16-May-2025 09:22:55 test_triangulation_test(): MATLAB/Octave version 6.4.0 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: -0.0115424 -0.460495 2: -0.346529 0.744855 3: -0.819471 -0.157142 4: -0.278213 -0.905326 5: -0.653671 -0.662067 6: -0.962052 0.133988 7: 0.0873599 -0.198571 8: 0.0619763 -0.655026 9: -0.587643 -0.0641372 10: 0.156129 0.900463 11: 0.423045 -0.148909 12: 0.489673 0.618431 13: 0.182501 0.964372 14: -0.479598 0.177433 15: 0.171373 -0.913275 16: 0.33414 -0.297049 17: -0.221875 -0.938689 18: 0.215664 0.515954 19: 0.0581255 0.663772 20: 0.88197 -0.445034 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: 0.614163 0.282454 2: -0.844684 0.333702 3: 0.907978 0.115672 4: -0.455291 0.480406 5: 0.0454714 0.717591 6: -0.272536 -0.432515 7: -0.698452 0.548848 8: 0.225717 0.393099 9: -0.0908102 0.933723 10: -0.336905 0.881222 11: 0.41955 0.12327 12: -0.325739 0.646732 13: -0.264586 -0.782129 14: -0.351834 0.914182 15: 0.548916 0.423467 16: -0.239817 0.503647 17: 0.6536 -0.209249 18: -0.728356 0.664652 19: -0.204595 0.685648 20: -0.920729 0.142809 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: -0.860811 0.824777 2: -0.439301 0.288713 3: -0.414345 0.0392054 4: 0.582733 -0.150455 5: 0.225379 0.895563 6: 0.431383 0.389399 7: -0.414629 -0.755018 8: 0.484333 0.647926 9: 0.708166 -0.62324 10: 0.471357 -0.694415 11: 0.707531 0.0380554 12: 0.764134 -0.732451 13: 0.43149 0.189862 14: 0.436212 0.825649 15: 0.732618 -0.70703 16: -0.991403 0.56867 17: 0.0530448 -0.621453 18: -0.30851 -0.970434 19: 0.727454 -0.389495 20: 0.879435 -0.811394 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: -0.360508 -0.303695 2: 0.497164 0.462945 3: -0.273573 0.393233 4: -0.352294 -0.321541 5: -0.227386 -0.804029 6: -0.490408 -0.452469 7: 0.0648117 -0.822257 8: 0.344618 -0.5067 9: 0.708414 0.00716441 10: 0.551795 0.26879 11: -0.519086 0.675762 12: 0.464015 0.103114 13: -0.614201 -0.0390319 14: -0.117653 0.83511 15: -0.531448 -0.758448 16: 0.660818 0.505714 17: 0.194273 0.534572 18: 0.623682 -0.204396 19: 0.374057 -0.81299 20: 0.74329 -0.112196 Test number = 5 Title: = "#5: The horn." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: 0.0408719 0.575379 2: 0.00380721 0.509994 3: 0.393939 0.596735 4: -0.457968 0.704395 5: -0.460192 0.793601 6: 0.0880653 0.842538 7: 0.407089 0.49601 8: 0.160411 0.702804 9: 0.603034 0.109675 10: -0.863094 0.334765 11: 0.78683 0.398768 12: 0.142546 0.28368 13: -0.00849301 0.778859 14: -0.237256 0.833445 15: 0.734151 0.3965 16: 0.129623 0.270089 17: 0.37414 0.914358 18: 0.770837 0.232031 19: 0.193935 0.58941 20: 0.825753 0.0120192 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: 0.335357 -0.62194 2: 0.781099 0.696003 3: -0.811449 -0.610898 4: -0.477565 -0.694906 5: 0.585732 0.28645 6: 0.0802099 -0.835439 7: 0.681093 -0.554445 8: -0.825084 0.649124 9: 0.243597 -0.843456 10: 0.521718 0.656143 11: 0.553662 0.574724 12: 0.623671 -0.736601 13: 0.538149 -0.608034 14: -0.622794 -0.649452 15: 0.865792 0.758431 16: -0.448058 0.46931 17: -0.199011 -0.993902 18: 0.0304614 0.658819 19: -0.747958 0.668885 20: -0.769506 0.566967 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: -0.226357 -4.50989 2: -3.51149 -2.67131 3: -5.12024 -2.18832 4: -5.19618 0.0614132 5: -0.166467 -0.0731459 6: -5.96807 -0.767054 7: 4.4881 -3.07465 8: -1.68329 -1.70841 9: 5.42819 -2.342 10: -0.84517 -3.80221 11: -4.76464 -3.3537 12: 6.13416 -1.32169 13: -4.85412 -1.41057 14: -4.90727 -4.08273 15: 3.56874 -3.04462 16: -1.47149 -0.592417 17: -2.8813 -4.47621 18: -5.46552 -1.38277 19: -6.23045 -0.926334 20: 1.60785 -3.40707 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: 0.892448 -0.0974194 2: 0.958088 0.0905974 3: 0.75314 -0.131525 4: 0.76363 -0.181485 5: 0.43953 -0.100518 6: 0.451091 -0.0799719 7: 0.740457 -0.138584 8: 0.786602 0.0778956 9: 0.736097 -0.101988 10: 0.44186 -0.110165 11: 0.945343 -0.164179 12: 0.708147 -0.0944432 13: 0.6799 0.0623328 14: 0.928676 0.194403 15: 0.77635 -0.0287528 16: 0.863147 0.17081 17: 0.438949 -0.105285 18: 0.634705 -0.162998 19: 0.488771 -0.10022 20: 0.980754 -0.153302 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: 0.557331 0.730088 2: 0.652967 0.888145 3: 0.847331 0.507947 4: 0.814474 0.48249 5: 0.763647 0.244979 6: 0.655991 0.586774 7: 0.0675937 0.383154 8: 0.549592 0.728963 9: 0.768809 0.552233 10: 0.0585351 0.31004 11: 0.318829 0.923596 12: 0.57325 0.561907 13: 0.270282 0.278498 14: 0.949589 0.00608978 15: 0.0495794 0.620499 16: 0.41424 0.264594 17: 0.255396 0.179113 18: 0.14137 0.552398 19: 0.800382 0.254688 20: 0.901962 0.424702 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: 0.467163 0.871073 2: 0.953921 0.0225778 3: 0.879349 0.241603 4: 0.260988 0.61385 5: 0.589497 0.389421 6: 0.287627 0.710975 7: 0.479041 0.357966 8: 0.962235 0.409771 9: 0.165182 0.463724 10: 0.856348 0.0779079 11: 0.327588 0.00556924 12: 0.7521 0.209731 13: 0.906447 0.383935 14: 0.936811 0.388129 15: 0.516795 0.953417 16: 0.98597 0.170452 17: 0.81595 0.505636 18: 0.697212 0.282746 19: 0.0840962 0.206896 20: 0.496106 0.115105 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: 0.361425 0.473293 2: 0.227986 0.0732532 3: 0.608493 0.155884 4: 0.826716 0.347074 5: 0.296307 0.708822 6: 0.40105 0.452911 7: 0.996759 0.184216 8: 0.434222 0.673994 9: 0.0865833 0.239687 10: 0.358551 0.982481 11: 0.11651 0.856248 12: 0.472381 0.220782 13: 0.123679 0.229734 14: 0.920958 0.193293 15: 0.532242 0.0689805 16: 0.455458 0.00253837 17: 0.263823 0.93622 18: 0.83392 0.179086 19: 0.0872435 0.24389 20: 0.36583 0.46681 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: 0.404685 0.491141 2: 0.439238 0.141136 3: 0.494686 0.863428 4: 0.371321 0.655976 5: 0.360925 0.0660316 6: 0.931381 0.160322 7: 0.738899 0.917358 8: 0.356571 0.820753 9: 0.628484 0.0393321 10: 0.389468 0.903909 11: 0.433647 0.873484 12: 0.115952 0.407998 13: 0.195975 0.839011 14: 0.919576 0.703603 15: 0.765151 0.124054 16: 0.919666 0.638981 17: 0.258124 0.894588 18: 0.458049 0.862061 19: 0.325877 0.320192 20: 0.30365 0.682093 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: 53.1424 84.1806 2: 37.145 30.9403 3: 14.3452 4.86143 4: 49.3265 32.2548 5: 14.5128 9.6618 6: 48.1632 56.004 7: 77.1745 22.8272 8: 50.6479 74.0837 9: 53.2248 58.5465 10: 54.0927 33.4236 11: 56.4737 33.8074 12: 14.228 11.5574 13: 30.703 29.718 14: 59.845 37.3244 15: 27.841 32.0832 16: 47.5576 70.3665 17: 24.8427 19.21 18: 54.2343 40.1531 19: 56.0405 31.9452 20: 53.9175 36.3443 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: 368.028 422.273 2: 527.96 346.938 3: 253.652 394.76 4: 516.966 514.402 5: 492.233 374.793 6: 298.172 781.65 7: 332.772 536.435 8: 313.129 368.265 9: 310.231 555.487 10: 205.209 306.296 11: 315.713 542.731 12: 359.22 783.848 13: 277.715 732.763 14: 478.14 433.294 15: 441.746 359.268 16: 292.022 644.652 17: 564.241 468.573 18: 154.373 310.106 19: 542.252 284.96 20: 440.145 415.607 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: -0.685131 -0.299026 2: -0.794586 -0.943016 3: -1.71279 0.224147 4: 1.24286 0.382869 5: -1.27645 0.344751 6: 0.191955 -0.622795 7: -5.38136 -0.291851 8: 2.85179 0.387481 9: -5.28168 -0.576651 10: 0.342814 -0.743473 11: -0.833533 0.9324 12: -5.60125 -0.965556 13: 4.16611 0.661675 14: 1.86005 0.0176402 15: 3.00011 0.836736 16: 1.02291 0.364967 17: 6.44005 0.637733 18: -5.6894 -0.616206 19: 4.8465 0.155058 20: 1.15817 -0.400097 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.) -0.806513 -0.435169 -0.880064 -0.474855 0.377777 0.815676 0.420260 0.907404 -0.553918 -0.317984 -0.867257 -0.497860 -0.863001 0.326254 -0.935389 0.353620 -0.285344 0.336333 -0.646938 0.762542 -0.206811 0.827046 -0.242590 0.970129 0.768381 -0.565184 0.805552 -0.592525 0.014150 -0.487524 0.029012 -0.999579 -0.084817 0.119248 -0.579610 0.814894 0.308804 0.574482 0.473467 0.880811 0.135190 0.410286 0.312950 0.949770 0.120131 0.823446 0.144360 0.989525 -0.318454 0.680150 -0.424034 0.905646 -0.360546 -0.085811 -0.972826 -0.231535 -0.161386 -0.591494 -0.263222 -0.964735 -0.428668 0.292783 -0.825770 0.564007 -0.908732 0.249608 -0.964285 0.264867 0.347616 0.804412 0.396682 0.917956 -0.464790 -0.001960 -0.999991 -0.004216 -0.690504 0.511131 -0.803754 0.594962 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.) 0.099544 -0.420723 0.092098 -0.389253 -0.412165 -0.644491 -0.538767 -0.842455 0.748757 0.114755 0.988459 0.151491 0.469672 0.087316 0.393262 0.073111 0.047432 0.643289 0.029413 0.398917 0.751197 -0.544463 0.809690 -0.586858 0.236786 0.401942 0.203031 0.344642 -0.801205 0.545852 -0.826431 0.563039 0.858868 0.045664 0.998590 0.053093 -0.613936 -0.163348 -0.386552 -0.102849 -0.155077 -0.471615 -0.124947 -0.379985 0.735518 0.144658 0.981203 0.192978 -0.459488 -0.232109 -0.357033 -0.180354 -0.254676 -0.654038 -0.362852 -0.931847 -0.668984 -0.603180 -0.742690 -0.669636 -0.775420 -0.002531 -0.999995 -0.003265 -0.013784 0.637911 -0.008641 0.399907 0.612247 -0.283872 0.362891 -0.168257 -0.021377 0.605793 -0.014106 0.399751 0.870777 -0.251677 0.960679 -0.277661 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.) -0.888476 0.478788 -1.000000 0.478788 -0.568754 -0.578212 -0.280501 -0.285165 0.706605 0.346226 1.000000 0.346226 0.953933 -0.341051 1.000000 -0.341051 0.935601 0.643925 1.000000 0.643925 -0.606345 -0.483966 -0.312627 -0.249529 0.330236 0.827061 0.330236 1.000000 0.781243 -0.775023 1.000000 -0.775023 -0.484622 -0.431364 -0.298783 -0.265948 0.025191 0.648825 0.015518 0.399699 0.409721 0.333440 0.310245 0.252484 -0.498955 -0.668492 -0.498955 -1.000000 -0.310070 0.929051 -0.310070 1.000000 0.707309 -0.712167 0.707309 -1.000000 0.990859 -0.197373 1.000000 -0.197373 0.424025 0.113821 0.386324 0.103700 -0.600529 0.144954 -0.388833 0.093856 -0.737773 0.917750 -0.737773 1.000000 0.508762 -0.965558 0.508762 -1.000000 0.598554 -0.344793 0.346606 -0.199660 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.) 0.079884 -0.732245 0.079884 -0.866025 0.445210 0.164441 0.433013 0.164441 0.221413 -0.691533 0.221413 -0.866025 -0.336569 -0.807327 -0.336569 -0.866025 0.408998 0.340608 0.375767 0.283051 -0.534285 -0.319497 -0.433013 -0.250000 0.584552 -0.568456 0.649989 -0.606237 -0.551532 0.625999 -0.616818 0.663691 0.768697 0.314871 0.805831 0.336310 0.437650 -0.479238 0.337228 -0.305301 -0.310203 0.536892 -0.216678 0.374901 -0.716497 -0.143614 -0.866938 -0.230471 0.395788 -0.775207 0.395788 -0.866025 0.809424 0.028736 0.939913 0.104074 0.788405 -0.105379 0.901471 -0.170657 0.514570 -0.831183 0.518730 -0.833585 0.504583 0.266658 0.433013 0.250000 -0.527616 -0.072362 -0.433013 -0.072362 -0.394860 0.589074 -0.593638 0.703839 0.055647 0.494825 0.043976 0.474610 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.) 0.664297 0.621788 0.730080 0.683362 0.223087 0.466461 0.400526 0.599297 0.454887 0.160958 0.582733 0.185028 0.363869 0.558534 0.407229 0.590239 -0.225092 0.915723 -0.238702 0.971093 0.207515 0.510810 0.365396 0.643559 0.600362 0.198030 0.580964 0.194190 0.507599 0.213522 0.573425 0.229008 0.629338 0.613191 0.716235 0.697859 0.834277 0.270706 0.951179 0.308639 0.649695 0.262011 0.570232 0.242177 -0.120656 0.698324 -0.028592 0.928470 0.292242 0.182825 0.292242 0.000000 0.227745 0.259398 0.227745 0.000000 -0.486059 0.845567 -0.498361 0.866969 0.338589 0.783210 0.286079 0.727527 -0.732369 0.605599 -0.770653 0.637256 0.560400 0.675555 0.638460 0.769655 0.498452 0.121633 0.590960 0.134157 0.019442 0.709282 0.109018 0.860756 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.) 0.818226 0.156481 0.999847 0.157186 0.969964 -0.366752 0.995381 -0.368037 -0.761641 0.045037 -0.999999 0.045059 0.980388 0.444208 0.990041 0.445085 -0.438391 0.532571 -0.385194 0.448563 0.718401 -0.321947 0.487460 -0.278758 0.804390 -0.474048 0.984353 -0.497246 -0.262127 -0.591935 -0.249169 -0.492106 0.732367 0.851201 0.762971 0.901720 0.022199 -0.789936 0.022200 -1.000000 0.647314 0.544844 0.441272 0.395970 0.820176 0.271362 0.998565 0.275092 -0.701395 0.428538 -0.470513 0.340801 -0.039001 0.846623 -0.039010 0.999999 0.775181 -0.657868 0.919769 -0.730222 -0.544074 -0.791033 -0.582888 -0.969800 0.927761 -0.549733 0.974721 -0.558571 0.190743 0.808875 0.192097 0.999659 -0.139430 -0.579037 -0.137754 -0.499278 0.274678 0.923121 0.276276 0.998540 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.) 5.217881 -1.077032 0.000000 1.000000 2.867152 -2.033991 0.000000 1.000000 -6.257508 0.398674 0.000000 1.000000 0.761148 -1.391086 0.000000 1.000000 1.057875 -2.113514 0.000000 1.000000 -0.795407 -0.172166 0.000000 1.000000 -1.494736 -4.124034 0.000000 -5.000000 3.335417 -4.079143 0.000000 -5.000000 -5.923952 0.733563 0.000000 1.000000 4.378708 -1.853415 0.000000 1.000000 2.929282 -4.660475 0.000000 -5.000000 1.855318 -3.380058 0.000000 -5.000000 -3.945496 -2.566720 0.000000 1.000000 0.017694 0.638065 0.000000 1.000000 4.340369 -4.195109 0.000000 -5.000000 2.701038 -4.419044 0.000000 -5.000000 1.838778 -3.451903 0.000000 -5.000000 -5.174686 -2.114264 0.000000 -5.000000 7.096272 -0.248923 0.000000 -5.000000 1.330247 -4.702018 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.) 0.632787 0.109629 0.628654 0.095807 0.302981 -0.028726 0.289867 -0.077670 0.692679 -0.176781 0.690474 -0.185012 0.864657 -0.076857 0.920757 -0.020757 0.883338 -0.004317 0.900000 0.000000 0.815101 -0.185883 0.806970 -0.216227 0.117356 -0.002267 0.110061 -0.029491 0.890230 0.098525 0.944378 0.044378 0.852938 0.043101 0.900000 0.000000 0.892578 0.234581 0.967157 0.254181 0.721864 -0.011361 0.699568 -0.009282 0.761383 -0.007427 0.699894 -0.004597 0.794889 0.070756 0.693997 0.034126 0.961351 -0.254029 0.960460 -0.257355 0.145615 0.017019 0.131606 -0.035264 0.916686 0.055180 0.935933 0.035933 0.444100 -0.076549 0.433488 -0.116153 0.124073 0.027369 0.108920 -0.029185 0.690170 -0.086036 0.672350 -0.069033 0.750224 0.083086 0.687507 0.048399 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.) 0.850845 0.059231 0.850845 0.000000 0.083170 0.498118 0.000000 0.498118 0.432491 0.098383 0.432491 0.000000 0.530595 0.633616 0.550000 0.486603 0.862256 0.179713 1.000000 0.179713 0.705380 0.853757 0.705380 1.000000 0.058037 0.617641 0.000000 0.617641 0.161439 0.614210 0.200000 0.663397 0.450460 0.881232 0.450460 1.000000 0.575544 0.778258 0.575544 1.000000 0.225979 0.055836 0.225979 0.000000 0.990611 0.242922 1.000000 0.242922 0.715283 0.185643 0.650000 0.313397 0.458891 0.786188 0.350000 0.750000 0.993993 0.041426 1.000000 0.041426 0.153133 0.966354 0.153133 1.000000 0.980460 0.564074 1.000000 0.564074 0.847264 0.418533 0.700000 0.400000 0.056396 0.821175 0.000000 0.821175 0.384334 0.341500 0.500000 0.400000 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.) 0.914051 0.352033 1.000000 0.352033 0.470469 0.826077 0.000000 0.000000 0.795086 0.551417 1.000000 0.551417 0.951628 0.420593 1.000000 0.420593 0.024049 0.724700 0.000000 0.724700 0.387878 0.169776 0.387878 0.000000 0.490486 0.823277 0.000000 0.000000 0.614616 0.775667 0.000000 0.000000 0.461650 0.745519 0.000000 0.000000 0.601479 0.443316 1.000000 0.443316 0.393832 0.214443 0.393832 0.000000 0.223394 0.687781 0.000000 0.687781 0.307558 0.856339 0.000000 0.000000 0.057929 0.665446 0.000000 0.665446 0.072889 0.530046 0.000000 0.530046 0.131195 0.112959 0.131195 0.000000 0.742271 0.726902 1.000000 0.726902 0.266748 0.850906 0.000000 0.000000 0.075170 0.224452 0.000000 0.224452 0.726636 0.572872 1.000000 0.572872 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.) 0.440696 0.168964 0.440696 0.000000 0.327746 0.323037 0.500000 0.500000 0.587403 0.438557 0.587403 0.500000 0.372921 0.289243 0.500000 0.500000 0.376608 0.104845 0.376608 0.000000 0.320683 0.986802 0.320683 1.000000 0.887533 0.468323 0.887533 0.500000 0.055983 0.403233 0.000000 0.403233 0.395923 0.938541 0.395923 1.000000 0.161283 0.271410 0.000000 0.271410 0.960061 0.072918 1.000000 0.072918 0.913972 0.380902 1.000000 0.380902 0.204419 0.574824 0.000000 0.574824 0.357951 0.310139 0.500000 0.500000 0.187000 0.969050 0.187000 1.000000 0.245757 0.052896 0.245757 0.000000 0.774245 0.066202 0.774245 0.000000 0.295360 0.651233 0.500000 0.651233 0.075811 0.522535 0.000000 0.522535 0.063232 0.426214 0.000000 0.426214 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.) 0.207072 0.779283 0.000000 0.779283 0.183158 0.898159 0.183158 1.000000 0.327097 0.053606 0.327097 0.000000 0.401157 0.119800 0.500000 0.119800 0.096176 0.642347 0.000000 0.642347 0.931703 0.121592 1.000000 0.121592 0.780908 0.072972 0.780908 0.000000 0.115312 0.224687 0.000000 0.224687 0.655501 0.002923 0.655501 0.000000 0.164979 0.458942 0.000000 0.458942 0.983833 0.323324 1.000000 0.323324 0.097075 0.909556 0.097075 1.000000 0.295606 0.598285 0.500000 0.598285 0.780556 0.279462 0.625000 0.250000 0.044093 0.746169 0.000000 0.746169 0.740905 0.399435 0.625000 0.399435 0.905163 0.024484 0.905163 0.000000 0.837376 0.733963 1.000000 0.733963 0.677854 0.610017 0.625000 0.610017 0.846320 0.882388 0.846320 1.000000 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.) 66.619626 26.441877 65.964470 25.399522 49.704023 88.209921 49.704023 90.000000 40.110347 37.724483 39.856573 38.692517 53.712545 35.738996 55.000000 39.686270 54.330985 63.470984 55.000000 63.470984 13.249095 10.990145 11.676882 11.460306 12.643036 11.241768 11.696749 11.526533 60.130486 30.672100 59.408604 28.486456 86.345008 8.104612 89.041116 8.705820 42.435407 29.959164 42.655598 29.087107 18.128824 23.853918 17.976159 23.968179 77.238798 24.834035 79.558958 26.949360 46.981535 75.948170 45.000000 75.948170 82.346259 13.614181 86.867574 15.517152 38.041796 28.072285 38.242898 27.600191 88.927402 5.171880 89.651572 5.268093 31.096910 30.031060 28.691792 33.852035 59.830685 33.426764 58.464422 28.781132 85.959462 3.388773 89.823556 3.752921 72.079972 27.346087 75.128489 31.121682 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.) 394.477690 520.528132 342.871133 512.342361 419.447332 582.972277 419.748399 585.282964 303.317948 178.832306 313.767583 169.748622 375.613970 515.000026 343.263513 509.868635 477.958667 480.424132 526.070548 523.554362 483.185156 552.265531 486.194480 558.680513 156.804159 388.042512 148.339825 396.615723 472.851903 356.302230 458.340250 297.551210 182.845376 395.751294 185.475291 405.184481 520.355393 360.253679 568.588892 365.760647 442.215830 559.054815 449.458583 575.262365 300.989291 204.733503 325.589859 183.348664 303.730692 201.404631 325.121552 182.809935 132.175727 369.104426 129.023627 371.292523 429.573788 335.533211 417.585707 322.616802 511.513937 388.997719 558.875668 404.149160 187.300350 287.566249 171.233860 254.645979 275.544317 308.688339 269.560816 293.202473 285.144401 181.385023 266.221396 161.569411 274.290185 588.994520 273.599402 588.599170 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.) 5.622975 0.569359 -8.000000 0.569359 -0.213913 -0.019476 -8.000000 -0.019476 3.533211 0.964901 -8.000000 0.964901 -0.904213 -0.019382 -8.000000 -0.019382 0.069955 -0.512720 -8.000000 -0.512720 5.915352 0.366456 -8.000000 0.366456 -4.391363 -0.499778 -8.000000 -0.499778 2.596253 0.961028 -8.000000 0.961028 4.780760 0.460721 -8.000000 0.460721 6.467267 0.243805 -8.000000 0.243805 0.729666 0.189673 -8.000000 0.189673 5.956770 0.566331 -8.000000 0.566331 5.117979 0.538701 -8.000000 0.538701 1.791002 0.847359 -8.000000 0.847359 3.674432 0.785711 -8.000000 0.785711 -2.007240 -0.570901 -8.000000 -0.570901 -5.649683 -0.042957 -8.000000 -0.042957 6.495733 0.812627 -8.000000 0.812627 -3.623430 -0.651054 -8.000000 -0.651054 -0.229761 -0.246912 -8.000000 -0.246912 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. 16-May-2025 09:22:59