#8: Pie slice with notch and hole." P08: Strang and Persson example #7 Pie slice with notch and hole. A uniform mesh density is requested. Number of boundary segments = 2 Number of fixed points = 6 Number of holes = 1 Test number: 9 Title: "#9: Jeff Borggaard's Box with 2 hexagonal holes." P09: Jeff Borggaard's example A square with 2 hexagonal holes. The square has "center" at (0.500000, 0.500000) and "radius" R1 = 0.500000 Hexagon 1 has "center" at (0.250000, 0.750000) and "radius" R2 = 0.100000 Hexagon 2 has "center" at (0.600000, 0.400000) and "radius" R3 = 0.100000 A uniform mesh density is requested. Number of boundary segments = 3 Number of fixed points = 16 Number of holes = 2 Test number: 10 Title: "#10: The unit square." P10: The unit square. Number of boundary segments = 1 Number of fixed points = 4 Number of holes = 0 Test number: 11 Title: "#11: The L-shaped region." P11: The L-shaped region. The lower left corner of the indentation is P = (0.500000, 0.500000) Number of boundary segments = 1 Number of fixed points = 6 Number of holes = 0 Test number: 12 Title: "#12: John Shadid's H-shaped region." P12: John Shadid's H-shaped region. Number of boundary segments = 1 Number of fixed points = 12 Number of holes = 0 Test number: 13 Title: "#13: The Sandia Fork region." P13: The Sandia Fork region. Number of boundary segments = 1 Number of fixed points = 8 Number of holes = 0 Test number: 14 Title: "#14: Marcus Garvie's Lake Alpha with Beta Island." P14: Marcus Garvie's Lake Alpha and Beta island. Number of boundary segments = 2 Number of fixed points = 101 Number of holes = 1 Test number: 15 Title: "#15: Sangbum Kim's forward step." P15: Sangbum Kim's forward step. Number of boundary segments = 1 Number of fixed points = 8 Number of holes = 0 test_triangulation_test02(): p00_test_num() reports the number of problems. p00_sample() returns sample points from the region. Test number = 1 Title: = "#1: The unit circle." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: 0.411884 -0.778558 2: -0.432087 -0.0758685 3: 0.586904 -0.373222 4: -0.819284 -0.388466 5: 0.950992 0.270328 6: -0.729671 -0.464003 7: -0.307006 -0.877437 8: 0.0248658 0.864588 9: 0.757384 -0.369255 10: 0.116015 -0.225268 11: 0.727288 -0.412192 12: 0.518643 0.161462 13: 0.219844 0.478912 14: 0.818706 0.240484 15: 0.412334 -0.331535 16: 0.732105 -0.0306508 17: 0.189816 -0.690665 18: 0.0662037 0.196546 19: 0.562498 0.570463 20: -0.122537 -0.189772 Test number = 2 Title: = "#2: The circle with concentric circular hole." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: -0.788469 0.369287 2: 0.0391082 -0.759651 3: -0.76942 0.134133 4: 0.0761733 -0.497317 5: -0.769974 -0.172098 6: -0.593718 0.333992 7: -0.276016 0.355721 8: 0.0251678 0.93565 9: -0.413952 0.187188 10: -0.604585 -0.344785 11: -0.693375 -0.216551 12: -0.975313 -0.0530888 13: -0.0379091 0.920605 14: -0.502488 -0.77032 15: -0.269293 0.450835 16: 0.23847 0.551797 17: -0.205629 0.741498 18: -0.0893662 0.779625 19: 0.501418 -0.254805 20: 0.966404 -0.0394943 Test number = 3 Title: = "#3: The unit square with circular hole." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: -0.6674 -0.953151 2: 0.921316 0.47607 3: 0.853064 0.902553 4: -0.0186138 -0.516277 5: -0.748997 -0.990345 6: 0.919629 0.534437 7: 0.425173 0.490004 8: -0.419884 0.762567 9: -0.692765 0.756693 10: 0.419378 0.0394935 11: 0.427604 0.3936 12: 0.983209 0.906115 13: -0.179403 0.754605 14: -0.738975 -0.891058 15: 0.534371 -0.645948 16: 0.468946 -0.355528 17: -0.84408 0.0534747 18: 0.972141 0.842135 19: 0.962971 -0.701667 20: 0.103559 0.397155 Test number = 4 Title: = "#4: The unit hexagon with hexagonal hole." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: -0.200259 -0.629041 2: 0.247188 0.671105 3: -0.206165 0.515719 4: 0.45041 0.176506 5: -0.0986823 -0.569541 6: -0.475273 -0.353814 7: -0.694382 0.278217 8: 0.50016 -0.0589187 9: -0.439393 0.177705 10: 0.516814 0.61967 11: -0.729958 -0.0359053 12: 0.488135 -0.0922303 13: -0.932766 -0.0283101 14: -0.891394 -0.067988 15: 0.194937 -0.86523 16: -0.495143 -0.272747 17: 0.65367 -0.576847 18: 0.883103 -0.190564 19: 0.0437585 -0.642737 20: 0.49017 0.334988 Test number = 5 Title: = "#5: The horn." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: -0.0612575 0.991731 2: 0.167792 0.957977 3: 0.679386 0.690609 4: 0.508475 0.274183 5: 0.146195 0.471853 6: 0.430118 0.181624 7: 0.282904 0.0534519 8: -0.63449 0.669911 9: 0.736088 0.47091 10: 0.239139 0.868476 11: -0.628609 0.708331 12: 0.227116 0.623443 13: 0.650615 0.422181 14: 0.38891 0.407687 15: -0.921094 0.201046 16: 0.681531 0.496774 17: -0.226845 0.555791 18: 0.533104 0.703183 19: 0.0882279 0.929539 20: 0.123675 0.581321 Test number = 6 Title: = "#6: The superellipse with superelliptical hole." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: 0.633893 -0.217972 2: -0.534789 -0.783499 3: -0.191406 0.865043 4: -0.970566 -0.35734 5: 0.517107 0.36675 6: 0.887668 -0.103318 7: 0.130716 -0.876714 8: -0.956935 0.0311636 9: -0.658812 0.150205 10: -0.864894 0.148137 11: -0.839248 -0.179737 12: 0.579764 0.51369 13: 0.563486 -0.944879 14: -0.689698 0.8982 15: 0.643166 -0.0832056 16: 0.970001 0.525097 17: 0.167702 0.889783 18: 0.210724 0.540218 19: -0.489243 0.506293 20: -0.30278 -0.655388 Test number = 7 Title: = "#7: Bicycle seat (implicit)." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: 4.07417 -4.61074 2: 5.69706 -1.64128 3: 1.63061 -1.70849 4: -1.80318 -2.39203 5: -5.83088 -2.70908 6: 0.351243 0.19178 7: -4.62105 -4.33913 8: -2.07696 -1.00626 9: 5.83925 -2.11873 10: -0.718282 0.59696 11: 5.4831 -0.185206 12: 7.42218 0.297626 13: -5.71782 -1.3369 14: -2.79721 -2.35984 15: -4.15441 -2.93387 16: -5.40616 -2.85313 17: -1.90371 -4.09445 18: -2.03581 -3.3614 19: 4.01911 -3.04059 20: -5.04929 -2.73982 Test number = 8 Title: = "#8: Pie slice with notch and hole." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: 0.82545 0.097298 2: 0.883784 0.0297154 3: 0.145752 -0.00476009 4: 0.476701 0.0698048 5: 0.908064 -0.143719 6: 0.721258 0.191822 7: 0.964212 -0.193206 8: 0.873598 -0.106683 9: 0.578116 0.110693 10: 0.0357253 -0.00528058 11: 0.71556 0.0164348 12: 0.746817 -0.139967 13: 0.676883 0.115922 14: 0.792387 -0.17918 15: 0.757512 -0.0650593 16: 0.485542 -0.0488435 17: 0.908449 -0.238496 18: 0.738992 -0.112386 19: 0.278585 -0.00852002 20: 0.859942 -0.11721 Test number = 9 Title: = "#9: Jeff Borggaard's Box with 2 hexagonal holes." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: 0.535671 0.0457733 2: 0.78232 0.997501 3: 0.816524 0.0480599 4: 0.955644 0.101507 5: 0.458688 0.284347 6: 0.391806 0.95488 7: 0.322904 0.624129 8: 0.142418 0.565209 9: 0.720433 0.0330046 10: 0.95653 0.613777 11: 0.821089 0.00224178 12: 0.950357 0.216236 13: 0.665145 0.19061 14: 0.595502 0.597653 15: 0.808396 0.831878 16: 0.91238 0.625481 17: 0.453125 0.987088 18: 0.798979 0.243799 19: 0.416955 0.0910784 20: 0.93774 0.496018 Test number = 10 Title: = "#10: The unit square." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: 0.590842 0.235096 2: 0.741032 0.736595 3: 0.360742 0.878054 4: 0.573907 0.519899 5: 0.364656 0.093898 6: 0.93378 0.342566 7: 0.0675434 0.135402 8: 0.660885 0.675748 9: 0.842899 0.525233 10: 0.910531 0.429121 11: 0.107761 0.00921679 12: 0.262137 0.894491 13: 0.701727 0.334003 14: 0.239264 0.932778 15: 0.111291 0.772144 16: 0.000859261 0.477669 17: 0.391035 0.589907 18: 0.849961 0.116049 19: 0.530413 0.930231 20: 0.616942 0.719946 Test number = 11 Title: = "#11: The L-shaped region." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: 0.425962 0.0851127 2: 0.919355 0.272306 3: 0.451265 0.936955 4: 0.52175 0.000445188 5: 0.0409474 0.0943 6: 0.276843 0.494055 7: 0.232097 0.764675 8: 0.805621 0.0915814 9: 0.757919 0.171289 10: 0.614004 0.387915 11: 0.375799 0.453894 12: 0.148189 0.448312 13: 0.163622 0.0154699 14: 0.253542 0.679348 15: 0.482422 0.788362 16: 0.0135498 0.703771 17: 0.181729 0.791924 18: 0.984085 0.434373 19: 0.235835 0.967429 20: 0.184811 0.136321 Test number = 12 Title: = "#12: John Shadid's H-shaped region." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: 0.743031 0.344819 2: 0.952935 0.149964 3: 0.290579 0.642866 4: 0.716244 0.882443 5: 0.879067 0.0616006 6: 0.70345 0.521834 7: 0.457143 0.31658 8: 0.319374 0.525912 9: 0.103951 0.966043 10: 0.821362 0.989845 11: 0.835994 0.153666 12: 0.0539945 0.483607 13: 0.924883 0.047961 14: 0.793935 0.279682 15: 0.940003 0.599416 16: 0.38084 0.741254 17: 0.44083 0.933301 18: 0.928712 0.70826 19: 0.199057 0.353315 20: 0.0447725 0.353674 Test number = 13 Title: = "#13: The Sandia Fork region." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: 16.1158 10.6324 2: 50.7381 32.0967 3: 51.0806 60.9956 4: 48.6726 45.5265 5: 47.7122 55.2979 6: 86.9201 3.64021 7: 53.1139 78.9106 8: 80.1756 16.1261 9: 50.2268 80.4587 10: 54.9933 86.6613 11: 19.4314 25.5136 12: 11.4535 4.74499 13: 15.8509 17.8688 14: 54.7173 76.167 15: 51.5763 39.5019 16: 39.9012 30.207 17: 89.4171 6.49956 18: 46.0818 49.0012 19: 66.7026 27.5339 20: 54.5059 85.6286 Test number = 14 Title: = "#14: Marcus Garvie's Lake Alpha with Beta Island." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: 409.816 481.449 2: 399.942 423.803 3: 340.535 384.584 4: 435.142 343.073 5: 367.812 403.835 6: 381.387 424.769 7: 177.78 268.383 8: 618.831 247.7 9: 334.773 603.696 10: 462.429 458.451 11: 113.262 335.47 12: 313.879 743.223 13: 404.626 498.062 14: 301.778 189.055 15: 269.473 720.45 16: 485.277 519.886 17: 236.006 297.557 18: 132.316 321.392 19: 595.352 252.624 20: 416.393 490.798 Test number = 15 Title: = "#15: Sangbum Kim's forward step." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: 1.75965 0.849294 2: 1.50508 -0.695165 3: -3.07169 -0.330655 4: -5.15305 -0.164666 5: 2.6711 0.523908 6: 7.24072 0.798108 7: 2.76875 0.0255655 8: -0.137541 -0.627425 9: -1.14691 -0.0287568 10: -2.43994 -0.362646 11: 1.56752 0.726657 12: -1.81184 0.839674 13: -0.430927 0.731848 14: -6.81052 -0.733466 15: 5.76931 0.714308 16: -7.61752 -0.240282 17: -2.88314 -0.583951 18: 6.41552 0.0837021 19: -0.0588572 0.206103 20: -0.0977468 0.954117 test_triangulation_test03(): p00_boundary_nearest() returns the nearest boundary point for a set of points. Test number = 1 Title: = "#1: The unit circle." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) -0.585292 0.173770 -0.958642 0.284615 0.857606 -0.252693 0.959227 -0.282636 0.277486 -0.094246 0.946876 -0.321598 0.345128 -0.605249 0.495350 -0.868693 -0.937064 -0.321468 -0.945888 -0.324495 -0.664449 -0.650060 -0.714804 -0.699325 -0.443978 0.194004 -0.916337 0.400409 0.220619 -0.487255 0.412469 -0.910972 -0.156997 -0.256068 -0.522689 -0.852523 0.547373 0.405216 0.803729 0.594995 0.782804 0.553531 0.816494 0.577354 -0.146141 -0.535260 -0.263388 -0.964690 0.643449 -0.045330 0.997528 -0.070274 0.333235 0.569657 0.504928 0.863162 0.390151 -0.809493 0.434172 -0.900830 0.066279 0.676244 0.097543 0.995231 -0.800440 -0.449722 -0.871820 -0.489826 -0.337537 -0.691749 -0.438527 -0.898718 -0.284830 -0.335908 -0.646736 -0.762714 0.284992 0.780524 0.342981 0.939342 Test number = 2 Title: = "#2: The circle with concentric circular hole." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) -0.503910 0.538873 -0.683014 0.730405 -0.834036 0.048703 -0.998299 0.058295 0.687125 -0.341410 0.895546 -0.444968 -0.918548 0.052973 -0.998341 0.057575 -0.518135 0.193615 -0.374694 0.140015 -0.867184 -0.341891 -0.930309 -0.366778 -0.186718 0.797094 -0.228074 0.973644 -0.284736 0.364133 -0.246396 0.315101 -0.840424 0.285919 -0.946713 0.322079 -0.768667 -0.387583 -0.892912 -0.450231 -0.199703 -0.569050 -0.132456 -0.377432 0.286481 0.370414 0.244714 0.316410 -0.538119 0.411187 -0.317833 0.242862 -0.708310 0.479028 -0.828350 0.560211 -0.066631 -0.893518 -0.074365 -0.997231 -0.685885 0.201339 -0.959514 0.281662 0.944986 -0.117873 0.992310 -0.123776 0.682825 0.426492 0.848151 0.529754 -0.673513 -0.355282 -0.884484 -0.466571 0.047524 0.588766 0.032182 0.398703 Test number = 3 Title: = "#3: The unit square with circular hole." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) 0.974990 -0.886974 1.000000 -0.886974 -0.707834 -0.646989 -1.000000 -0.646989 -0.726060 -0.225993 -1.000000 -0.225993 -0.570205 0.954021 -0.570205 1.000000 -0.656774 0.653857 -1.000000 0.653857 0.525675 0.831716 0.525675 1.000000 -0.413087 -0.561796 -0.236957 -0.322260 0.905193 0.067309 1.000000 0.067309 0.691722 -0.469214 1.000000 -0.469214 0.535522 0.895859 0.535522 1.000000 -0.481760 0.684144 -0.481760 1.000000 -0.704458 -0.998966 -0.704458 -1.000000 -0.206980 0.847325 -0.206980 1.000000 -0.566772 0.463238 -0.309713 0.253136 0.584599 -0.962161 0.584599 -1.000000 -0.529187 0.080698 -0.395429 0.060301 0.028369 0.931521 0.028369 1.000000 0.262087 -0.757438 0.262087 -1.000000 -0.592114 0.944575 -0.592114 1.000000 -0.639323 0.626497 -1.000000 0.626497 Test number = 4 Title: = "#4: The unit hexagon with hexagonal hole." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) -0.468509 0.073624 -0.433013 0.073624 -0.353855 -0.865949 -0.353855 -0.866025 -0.602597 -0.210293 -0.433013 -0.210293 0.180105 0.564253 0.107257 0.438075 -0.323717 -0.703381 -0.323717 -0.866025 0.211806 -0.601266 0.115005 -0.433602 0.365866 -0.591929 0.585154 -0.718535 0.642517 -0.118407 0.433013 -0.118407 -0.596886 -0.644772 -0.620027 -0.658133 -0.578485 -0.332603 -0.433013 -0.250000 -0.735533 0.097164 -0.891810 0.187390 -0.121717 0.603720 -0.046376 0.473225 0.064020 -0.526811 0.036406 -0.478981 -0.517228 0.016711 -0.433013 0.016711 0.063487 0.715888 0.063487 0.866025 -0.562878 -0.529888 -0.661271 -0.586695 -0.640143 0.255417 -0.799437 0.347385 0.687802 0.438223 0.732194 0.463853 -0.782535 -0.326186 -0.804391 -0.338805 -0.052499 0.493387 -0.042237 0.475614 Test number = 5 Title: = "#5: The horn." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) -0.520937 0.687550 -0.603906 0.797056 0.629136 0.170027 0.586625 0.163004 0.722739 0.305221 0.564977 0.262333 0.488564 0.245459 0.563898 0.266270 0.134214 0.418911 0.386911 0.617066 0.523685 0.433007 0.505448 0.424457 0.201219 0.320124 0.482673 0.469987 0.107717 0.668133 0.205035 0.796199 0.743895 0.027477 0.743895 0.000000 0.777611 0.280729 0.940583 0.339564 -0.243229 0.758207 -0.305462 0.952204 0.129509 0.334924 0.150000 0.000000 0.343790 0.933249 0.345671 0.938356 0.450509 0.309515 0.539709 0.341976 -0.055528 0.736807 0.023521 0.905887 0.985980 0.040692 0.999149 0.041235 0.043642 0.436010 0.313214 0.700946 0.809188 0.407153 0.893294 0.449472 0.841578 0.098679 0.841578 0.000000 0.228689 0.601160 0.322753 0.691106 Test number = 6 Title: = "#6: The superellipse with superelliptical hole." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) 0.192805 -0.591034 0.187776 -0.497495 0.763183 -0.438452 0.988476 -0.461359 0.102048 0.808824 0.102252 0.999973 0.763632 0.553008 0.965433 0.601914 0.507320 0.630347 0.387672 0.446970 0.935450 0.219818 0.999408 0.220505 -0.672949 0.006308 -0.500000 0.006307 0.752660 -0.460918 0.985335 -0.489433 -0.954541 -0.160178 -0.999835 -0.160365 0.826980 0.234698 0.999210 0.236996 -0.601833 0.399440 -0.468543 0.345839 -0.883647 -0.774231 -0.891298 -0.779346 0.547984 0.659614 0.394303 0.442464 -0.165691 0.632814 -0.161161 0.498645 -0.976787 -0.358809 -0.995788 -0.359705 0.376491 0.765243 0.390347 0.994145 -0.466045 -0.863669 -0.480208 -0.986432 0.366234 -0.480979 0.358060 -0.463274 -0.687414 -0.097401 -0.499830 -0.096069 0.331255 0.516381 0.319653 0.477667 Test number = 7 Title: = "#7: Bicycle seat (implicit)." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) -6.219812 -0.398502 0.000000 1.000000 3.440323 -3.852362 0.000000 -5.000000 -2.322782 -2.713050 0.000000 1.000000 1.952345 -1.883841 0.000000 1.000000 3.499920 -4.507397 0.000000 -5.000000 1.573116 -2.629736 0.000000 1.000000 1.471652 -0.007434 0.000000 1.000000 -0.391966 -4.364799 0.000000 -5.000000 -0.513947 -4.513197 0.000000 -5.000000 6.623728 -1.506297 0.000000 -5.000000 0.407814 -1.748367 0.000000 1.000000 -1.924456 -3.830720 0.000000 -5.000000 0.765889 -1.366460 0.000000 1.000000 -0.376029 0.854880 0.000000 1.000000 6.565808 -1.389982 0.000000 -5.000000 -2.327618 -4.177720 0.000000 -5.000000 6.420744 -1.473485 0.000000 -5.000000 -0.397933 -4.055100 0.000000 -5.000000 7.065785 -1.635882 0.000000 -5.000000 4.660475 -2.930651 0.000000 -5.000000 Test number = 8 Title: = "#8: Pie slice with notch and hole." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) 0.935695 -0.208779 0.925210 -0.247909 0.880678 0.057241 0.918959 0.018959 0.620980 0.166346 0.612513 0.099214 0.536902 -0.097170 0.545539 -0.083869 0.912011 -0.047667 0.929839 -0.029839 0.894902 -0.122377 0.958640 -0.058640 0.571840 -0.120623 0.577266 -0.097381 0.440604 -0.047693 0.504197 -0.028665 0.615180 0.106052 0.614169 0.098991 0.454485 -0.009278 0.500203 -0.006363 0.181391 -0.019643 0.174151 -0.046664 0.198011 -0.018577 0.189391 -0.050747 0.833105 -0.161652 0.817710 -0.219105 0.709072 -0.035594 0.695066 -0.031023 0.651849 0.113320 0.641606 0.090934 0.910623 0.099292 0.954958 0.054958 0.164355 0.013655 0.149931 -0.040174 0.097044 0.024271 0.084476 -0.022635 0.373978 0.079092 0.505612 0.033029 0.474151 0.031674 0.503024 0.024407 Test number = 9 Title: = "#9: Jeff Borggaard's Box with 2 hexagonal holes." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) 0.260537 0.523677 0.260537 0.663397 0.455914 0.796282 0.350000 0.750000 0.318609 0.610289 0.300000 0.663397 0.929041 0.018247 0.929041 0.000000 0.691428 0.487077 0.660151 0.469020 0.635961 0.895467 0.635961 1.000000 0.197163 0.179532 0.197163 0.000000 0.063566 0.805415 0.000000 0.805415 0.097504 0.711233 0.153663 0.743656 0.122863 0.865771 0.193346 0.825078 0.444961 0.087112 0.444961 0.000000 0.981279 0.809867 1.000000 0.809867 0.934461 0.102789 1.000000 0.102789 0.000509 0.213431 0.000000 0.213431 0.523676 0.033079 0.523676 0.000000 0.427964 0.509196 0.529274 0.450705 0.095375 0.356558 0.000000 0.356558 0.401757 0.545667 0.300000 0.663397 0.743077 0.198590 0.650000 0.313397 0.030092 0.324173 0.000000 0.324173 Test number = 10 Title: = "#10: The unit square." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) 0.876172 0.768568 1.000000 0.768568 0.110653 0.716544 0.000000 0.716544 0.287472 0.367611 0.000000 0.367611 0.307709 0.507534 0.000000 0.507534 0.953279 0.483002 1.000000 0.483002 0.333814 0.385636 0.000000 0.385636 0.736820 0.985712 0.000000 0.000000 0.767580 0.089684 0.767580 0.000000 0.984862 0.566128 1.000000 0.566128 0.063465 0.617678 0.000000 0.617678 0.152617 0.923493 0.000000 0.000000 0.436088 0.723991 0.000000 0.000000 0.585841 0.690436 0.000000 0.000000 0.465537 0.203615 0.465537 0.000000 0.106711 0.832276 0.000000 0.832276 0.861544 0.605001 1.000000 0.605001 0.743484 0.460846 1.000000 0.460846 0.692970 0.824646 0.000000 0.000000 0.666641 0.805079 0.000000 0.000000 0.136509 0.596538 0.000000 0.596538 Test number = 11 Title: = "#11: The L-shaped region." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) 0.709739 0.330649 0.709739 0.500000 0.189566 0.333645 0.000000 0.333645 0.058098 0.139459 0.000000 0.139459 0.383143 0.333094 0.500000 0.500000 0.794754 0.158478 0.794754 0.000000 0.075265 0.747239 0.000000 0.747239 0.672940 0.178162 0.672940 0.000000 0.302622 0.884947 0.302622 1.000000 0.434594 0.179550 0.434594 0.000000 0.442796 0.420449 0.500000 0.500000 0.504959 0.115932 0.504959 0.000000 0.450290 0.853276 0.500000 0.853276 0.917079 0.290372 1.000000 0.290372 0.847418 0.008118 0.847418 0.000000 0.527578 0.191265 0.527578 0.000000 0.390002 0.423626 0.500000 0.500000 0.629893 0.434474 0.629893 0.500000 0.208187 0.513911 0.000000 0.513911 0.561130 0.309521 0.561130 0.500000 0.131010 0.095888 0.131010 0.000000 Test number = 12 Title: = "#12: John Shadid's H-shaped region." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) 0.375538 0.913022 0.375538 1.000000 0.562703 0.306977 0.562703 0.250000 0.681051 0.351499 0.625000 0.375000 0.287697 0.942796 0.287697 1.000000 0.242448 0.641930 0.000000 0.641930 0.269836 0.503574 0.500000 0.503574 0.488795 0.450658 0.500000 0.450658 0.371132 0.862784 0.500000 0.862784 0.794192 0.612168 0.625000 0.612168 0.008357 0.226310 0.000000 0.226310 0.380518 0.937586 0.380518 1.000000 0.197050 0.316274 0.000000 0.316274 0.794868 0.507770 0.625000 0.507770 0.872788 0.480410 1.000000 0.480410 0.732144 0.384633 0.625000 0.384633 0.499015 0.256282 0.500000 0.250000 0.319915 0.107349 0.319915 0.000000 0.976478 0.680772 1.000000 0.680772 0.827197 0.690286 1.000000 0.690286 0.644026 0.835478 0.625000 0.835478 Test number = 13 Title: = "#13: The Sandia Fork region." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) 80.264685 16.128483 76.475193 14.109009 43.256130 38.465874 43.092522 39.399070 73.010171 27.957906 75.419082 30.884791 53.671337 43.947110 55.000000 43.947110 13.992210 8.679432 11.113732 9.373269 23.932368 26.845233 22.134399 28.696834 17.870061 17.707925 14.968163 19.307262 44.951641 30.716602 45.134689 29.602850 27.500977 26.996119 24.391108 30.727588 52.016994 87.709245 52.016994 90.000000 19.669002 22.762767 18.007352 24.009800 25.190249 21.762802 27.447164 19.783064 48.716932 69.197809 45.000000 69.197809 47.306367 67.033870 45.000000 67.033870 12.035648 8.929115 11.062473 9.158003 11.114881 8.178109 10.856339 8.232484 52.657340 64.837819 55.000000 64.837819 30.361461 25.028716 31.481030 23.601859 17.015957 13.412190 12.946205 15.067059 50.566111 81.984226 55.000000 81.984226 Test number = 14 Title: = "#14: Marcus Garvie's Lake Alpha with Beta Island." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) 377.730142 375.804915 390.852298 327.392608 214.994307 232.088377 209.033438 227.186129 286.854301 243.433118 270.684780 255.554400 629.736371 266.415304 630.829050 266.953371 474.874394 304.686614 470.113795 292.825684 504.795174 473.844016 543.281733 501.523345 566.632546 337.164484 572.942396 338.665139 298.786941 149.794899 301.918616 148.234151 459.155173 564.790279 461.441859 569.907336 166.718798 301.004416 139.363843 274.678351 447.324960 544.757391 459.042911 570.979366 296.029091 313.965766 274.553000 291.273570 360.645385 575.903638 363.013469 582.898365 447.358279 399.577393 412.591160 327.252380 331.892974 568.650447 354.263030 585.860850 540.635899 294.157917 544.012725 267.782931 295.718686 219.484877 270.684780 255.554400 215.668790 326.758310 238.207360 303.467850 265.497167 605.925799 264.130605 605.143684 568.247662 362.531044 568.948490 362.611060 Test number = 15 Title: = "#15: Sangbum Kim's forward step." Spatial dimension M = 2 Number of samples N = 20 Pairs of Point and Nearest Boundary Point: (This data can be passed to the PLOT_POINTS routine and plotted with the DASH option.) -1.134597 0.603399 -8.000000 0.603399 6.159015 0.758325 -8.000000 0.758325 -0.739817 -0.869282 -8.000000 -0.869282 -0.038196 0.639531 -8.000000 0.639531 -2.168314 -0.450691 -8.000000 -0.450691 -5.677831 -0.727450 -8.000000 -0.727450 6.410809 0.455139 -8.000000 0.455139 -7.097550 -0.564502 -8.000000 -0.564502 4.248931 0.302652 -8.000000 0.302652 -0.456592 0.740540 -8.000000 0.740540 -1.116575 -0.994705 -8.000000 -0.994705 7.011294 0.839921 -8.000000 0.839921 -1.886471 0.372222 -8.000000 0.372222 -5.613147 -0.599119 -8.000000 -0.599119 0.717455 0.795640 -8.000000 0.795640 1.419831 -0.018115 -8.000000 -0.018115 4.172506 0.154074 -8.000000 0.154074 0.099628 0.970597 -8.000000 0.970597 0.871610 -0.160648 -8.000000 -0.160648 1.796564 0.233486 -8.000000 0.233486 test_triangulation_test05(): p00_points_eps() makes an EPS file containing an image of a set of points, and the boundary. Test number = 1 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.050000 Title: = "#1: The unit circle." Boundary image file is "p01_points.eps". Test number = 2 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.050000 Title: = "#2: The circle with concentric circular hole." Boundary image file is "p02_points.eps". Test number = 3 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.050000 Title: = "#3: The unit square with circular hole." Boundary image file is "p03_points.eps". Test number = 4 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.043301 Title: = "#4: The unit hexagon with hexagonal hole." Boundary image file is "p04_points.eps". Test number = 5 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.025000 Title: = "#5: The horn." Boundary image file is "p05_points.eps". Test number = 6 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.050000 Title: = "#6: The superellipse with superelliptical hole." Boundary image file is "p06_points.eps". Test number = 7 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.150000 Title: = "#7: Bicycle seat (implicit)." Boundary image file is "p07_points.eps". Test number = 8 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.012941 Title: = "#8: Pie slice with notch and hole." Boundary image file is "p08_points.eps". Test number = 9 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.025000 Title: = "#9: Jeff Borggaard's Box with 2 hexagonal holes." Boundary image file is "p09_points.eps". Test number = 10 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.025000 Title: = "#10: The unit square." Boundary image file is "p10_points.eps". Test number = 11 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.025000 Title: = "#11: The L-shaped region." Boundary image file is "p11_points.eps". Test number = 12 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.025000 Title: = "#12: John Shadid's H-shaped region." Boundary image file is "p12_points.eps". Test number = 13 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 2.500000 Title: = "#13: The Sandia Fork region." Boundary image file is "p13_points.eps". Test number = 14 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 13.350000 Title: = "#14: Marcus Garvie's Lake Alpha with Beta Island." Boundary image file is "p14_points.eps". Test number = 15 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.050000 Title: = "#15: Sangbum Kim's forward step." Boundary image file is "p15_points.eps". test_triangulation_test06 P00_POLY_WRITE creates a POLY file out of the boundary data for each problem. The number of tests available = 15 test_triangulation_test07 P00_HEX_GRID returns points inside a region that lie on a hexagonal grid. P00_HEX_GRID_COUNT counts the number of hex grid points inside a region. DTABLE_WRITE writes sets of points to a file. We use a hex grid spacing of H = 0.025000 P00_HEX_GRID_COUNT reports that the number of hex grid points will be 409 A few of the points: Row: 1 2 Col 1: 0.4875 0.0216506 2: 0.475 1.38778e-17 3: 0.4875 -0.0216506 4: 0.5 0.0433013 5: 0.475 0.0433013 The hex grid points were written to the file "p08_hex_grid_points.txt" test_triangulation_test(): Normal end of execution. 07-Jun-2023 08:04:36