10-May-2026 09:07:19 test_triangulation_test(): MATLAB/Octave version 11.1.0 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: -0.855887 0.206275 2: 0.583763 -0.298095 3: -0.207991 0.405175 4: 0.180443 -0.68797 5: -0.88145 -0.0521893 6: -0.786891 -0.542732 7: -0.504277 -0.295001 8: -0.353335 -0.874285 9: -0.0940406 -0.10875 10: 0.821334 0.387674 11: 0.824006 -0.345248 12: -0.603213 0.723209 13: 0.0993378 -0.673605 14: -0.54063 0.482045 15: 0.117953 0.943521 16: 0.191759 -0.0243841 17: 0.754468 -0.237751 18: 0.457261 -0.822968 19: 0.0269355 0.101898 20: 0.414056 -0.529265 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: -0.724725 0.595576 2: 0.28396 -0.455347 3: 0.563336 0.184575 4: -0.190448 -0.955978 5: -0.339462 -0.484863 6: -0.580829 0.557321 7: 0.180143 -0.562144 8: 0.454144 -0.259235 9: -0.162808 -0.92762 10: -0.867983 -0.083962 11: -0.823734 0.100216 12: -0.92523 0.324666 13: -0.855141 -0.0114471 14: -0.312377 -0.451743 15: -0.803146 -0.124988 16: -0.417161 0.497379 17: 0.261146 0.880935 18: 0.220509 -0.657875 19: -0.254789 0.680464 20: 0.591657 0.36115 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: -0.190325 0.459481 2: 0.163358 -0.739669 3: -0.456281 0.541927 4: -0.605692 0.357892 5: 0.4693 0.347733 6: -0.473523 0.593313 7: 0.0582986 -0.999702 8: 0.140457 -0.739201 9: 0.528233 -0.265241 10: -0.925943 0.457547 11: 0.920969 0.873626 12: 0.88752 -0.15962 13: -0.824336 -0.121046 14: 0.163805 -0.54176 15: 0.171865 -0.559916 16: 0.799161 -0.0605907 17: -0.487203 0.395746 18: 0.335862 0.957871 19: -0.11335 -0.556537 20: 0.201432 -0.816762 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: 0.372906 -0.79491 2: 0.651467 -0.122107 3: 0.383988 0.600846 4: 0.0626686 0.513851 5: -0.238347 0.826219 6: 0.55591 -0.660475 7: 0.369516 -0.581107 8: 0.587725 0.0986957 9: -0.286108 0.463273 10: -0.447 -0.274763 11: 0.279586 -0.473888 12: -0.471386 0.0131848 13: -0.45474 0.231468 14: 0.539556 0.214822 15: 0.606704 -0.559949 16: 0.266559 0.789675 17: 0.507485 -0.0266043 18: -0.800495 0.284963 19: -0.378359 0.618524 20: -0.29722 -0.457921 Test number = 5 Title: = "#5: The horn." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: -0.0377474 0.505171 2: 0.75246 0.361266 3: 0.490164 0.00954681 4: 0.679386 0.0600857 5: 0.34943 0.338495 6: -0.339149 0.922879 7: 0.385846 0.745808 8: 0.740098 0.00347648 9:-0.000400189 0.691322 10: -0.00687392 0.799744 11: 0.711282 0.0561392 12: 0.354045 0.0712214 13: -0.0693956 0.980118 14: -0.37353 0.737829 15: 0.246163 0.588704 16: 0.212858 0.28588 17: 0.501789 0.493907 18: 0.398824 0.749433 19: -0.273813 0.942897 20: 0.481148 0.376 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: -0.516276 -0.0316799 2: -0.888506 -0.274733 3: -0.614023 -0.628838 4: 0.0376639 -0.583329 5: 0.192026 -0.77033 6: -0.217124 -0.867562 7: -0.97528 0.214851 8: -0.60077 -0.692175 9: 0.270185 0.525193 10: -0.712036 0.421623 11: 0.472229 0.618976 12: 0.440695 0.927014 13: 0.156483 -0.692123 14: 0.445984 -0.751604 15: 0.279939 0.498398 16: -0.402475 0.665261 17: -0.34775 -0.955104 18: 0.622925 0.952123 19: -0.820072 0.251145 20: 0.963364 -0.0667276 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: -0.945952 -1.43764 2: -4.50908 -1.59197 3: -2.20665 -4.55931 4: -1.05294 0.296723 5: -6.43538 -1.06294 6: -0.554272 -4.29541 7: -0.482578 -4.83152 8: -6.22114 -0.0420791 9: -3.29123 -3.36946 10: -2.79458 -2.37198 11: 4.79081 -2.29767 12: -3.25757 -2.9134 13: 6.05303 0.0630938 14: 4.28381 -1.34784 15: -5.85903 0.565578 16: -0.449253 -0.920571 17: -5.72227 -3.442 18: 1.39518 -1.54023 19: -0.0496886 0.150899 20: -0.978971 -1.69933 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: 0.880975 0.128465 2: 0.288261 -0.0393091 3: 0.58386 0.135014 4: 0.70237 0.00666297 5: 0.841493 -0.0417589 6: 0.906941 0.0472715 7: 0.467896 0.0961681 8: 0.46521 0.0657403 9: 0.591896 0.130581 10: 0.971049 -0.10649 11: 0.607701 -0.152598 12: 0.902957 -0.190057 13: 0.21927 -0.0198559 14: 0.34215 -0.00395834 15: 0.677695 -0.142605 16: 0.671418 -0.128341 17: 0.752759 -0.152686 18: 0.771489 0.074635 19: 0.932902 0.188436 20: 0.657257 -0.17317 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: 0.407588 0.120759 2: 0.477405 0.5212 3: 0.0263557 0.978458 4: 0.289432 0.0547294 5: 0.665404 0.817892 6: 0.201023 0.423016 7: 0.0696476 0.488207 8: 0.786384 0.34347 9: 0.65568 0.72279 10: 0.0407804 0.950484 11: 0.735777 0.765195 12: 0.426223 0.62595 13: 0.981087 0.593988 14: 0.460726 0.486784 15: 0.278596 0.624023 16: 0.124652 0.525894 17: 0.920489 0.883532 18: 0.0772415 0.701374 19: 0.603838 0.162131 20: 0.69188 0.527459 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: 0.888966 0.0610495 2: 0.492073 0.108215 3: 0.778923 0.753262 4: 0.240598 0.127411 5: 0.147149 0.271139 6: 0.268023 0.579755 7: 0.383087 0.100405 8: 0.28115 0.840485 9: 0.799439 0.203421 10: 0.329562 0.422333 11: 0.277141 0.726124 12: 0.176343 0.0885864 13: 0.573751 0.0932893 14: 0.0428771 0.367496 15: 0.337874 0.205179 16: 0.697871 0.134815 17: 0.242406 0.372326 18: 0.0537626 0.901539 19: 0.497475 0.258874 20: 0.473419 0.837335 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: 0.972483 0.376042 2: 0.277544 0.0475445 3: 0.71365 0.213948 4: 0.249398 0.196534 5: 0.398502 0.935193 6: 0.70453 0.013136 7: 0.277619 0.383739 8: 0.539604 0.167184 9: 0.328855 0.11352 10: 0.39463 0.167234 11: 0.973027 0.14135 12: 0.211707 0.420426 13: 0.344069 0.363269 14: 0.0328643 0.223525 15: 0.421927 0.116305 16: 0.610551 0.429643 17: 0.0537698 0.826152 18: 0.213007 0.306708 19: 0.766188 0.333428 20: 0.294978 0.157385 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: 0.999268 0.51197 2: 0.0974386 0.191273 3: 0.0498969 0.391848 4: 0.0535561 0.739215 5: 0.329462 0.928338 6: 0.00119303 0.440561 7: 0.219646 0.59542 8: 0.37733 0.668282 9: 0.74276 0.815986 10: 0.0942935 0.213492 11: 0.0434584 0.250451 12: 0.202246 0.452027 13: 0.329283 0.145183 14: 0.141066 0.312895 15: 0.217028 0.458029 16: 0.274284 0.605073 17: 0.881144 0.0938203 18: 0.870929 0.983134 19: 0.484321 0.636011 20: 0.35399 0.417752 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: 54.7365 63.12 2: 67.6644 29.9385 3: 46.0274 77.8297 4: 52.7283 61.7008 5: 17.7631 16.0275 6: 52.4485 32.1464 7: 65.4811 31.7519 8: 76.8088 18.5045 9: 54.4978 65.3153 10: 85.2672 1.88099 11: 23.5483 22.2123 12: 45.442 84.0526 13: 53.5438 89.7867 14: 19.9943 22.2062 15: 45.7662 68.421 16: 49.381 69.9733 17: 46.4826 88.762 18: 68.0855 35.622 19: 13.8448 3.88173 20: 82.0377 11.5087 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: 282.239 201.306 2: 431.145 539.403 3: 462.183 396.723 4: 438.255 438.848 5: 266.607 673.461 6: 112.258 339.26 7: 246.628 214.25 8: 304.218 342.14 9: 337.531 328.214 10: 436.298 512.522 11: 326.57 534.628 12: 224.908 700.704 13: 420.154 486.871 14: 252.818 216.065 15: 282.784 378.367 16: 304.722 285.908 17: 271.26 599.518 18: 354.604 781.524 19: 558.086 462.749 20: 201.538 286.994 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: 3.59315 0.161591 2: -6.14217 -0.0253828 3: 0.534256 0.437717 4: 5.70305 0.0534434 5: 0.471677 -0.330423 6: -7.62775 -0.405677 7: 6.91686 0.921642 8: 2.59453 0.324988 9: -1.93502 0.331888 10: 0.400531 0.480514 11: -3.94702 -0.733943 12: 1.695 -0.956646 13: -7.16286 -0.148857 14: -5.83103 -0.616134 15: -2.72028 -0.152211 16: -6.99199 -0.540809 17: -5.69001 -0.45772 18: 2.10236 0.465041 19: 2.10788 0.951892 20: 1.92533 0.413148 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.) -0.188052 -0.791490 -0.231158 -0.972916 0.090412 -0.691681 0.129610 -0.991565 0.853019 -0.110488 0.991716 -0.128453 -0.390971 -0.605845 -0.542228 -0.840231 -0.536925 -0.287747 -0.881406 -0.472360 0.016789 0.375952 0.044613 0.999004 0.655784 0.485631 0.803636 0.595121 -0.762793 -0.226869 -0.958504 -0.285078 0.578353 0.278420 0.901030 0.433757 0.490690 -0.625882 0.616986 -0.786974 -0.598460 -0.582419 -0.716646 -0.697437 0.589587 0.386518 0.836307 0.548261 -0.360135 0.254376 -0.816794 0.576930 0.532479 0.596318 0.666052 0.745905 0.216689 -0.122295 0.870874 -0.491506 -0.362212 -0.138482 -0.934062 -0.357112 0.370335 -0.469978 0.618923 -0.785452 -0.330909 0.462682 -0.581728 0.813383 -0.564454 -0.355816 -0.845949 -0.533263 -0.883783 0.292608 -0.949322 0.314307 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.) -0.664740 0.288674 -0.917243 0.398327 -0.511289 -0.758723 -0.558835 -0.829279 0.230701 0.884058 0.252501 0.967597 0.055537 0.802778 0.069016 0.997616 -0.728212 -0.630119 -0.756202 -0.654339 -0.875504 0.337326 -0.933133 0.359530 -0.493880 -0.363407 -0.322179 -0.237066 -0.546465 0.102281 -0.393172 0.073589 -0.083163 -0.913141 -0.090698 -0.995878 0.292540 0.838311 0.329478 0.944163 -0.551786 -0.610363 -0.670615 -0.741806 -0.821624 0.111660 -0.990891 0.134663 0.507645 -0.341658 0.331843 -0.223339 -0.412739 0.840616 -0.440736 0.897637 -0.048074 0.919296 -0.052223 0.998635 0.438770 -0.786163 0.487350 -0.873207 0.468820 -0.651995 0.583799 -0.811898 0.135632 -0.635261 0.083520 -0.391183 -0.239018 0.366842 -0.218362 0.335139 0.640820 -0.189704 0.383547 -0.113542 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.) 0.225063 0.542198 0.153351 0.369437 0.835956 -0.411677 1.000000 -0.411677 -0.747526 0.375857 -1.000000 0.375857 0.051530 -0.676117 0.030398 -0.398843 -0.849383 -0.582814 -1.000000 -0.582814 0.253534 -0.941527 0.253534 -1.000000 -0.413069 -0.546588 -0.241167 -0.319121 -0.490860 -0.736234 -0.490860 -1.000000 0.018247 -0.816746 0.018247 -1.000000 0.911619 0.187760 1.000000 0.187760 0.820609 0.314708 1.000000 0.314708 0.508639 0.841952 0.508639 1.000000 -0.508960 0.869744 -0.508960 1.000000 0.330081 0.835782 0.330081 1.000000 -0.480787 -0.942060 -0.480787 -1.000000 -0.533417 -0.600832 -0.533417 -1.000000 0.403709 -0.301372 0.320537 -0.239283 0.049232 0.727883 0.049232 1.000000 0.415967 0.130482 0.381663 0.119722 -0.613983 0.960617 -0.613983 1.000000 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.) -0.542556 -0.276824 -0.433013 -0.250000 -0.199498 0.863828 -0.199498 0.866025 -0.580898 -0.308738 -0.433013 -0.250000 0.513781 0.554598 0.638297 0.626488 0.723125 0.119598 0.878994 0.209589 -0.608533 -0.173069 -0.433013 -0.173069 0.038093 -0.566864 -0.000000 -0.500000 0.073132 -0.838299 0.073132 -0.866025 -0.457961 -0.694433 -0.563792 -0.755535 -0.352849 -0.772625 -0.352849 -0.866025 0.327078 0.814649 0.327078 0.866025 -0.586448 0.108854 -0.433013 0.108854 0.005975 0.645606 0.000000 0.500000 0.769963 0.312146 0.807327 0.333719 0.233631 0.826060 0.233631 0.866025 -0.536383 0.495802 -0.669407 0.572603 0.526740 -0.268104 0.433013 -0.250000 -0.244815 -0.659438 -0.244815 -0.866025 -0.329461 -0.389760 -0.294831 -0.329779 -0.405478 0.725884 -0.405478 0.866025 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.) -0.229060 0.742425 -0.294816 0.955554 -0.103236 0.871675 -0.077713 0.946642 0.347912 0.193201 0.347912 0.000000 0.171118 0.166250 0.171118 0.000000 -0.547354 0.547516 -0.707002 0.707211 0.932492 0.187431 0.980392 0.197059 0.072013 0.536715 0.260395 0.750919 -0.303956 0.900551 -0.319798 0.947486 0.461497 0.629837 0.407265 0.590189 -0.128113 0.642529 -0.010302 0.920943 -0.322690 0.643345 -0.448344 0.893861 -0.314424 0.560707 -0.489111 0.872222 0.617378 0.432700 0.520228 0.391382 -0.617663 0.717502 -0.652410 0.757866 0.146846 0.342575 0.150000 0.000000 0.397385 0.860814 0.419133 0.907925 -0.269960 0.599907 -0.410367 0.911920 -0.696201 0.638199 -0.737146 0.675733 0.608714 0.046835 0.598924 0.046380 0.416312 0.438804 0.480808 0.473473 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.) 0.731781 -0.601909 0.941123 -0.681346 -0.103245 0.506552 -0.103185 0.499773 0.237380 0.768347 0.240603 0.999161 -0.219868 -0.741657 -0.203098 -0.496562 0.327551 -0.939712 0.329622 -0.997036 0.602695 -0.944371 0.607617 -0.964028 -0.872704 -0.603828 -0.958622 -0.627981 0.334910 -0.891983 0.339031 -0.996681 0.303255 0.547130 0.290030 0.485205 -0.438878 -0.612344 -0.363916 -0.460478 -0.143637 -0.929677 -0.143846 -0.999893 0.712626 0.274597 0.492402 0.246851 -0.030123 -0.792401 -0.030130 -1.000000 -0.667082 -0.794480 -0.729723 -0.920018 -0.583974 -0.230659 -0.495018 -0.222573 0.614703 -0.942122 0.619737 -0.960886 0.033151 0.782259 0.033159 1.000000 -0.735671 -0.465948 -0.984232 -0.498181 0.737480 -0.496432 0.978682 -0.536072 -0.487252 -0.710181 -0.529898 -0.979678 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.) 0.902660 0.489995 0.000000 1.000000 5.645981 -0.086337 0.000000 1.000000 0.212877 -3.125465 0.000000 -5.000000 -4.464644 -1.011386 0.000000 1.000000 -4.418933 -2.162285 0.000000 1.000000 -0.294628 -3.221220 0.000000 -5.000000 -3.221049 -3.791811 0.000000 -5.000000 -1.241687 -1.916566 0.000000 1.000000 6.061583 -0.269751 0.000000 1.000000 -1.645938 -1.481955 0.000000 1.000000 0.837257 -1.404098 0.000000 1.000000 4.791183 -3.949108 0.000000 -5.000000 3.511511 -1.094386 0.000000 1.000000 -1.797815 -3.575238 0.000000 -5.000000 -6.001104 0.797067 0.000000 1.000000 -6.235789 -0.692599 0.000000 -5.000000 0.495959 -1.950720 0.000000 1.000000 -5.502541 0.385117 0.000000 1.000000 -0.561136 -0.771143 0.000000 1.000000 0.550456 -4.272204 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.) 0.918559 0.206244 0.975708 0.219076 0.875465 0.129119 0.952292 0.052292 0.900014 -0.084055 0.942034 -0.042034 0.717165 0.095655 0.677463 0.063242 0.828497 0.088727 0.908612 0.008612 0.368557 -0.003120 0.344649 -0.092348 0.883235 0.016851 0.900043 0.000043 0.964146 -0.173753 0.984146 -0.177358 0.370692 0.020147 0.340824 -0.091323 0.963040 0.228531 0.972980 0.230890 0.191137 0.017796 0.173884 -0.046592 0.265883 -0.059673 0.262991 -0.070468 0.681014 -0.079022 0.671585 -0.069825 0.826927 0.070856 0.900000 0.000000 0.635445 -0.155690 0.631800 -0.169290 0.747974 -0.112892 0.726092 -0.194556 0.581704 -0.110206 0.583622 -0.098650 0.467944 0.091292 0.517743 0.056866 0.296345 0.027401 0.269643 -0.072251 0.228033 0.050293 0.200184 -0.053639 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.) 0.905775 0.693517 1.000000 0.693517 0.820393 0.013206 0.820393 0.000000 0.397055 0.576251 0.300000 0.663397 0.945251 0.916627 1.000000 0.916627 0.513207 0.080023 0.513207 0.000000 0.382341 0.822056 0.326884 0.790038 0.922658 0.269029 1.000000 0.269029 0.415491 0.080228 0.415491 0.000000 0.679077 0.263414 0.650000 0.313397 0.507361 0.572347 0.550000 0.486603 0.209879 0.246113 0.000000 0.246113 0.073889 0.118142 0.000000 0.118142 0.935444 0.173440 1.000000 0.173440 0.734013 0.460237 0.682420 0.430450 0.705238 0.159707 0.705238 0.000000 0.197390 0.433830 0.000000 0.433830 0.678491 0.202736 0.650000 0.313397 0.021384 0.631602 0.000000 0.631602 0.102742 0.688950 0.164621 0.724676 0.568339 0.975135 0.568339 1.000000 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.) 0.855854 0.427892 1.000000 0.427892 0.521006 0.359780 0.521006 0.000000 0.926086 0.177788 1.000000 0.177788 0.481938 0.066799 0.481938 0.000000 0.283610 0.295217 0.000000 0.295217 0.378326 0.586576 0.000000 0.586576 0.162068 0.326657 0.000000 0.326657 0.244589 0.440544 0.000000 0.440544 0.980555 0.935747 1.000000 0.935747 0.219532 0.204207 0.219532 0.000000 0.379881 0.463414 0.000000 0.463414 0.526300 0.906725 0.000000 0.000000 0.329354 0.958878 0.000000 0.000000 0.847337 0.884613 0.000000 0.000000 0.429366 0.656776 0.000000 0.000000 0.880509 0.586126 1.000000 0.586126 0.066553 0.061461 0.066553 0.000000 0.721822 0.748956 0.000000 0.000000 0.035595 0.788682 0.000000 0.788682 0.912419 0.187926 1.000000 0.187926 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.) 0.677323 0.019348 0.677323 0.000000 0.315630 0.347502 0.500000 0.500000 0.658233 0.373230 0.658233 0.500000 0.952711 0.173540 1.000000 0.173540 0.408925 0.279054 0.500000 0.500000 0.076194 0.730883 0.000000 0.730883 0.470782 0.469868 0.500000 0.500000 0.406190 0.296529 0.500000 0.500000 0.412232 0.673098 0.500000 0.673098 0.062044 0.151844 0.000000 0.151844 0.106020 0.320475 0.000000 0.320475 0.097659 0.211267 0.000000 0.211267 0.042354 0.261288 0.000000 0.261288 0.792564 0.366740 0.792564 0.500000 0.828411 0.184493 1.000000 0.184493 0.105768 0.862407 0.000000 0.862407 0.498860 0.774265 0.500000 0.774265 0.260358 0.307511 0.500000 0.500000 0.166354 0.017776 0.166354 0.000000 0.116804 0.736502 0.000000 0.736502 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.) 0.784594 0.656975 0.625000 0.656975 0.273707 0.831845 0.273707 1.000000 0.546994 0.365767 0.546994 0.375000 0.662043 0.388191 0.625000 0.388191 0.384480 0.426395 0.500000 0.426395 0.722185 0.398649 0.625000 0.398649 0.265219 0.635849 0.500000 0.635849 0.000495 0.069406 0.000000 0.069406 0.799869 0.549488 0.625000 0.549488 0.693724 0.007113 0.693724 0.000000 0.123353 0.634040 0.000000 0.634040 0.228947 0.758270 0.000000 0.758270 0.124279 0.830590 0.000000 0.830590 0.819549 0.480298 1.000000 0.480298 0.308724 0.024558 0.308724 0.000000 0.446287 0.922073 0.500000 0.922073 0.246842 0.482277 0.000000 0.482277 0.907763 0.259745 1.000000 0.259745 0.317029 0.118203 0.317029 0.000000 0.858704 0.499357 1.000000 0.499357 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.) 16.834454 1.796599 20.043920 1.622740 79.139976 8.571684 78.780670 8.465992 75.532826 29.440211 76.207757 30.218429 61.618880 37.887717 61.727580 38.242174 51.476484 61.731712 55.000000 61.731712 16.274160 16.195388 13.941991 17.315312 24.822578 25.299753 21.784358 28.352735 51.721391 49.321216 55.000000 49.321216 40.169899 28.719269 40.284868 28.383379 29.790886 32.811124 29.022814 34.058151 50.935053 68.502602 55.000000 68.502602 48.815190 64.314648 45.000000 64.314648 48.367662 63.641606 45.000000 63.641606 79.558551 23.666110 81.224820 25.000212 18.930115 17.542213 15.168353 19.666123 47.210831 34.418785 47.576856 29.901979 86.282532 16.166098 86.537299 16.279613 50.730821 40.678703 55.000000 40.678703 74.965972 21.172634 72.880073 19.403667 65.629684 26.332256 65.312473 25.797833 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.) 502.970146 304.516563 480.204521 288.237049 533.989852 440.551027 564.496325 432.965819 345.979926 333.362122 369.246541 312.234496 546.854777 375.771200 565.995170 381.894383 389.318083 403.698677 349.331830 431.314540 424.718002 362.942087 412.591160 327.252380 387.427772 583.545035 387.159716 584.880943 283.566611 167.748797 272.207042 155.853392 408.893529 551.853194 413.357686 586.115630 454.282286 326.165015 448.520827 299.687934 538.203288 492.416004 545.867460 497.928036 434.837389 391.862522 412.591160 327.252380 197.525626 275.144548 184.388266 248.226071 348.364871 528.068869 341.636630 520.125190 515.137911 285.531138 510.928958 266.303225 451.240911 565.354072 454.634970 572.949166 542.620110 315.595771 576.511939 323.656178 394.451684 550.463118 387.530659 584.955375 293.106086 251.788881 276.775786 263.821160 334.088048 200.047442 337.167553 197.553351 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.) -2.263377 -0.613693 -8.000000 -0.613693 -1.023971 -0.836431 -8.000000 -0.836431 3.234416 0.237169 -8.000000 0.237169 1.620205 0.755298 -8.000000 0.755298 3.995001 0.342595 -8.000000 0.342595 3.401740 0.614746 -8.000000 0.614746 4.263986 0.054660 -8.000000 0.054660 1.098070 0.028886 -8.000000 0.028886 -0.301849 0.038581 -8.000000 0.038581 -1.697632 -0.582815 -8.000000 -0.582815 5.968684 0.084123 -8.000000 0.084123 2.026418 0.932250 -8.000000 0.932250 -0.114320 -0.451567 -8.000000 -0.451567 5.210537 0.711702 -8.000000 0.711702 -3.711305 -0.579993 -8.000000 -0.579993 -0.788395 -0.714867 -8.000000 -0.714867 -4.171434 -0.278184 -8.000000 -0.278184 -6.619715 -0.339700 -8.000000 -0.339700 -2.175077 -0.577608 -8.000000 -0.577608 -1.843689 0.522218 -8.000000 0.522218 test_triangulation_test04(): p00_boundary_eps() makes an image of the boundary. The boundary will be drawn to a relative fineness of H_RELATIVE = 0.050000 The boundary nodes will NOT be shown. Test number = 1 Title: = "#1: The unit circle.". H = 0.100000 Graphics saved as "p01_boundary.png" Boundary image file is "p01_boundary.png". Test number = 2 Title: = "#2: The circle with concentric circular hole.". H = 0.100000 Graphics saved as "p02_boundary.png" Boundary image file is "p02_boundary.png". Test number = 3 Title: = "#3: The unit square with circular hole.". H = 0.100000 Graphics saved as "p03_boundary.png" Boundary image file is "p03_boundary.png". Test number = 4 Title: = "#4: The unit hexagon with hexagonal hole.". H = 0.100000 Graphics saved as "p04_boundary.png" Boundary image file is "p04_boundary.png". Test number = 5 Title: = "#5: The horn.". H = 0.100000 Graphics saved as "p05_boundary.png" Boundary image file is "p05_boundary.png". Test number = 6 Title: = "#6: The superellipse with superelliptical hole.". H = 0.100000 Graphics saved as "p06_boundary.png" Boundary image file is "p06_boundary.png". Test number = 7 Title: = "#7: Bicycle seat (implicit).". H = 0.785398 Graphics saved as "p07_boundary.png" Boundary image file is "p07_boundary.png". Test number = 8 Title: = "#8: Pie slice with notch and hole.". H = 0.050000 Graphics saved as "p08_boundary.png" Boundary image file is "p08_boundary.png". Test number = 9 Title: = "#9: Jeff Borggaard's Box with 2 hexagonal holes.". H = 0.050000 Graphics saved as "p09_boundary.png" Boundary image file is "p09_boundary.png". Test number = 10 Title: = "#10: The unit square.". H = 0.050000 Graphics saved as "p10_boundary.png" Boundary image file is "p10_boundary.png". Test number = 11 Title: = "#11: The L-shaped region.". H = 0.050000 Graphics saved as "p11_boundary.png" Boundary image file is "p11_boundary.png". Test number = 12 Title: = "#12: John Shadid's H-shaped region.". H = 0.050000 Graphics saved as "p12_boundary.png" Boundary image file is "p12_boundary.png". Test number = 13 Title: = "#13: The Sandia Fork region.". H = 5.000000 Graphics saved as "p13_boundary.png" Boundary image file is "p13_boundary.png". Test number = 14 Title: = "#14: Marcus Garvie's Lake Alpha with Beta Island.". H = 32.700000 Graphics saved as "p14_boundary.png" Boundary image file is "p14_boundary.png". Test number = 15 Title: = "#15: Sangbum Kim's forward step.". H = 0.800000 Graphics saved as "p15_boundary.png" Boundary image file is "p15_boundary.png". test_triangulation_test05(): p00_points_plot() makes an image of sample points, and the boundary. Test number = 1 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.050000 Title: = "#1: The unit circle." Graphics saved as "p01_points.png" Test number = 2 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.050000 Title: = "#2: The circle with concentric circular hole." Graphics saved as "p02_points.png" Test number = 3 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.050000 Title: = "#3: The unit square with circular hole." Graphics saved as "p03_points.png" Test number = 4 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.043301 Title: = "#4: The unit hexagon with hexagonal hole." Graphics saved as "p04_points.png" Test number = 5 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.025000 Title: = "#5: The horn." Graphics saved as "p05_points.png" Test number = 6 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.050000 Title: = "#6: The superellipse with superelliptical hole." Graphics saved as "p06_points.png" Test number = 7 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.150000 Title: = "#7: Bicycle seat (implicit)." Graphics saved as "p07_points.png" Test number = 8 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.012941 Title: = "#8: Pie slice with notch and hole." Graphics saved as "p08_points.png" 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." Graphics saved as "p09_points.png" Test number = 10 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.025000 Title: = "#10: The unit square." Graphics saved as "p10_points.png" Test number = 11 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.025000 Title: = "#11: The L-shaped region." Graphics saved as "p11_points.png" Test number = 12 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.025000 Title: = "#12: John Shadid's H-shaped region." Graphics saved as "p12_points.png" Test number = 13 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 2.500000 Title: = "#13: The Sandia Fork region." Graphics saved as "p13_points.png" 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." Graphics saved as "p14_points.png" Test number = 15 Spatial dimension = 2 Relative spacing = 0.025000 Actual spacing H = 0.050000 Title: = "#15: Sangbum Kim's forward step." Graphics saved as "p15_points.png" 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. 10-May-2026 09:07:34