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GeezerVison is showing github.com — solvespace/src/polygon.cpp at python · realthunder/solvespace Expand file tree/ Copy pathpolygon.cppMore file actions 865 lines (755 loc) · 24.9 KB / Copy pathpolygon.cppFile metadata and controls865 lines (755 loc) · 24.9 KB 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 //----------------------------------------------------------------------------- // Operations on polygons (planar, of line segment edges). // // Copyright 2008-2013 Jonathan Westhues. //----------------------------------------------------------------------------- #include "solvespace.h" Vector STriangle::Normal(void) { Vector ab = b.Minus(a), bc = c.Minus(b); return ab.Cross(bc); } double STriangle::MinAltitude(void) { double altA = a.DistanceToLine(b, c.Minus(b)), altB = b.DistanceToLine(c, a.Minus(c)), altC = c.DistanceToLine(a, b.Minus(a)); return min(altA, min(altB, altC)); } bool STriangle::ContainsPoint(Vector p) { Vector n = Normal(); if(MinAltitude() < LENGTH_EPS) { // shouldn't happen; zero-area triangle return false; } return ContainsPointProjd(n.WithMagnitude(1), p); } bool STriangle::ContainsPointProjd(Vector n, Vector p) { Vector ab = b.Minus(a), bc = c.Minus(b), ca = a.Minus(c); Vector no_ab = n.Cross(ab); if(no_ab.Dot(p) < no_ab.Dot(a) - LENGTH_EPS) return false; Vector no_bc = n.Cross(bc); if(no_bc.Dot(p) < no_bc.Dot(b) - LENGTH_EPS) return false; Vector no_ca = n.Cross(ca); if(no_ca.Dot(p) < no_ca.Dot(c) - LENGTH_EPS) return false; return true; } void STriangle::FlipNormal(void) { swap(a, b); swap(an, bn); } STriangle STriangle::From(STriMeta meta, Vector a, Vector b, Vector c) { STriangle tr = {}; tr.meta = meta; tr.a = a; tr.b = b; tr.c = c; return tr; } SEdge SEdge::From(Vector a, Vector b) { SEdge se = {}; se.a = a; se.b = b; return se; } bool SEdge::EdgeCrosses(Vector ea, Vector eb, Vector *ppi, SPointList *spl) { Vector d = eb.Minus(ea); double t_eps = LENGTH_EPS/d.Magnitude(); double t, tthis; bool skew; Vector pi; bool inOrEdge0, inOrEdge1; Vector dthis = b.Minus(a); double tthis_eps = LENGTH_EPS/dthis.Magnitude(); if((ea.Equals(a) && eb.Equals(b)) || (eb.Equals(a) && ea.Equals(b))) { if(ppi) *ppi = a; if(spl) spl->Add(a); return true; } // Can't just test if distance between d and a equals distance between d and b; // they could be on opposite sides, since we don't have the sign. double m = sqrt(d.Magnitude()*dthis.Magnitude()); if(sqrt(fabs(d.Dot(dthis))) > (m - LENGTH_EPS)) { // The edges are parallel. if(fabs(a.DistanceToLine(ea, d)) > LENGTH_EPS) { // and not coincident, so can't be interesecting return false; } // The edges are coincident. Make sure that neither endpoint lies // on the other bool inters = false; double t; t = a.Minus(ea).DivPivoting(d); if(t > t_eps && t < (1 - t_eps)) inters = true; t = b.Minus(ea).DivPivoting(d); if(t > t_eps && t < (1 - t_eps)) inters = true; t = ea.Minus(a).DivPivoting(dthis); if(t > tthis_eps && t < (1 - tthis_eps)) inters = true; t = eb.Minus(a).DivPivoting(dthis); if(t > tthis_eps && t < (1 - tthis_eps)) inters = true; if(inters) { if(ppi) *ppi = a; if(spl) spl->Add(a); return true; } else { // So coincident but disjoint, okay. return false; } } // Lines are not parallel, so look for an intersection. pi = Vector::AtIntersectionOfLines(ea, eb, a, b, &skew, &t, &tthis); if(skew) return false; inOrEdge0 = (t > -t_eps) && (t < (1 + t_eps)); inOrEdge1 = (tthis > -tthis_eps) && (tthis < (1 + tthis_eps)); if(inOrEdge0 && inOrEdge1) { if(a.Equals(ea) || b.Equals(ea) || a.Equals(eb) || b.Equals(eb)) { // Not an intersection if we share an endpoint with an edge return false; } // But it's an intersection if a vertex of one edge lies on the // inside of the other (or if they cross away from either's // vertex). if(ppi) *ppi = pi; if(spl) spl->Add(pi); return true; } return false; } void SEdgeList::Clear(void) { l.Clear(); } void SEdgeList::AddEdge(Vector a, Vector b, int auxA, int auxB) { SEdge e = {}; e.a = a; e.b = b; e.auxA = auxA; e.auxB = auxB; l.Add(&e); } bool SEdgeList::AssembleContour(Vector first, Vector last, SContour *dest, SEdge *errorAt, bool keepDir) { int i; dest->AddPoint(first); dest->AddPoint(last); do { for(i = 0; i < l.n; i++) { SEdge *se = &(l.elem[i]); if(se->tag) continue; if(se->a.Equals(last)) { dest->AddPoint(se->b); last = se->b; se->tag = 1; break; } // Don't allow backwards edges if keepDir is true. if(!keepDir && se->b.Equals(last)) { dest->AddPoint(se->a); last = se->a; se->tag = 1; break; } } if(i >= l.n) { // Couldn't assemble a closed contour; mark where. if(errorAt) { errorAt->a = first; errorAt->b = last; } return false; } } while(!last.Equals(first)); return true; } bool SEdgeList::AssemblePolygon(SPolygon *dest, SEdge *errorAt, bool keepDir) { dest->Clear(); bool allClosed = true; for(;;) { Vector first = Vector::From(0, 0, 0); Vector last = Vector::From(0, 0, 0); int i; for(i = 0; i < l.n; i++) { if(!l.elem[i].tag) { first = l.elem[i].a; last = l.elem[i].b; l.elem[i].tag = 1; break; } } if(i >= l.n) { return allClosed; } // Create a new empty contour in our polygon, and finish assembling // into that contour. dest->AddEmptyContour(); if(!AssembleContour(first, last, &(dest->l.elem[dest->l.n-1]), errorAt, keepDir)) { allClosed = false; } // But continue assembling, even if some of the contours are open } } //----------------------------------------------------------------------------- // Test if the specified edge crosses any of the edges in our list. Two edges // are not considered to cross if they share an endpoint (within LENGTH_EPS), // but they are considered to cross if they are coincident and overlapping. // If pi is not NULL, then a crossing is returned in that. //----------------------------------------------------------------------------- int SEdgeList::AnyEdgeCrossings(Vector a, Vector b, Vector *ppi, SPointList *spl) { int cnt = 0; SEdge *se; for(se = l.First(); se; se = l.NextAfter(se)) { if(se->EdgeCrosses(a, b, ppi, spl)) { cnt++; } } return cnt; } //----------------------------------------------------------------------------- // Returns true if the intersecting edge list contains an edge that shares // an endpoint with one of our edges. //----------------------------------------------------------------------------- bool SEdgeList::ContainsEdgeFrom(SEdgeList *sel) { SEdge *se; for(se = l.First(); se; se = l.NextAfter(se)) { if(sel->ContainsEdge(se)) return true; } return false; } bool SEdgeList::ContainsEdge(SEdge *set) { SEdge *se; for(se = l.First(); se; se = l.NextAfter(se)) { if((se->a).Equals(set->a) && (se->b).Equals(set->b)) return true; if((se->b).Equals(set->a) && (se->a).Equals(set->b)) return true; } return false; } //----------------------------------------------------------------------------- // Remove unnecessary edges: if two are anti-parallel then remove both, and if // two are parallel then remove one. //----------------------------------------------------------------------------- void SEdgeList::CullExtraneousEdges(void) { l.ClearTags(); int i, j; for(i = 0; i < l.n; i++) { SEdge *se = &(l.elem[i]); for(j = i+1; j < l.n; j++) { SEdge *set = &(l.elem[j]); if((set->a).Equals(se->a) && (set->b).Equals(se->b)) { // Two parallel edges exist; so keep only the first one. set->tag = 1; } if((set->a).Equals(se->b) && (set->b).Equals(se->a)) { // Two anti-parallel edges exist; so keep neither. se->tag = 1; set->tag = 1; } } } l.RemoveTagged(); } //----------------------------------------------------------------------------- // Make a kd-tree of edges. This is used for O(log(n)) implementations of stuff // that would naively be O(n). //----------------------------------------------------------------------------- SKdNodeEdges *SKdNodeEdges::Alloc(void) { SKdNodeEdges *ne = (SKdNodeEdges *)AllocTemporary(sizeof(SKdNodeEdges)); *ne = {}; return ne; } SEdgeLl *SEdgeLl::Alloc(void) { SEdgeLl *sell = (SEdgeLl *)AllocTemporary(sizeof(SEdgeLl)); *sell = {}; return sell; } SKdNodeEdges *SKdNodeEdges::From(SEdgeList *sel) { SEdgeLl *sell = NULL; SEdge *se; for(se = sel->l.First(); se; se = sel->l.NextAfter(se)) { SEdgeLl *n = SEdgeLl::Alloc(); n->se = se; n->next = sell; sell = n; } return SKdNodeEdges::From(sell); } SKdNodeEdges *SKdNodeEdges::From(SEdgeLl *sell) { SKdNodeEdges *n = SKdNodeEdges::Alloc(); // Compute the midpoints (just mean, though median would be better) of // each component. Vector ptAve = Vector::From(0, 0, 0); SEdgeLl *flip; int totaln = 0; for(flip = sell; flip; flip = flip->next) { ptAve = ptAve.Plus(flip->se->a); ptAve = ptAve.Plus(flip->se->b); totaln++; } ptAve = ptAve.ScaledBy(1.0 / (2*totaln)); // For each component, see how it splits. int ltln[3] = { 0, 0, 0 }, gtln[3] = { 0, 0, 0 }; double badness[3]; for(flip = sell; flip; flip = flip->next) { for(int i = 0; i < 3; i++) { if(flip->se->a.Element(i) < ptAve.Element(i) + KDTREE_EPS || flip->se->b.Element(i) < ptAve.Element(i) + KDTREE_EPS) { ltln[i]++; } if(flip->se->a.Element(i) > ptAve.Element(i) - KDTREE_EPS || flip->se->b.Element(i) > ptAve.Element(i) - KDTREE_EPS) { gtln[i]++; } } } for(int i = 0; i < 3; i++) { badness[i] = pow((double)ltln[i], 4) + pow((double)gtln[i], 4); } // Choose the least bad coordinate to split along. if(badness[0] < badness[1] && badness[0] < badness[2]) { n->which = 0; } else if(badness[1] < badness[2]) { n->which = 1; } else { n->which = 2; } n->c = ptAve.Element(n->which); if(totaln < 3 || totaln == gtln[n->which] || totaln == ltln[n->which]) { n->edges = sell; // and we're a leaf node return n; } // Sort the edges according to which side(s) of the split plane they're on. SEdgeLl *gtl = NULL, *ltl = NULL; for(flip = sell; flip; flip = flip->next) { if(flip->se->a.Element(n->which) < n->c + KDTREE_EPS || flip->se->b.Element(n->which) < n->c + KDTREE_EPS) { SEdgeLl *selln = SEdgeLl::Alloc(); selln->se = flip->se; selln->next = ltl; ltl = selln; } if(flip->se->a.Element(n->which) > n->c - KDTREE_EPS || flip->se->b.Element(n->which) > n->c - KDTREE_EPS) { SEdgeLl *selln = SEdgeLl::Alloc(); selln->se = flip->se; selln->next = gtl; gtl = selln; } } n->lt = SKdNodeEdges::From(ltl); n->gt = SKdNodeEdges::From(gtl); return n; } int SKdNodeEdges::AnyEdgeCrossings(Vector a, Vector b, int cnt, Vector *pi, SPointList *spl) { int inters = 0; if(gt && lt) { if(a.Element(which) < c + KDTREE_EPS || b.Element(which) < c + KDTREE_EPS) { inters += lt->AnyEdgeCrossings(a, b, cnt, pi, spl); } if(a.Element(which) > c - KDTREE_EPS || b.Element(which) > c - KDTREE_EPS) { inters += gt->AnyEdgeCrossings(a, b, cnt, pi, spl); } } else { SEdgeLl *sell; for(sell = edges; sell; sell = sell->next) { SEdge *se = sell->se; if(se->tag == cnt) continue; if(se->EdgeCrosses(a, b, pi, spl)) { inters++; } se->tag = cnt; } } return inters; } //----------------------------------------------------------------------------- // We have an edge list that contains only collinear edges, maybe with more // splits than necessary. Merge any collinear segments that join. //----------------------------------------------------------------------------- static Vector LineStart, LineDirection; static int ByTAlongLine(const void *av, const void *bv) { SEdge *a = (SEdge *)av, *b = (SEdge *)bv; double ta = (a->a.Minus(LineStart)).DivPivoting(LineDirection), tb = (b->a.Minus(LineStart)).DivPivoting(LineDirection); return (ta > tb) ? 1 : -1; } void SEdgeList::MergeCollinearSegments(Vector a, Vector b) { LineStart = a; LineDirection = b.Minus(a); qsort(l.elem, l.n, sizeof(l.elem[0]), ByTAlongLine); l.ClearTags(); int i; for(i = 1; i < l.n; i++) { SEdge *prev = &(l.elem[i-1]), *now = &(l.elem[i]); if((prev->b).Equals(now->a) && prev->auxA == now->auxA) { // The previous segment joins up to us; so merge it into us. prev->tag = 1; now->a = prev->a; } } l.RemoveTagged(); } void SPointList::Clear(void) { l.Clear(); } bool SPointList::ContainsPoint(Vector pt) { return (IndexForPoint(pt) >= 0); } int SPointList::IndexForPoint(Vector pt) { int i; for(i = 0; i < l.n; i++) { SPoint *p = &(l.elem[i]); if(pt.Equals(p->p)) { return i; } } // Not found, so return negative to indicate that. return -1; } void SPointList::IncrementTagFor(Vector pt) { SPoint *p; for(p = l.First(); p; p = l.NextAfter(p)) { if(pt.Equals(p->p)) { (p->tag)++; return; } } SPoint pa; pa.p = pt; pa.tag = 1; l.Add(&pa); } void SPointList::Add(Vector pt) { SPoint p = {}; p.p = pt; l.Add(&p); } void SContour::AddPoint(Vector p) { SPoint sp; sp.tag = 0; sp.p = p; l.Add(&sp); } void SContour::MakeEdgesInto(SEdgeList *el) { int i; for(i = 0; i < (l.n - 1); i++) { el->AddEdge(l.elem[i].p, l.elem[i+1].p); } } void SContour::CopyInto(SContour *dest) { SPoint *sp; for(sp = l.First(); sp; sp = l.NextAfter(sp)) { dest->AddPoint(sp->p); } } void SContour::FindPointWithMinX(void) { SPoint *sp; xminPt = Vector::From(1e10, 1e10, 1e10); for(sp = l.First(); sp; sp = l.NextAfter(sp)) { if(sp->p.x < xminPt.x) { xminPt = sp->p; } } } Vector SContour::ComputeNormal(void) { Vector n = Vector::From(0, 0, 0); for(int i = 0; i < l.n - 2; i++) { Vector u = (l.elem[i+1].p).Minus(l.elem[i+0].p).WithMagnitude(1); Vector v = (l.elem[i+2].p).Minus(l.elem[i+1].p).WithMagnitude(1); Vector nt = u.Cross(v); if(nt.Magnitude() > n.Magnitude()) { n = nt; } } return n.WithMagnitude(1); } Vector SContour::AnyEdgeMidpoint(void) { if(l.n < 2) oops(); return ((l.elem[0].p).Plus(l.elem[1].p)).ScaledBy(0.5); } bool SContour::IsClockwiseProjdToNormal(Vector n) { // Degenerate things might happen as we draw; doesn't really matter // what we do then. if(n.Magnitude() < 0.01) return true; return (SignedAreaProjdToNormal(n) < 0); } double SContour::SignedAreaProjdToNormal(Vector n) { // An arbitrary 2d coordinate system that has n as its normal Vector u = n.Normal(0); Vector v = n.Normal(1); double area = 0; for(int i = 0; i < (l.n - 1); i++) { double u0 = (l.elem[i ].p).Dot(u); double v0 = (l.elem[i ].p).Dot(v); double u1 = (l.elem[i+1].p).Dot(u); double v1 = (l.elem[i+1].p).Dot(v); area += ((v0 + v1)/2)*(u1 - u0); } return area; } bool SContour::ContainsPointProjdToNormal(Vector n, Vector p) { Vector u = n.Normal(0); Vector v = n.Normal(1); double up = p.Dot(u); double vp = p.Dot(v); bool inside = false; for(int i = 0; i < (l.n - 1); i++) { double ua = (l.elem[i ].p).Dot(u); double va = (l.elem[i ].p).Dot(v); // The curve needs to be exactly closed; approximation is death. double ub = (l.elem[(i+1)%(l.n-1)].p).Dot(u); double vb = (l.elem[(i+1)%(l.n-1)].p).Dot(v); if ((((va <= vp) && (vp < vb)) || ((vb <= vp) && (vp < va))) && (up < (ub - ua) * (vp - va) / (vb - va) + ua)) { inside = !inside; } } return inside; } void SContour::Reverse(void) { l.Reverse(); } void SPolygon::Clear(void) { int i; for(i = 0; i < l.n; i++) { (l.elem[i]).l.Clear(); } l.Clear(); } void SPolygon::AddEmptyContour(void) { SContour c = {}; l.Add(&c); } void SPolygon::MakeEdgesInto(SEdgeList *el) { int i; for(i = 0; i < l.n; i++) { (l.elem[i]).MakeEdgesInto(el); } } Vector SPolygon::ComputeNormal(void) { if(l.n < 1) return Vector::From(0, 0, 0); return (l.elem[0]).ComputeNormal(); } double SPolygon::SignedArea(void) { SContour *sc; double area = 0; // This returns the true area only if the contours are all oriented // correctly, with the holes backwards from the outer contours. for(sc = l.First(); sc; sc = l.NextAfter(sc)) { area += sc->SignedAreaProjdToNormal(normal); } return area; } bool SPolygon::ContainsPoint(Vector p) { return (WindingNumberForPoint(p) % 2) == 1; } int SPolygon::WindingNumberForPoint(Vector p) { int winding = 0; int i; for(i = 0; i < l.n; i++) { SContour *sc = &(l.elem[i]); if(sc->ContainsPointProjdToNormal(normal, p)) { winding++; } } return winding; } void SPolygon::FixContourDirections(void) { // At output, the contour's tag will be 1 if we reversed it, else 0. l.ClearTags(); // Outside curve looks counterclockwise, projected against our normal. int i, j; for(i = 0; i < l.n; i++) { SContour *sc = &(l.elem[i]); if(sc->l.n < 2) continue; // The contours may not intersect, but they may share vertices; so // testing a vertex for point-in-polygon may fail, but the midpoint // of an edge is okay. Vector pt = (((sc->l.elem[0]).p).Plus(sc->l.elem[1].p)).ScaledBy(0.5); sc->timesEnclosed = 0; bool outer = true; for(j = 0; j < l.n; j++) { if(i == j) continue; SContour *sct = &(l.elem[j]); if(sct->ContainsPointProjdToNormal(normal, pt)) { outer = !outer; (sc->timesEnclosed)++; } } bool clockwise = sc->IsClockwiseProjdToNormal(normal); if((clockwise && outer) || (!clockwise && !outer)) { sc->Reverse(); sc->tag = 1; } } } bool SPolygon::IsEmpty(void) { if(l.n == 0 || l.elem[0].l.n == 0) return true; return false; } Vector SPolygon::AnyPoint(void) { if(IsEmpty()) oops(); return l.elem[0].l.elem[0].p; } bool SPolygon::SelfIntersecting(Vector *intersectsAt) { SEdgeList el = {}; MakeEdgesInto(&el); SKdNodeEdges *kdtree = SKdNodeEdges::From(&el); int cnt = 1; el.l.ClearTags(); bool ret = false; SEdge *se; for(se = el.l.First(); se; se = el.l.NextAfter(se)) { int inters = kdtree->AnyEdgeCrossings(se->a, se->b, cnt, intersectsAt); if(inters != 1) { ret = true; break; } cnt++; } el.Clear(); return ret; } //----------------------------------------------------------------------------- // Low-quality routines to cutter radius compensate a polygon. Assumes the // polygon is in the xy plane, and the contours all go in the right direction // with respect to normal (0, 0, -1). //----------------------------------------------------------------------------- void SPolygon::OffsetInto(SPolygon *dest, double r) { int i; dest->Clear(); for(i = 0; i < l.n; i++) { SContour *sc = &(l.elem[i]); dest->AddEmptyContour(); sc->OffsetInto(&(dest->l.elem[dest->l.n-1]), r); } } //----------------------------------------------------------------------------- // Calculate the intersection point of two lines. Returns true for success, // false if they're parallel. //----------------------------------------------------------------------------- static bool IntersectionOfLines(double x0A, double y0A, double dxA, double dyA, double x0B, double y0B, double dxB, double dyB, double *xi, double *yi) { double A[2][2]; double b[2]; // The line is given to us in the form: // (x(t), y(t)) = (x0, y0) + t*(dx, dy) // so first rewrite it as // (x - x0, y - y0) dot (dy, -dx) = 0 // x*dy - x0*dy - y*dx + y0*dx = 0 // x*dy - y*dx = (x0*dy - y0*dx) // So write the matrix, pre-pivoted. if(fabs(dyA) > fabs(dyB)) { A[0][0] = dyA; A[0][1] = -dxA; b[0] = x0A*dyA - y0A*dxA; A[1][0] = dyB; A[1][1] = -dxB; b[1] = x0B*dyB - y0B*dxB; } else { A[1][0] = dyA; A[1][1] = -dxA; b[1] = x0A*dyA - y0A*dxA; A[0][0] = dyB; A[0][1] = -dxB; b[0] = x0B*dyB - y0B*dxB; } // Check the determinant; if it's zero then no solution. if(fabs(A[0][0]*A[1][1] - A[0][1]*A[1][0]) < LENGTH_EPS) { return false; } // Solve double v = A[1][0] / A[0][0]; A[1][0] -= A[0][0]*v; A[1][1] -= A[0][1]*v; b[1] -= b[0]*v; // Back-substitute. *yi = b[1] / A[1][1]; *xi = (b[0] - A[0][1]*(*yi)) / A[0][0]; return true; } void SContour::OffsetInto(SContour *dest, double r) { int i; for(i = 0; i < l.n; i++) { Vector a, b, c; Vector dp, dn; double thetan, thetap; a = l.elem[WRAP(i-1, (l.n-1))].p; b = l.elem[WRAP(i, (l.n-1))].p; c = l.elem[WRAP(i+1, (l.n-1))].p; dp = a.Minus(b); thetap = atan2(dp.y, dp.x); dn = b.Minus(c); thetan = atan2(dn.y, dn.x); // A short line segment in a badly-generated polygon might look // okay but screw up our sense of direction. if(dp.Magnitude() < LENGTH_EPS || dn.Magnitude() < LENGTH_EPS) { continue; } if(thetan > thetap && (thetan - thetap) > PI) { thetap += 2*PI; } if(thetan < thetap && (thetap - thetan) > PI) { thetan += 2*PI; } if(fabs(thetan - thetap) < (1*PI)/180) { Vector p = { b.x - r*sin(thetap), b.y + r*cos(thetap), 0 }; dest->AddPoint(p); } else if(thetan < thetap) { // This is an inside corner. We have two edges, Ep and En. Move // out from their intersection by radius, normal to En, and // then draw a line parallel to En. Move out from their // intersection by radius, normal to Ep, and then draw a second // line parallel to Ep. The point that we want to generate is // the intersection of these two lines--it removes as much // material as we can without removing any that we shouldn't. double px0, py0, pdx, pdy; double nx0, ny0, ndx, ndy; double x = 0.0, y = 0.0; px0 = b.x - r*sin(thetap); py0 = b.y + r*cos(thetap); pdx = cos(thetap); pdy = sin(thetap); nx0 = b.x - r*sin(thetan); ny0 = b.y + r*cos(thetan); ndx = cos(thetan); ndy = sin(thetan); IntersectionOfLines(px0, py0, pdx, pdy, nx0, ny0, ndx, ndy, &x, &y); dest->AddPoint(Vector::From(x, y, 0)); } else { if(fabs(thetap - thetan) < (6*PI)/180) { Vector pp = { b.x - r*sin(thetap), b.y + r*cos(thetap), 0 }; dest->AddPoint(pp); Vector pn = { b.x - r*sin(thetan), b.y + r*cos(thetan), 0 }; dest->AddPoint(pn); } else { double theta; for(theta = thetap; theta <= thetan; theta += (6*PI)/180) { Vector p = { b.x - r*sin(theta), b.y + r*cos(theta), 0 }; dest->AddPoint(p); } } } } } |
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