08-Oct-2025 20:42:24 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: 0.00183265 -0.932509 2: -0.392794 -0.76627 3: -0.304644 0.73461 4: -0.587255 0.552018 5: -0.934652 0.00663981 6: -0.768472 -0.261577 7: -0.984329 -0.146528 8: 0.248286 0.957484 9: 0.153848 0.000685714 10: 0.392983 -0.239727 11: 0.952087 0.227015 12: -0.152792 0.80536 13: -0.759739 0.497193 14: -0.42905 0.854319 15: 0.136324 -0.409972 16: 0.307553 -0.63071 17: -0.390998 -0.145117 18: 0.500684 -0.213673 19: 0.591482 0.189692 20: -0.0152033 -0.526194 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: -0.485613 0.196937 2: 0.805214 0.133068 3: 0.385555 0.638324 4: 0.722033 0.670552 5: 0.692519 -0.260282 6: 0.70248 0.565721 7: -0.263702 -0.374596 8: 0.889081 0.0501386 9: -0.973675 -0.0121179 10: 0.346064 -0.748282 11: -0.210019 0.969723 12: 0.490456 -0.70029 13: -0.0275422 -0.400921 14: 0.824579 0.2332 15: -0.585213 -0.381784 16: 0.0250934 -0.528753 17: 0.136521 0.932512 18: 0.502237 -0.774873 19: -0.789832 0.105058 20: -0.283917 -0.834061 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: -0.872811 -0.995094 2: -0.37417 -0.971433 3: -0.710797 0.774932 4: -0.564773 0.31443 5: -0.808785 -0.535329 6: 0.838197 -0.481112 7: -0.0141474 -0.9801 8: -0.311004 -0.497368 9: 0.446243 0.384612 10: 0.580347 0.464688 11: -0.0362703 -0.465888 12: 0.40556 0.839483 13: 0.488941 0.428269 14: 0.803287 0.98823 15: 0.755768 -0.59909 16: -0.398167 0.973479 17: -0.865866 0.653104 18: 0.756874 -0.862064 19: -0.694645 0.245969 20: -0.332776 -0.497675 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: 0.123398 0.86122 2: 0.698809 -0.185403 3: -0.4593 0.329383 4: -0.550696 0.75837 5: -0.242245 -0.47398 6: -0.594629 -0.121449 7: 0.825852 -0.253214 8: -0.797921 -0.14752 9: -0.656739 0.0934569 10: -0.501578 -0.544668 11: -0.117301 0.73323 12: 0.264267 0.657786 13: -0.271862 0.507229 14: -0.581831 0.641571 15: -0.0192829 -0.546377 16: -0.213404 0.672191 17: 0.324517 0.598315 18: 0.840914 0.0929484 19: 0.417664 0.356956 20: 0.542645 0.414028 Test number = 5 Title: = "#5: The horn." Spatial dimension M = 2 Number of samples N = 20 The sample points: Row: 1 2 Col 1: 0.996544 0.0342043 2: 0.265078 0.0386626 3: 0.968574 0.0105626 4: 0.466157 0.215663 5: 0.61219 0.574282 6: 0.302503 0.222365 7: 0.785213 0.0876854 8: 0.05285 0.484811 9: 0.490135 0.357801 10: 0.793959 0.500302 11: 0.856631 0.123368 12: 0.245803 0.153822 13: 0.341302 0.757045 14: -0.773686 0.446738 15: 0.24182 0.348839 16: 0.738548 0.656937 17: 0.766222 0.413376 18: 0.102435 0.667858 19: 0.863804 0.271334 20: 0.18743 0.709261 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: 0.251304 0.815102 2: 0.673422 -0.299038 3: -0.719986 -0.838884 4: -0.301248 -0.806414 5: -0.487393 0.826136 6: -0.236696 0.64165 7: 0.421033 -0.939921 8: -0.496451 0.598795 9: 0.674256 0.330549 10: 0.354528 -0.86784 11: -0.549304 0.722052 12: 0.67378 -0.535934 13: -0.693542 -0.836933 14: 0.411125 0.626451 15: 0.82165 -0.44513 16: 0.744168 0.489704 17: 0.450544 -0.53301 18: -0.215182 -0.859528 19: 0.552857 -0.681257 20: 0.623007 0.305221 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:-0.000756914 -3.73297 2: -0.0456944 -4.02902 3: -1.57397 -2.72179 4: 5.59263 -0.239687 5: 2.62485 -4.73925 6: 0.715471 0.280548 7: -2.05751 -3.92282 8: 2.78218 -2.43208 9: -2.01485 -0.683289 10: -4.62753 -0.125452 11: 4.88273 -3.14418 12: 5.92609 -3.33687 13: 7.14102 -0.509519 14: -6.5408 -1.10041 15: -0.986369 -4.92998 16: -7.17444 -1.32944 17: 6.7137 -1.67722 18: 3.64996 -4.74225 19: -2.99681 -1.82911 20: 3.57799 -2.63074 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: 0.70246 -0.124934 2: 0.77657 -0.0281001 3: 0.757193 -0.0154934 4: 0.751734 -0.0400975 5: 0.803629 -0.0295971 6: 0.332271 -0.0592193 7: 0.426726 0.0774922 8: 0.198191 -0.0248313 9: 0.415287 0.089356 10: 0.871638 -0.217802 11: 0.759084 0.120752 12: 0.559455 0.109305 13: 0.90007 -0.00949414 14: 0.839574 0.0136907 15: 0.732902 0.0616677 16: 0.315294 0.0542519 17: 0.794858 -0.020218 18: 0.413257 0.10632 19: 0.317465 0.0109735 20: 0.356245 -0.0567789 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: 0.611693 0.619514 2: 0.389512 0.803797 3: 0.111772 0.113955 4: 0.518292 0.780844 5: 0.365977 0.295991 6: 0.17543 0.399475 7: 0.694017 0.807224 8: 0.857925 0.22019 9: 0.898349 0.337216 10: 0.494413 0.61595 11: 0.982716 0.751515 12: 0.173165 0.0197971 13: 0.345632 0.323741 14: 0.792369 0.999523 15: 0.470872 0.988202 16: 0.584403 0.769957 17: 0.12233 0.732565 18: 0.334257 0.928761 19: 0.443847 0.407611 20: 0.093761 0.877432 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: 0.861283 0.0464887 2: 0.195475 0.5879 3: 0.809455 0.364984 4: 0.166753 0.682295 5: 0.866069 0.347348 6: 0.759876 0.701855 7: 0.349547 0.354966 8: 0.461525 0.118822 9: 0.908468 0.061482 10: 0.770142 0.715942 11: 0.096576 0.485511 12: 0.324036 0.930121 13: 0.268928 0.975636 14: 0.971884 0.636534 15: 0.703279 0.434675 16: 0.547596 0.602062 17: 0.651727 0.578056 18: 0.600291 0.0598955 19: 0.585476 0.759548 20: 0.669084 0.491209 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: 0.720835 0.279531 2: 0.954298 0.0333246 3: 0.0614182 0.411884 4: 0.745424 0.23581 5: 0.0124871 0.988159 6: 0.304879 0.999516 7: 0.880236 0.150004 8: 0.215809 0.372919 9: 0.692275 0.357295 10: 0.28131 0.884071 11: 0.692004 0.427938 12: 0.00223197 0.635081 13: 0.445538 0.653334 14: 0.166876 0.0672291 15: 0.388032 0.383544 16: 0.9406 0.445668 17: 0.578562 0.35323 18: 0.573373 0.313097 19: 0.389807 0.604261 20: 0.189113 0.994234 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: 0.704787 0.979488 2: 0.850295 0.680949 3: 0.974755 0.360726 4: 0.351488 0.416556 5: 0.460556 0.593983 6: 0.178609 0.272364 7: 0.394167 0.709438 8: 0.446129 0.569755 9: 0.788165 0.200123 10: 0.346721 0.816639 11: 0.0745237 0.469731 12: 0.941782 0.809523 13: 0.197109 0.346484 14: 0.73616 0.908833 15: 0.258772 0.115335 16: 0.263554 0.815062 17: 0.273805 0.807854 18: 0.264221 0.601066 19: 0.422672 0.914209 20: 0.345298 0.573884 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: 48.0226 49.3328 2: 29.0046 29.4697 3: 89.3911 6.02596 4: 55.6756 31.7523 5: 49.0388 56.2102 6: 39.7429 34.4452 7: 53.4983 67.5254 8: 16.183 0.365904 9: 25.3592 28.5814 10: 70.7426 28.5407 11: 15.5061 2.52932 12: 78.5724 23.4475 13: 50.4046 36.8918 14: 46.1621 37.2854 15: 81.3737 16.5109 16: 39.4302 28.4189 17: 13.0273 3.35837 18: 40.0938 35.4604 19: 51.0867 67.1705 20: 49.1157 64.7469 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: 367.316 457.341 2: 175.491 298.922 3: 461.198 446.116 4: 408.827 585.658 5: 440.031 560.898 6: 435.023 368.678 7: 256.583 756.532 8: 209.242 287.385 9: 253.654 246.695 10: 336.681 556.328 11: 299.138 275.449 12: 269.911 688.066 13: 504.959 341.947 14: 526.358 477.933 15: 448.01 353.107 16: 245.277 398.373 17: 384.835 764.794 18: 387.69 572.579 19: 400.365 494.973 20: 239.17 327.41 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: -0.423672 0.918932 2: -6.58496 -0.644648 3: -3.31706 -0.974959 4: -2.67888 -0.807069 5: -2.07026 -0.163016 6: 1.8826 -0.370535 7: -3.55495 -0.586524 8: 6.80902 0.966848 9: -1.3296 -0.320731 10: 5.56688 0.44634 11: -0.158194 0.995241 12: 3.24387 0.142993 13: -0.314323 -0.765884 14: 0.157921 0.61752 15: 1.02216 0.881195 16: 7.54411 0.148448 17: 6.89539 0.253255 18: -0.642783 0.00457442 19: -7.09715 -0.66725 20: 0.807271 -0.339417 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.) 0.175253 0.010433 0.998233 0.059428 0.677081 -0.395449 0.863510 -0.504332 -0.422237 -0.352478 -0.767672 -0.640843 -0.342658 0.568250 -0.516387 0.856355 -0.355113 -0.088728 -0.970175 -0.242407 -0.724473 0.550271 -0.796336 0.604855 -0.274135 0.411828 -0.554116 0.832439 -0.435386 -0.478691 -0.672852 -0.739777 -0.690738 -0.207965 -0.957542 -0.288293 0.165898 0.626320 0.256048 0.966664 -0.863925 -0.215514 -0.970266 -0.242042 -0.323880 0.407800 -0.621928 0.783074 0.340672 -0.700548 0.437326 -0.899303 -0.356398 0.675405 -0.466692 0.884420 -0.378281 0.915902 -0.381737 0.924271 -0.685984 -0.611855 -0.746279 -0.665634 -0.071676 -0.526464 -0.134901 -0.990859 -0.467917 -0.398021 -0.761705 -0.647924 -0.467947 -0.702522 -0.554371 -0.832270 -0.091875 -0.274064 -0.317847 -0.948142 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.) 0.445211 -0.646129 0.567392 -0.823448 0.947692 0.237552 0.969991 0.243142 0.838867 0.371688 0.914273 0.405099 -0.915696 -0.236259 -0.968290 -0.249829 0.410048 0.595163 0.567349 0.823477 -0.599336 -0.281606 -0.362028 -0.170104 -0.467442 0.427343 -0.295222 0.269897 0.076923 -0.618515 0.049366 -0.396942 0.536088 -0.818959 0.547689 -0.836682 -0.195155 0.397292 -0.176358 0.359024 0.354571 -0.474008 0.239596 -0.320303 -0.675457 -0.717503 -0.685451 -0.728119 -0.339113 -0.561007 -0.206923 -0.342320 -0.250288 0.331450 -0.241047 0.319212 -0.181731 0.671337 -0.104518 0.386103 -0.196993 0.681198 -0.277804 0.960638 -0.096088 -0.752411 -0.126678 -0.991944 -0.672923 -0.448751 -0.831973 -0.554817 0.834925 -0.265873 0.952855 -0.303427 -0.035950 -0.936911 -0.038342 -0.999265 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.) -0.474442 -0.287674 -0.342037 -0.207391 0.725985 0.444701 1.000000 0.444701 -0.793482 0.923773 -0.793482 1.000000 -0.672008 -0.882455 -0.672008 -1.000000 -0.048459 -0.705485 -0.048459 -1.000000 0.386210 0.786140 0.386210 1.000000 -0.992014 0.204942 -1.000000 0.204942 0.262005 0.422775 0.210709 0.340003 -0.979594 0.881666 -1.000000 0.881666 0.484105 0.072622 0.395574 0.059341 0.541686 -0.854948 0.541686 -1.000000 -0.772240 -0.090808 -1.000000 -0.090808 0.268563 -0.894961 0.268563 -1.000000 0.456872 -0.046136 0.397976 -0.040189 0.644589 -0.428109 1.000000 -0.428109 -0.680467 0.797641 -0.680467 1.000000 -0.779534 0.735923 -1.000000 0.735923 -0.346184 0.468666 -0.237658 0.321743 0.968686 0.030293 1.000000 0.030293 0.569291 0.877048 0.569291 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.) 0.427454 0.606907 0.594065 0.703100 0.236618 0.641116 0.236618 0.866025 0.081267 -0.578394 0.027005 -0.484409 -0.842916 0.151066 -0.895315 0.181319 -0.646494 0.214144 -0.818896 0.313681 0.654650 -0.468476 0.710806 -0.500898 0.636101 0.203222 0.433013 0.203222 -0.514232 -0.613370 -0.612961 -0.670371 -0.315250 0.762483 -0.315250 0.866025 0.365696 0.680715 0.365696 0.866025 0.464618 0.101224 0.433013 0.101224 0.585613 -0.074291 0.433013 -0.074291 -0.665568 0.294300 -0.788956 0.365539 0.491154 0.001455 0.433013 0.001455 0.062885 0.623207 0.000000 0.500000 -0.217785 -0.674424 -0.217785 -0.866025 0.029233 0.538847 0.005104 0.497053 0.559813 0.005266 0.433013 0.005266 0.668311 0.286192 0.793153 0.358270 -0.064815 0.607780 -0.001941 0.498879 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.) -0.028762 0.784286 0.027836 0.903856 -0.953953 0.186746 -0.981373 0.192114 -0.477957 0.564041 -0.646487 0.762925 0.062944 0.604828 0.207805 0.794086 -0.859325 0.500432 -0.864147 0.503240 0.605687 0.375482 0.536834 0.349775 -0.478948 0.852087 -0.489989 0.871729 0.661437 0.720284 0.676378 0.736555 0.001167 0.533735 0.200830 0.799377 -0.369384 0.636005 -0.502228 0.864735 0.379741 0.579491 0.402618 0.596493 0.119633 0.336926 0.150000 0.000000 0.685155 0.324493 0.558082 0.286494 -0.057693 0.466765 0.191377 0.806395 0.205305 0.465999 0.392383 0.610024 0.528462 0.237574 0.568788 0.247892 0.838799 0.451215 0.880666 0.473737 -0.669676 0.702933 -0.689772 0.724027 -0.895448 0.361208 -0.927391 0.374094 -0.207902 0.528276 -0.366210 0.930532 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.) 0.632680 -0.222966 0.495891 -0.212242 0.524015 0.152676 0.498930 0.151967 -0.840870 -0.786928 -0.868986 -0.809671 -0.522594 -0.405386 -0.457099 -0.370506 0.792198 -0.521860 0.975251 -0.555730 -0.358924 -0.601161 -0.321149 -0.477215 0.733276 -0.831107 0.774432 -0.894534 -0.292051 -0.707831 -0.259801 -0.490628 0.703202 -0.334956 0.485423 -0.289000 -0.885715 -0.428334 -0.990724 -0.437368 -0.914729 0.501145 -0.982547 0.510666 -0.480936 -0.484548 -0.419193 -0.421693 -0.959468 0.379304 -0.994674 0.381287 -0.711812 -0.177543 -0.498353 -0.169191 0.154026 -0.857641 0.154551 -0.999857 -0.136476 -0.906088 -0.136717 -0.999913 -0.782322 0.045208 -0.999999 0.045229 0.927644 -0.032058 1.000000 -0.032059 0.571459 0.685726 0.660010 0.948754 -0.432794 0.894889 -0.441239 0.990386 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.) -3.249029 -1.504816 0.000000 1.000000 1.535865 -3.093500 0.000000 -5.000000 -6.448232 -0.038821 0.000000 1.000000 -0.750821 -0.530733 0.000000 1.000000 1.421334 -4.248557 0.000000 -5.000000 5.992101 -2.064056 0.000000 -5.000000 -3.777303 -1.523151 0.000000 1.000000 7.298429 -1.148461 0.000000 -5.000000 5.153787 -2.416341 0.000000 -5.000000 -3.539436 -3.417929 0.000000 -5.000000 4.846670 -2.957099 0.000000 -5.000000 0.929231 0.468741 0.000000 1.000000 -6.277365 -1.179963 0.000000 -5.000000 5.848431 0.627778 0.000000 1.000000 -6.295420 0.147620 0.000000 1.000000 -3.701278 -1.205154 0.000000 1.000000 3.356628 -2.924644 0.000000 -5.000000 0.865296 -3.359039 0.000000 -5.000000 -0.569900 -1.238562 0.000000 1.000000 0.478751 -3.063747 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.) 0.732707 0.007739 0.699830 0.005822 0.877568 -0.059877 0.918723 -0.018723 0.679540 -0.090590 0.665979 -0.075145 0.351341 -0.007613 0.329709 -0.088345 0.456519 0.115911 0.522212 0.062841 0.922125 0.209348 0.975184 0.221394 0.904285 -0.110980 0.957632 -0.057632 0.217880 -0.014981 0.207030 -0.055473 0.256748 -0.056027 0.253556 -0.067940 0.383896 0.017949 0.353692 -0.094772 0.483260 -0.083440 0.518644 -0.058149 0.945871 0.048488 0.947179 0.047179 0.503723 -0.064354 0.516863 -0.055571 0.908648 0.042849 0.925748 0.025748 0.070946 -0.013974 0.069687 -0.018672 0.640007 -0.135148 0.630922 -0.169055 0.829979 0.044414 0.900000 0.000000 0.791192 -0.041736 0.697699 -0.021327 0.900503 -0.024667 0.912585 -0.012585 0.438714 0.039168 0.502824 0.023599 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.) 0.366029 0.048906 0.366029 0.000000 0.311803 0.629586 0.300000 0.663397 0.165844 0.036199 0.165844 0.000000 0.879011 0.846055 1.000000 0.846055 0.942889 0.903163 1.000000 0.903163 0.643564 0.519405 0.643564 0.486603 0.484881 0.151013 0.484881 0.000000 0.361923 0.842367 0.312984 0.814113 0.398208 0.297498 0.518936 0.367201 0.427981 0.445491 0.501693 0.402933 0.292280 0.420758 0.500000 0.400000 0.440732 0.477868 0.518901 0.432738 0.671733 0.927469 0.671733 1.000000 0.413785 0.416393 0.500000 0.400000 0.458475 0.434463 0.504542 0.407866 0.110091 0.526508 0.000000 0.526508 0.573885 0.692159 0.573885 0.486603 0.227183 0.261131 0.000000 0.261131 0.496011 0.910439 0.496011 1.000000 0.748691 0.877201 0.748691 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.) 0.752706 0.771233 0.000000 0.000000 0.293235 0.890295 0.000000 0.000000 0.404474 0.052583 0.404474 0.000000 0.433900 0.776334 0.000000 0.000000 0.158740 0.598571 0.000000 0.598571 0.238990 0.959249 0.000000 0.000000 0.815057 0.229233 1.000000 0.229233 0.316559 0.234740 0.316559 0.000000 0.132588 0.505202 0.000000 0.505202 0.815374 0.230182 1.000000 0.230182 0.367447 0.361801 0.367447 0.000000 0.914819 0.082468 0.914819 0.000000 0.918251 0.654155 1.000000 0.654155 0.523843 0.669130 0.000000 0.000000 0.120272 0.200166 0.000000 0.200166 0.898047 0.012392 0.898047 0.000000 0.893218 0.663139 1.000000 0.663139 0.572948 0.066624 0.572948 0.000000 0.501393 0.136379 0.501393 0.000000 0.515986 0.205848 0.515986 0.000000 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.) 0.441853 0.050719 0.441853 0.000000 0.308536 0.745202 0.500000 0.745202 0.550564 0.259709 0.550564 0.500000 0.079731 0.050761 0.079731 0.000000 0.801820 0.138778 0.801820 0.000000 0.363776 0.249415 0.363776 0.000000 0.265748 0.740522 0.500000 0.740522 0.201591 0.633011 0.000000 0.633011 0.292175 0.318113 0.500000 0.500000 0.075078 0.606486 0.000000 0.606486 0.166074 0.310923 0.000000 0.310923 0.445614 0.679818 0.500000 0.679818 0.454622 0.055328 0.454622 0.000000 0.518930 0.231681 0.518930 0.000000 0.168461 0.983329 0.168461 1.000000 0.724298 0.372231 0.724298 0.500000 0.289434 0.001359 0.289434 0.000000 0.448518 0.286886 0.500000 0.500000 0.781339 0.321753 0.781339 0.500000 0.243974 0.898854 0.243974 1.000000 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.) 0.795640 0.524890 0.625000 0.524890 0.300570 0.468066 0.500000 0.468066 0.349871 0.047960 0.349871 0.000000 0.447681 0.155868 0.500000 0.155868 0.797142 0.085400 0.797142 0.000000 0.967013 0.548157 1.000000 0.548157 0.405668 0.653554 0.500000 0.653554 0.050865 0.521702 0.000000 0.521702 0.635470 0.891021 0.625000 0.891021 0.382092 0.945850 0.382092 1.000000 0.882566 0.328692 1.000000 0.328692 0.629728 0.773494 0.625000 0.773494 0.649609 0.744200 0.625000 0.744200 0.665860 0.832954 0.625000 0.832954 0.090561 0.990571 0.090561 1.000000 0.977902 0.473086 1.000000 0.473086 0.182951 0.027883 0.182951 0.000000 0.307856 0.187160 0.307856 0.000000 0.196268 0.509505 0.000000 0.509505 0.315281 0.075265 0.315281 0.000000 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.) 83.158160 6.956682 79.360768 6.159978 54.597764 41.360265 55.000000 41.360265 80.750057 21.874523 82.594300 23.186454 12.525822 9.020594 11.110826 9.361204 27.923745 32.707253 27.621880 33.154483 31.475113 27.676086 33.312773 24.930633 36.186120 36.690411 35.905899 37.434694 28.924331 27.810134 31.880235 23.909708 58.042931 29.592743 57.868190 28.949811 62.411747 35.042634 63.354664 37.704813 15.681522 0.153036 20.000298 0.133777 15.115142 18.636368 14.718955 18.848021 46.873864 45.845464 45.000000 45.845464 54.945940 88.507154 55.000000 88.507154 22.776301 18.364701 25.129756 16.777096 17.251192 1.460145 20.029775 1.336259 14.144653 9.642034 11.372308 10.387559 84.637741 5.365295 89.528602 6.122876 78.917998 9.152472 78.601660 9.052352 23.465129 18.691836 25.474140 17.276637 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.) 605.376373 264.207760 594.727332 243.608433 250.943273 740.459661 243.977559 747.382369 216.694333 352.578474 216.551450 396.520640 545.935499 323.193810 574.979139 330.101185 566.271706 459.894676 567.122259 459.826401 197.475711 304.552793 236.882035 296.763222 365.168317 427.953459 349.331830 431.314540 265.637514 370.439621 277.862768 405.329700 485.163700 451.461280 547.198937 496.076692 560.245407 438.949264 565.413112 438.534443 444.510583 435.512819 350.165086 442.525230 212.796308 358.059207 216.551450 396.520640 135.947165 328.947190 110.183441 343.586578 143.930832 346.656917 122.330790 361.651043 274.334059 361.403148 288.428428 401.627562 460.462865 422.707550 558.006680 406.865520 305.086509 276.820293 284.662300 280.720630 369.167997 778.393158 371.605831 790.771481 307.112779 180.288329 316.121846 172.456906 346.422703 385.354357 328.804650 412.430550 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.) -1.094799 -0.712465 -8.000000 -0.712465 2.903115 0.108968 -8.000000 0.108968 3.575812 0.026641 -8.000000 0.026641 -7.124838 -0.938887 -8.000000 -0.938887 -1.028292 0.172595 -8.000000 0.172595 1.358117 0.846456 -8.000000 0.846456 1.519263 -0.062409 -8.000000 -0.062409 -1.310483 -0.279439 -8.000000 -0.279439 2.476144 0.918702 -8.000000 0.918702 6.372933 0.519973 -8.000000 0.519973 -5.632310 -0.165863 -8.000000 -0.165863 4.885397 0.424235 -8.000000 0.424235 -6.659522 -0.393209 -8.000000 -0.393209 -1.467212 0.154723 -8.000000 0.154723 1.294092 0.163939 -8.000000 0.163939 1.122622 -0.872008 -8.000000 -0.872008 -0.476916 0.063979 -8.000000 0.063979 -3.515235 -0.698642 -8.000000 -0.698642 -7.716102 -0.143630 -8.000000 -0.143630 3.866622 0.607791 -8.000000 0.607791 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. 08-Oct-2025 20:42:28