1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893
|
# -*- tcl -*-
# Tests for geometry library.
#
# Copyright (c) 2001 by Ideogramic ApS and other parties.
# All rights reserved.
#
# RCS: @(#) $Id: geometry.test,v 1.13 2010/04/06 17:02:25 andreas_kupries Exp $
# -------------------------------------------------------------------------
source [file join \
[file dirname [file dirname [file join [pwd] [info script]]]] \
devtools testutilities.tcl]
testsNeedTcl 8.5
testsNeedTcltest 1.0
support {
useLocal math.tcl math
}
testing {
useLocal geometry.tcl math::geometry
}
# -------------------------------------------------------------------------
proc withFourDecimals {args} {
set res {}
foreach arg $args {lappend res [expr (round(10000*$arg))/10000.0]}
return $res
}
if { [info commands lmap] eq {} } {
proc lmap {var list body} {
upvar 1 $var _$var
set __$var {}
foreach _$var $list {
lappend __$var [uplevel 1 $body]
}
set __$var
}
}
#
# Custom matching procedure:
# Expect an accuracy of at least four decimals
#
proc matchNumbers {expected actual} {
set match 1
foreach a $actual e $expected {
if {abs($a-$e) > 1.0e-4} {
set match 0
break
}
}
return $match
}
customMatch numbers matchNumbers
# -------------------------------------------------------------------------
###
# calculateDistanceToLine
###
test geometry-1.1 {geometry::calculateDistanceToLine, simple} {
eval withFourDecimals [::math::geometry::calculateDistanceToLine {6 4} {1 1 7 1}]
} 3.0
test geometry-1.2 {geometry::calculateDistanceToLine, on line segment} {
eval withFourDecimals [::math::geometry::calculateDistanceToLine {3 2} {1 1 5 3}]
} 0.0
test geometry-1.3 {geometry::calculateDistanceToLine, on first end} {
eval withFourDecimals [::math::geometry::calculateDistanceToLine {1 1} {1 1 7 1}]
} 0.0
test geometry-1.4 {geometry::calculateDistanceToLine, on second end} {
eval withFourDecimals [::math::geometry::calculateDistanceToLine {7 1} {1 1 7 1}]
} 0.0
test geometry-1.5 {geometry::calculateDistanceToLine, not on line segment, between line segment ends} {
eval withFourDecimals [::math::geometry::calculateDistanceToLine {3 1} {1 1 7 3}]
} 0.6325
test geometry-1.6 {geometry::calculateDistanceToLine, not on infinite line, beyond first line segment end} {
eval withFourDecimals [::math::geometry::calculateDistanceToLine {0 -2} {1 1 7 3}]
} 2.5298
test geometry-1.7 {geometry::calculateDistanceToLine, not on infinite line, beyond second line segment end} {
eval withFourDecimals [::math::geometry::calculateDistanceToLine {10 2} {1 1 7 3}]
} 1.8974
test geometry-1.8 {geometry::calculateDistanceToLine, on infinite line, beyond first line segment end} {
eval withFourDecimals [::math::geometry::calculateDistanceToLine {-1 0} {1 1 5 3}]
} 0.0
test geometry-1.9 {geometry::calculateDistanceToLine, on infinite line, beyond second line segment end} {
eval withFourDecimals [::math::geometry::calculateDistanceToLine {9 5} {1 1 5 3}]
} 0.0
###
# calculateDistanceToLineSegment
###
test geometry-2.1 {geometry::calculateDistanceToLineSegment, simple} {
eval withFourDecimals [::math::geometry::calculateDistanceToLineSegment {6 4} {1 1 7 1}]
} 3.0
test geometry-2.2 {geometry::calculateDistanceToLineSegment, on linesegment} {
eval withFourDecimals [::math::geometry::calculateDistanceToLineSegment {3 2} {1 1 5 3}]
} 0.0
test geometry-2.3 {geometry::calculateDistanceToLineSegment, on first end} {
eval withFourDecimals [::math::geometry::calculateDistanceToLineSegment {1 1} {1 1 7 1}]
} 0.0
test geometry-2.4 {geometry::calculateDistanceToLineSegment, on second end} {
eval withFourDecimals [::math::geometry::calculateDistanceToLineSegment {7 1} {1 1 7 1}]
} 0.0
test geometry-2.5 {geometry::calculateDistanceToLineSegment, not on linesegment, between linesegment ends} {
eval withFourDecimals [::math::geometry::calculateDistanceToLineSegment {3 1} {1 1 7 3}]
} 0.6325
test geometry-2.6 {geometry::calculateDistanceToLineSegment, not on infinite line, beyond first line segment end} {
eval withFourDecimals [::math::geometry::calculateDistanceToLineSegment {0 -2} {1 1 7 3}]
} 3.1623
test geometry-2.7 {geometry::calculateDistanceToLineSegment, not on infinite line, beyond second line segment end} {
eval withFourDecimals [::math::geometry::calculateDistanceToLineSegment {10 2} {1 1 7 3}]
} 3.1623
test geometry-2.8 {geometry::calculateDistanceToLineSegment, on infinite line, beyond first line segment end} {
eval withFourDecimals [::math::geometry::calculateDistanceToLineSegment {-1 0} {1 1 5 3}]
} 2.2361
test geometry-2.9 {geometry::calculateDistanceToLineSegment, on infinite line, beyond second line segment end} {
eval withFourDecimals [::math::geometry::calculateDistanceToLineSegment {9 5} {1 1 5 3}]
} 4.4721
###
# findClosestPointOnLine
###
test geometry-3.1 {geometry::findClosestPointOnLine, between end points} {
eval withFourDecimals [::math::geometry::findClosestPointOnLine {5 10} {0 0 10 10}]
} {7.5 7.5}
test geometry-3.2 {geometry::findClosestPointOnLine, before first point} {
eval withFourDecimals [::math::geometry::findClosestPointOnLine {-10 0} {0 0 10 10}]
} {-5.0 -5.0}
###
# findClosestPointOnLineSegment
###
###
# findClosestPointOnPolyline
###
test geometry-5.1 {geometry::findClosestPointOnPolyline, one linesegment} {
eval withFourDecimals [::math::geometry::findClosestPointOnPolyline {6 4} {1 1 7 1}]
} {6.0 1.0}
test geometry-5.2 {geometry::findClosestPointOnPolyline, two linesegments} {
eval withFourDecimals [::math::geometry::findClosestPointOnPolyline {5 5} {1 1 1 5 14 10}]
} {4.4845 6.3402}
test geometry-5.3 {geometry::findClosestPointOnPolyline, point lies on a linesegment} {
eval withFourDecimals [::math::geometry::findClosestPointOnPolyline {5 5} {1 1 8 8}]
} {5.0 5.0}
###
# calculateDistanceToPolyline
###
test geometry-6.1 {geometry::calculateDistanceToPolyline, one line segment} {
eval withFourDecimals [::math::geometry::calculateDistanceToPolyline {6 4} {4 6 1 2}]
} 2.8
test geometry-6.2 {geometry::calculateDistanceToPolyline, two line segments} {
eval withFourDecimals [::math::geometry::calculateDistanceToPolyline {6 9} {4 6 1 2 4 12}]
} 2.7777
test geometry-6.3 {geometry::calculateDistanceToPolyline, three line segments} {
eval withFourDecimals [::math::geometry::calculateDistanceToPolyline {6 4} {4 6 1 2 10 8 12 4}]
} 1.1094
test geometry-6.4 {geometry::calculateDistanceToPolyline, on first point} {
eval withFourDecimals [::math::geometry::calculateDistanceToPolyline {4 6} {4 6 1 2 5 1}]
} 0.0
test geometry-6.5 {geometry::calculateDistanceToPolyline, on second point} {
eval withFourDecimals [::math::geometry::calculateDistanceToPolyline {1 2} {4 6 1 2 5 1}]
} 0.0
test geometry-6.6 {geometry::calculateDistanceToPolyline, on third point} {
eval withFourDecimals [::math::geometry::calculateDistanceToPolyline {5 1} {4 6 1 2 5 1}]
} 0.0
test geometry-6.7 {geometry::calculateDistanceToPolyline, on first line segment} {
eval withFourDecimals [::math::geometry::calculateDistanceToPolyline {2 2} {4 6 1 0 5 4}]
} 0.0
test geometry-6.8 {geometry::calculateDistanceToPolyline, on second line segment} {
eval withFourDecimals [::math::geometry::calculateDistanceToPolyline {3 2} {4 6 1 0 5 4}]
} 0.0
###
# lineSegmentsIntersect
###
test geometry-7.1 {geometry::lineSegmentsIntersect, } {
::math::geometry::lineSegmentsIntersect {0 0 10 10} {0 10 10 0}
} 1
###
# polylinesIntersect
###
test geometry-8.1 {geometry::polylinesIntersect, } {
::math::geometry::polylinesIntersect {0 0 0 2 10 10} {0 10 2 10 10 0}
} 1
###
# findLineIntersection
###
test geometry-9.1 {geometry::findLineIntersection, first line vertical} {
eval withFourDecimals [::math::geometry::findLineIntersection {7 8 7 28} {3 14 17 21}]
} {7.0 16.0}
test geometry-9.2 {geometry::findLineIntersection, second line vertical} {
eval withFourDecimals [::math::geometry::findLineIntersection {3 14 17 21} {7 8 7 28}]
} {7.0 16.0}
test geometry-9.3 {geometry::findLineIntersection, both lines vertical - coincident} {
::math::geometry::findLineIntersection {7 8 7 28} {7 14 7 21}
} "coincident"
test geometry-9.4 {geometry::findLineIntersection, both lines vertical - no intersection} {
::math::geometry::findLineIntersection {7 8 7 28} {8 14 8 21}
} "none"
test geometry-9.5 {geometry::findLineIntersection, first line horizontal} {
eval withFourDecimals [::math::geometry::findLineIntersection {2 3 10 3} {4 5 7 2}]
} {6.0 3.0}
test geometry-9.6 {geometry::findLineIntersection, second line horizontal} {
eval withFourDecimals [::math::geometry::findLineIntersection {4 5 7 2} {2 3 10 3}]
} {6.0 3.0}
test geometry-9.7 {geometry::findLineIntersection, both lines horizontal - coincident} {
::math::geometry::findLineIntersection {8 7 28 7} {14 7 21 7}
} "coincident"
test geometry-9.8 {geometry::findLineIntersection, both lines horizontal - no intersection} {
::math::geometry::findLineIntersection {8 7 28 7} {14 8 21 8}
} "none"
test geometry-9.9 {geometry::findLineIntersection, both lines skaeve - with intersection} {
eval withFourDecimals [::math::geometry::findLineIntersection {3 2 9 4} {4 5 7 2}]
} {6.0 3.0}
test geometry-9.10 {geometry::findLineIntersection, both lines skaeve - coincident} {
::math::geometry::findLineIntersection {3 2 9 4} {6 3 12 5}
} "coincident"
test geometry-9.11 {geometry::findLineIntersection, both lines skaeve - no intersection} {
::math::geometry::findLineIntersection {3 2 9 4} {3 12 9 14}
} "none"
test geometry-9.12 {geometry::findLineIntersection, vertical} {
eval withFourDecimals [::math::geometry::findLineIntersection {110.0 130.0 110.0 30.0} {180.0 200.0 280.0 200.0}]
} {110.0 200.0}
test geometry-9.13 {geometry::findLineIntersection, vertical, ints} {
eval withFourDecimals [::math::geometry::findLineIntersection {110 130 110 30} {180 200 280 200}]
} {110.0 200.0}
test geometry-9.14 {geometry::findLineIntersection, very near vertical, flipped direction} {
# This test checks the numerical stability of the algorithm
eval withFourDecimals [::math::geometry::findLineIntersection {110.0 130.0 109.99999999999999 230.0} {180.0 200.0 280.0 200.0}]
} {110.0 200.0}
test geometry-9.15 {geometry::findLineIntersection, vertical, flipped direction} {
eval withFourDecimals [::math::geometry::findLineIntersection {110 130 110 230} {180 200 280 200}]
} {110.0 200.0}
###
# findLineSegmentIntersection
###
test geometry-10.1 {geometry::findLineSegmentIntersection, both lines vertical - no overlap} {
::math::geometry::findLineSegmentIntersection {1 1 1 2} {1 3 1 4}
} "none"
test geometry-10.2 {geometry::findLineSegmentIntersection, both lines vertical - with overlap} {
::math::geometry::findLineSegmentIntersection {1 1 1 2} {1 1.5 1 19}
} "coincident"
test geometry-10.3 {geometry::findLineSegmentIntersection, both lines skaeve - with intersection} {
eval withFourDecimals [::math::geometry::findLineSegmentIntersection {3 2 9 4} {4 5 7 2}]
} {6.0 3.0}
test geometry-10.4 {geometry::findLineSegmentIntersection, both lines skaeve - coincident} {
::math::geometry::findLineSegmentIntersection {3 2 9 4} {6 3 12 5}
} "coincident"
test geometry-10.5 {geometry::findLineSegmentIntersection, both lines skaeve - parallel but not coincident} {
::math::geometry::findLineSegmentIntersection {3 2 6 3} {9 4 12 5}
} "none"
test geometry-10.6 {geometry::findLineSegmentIntersection, both lines skaeve - no intersection} {
::math::geometry::findLineSegmentIntersection {3 2 9 4} {4 5 5 4}
} "none"
###
# movePointInDirection
###
test geometry-11.1 {geometry::movePointInDirection, going up} {
eval withFourDecimals [::math::geometry::movePointInDirection {0 0} 90 1]
} {0.0 1.0}
test geometry-11.2 {geometry::movePointInDirection, going up 2} {
eval withFourDecimals [::math::geometry::movePointInDirection {0 0} 90 5.7]
} {0.0 5.7}
test geometry-11.3 {geometry::movePointInDirection, going down} {
eval withFourDecimals [::math::geometry::movePointInDirection {0 0} 270 5.7]
} {0.0 -5.7}
test geometry-11.4 {geometry::movePointInDirection, going left} {
eval withFourDecimals [::math::geometry::movePointInDirection {0 0} 180 5.7]
} {-5.7 0.0}
test geometry-11.5 {geometry::movePointInDirection, going right} {
eval withFourDecimals [::math::geometry::movePointInDirection {0 0} 0 5.7]
} {5.7 0.0}
test geometry-11.6 {geometry::movePointInDirection, going up and right} {
eval withFourDecimals [::math::geometry::movePointInDirection {0 0} 45 5.7]
} {4.0305 4.0305}
test geometry-11.7 {geometry::movePointInDirection, going up and left} {
eval withFourDecimals [::math::geometry::movePointInDirection {0 0} 135 5.7]
} {-4.0305 4.0305}
test geometry-11.8 {geometry::movePointInDirection, (3,4,5)-triangle} {
set pi [expr 4*atan(1)]
set angleInRadians [expr asin(0.6)]
set angleInDegrees [expr $angleInRadians/$pi*180]
eval withFourDecimals [::math::geometry::movePointInDirection {0 0} $angleInDegrees 5]
} {4.0 3.0}
test geometry-11.9 {geometry::movePointInDirection, going up and left from (3,6)} {
eval withFourDecimals [::math::geometry::movePointInDirection {3 6} 135 5.7]
} {-1.0305 10.0305}
test geometry-11.10 {geometry::movePointInDirection, negative angle} {
eval withFourDecimals [::math::geometry::movePointInDirection {0 0} -90 5.7]
} {0.0 -5.7}
test geometry-11.11 {geometry::movePointInDirection, negative angle 2} {
eval withFourDecimals [::math::geometry::movePointInDirection {0 0} -135 5.7]
} {-4.0305 -4.0305}
test geometry-11.12 {geometry::movePointInDirection, big angle (>360)} {
eval withFourDecimals [::math::geometry::movePointInDirection {0 0} 450 5.7]
} {0.0 5.7}
###
# Angle
###
test geometry-12.1 {geometry::angle, going right} {
withFourDecimals [::math::geometry::angle {0 0 10 0}]
} 0.0
test geometry-12.2 {geometry::angle, going up} {
withFourDecimals [::math::geometry::angle {0 0 0 10}]
} 90.0
test geometry-12.3 {geometry::angle, going left} {
withFourDecimals [::math::geometry::angle {0 0 -10 0}]
} 180.0
test geometry-12.4 {geometry::angle, going down} {
withFourDecimals [::math::geometry::angle {0 0 0 -10}]
} 270.0
test geometry-12.5 {geometry::angle, going up and right} {
withFourDecimals [::math::geometry::angle {0 0 10 10}]
} 45.0
test geometry-12.6 {geometry::angle, going up and left} {
withFourDecimals [::math::geometry::angle {0 0 -10 10}]
} 135.0
test geometry-12.7 {geometry::angle, going down and left} {
withFourDecimals [::math::geometry::angle {0 0 -10 -10}]
} 225.0
test geometry-12.8 {geometry::angle, going down and right} {
withFourDecimals [::math::geometry::angle {0 0 10 -10}]
} 315.0
test geometry-12.9 {geometry::angle, going up and right from (3,6)} {
withFourDecimals [::math::geometry::angle {3 6 10 9}]
} 23.1986
###
# intervalsOverlap
###
test geometry-13.1 {geometry::intervalsOverlap, strict, overlap} {
math::geometry::intervalsOverlap 2 4 3 6 1
} 1
test geometry-13.2 {geometry::intervalsOverlap, strict, no overlap} {
math::geometry::intervalsOverlap 2 4 4 6 1
} 0
test geometry-13.3 {geometry::intervalsOverlap, not strict, overlap} {
math::geometry::intervalsOverlap 2 4 3 6 0
} 1
test geometry-13.4 {geometry::intervalsOverlap, not strict, no overlap} {
math::geometry::intervalsOverlap 2 4 5 6 0
} 0
test geometry-13.5 {geometry::intervalsOverlap, first interval wrong order} {
math::geometry::intervalsOverlap 4 2 3 5 0
} 1
test geometry-13.6 {geometry::intervalsOverlap, second interval wrong order} {
math::geometry::intervalsOverlap 2 4 5 3 0
} 1
test geometry-13.7 {geometry::intervalsOverlap, both interval wrong order} {
math::geometry::intervalsOverlap 4 2 5 3 0
} 1
###
# rectanglesOverlap
###
test geometry-14.1 {geometry::rectanglesOverlap, strict, overlap} {
math::geometry::rectanglesOverlap {0 10} {10 0} {5 10} {20 0} 1
} 1
test geometry-14.2 {geometry::rectanglesOverlap, strict, no overlap} {
math::geometry::rectanglesOverlap {0 10} {10 0} {10 10} {20 0} 1
} 0
test geometry-14.3 {geometry::rectanglesOverlap, not strict, overlap} {
math::geometry::rectanglesOverlap {0 10} {10 0} {5 10} {20 0} 0
} 1
test geometry-14.4 {geometry::rectanglesOverlap, not strict, no overlap} {
math::geometry::rectanglesOverlap {0 10} {10 0} {12 10} {20 0} 0
} 0
###
# pointInsidePolygon
###
test geometry-15.1 {geometry::pointInsidePolygon, simple inside} {
math::geometry::pointInsidePolygon {5 5} {4 4 4 6 6 6 6 4}
} 1
test geometry-15.2 {geometry::pointInsidePolygon, simple not inside} {
math::geometry::pointInsidePolygon {5 5} {6 6 6 7 7 7}
} 0
test geometry-15.3 {geometry::pointInsidePolygon, point on polygon's sides} {
math::geometry::pointInsidePolygon {5 5} {5 4 5 6 7 7}
} 0
test geometry-15.4 {geometry::pointInsidePolygon, point identical with one of polygon's points} {
math::geometry::pointInsidePolygon {5 5} {5 4 5 5 7 7}
} 0
test geometry-15.5 {geometry::pointInsidePolygon, point not in polygon's bbox} {
math::geometry::pointInsidePolygon {5 5} {8 8 8 9 9 9 9 8}
} 0
#
# Note: outcome changed, because of ticket dc49af96c2
# This is an edge case anyway
#
test geometry-15.6 {geometry::pointInsidePolygon, hour-glass with center on point} {
math::geometry::pointInsidePolygon {5 5} {4 4 6 6 6 4 4 6}
} 1
test geometry-15.7 {geometry::pointInsidePolygon, hour-glass with point inside one of the areas} {
math::geometry::pointInsidePolygon {5 5} {3 2 5 11 3 11 11 6}
} 1
test geometry-15.8 {geometry::pointInsidePolygon, hour-glass with point on left side} {
math::geometry::pointInsidePolygon {5 5} {4 1 8 8 6 8 8 1}
} 0
test geometry-15.9 {geometry::pointInsidePolygon, hour-glass with point on right side} {
math::geometry::pointInsidePolygon {5 5} {2 4 6 9 2 9 5 4}
} 0
test geometry-15.10 {geometry::pointInsidePolygon, infinityLine crosses point instead of line segment} {
math::geometry::pointInsidePolygon {5 5} {4 4 4 7 7 7 7 4}
} 1
test geometry-15.11 {geometry::pointInsidePolygon, polygon already closed} {
math::geometry::pointInsidePolygon {5 5} {4 4 4 6 6 6 6 4 4 4}
} 1
test geometry-15.12 {geometry::pointInsidePolygon, polygon with zero-length side} {
math::geometry::pointInsidePolygon {5 5} {4 4 4 6 6 6 6 6 6 4}
} 1
test geometry-15.13 {geometry::pointInsidePolygon, edge case polygon/point, ticket c1ca34ead3} {
math::geometry::pointInsidePolygon {3.0 -1.5} {2.0 2.0 -2.0 2.0 -2.0 -2.0 2.0 -2.0}
} 0
test geometry-15.14 {geometry::pointInsidePolygon, point well outside polygon, negative coordinates, ticket dc49af96c2} {
math::geometry::pointInsidePolygon {838 456} {-764 -677 -668 -1341 -124 -797 -508 -406}
} 0
test geometry-15.15 {geometry::pointInsidePolygon, point well outside polygons, mixture of negative nd positive coordinates, ticket dc49af96c2} {
set polygons {
"-764 -677 -668 -1341 -124 -797 -508 -406"
"764 -677 668 -1341 124 -797 508 -406"
"-764 677 -668 1341 -124 797 -508 406"
"764 677 668 1341 124 797 508 406"
}
set point "838 456"
return [lmap polygon $polygons {::math::geometry::pointInsidePolygon $point $polygon}]
} {0 0 0 0}
test geometry-15.16 {geometry::pointInsidePolygon, point on boundary of adjacent polygons} {
# Points on the edge should belong to exactly one polygon
set polygons {
"0 0 0 100 100 100 100 0"
"0 0 0 100 -100 100 -100 0"
}
set point "0 50"
return [lmap polygon $polygons {::math::geometry::pointInsidePolygon $point $polygon}]
} {1 0}
test geometry-15.17 {geometry::pointInsidePolygon, point on boundary of adjacent polygons, second test} {
# Points on the edge should belong to exactly one polygon
set polygons {
"0 0 0 100 100 100 100 0"
"0 0 0 -100 100 -100 100 0"
}
set point "50 0"
return [lmap polygon $polygons {::math::geometry::pointInsidePolygon $point $polygon}]
} {1 0}
test geometry-15.18 {geometry::pointInsidePolygonAlt, point well outside polygons, mixture of negative nd positive coordinates, ticket dc49af96c2} {
set polygons {
"-764 -677 -668 -1341 -124 -797 -508 -406"
"764 -677 668 -1341 124 -797 508 -406"
"-764 677 -668 1341 -124 797 -508 406"
"764 677 668 1341 124 797 508 406"
}
set point "838 456"
return [lmap polygon $polygons {::math::geometry::pointInsidePolygonAlt $point $polygon}]
} {0 0 0 0}
test geometry-15.19 {geometry::pointInsidePolygonAlt, point in self-intersection polygon} {
# The winding number algorithm should tell the point is inside the polygon, the crossing number
# algorithm will report it to be outside
set polygon {-50 0 50 0 50 50 -25 10 25 10 -50 50}
set point "0 12"
return [list [::math::geometry::pointInsidePolygonAlt $point $polygon] \
[::math::geometry::pointInsidePolygon $point $polygon]]
} {1 0}
###
# rectangleInsidePolygon
###
test geometry-16.1 {geometry::rectangleInsidePolygon, simple} {
math::geometry::rectangleInsidePolygon {0 10} {10 0} {-10 -10 0 11 11 11 11 0}
} 1
test geometry-16.2 {geometry::rectangleInsidePolygon, rectangle and polygon identical} {
math::geometry::rectangleInsidePolygon {5 5} {7 7} {5 5 5 7 7 7 7 5}
} 0
test geometry-16.3 {geometry::rectangleInsidePolygon, bboxes don't overlap} {
math::geometry::rectangleInsidePolygon {5 5} {7 7} {8 8 8 9 9 9 9 8}
} 0
test geometry-16.4 {geometry::rectangleInsidePolygon, polygon point is inside the rectangle} {
math::geometry::rectangleInsidePolygon {5 5} {7 7} {4 4 4 8 6 6}
} 0
test geometry-16.5 {geometry::rectangleInsidePolygon, hour-glass with center inside rectangle} {
math::geometry::rectangleInsidePolygon {5 5} {7 7} {5 3 7 9 5 9 7 3}
} 0
test geometry-16.6 {geometry::rectangleInsidePolygon, hour-glass with rectangle inside one of the areas} {
math::geometry::rectangleInsidePolygon {5 5} {7 7} {3 2 5 11 3 11 11 6}
} 1
test geometry-16.7 {geometry::rectangleInsidePolygon, hour-glass with rectangle on left side} {
math::geometry::rectangleInsidePolygon {5 5} {6 6} {4 1 8 8 6 8 8 1}
} 0
test geometry-16.8 {geometry::rectangleInsidePolygon, hour-glass with rectangle on right side} {
math::geometry::rectangleInsidePolygon {5 5} {6 6} {2 4 6 9 2 9 5 4}
} 0
test geometry-16.9 {geometry::rectangleInsidePolygon, infinityLine crosses point instead of line segment} {
math::geometry::rectangleInsidePolygon {5 5} {6 6} {4 4 4 7 7 7 7 4}
} 1
###
###
test geometry-17.0 {point constructor} {
math::geometry::p 1 4
} {1 4}
test geometry-17.1 {vector addition} {
math::geometry::+ {1 4} {5 3}
} {6 7}
test geometry-17.2 {vector difference} {
math::geometry::- {6 7} {5 3}
} {1 4}
test geometry-17.3 {vector distance} {
withFourDecimals [math::geometry::distance {6 7} {5 3}]
} 4.1231
test geometry-17.4 {vector length} {
withFourDecimals [math::geometry::length {1 1}]
} 1.4142
test geometry-17.5 {vector scale} {
math::geometry::s* 5 {1 1}
} {5 5}
test geometry-17.6 {vector direction} {
eval withFourDecimals [math::geometry::direction 0]
} {1.0 0.0}
test geometry-17.7 {vector direction} {
eval withFourDecimals [math::geometry::direction 90]
} {0.0 -1.0}
test geometry-17.8 {vector vertical} {
math::geometry::v 90
} {0 90}
test geometry-17.9 {vector horizontal} {
math::geometry::h 90
} {90 0}
test geometry-17.10 {point between} {
math::geometry::between {0 0} {4 4} 0
} {0 0}
test geometry-17.11 {point between} {
math::geometry::between {0 0} {4 4} 1
} {4 4}
test geometry-17.12 {point between} {
math::geometry::between {0 0} {4 4} 0.5
} {2.0 2.0}
test geometry-17.13 {octant} {
math::geometry::octant {-10 -12}
} northwest
###
# calculateDistanceToPolygon
###
test geometry-18.1 {geometry::calculateDistanceToPolygon, non-closed polygon, point on polygon} {
eval withFourDecimals [::math::geometry::calculateDistanceToPolygon {2.0 0.5} {2.0 2.0 -2.0 2.0 -2.0 -2.0 2.0 -2.0}]
} 0.0
###
# transformations
###
test geometry-19.1 {geometry::translate over (1,-1)} {
eval withFourDecimals [::math::geometry::translate {1.0 -1.0} {0.0 0.0 1.0 1.0}]
} {1.0 -1.0 2.0 0.0}
test geometry-19.2 {geometry::rotate over 90 degrees} {
eval withFourDecimals [::math::geometry::rotate 90.0 {0.0 0.0 1.0 1.0 0.0 1.0}]
} {0.0 0.0 -1.0 1.0 -1.0 0.0}
test geometry-19.3 {geometry::reflect in x-axis} {
eval withFourDecimals [::math::geometry::reflect 180.0 {0.0 0.0 1.0 1.0 0.0 1.0}]
} {0.0 0.0 1.0 -1.0 0.0 -1.0}
test geometry-19.4 {geometry::reflect in y-axis} {
eval withFourDecimals [::math::geometry::reflect 90.0 {0.0 0.0 1.0 1.0 0.0 1.0}]
} {0.0 0.0 -1.0 1.0 0.0 1.0}
test geometry-19.5 {geometry::radToDeg} {
::math::geometry::radToDeg [expr {acos(-1.0)}]
} 180.0
test geometry-19.6 {geometry::degToRad} {
::math::geometry::degToRad 180.0
} [expr {acos(-1.0)}]
###
# areaPolygon
###
test geometry-20.1 {geometry::areaPolygon, closed polygon} {
eval withFourDecimals [::math::geometry::areaPolygon {-10 -10 10 -10 10 10 -10 10 -10 -10}]
} 400.0
test geometry-20.2 {geometry::areaPolygon, non-closed polygon} {
eval withFourDecimals [::math::geometry::areaPolygon {-10 -10 10 -10 10 10 -10 10}]
} 400.0
test geometry-20.3 {geometry::areaPolygon, closed triangle} {
eval withFourDecimals [::math::geometry::areaPolygon {-10 -10 10 -10 10 10 -10 -10}]
} 200.0
test geometry-20.4 {geometry::areaPolygon, open triangle} {
eval withFourDecimals [::math::geometry::areaPolygon {-10 -10 10 -10 10 10}]
} 200.0
test geometry-20.4 {geometry::areaPolygon, self-intersecting polygon} {
eval withFourDecimals [::math::geometry::areaPolygon {-10 -10 10 -10 -10 10 10 10 -10 -10}]
} 0.0
##
# areaPolygon
##
test geometry-20.0 {geometry::areaPolygon} {
math::geometry::areaPolygon {-10 -10 10 -10 10 10 -10 10}
} 400.0
##
# circle procedures
##
# circle construction
test circle-0.1 {construct circle} -body {
set circle [::math::geometry::circle {1.0 2.0} 3.0]
} -result {1.0 2.0 3.0}
test circle-0.2 {construct circle from two points} -body {
set circle [::math::geometry::circleTwoPoints {1.0 0.0} {-1.0 0.0}]
} -result {0.0 0.0 1.0}
test circle-0.3 {construct circle from two points (2)} -body {
set circle [::math::geometry::circleTwoPoints {0.0 1.0} {0.0 -1.0}]
} -result {0.0 0.0 1.0}
# points inside/outside circles
test circle-1.0 {point in circle} -body {
set circle [::math::geometry::circle {1.0 0.0} 3.0]
set point [::math::geometry::p 0.0 0.0]
::math::geometry::pointInsideCircle $point $circle
} -result 1
test circle-1.1 {point outside circle} -body {
set circle [::math::geometry::circle {1.0 0.0} 3.0]
set point [::math::geometry::p 5.0 0.0]
::math::geometry::pointInsideCircle $point $circle
} -result 0
test circle-1.2 {point on circle edge} -body {
set circle [::math::geometry::circle {1.0 0.0} 3.0]
set point [::math::geometry::p -2.0 0.0]
::math::geometry::pointInsideCircle $point $circle
} -result 1
# lines intersecting circles
test circle-2.0 {line through circle} -body {
set circle [::math::geometry::circle {1.0 0.0} 3.0]
set line {0.0 -10.0 0.0 10.0}
::math::geometry::lineIntersectsCircle $line $circle
} -result 1
test circle-2.1 {line not through circle} -body {
set circle [::math::geometry::circle {1.0 0.0} 3.0]
set line {10.0 -10.0 10.0 10.0}
::math::geometry::lineIntersectsCircle $line $circle
} -result 0
test circle-2.2 {line on edge of circle} -body {
set circle [::math::geometry::circle {1.0 0.0} 3.0]
set line {-2.0 -10.0 -2.0 10.0}
::math::geometry::lineIntersectsCircle $line $circle
} -result 1
# line segment intersecting circle
test circle-3.0 {line segment intersecting circle} -body {
set circle [::math::geometry::circle {1.0 0.0} 3.0]
set line {0.0 -10.0 0.0 10.0}
::math::geometry::lineSegmentIntersectsCircle $line $circle
} -result 1
test circle-3.1 {line segment outside circle} -body {
set circle [::math::geometry::circle {1.0 0.0} 3.0]
set line {0.0 5.0 0.0 10.0}
::math::geometry::lineSegmentIntersectsCircle $line $circle
} -result 0
test circle-3.2 {line segment completely inside circle} -body {
set circle [::math::geometry::circle {1.0 0.0} 3.0]
set line {1.0 0.0 1.0 1.0}
::math::geometry::lineSegmentIntersectsCircle $line $circle
} -result 0
test circle-3.3 {line segment touching circle} -body {
set circle [::math::geometry::circle {1.0 0.0} 3.0]
set line {-2.0 0.0 -5.0 0.0}
::math::geometry::lineIntersectsCircle $line $circle
} -result 1
#
# Private procedures
#
test circlePrivate-1.1 {intersect vertical line with circle (two points)} -body {
set circle [::math::geometry::circle {0.0 0.0} 5.0]
set line {3.0 4.0 3.0 -4.0}
::math::geometry::IntersectionVerticalLineCircle $line $circle
} -result {{3.0 4.0} {3.0 -4.0}}
test circlePrivate-1.2 {intersect vertical line with circle (two points, version 2)} -body {
set circle [::math::geometry::circle {0.0 0.0} 5.0]
set line {3.0 40.0 3.0 -40.0}
::math::geometry::IntersectionVerticalLineCircle $line $circle
} -result {{3.0 4.0} {3.0 -4.0}}
test circlePrivate-1.2 {intersect vertical line with circle (one point)} -body {
set circle [::math::geometry::circle {0.0 0.0} 5.0]
set line {5.0 40.0 5.0 -40.0}
::math::geometry::IntersectionVerticalLineCircle $line $circle
} -result {5.0 0.0}
test circlePrivate-1.2 {intersect vertical line with circle (no points)} -body {
set circle [::math::geometry::circle {0.0 0.0} 5.0]
set line {15.0 40.0 15.0 -40.0}
::math::geometry::IntersectionVerticalLineCircle $line $circle
} -result {}
# Coordinates: sqrt(3)/2
test circlePrivate-2.1 {intersect two circles (two points)} -body {
set circle1 [::math::geometry::circle {0.0 0.0} 1.0]
set circle2 [::math::geometry::circle {1.0 0.0} 1.0]
concat {*}[::math::geometry::IntersectionCircleCircle $circle1 $circle2]
} -result {0.5 0.8660254 0.5 -0.8660254} -match numbers
test circlePrivate-2.2 {intersect two circles (one point right)} -body {
set circle1 [::math::geometry::circle {0.0 0.0} 5.0]
set circle2 [::math::geometry::circle {10.0 0.0} 5.0]
::math::geometry::IntersectionCircleCircle $circle1 $circle2
} -result {5.0 0.0}
test circlePrivate-2.3 {intersect two circles (one point left)} -body {
set circle1 [::math::geometry::circle {0.0 0.0} 5.0]
set circle2 [::math::geometry::circle {5.0 0.0} 10.0]
::math::geometry::IntersectionCircleCircle $circle1 $circle2
} -result {-5.0 0.0}
test circlePrivate-2.4 {intersect two circles (no points)} -body {
set circle1 [::math::geometry::circle {0.0 0.0} 5.0]
set circle2 [::math::geometry::circle {15.0 0.0} 5.0]
::math::geometry::IntersectionCircleCircle $circle1 $circle2
} -result {}
test circlePrivate-2.4 {intersect two concentric circles} -body {
set circle1 [::math::geometry::circle {0.0 0.0} 5.0]
set circle2 [::math::geometry::circle {0.0 0.0} 7.0]
::math::geometry::IntersectionCircleCircle $circle1 $circle2
} -result {}
#
# Intersection procedures
#
test circleIntersect-1.1 {intersect a vertical line and a circle (two points)} -body {
set line {0.0 0.0 0.0 5.0}
set circle [::math::geometry::circle {0.0 0.0} 7.0]
concat {*}[::math::geometry::intersectionLineWithCircle $line $circle]
} -result {0.0 7.0 0.0 -7.0} -match numbers
# Coordinates in answer: 7*sqrt(2)/2
test circleIntersect-1.2 {intersect a diagonal line and a circle (two points)} -body {
set line {-5.0 -5.0 5.0 5.0}
set circle [::math::geometry::circle {0.0 0.0} 7.0]
concat {*}[::math::geometry::intersectionLineWithCircle $line $circle]
} -result {4.94975 4.94975 -4.94975 -4.94975} -match numbers
test circleIntersect-1.3 {intersect a horizontal line and a circle (one point)} -body {
set line {-5.0 5.0 5.0 5.0}
set circle [::math::geometry::circle {0.0 0.0} 5.0]
concat {*}[::math::geometry::intersectionLineWithCircle $line $circle]
} -result {0.0 5.0} -match numbers
test circleIntersect-2.1 {intersect two circles, arranged horizontally (two points)} -body {
set circle1 [::math::geometry::circle {0.0 0.0} 1.0]
set circle2 [::math::geometry::circle {1.0 0.0} 1.0]
concat {*}[::math::geometry::intersectionCircleWithCircle $circle1 $circle2]
} -result {0.5 0.8660254 0.5 -0.8660254} -match numbers
test circleIntersect-2.2 {intersect two circles, arranged vertically (two points)} -body {
set circle1 [::math::geometry::circle {0.0 0.0} 1.0]
set circle2 [::math::geometry::circle {0.0 1.0} 1.0]
concat {*}[::math::geometry::intersectionCircleWithCircle $circle1 $circle2]
} -result {-0.8660254 0.5 0.8660254 0.5} -match numbers
test circleTangent-1.1 {tangent lines to a circle} -body {
set circle [::math::geometry::circle {0.0 0.0} 1.0]
set point [::math::geometry::p 1.0 1.0]
concat {*}[::math::geometry::tangentLinesToCircle $point $circle]
} -result {1.0 1.0 0.0 1.0 1.0 1.0 1.0 0.0} -match numbers
test circleTangent-1.2 {tangent lines to a circle - point at circumference} -body {
set circle [::math::geometry::circle {0.0 0.0} 1.0]
set point [::math::geometry::p 0.0 1.0]
concat {*}[::math::geometry::tangentLinesToCircle $point $circle]
} -result {0.0 1.0 1.0 1.0} -match numbers
test circleTangent-1.3 {tangent lines to a circle - point inside the circle} -body {
set circle [::math::geometry::circle {0.0 0.0} 1.0]
set point [::math::geometry::p 0.5 0.5]
concat {*}[::math::geometry::tangentLinesToCircle $point $circle]
} -result {} -match numbers
###
testsuiteCleanup
|