501 lines
15 KiB
C++
501 lines
15 KiB
C++
#include "../solvespace.h"
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void SPolygon::UvTriangulateInto(SMesh *m, SSurface *srf) {
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if(l.n <= 0) return;
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SDWORD in = GetMilliseconds();
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normal = Vector::From(0, 0, 1);
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while(l.n > 0) {
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FixContourDirections();
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l.ClearTags();
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// Find a top-level contour, and start with that. Then build bridges
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// in order to merge all its islands into a single contour.
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SContour *top;
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for(top = l.First(); top; top = l.NextAfter(top)) {
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if(top->timesEnclosed == 0) {
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break;
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}
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}
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if(!top) {
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dbp("polygon has no top-level contours?");
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return;
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}
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// Start with the outer contour
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SContour merged;
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ZERO(&merged);
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top->tag = 1;
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top->CopyInto(&merged);
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(merged.l.n)--;
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// List all of the edges, for testing whether bridges work.
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SEdgeList el;
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ZERO(&el);
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top->MakeEdgesInto(&el);
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List<Vector> vl;
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ZERO(&vl);
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// And now find all of its holes. Note that we will also find any
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// outer contours that lie entirely within this contour, and any
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// holes for those contours. But that's okay, because we can merge
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// those too.
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SContour *sc;
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for(sc = l.First(); sc; sc = l.NextAfter(sc)) {
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if(sc->timesEnclosed != 1) continue;
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if(sc->l.n < 2) continue;
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// Test the midpoint of an edge. Our polygon may not be self-
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// intersecting, but two contours may share a vertex; so a
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// vertex could be on the edge of another polygon, in which
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// case ContainsPointProjdToNormal returns indeterminate.
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Vector tp = sc->AnyEdgeMidpoint();
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if(top->ContainsPointProjdToNormal(normal, tp)) {
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sc->tag = 2;
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sc->MakeEdgesInto(&el);
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sc->FindPointWithMinX();
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}
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}
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// dbp("finished finding holes: %d ms", GetMilliseconds() - in);
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for(;;) {
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double xmin = 1e10;
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SContour *scmin = NULL;
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for(sc = l.First(); sc; sc = l.NextAfter(sc)) {
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if(sc->tag != 2) continue;
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if(sc->xminPt.x < xmin) {
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xmin = sc->xminPt.x;
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scmin = sc;
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}
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}
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if(!scmin) break;
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if(!merged.BridgeToContour(scmin, &el, &vl)) {
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dbp("couldn't merge our hole");
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return;
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}
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// dbp(" bridged to contour: %d ms", GetMilliseconds() - in);
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scmin->tag = 3;
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}
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// dbp("finished merging holes: %d ms", GetMilliseconds() - in);
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merged.UvTriangulateInto(m, srf);
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// dbp("finished ear clippping: %d ms", GetMilliseconds() - in);
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merged.l.Clear();
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el.Clear();
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vl.Clear();
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l.RemoveTagged();
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}
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}
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bool SContour::BridgeToContour(SContour *sc,
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SEdgeList *avoidEdges, List<Vector> *avoidPts)
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{
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int i, j;
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// Start looking for a bridge on our new hole near its leftmost (min x)
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// point.
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int sco = 0;
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for(i = 0; i < (sc->l.n - 1); i++) {
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if((sc->l.elem[i].p).EqualsExactly(sc->xminPt)) {
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sco = i;
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}
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}
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// And start looking on our merged contour at whichever point is nearest
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// to the leftmost point of the new segment.
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int thiso = 0;
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double dmin = 1e10;
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for(i = 0; i < l.n; i++) {
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Vector p = l.elem[i].p;
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double d = (p.Minus(sc->xminPt)).MagSquared();
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if(d < dmin) {
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dmin = d;
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thiso = i;
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}
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}
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int thisp, scp;
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Vector a, b, *f;
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// First check if the contours share a point; in that case we should
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// merge them there, without a bridge.
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for(i = 0; i < l.n; i++) {
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thisp = WRAP(i+thiso, l.n);
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a = l.elem[thisp].p;
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for(f = avoidPts->First(); f; f = avoidPts->NextAfter(f)) {
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if(f->Equals(a)) break;
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}
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if(f) continue;
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for(j = 0; j < (sc->l.n - 1); j++) {
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scp = WRAP(j+sco, (sc->l.n - 1));
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b = sc->l.elem[scp].p;
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if(a.Equals(b)) {
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goto haveEdge;
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}
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}
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}
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// If that fails, look for a bridge that does not intersect any edges.
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for(i = 0; i < l.n; i++) {
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thisp = WRAP(i+thiso, l.n);
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a = l.elem[thisp].p;
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for(f = avoidPts->First(); f; f = avoidPts->NextAfter(f)) {
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if(f->Equals(a)) break;
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}
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if(f) continue;
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for(j = 0; j < (sc->l.n - 1); j++) {
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scp = WRAP(j+sco, (sc->l.n - 1));
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b = sc->l.elem[scp].p;
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for(f = avoidPts->First(); f; f = avoidPts->NextAfter(f)) {
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if(f->Equals(b)) break;
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}
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if(f) continue;
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if(avoidEdges->AnyEdgeCrossings(a, b) > 0) {
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// doesn't work, bridge crosses an existing edge
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} else {
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goto haveEdge;
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}
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}
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}
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// Tried all the possibilities, didn't find an edge
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return false;
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haveEdge:
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SContour merged;
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ZERO(&merged);
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for(i = 0; i < l.n; i++) {
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merged.AddPoint(l.elem[i].p);
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if(i == thisp) {
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// less than or equal; need to duplicate the join point
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for(j = 0; j <= (sc->l.n - 1); j++) {
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int jp = WRAP(j + scp, (sc->l.n - 1));
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merged.AddPoint((sc->l.elem[jp]).p);
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}
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// and likewise duplicate join point for the outer curve
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merged.AddPoint(l.elem[i].p);
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}
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}
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// and future bridges mustn't cross our bridge, and it's tricky to get
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// things right if two bridges come from the same point
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avoidEdges->AddEdge(a, b);
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avoidPts->Add(&a);
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avoidPts->Add(&b);
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l.Clear();
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l = merged.l;
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return true;
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}
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bool SContour::IsEar(int bp, double scaledEps) {
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int ap = WRAP(bp-1, l.n),
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cp = WRAP(bp+1, l.n);
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STriangle tr;
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ZERO(&tr);
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tr.a = l.elem[ap].p;
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tr.b = l.elem[bp].p;
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tr.c = l.elem[cp].p;
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if((tr.a).Equals(tr.c)) {
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// This is two coincident and anti-parallel edges. Zero-area, so
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// won't generate a real triangle, but we certainly can clip it.
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return true;
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}
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Vector n = Vector::From(0, 0, -1);
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if((tr.Normal()).Dot(n) < scaledEps) {
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// This vertex is reflex, or between two collinear edges; either way,
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// it's not an ear.
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return false;
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}
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// Accelerate with an axis-aligned bounding box test
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Vector maxv = tr.a, minv = tr.a;
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(tr.b).MakeMaxMin(&maxv, &minv);
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(tr.c).MakeMaxMin(&maxv, &minv);
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int i;
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for(i = 0; i < l.n; i++) {
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if(i == ap || i == bp || i == cp) continue;
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Vector p = l.elem[i].p;
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if(p.OutsideAndNotOn(maxv, minv)) continue;
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// A point on the edge of the triangle is considered to be inside,
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// and therefore makes it a non-ear; but a point on the vertex is
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// "outside", since that's necessary to make bridges work.
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if(p.EqualsExactly(tr.a)) continue;
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if(p.EqualsExactly(tr.b)) continue;
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if(p.EqualsExactly(tr.c)) continue;
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if(tr.ContainsPointProjd(n, p)) {
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return false;
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}
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}
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return true;
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}
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void SContour::ClipEarInto(SMesh *m, int bp, double scaledEps) {
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int ap = WRAP(bp-1, l.n),
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cp = WRAP(bp+1, l.n);
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STriangle tr;
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ZERO(&tr);
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tr.a = l.elem[ap].p;
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tr.b = l.elem[bp].p;
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tr.c = l.elem[cp].p;
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if(tr.Normal().MagSquared() < scaledEps*scaledEps) {
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// A vertex with more than two edges will cause us to generate
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// zero-area triangles, which must be culled.
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} else {
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m->AddTriangle(&tr);
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}
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// By deleting the point at bp, we may change the ear-ness of the points
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// on either side.
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l.elem[ap].ear = SPoint::UNKNOWN;
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l.elem[cp].ear = SPoint::UNKNOWN;
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l.ClearTags();
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l.elem[bp].tag = 1;
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l.RemoveTagged();
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}
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void SContour::UvTriangulateInto(SMesh *m, SSurface *srf) {
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Vector tu, tv;
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srf->TangentsAt(0.5, 0.5, &tu, &tv);
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double s = sqrt(tu.MagSquared() + tv.MagSquared());
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// We would like to apply our tolerances in xyz; but that would be a lot
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// of work, so at least scale the epsilon semi-reasonably. That's
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// perfect for square planes, less perfect for anything else.
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double scaledEps = LENGTH_EPS / s;
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int i;
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// Clean the original contour by removing any zero-length edges.
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l.ClearTags();
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for(i = 1; i < l.n; i++) {
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if((l.elem[i].p).Equals(l.elem[i-1].p)) {
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l.elem[i].tag = 1;
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}
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}
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l.RemoveTagged();
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// Now calculate the ear-ness of each vertex
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for(i = 0; i < l.n; i++) {
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(l.elem[i]).ear = IsEar(i, scaledEps) ? SPoint::EAR : SPoint::NOT_EAR;
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}
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bool toggle = false;
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while(l.n > 3) {
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// Some points may have changed ear-ness, so recalculate
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for(i = 0; i < l.n; i++) {
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if(l.elem[i].ear == SPoint::UNKNOWN) {
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(l.elem[i]).ear = IsEar(i, scaledEps) ?
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SPoint::EAR : SPoint::NOT_EAR;
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}
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}
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int bestEar = -1;
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double bestChordTol = VERY_POSITIVE;
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// Alternate the starting position so we generate strip-like
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// triangulations instead of fan-like
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toggle = !toggle;
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int offset = toggle ? -1 : 0;
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for(i = 0; i < l.n; i++) {
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int ear = WRAP(i+offset, l.n);
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if(l.elem[ear].ear == SPoint::EAR) {
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if(srf->degm == 1 && srf->degn == 1) {
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// This is a plane; any ear is a good ear.
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bestEar = ear;
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break;
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}
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// If we are triangulating a curved surface, then try to
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// clip ears that have a small chord tolerance from the
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// surface.
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Vector prev = l.elem[WRAP((i+offset-1), l.n)].p,
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next = l.elem[WRAP((i+offset+1), l.n)].p;
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double tol = srf->ChordToleranceForEdge(prev, next);
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if(tol < bestChordTol - scaledEps) {
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bestEar = ear;
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bestChordTol = tol;
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}
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if(bestChordTol < 0.1*SS.ChordTolMm()) {
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break;
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}
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}
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}
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if(bestEar < 0) {
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dbp("couldn't find an ear! fail");
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return;
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}
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ClipEarInto(m, bestEar, scaledEps);
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}
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ClipEarInto(m, 0, scaledEps); // add the last triangle
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}
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double SSurface::ChordToleranceForEdge(Vector a, Vector b) {
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Vector as = PointAt(a.x, a.y), bs = PointAt(b.x, b.y);
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double worst = VERY_NEGATIVE;
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int i;
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for(i = 1; i <= 3; i++) {
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Vector p = a. Plus((b. Minus(a )).ScaledBy(i/4.0)),
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ps = as.Plus((bs.Minus(as)).ScaledBy(i/4.0));
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Vector pps = PointAt(p.x, p.y);
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worst = max(worst, (pps.Minus(ps)).MagSquared());
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}
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return sqrt(worst);
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}
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Vector SSurface::PointAtMaybeSwapped(double u, double v, bool swapped) {
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if(swapped) {
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return PointAt(v, u);
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} else {
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return PointAt(u, v);
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}
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}
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void SSurface::MakeTriangulationGridInto(List<double> *l, double vs, double vf,
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bool swapped)
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{
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double worst = 0;
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// Try piecewise linearizing four curves, at u = 0, 1/3, 2/3, 1; choose
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// the worst chord tolerance of any of those.
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int i;
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for(i = 0; i <= 3; i++) {
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double u = i/3.0;
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// This chord test should be identical to the one in SBezier::MakePwl
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// to make the piecewise linear edges line up with the grid more or
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// less.
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Vector ps = PointAtMaybeSwapped(u, vs, swapped),
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pf = PointAtMaybeSwapped(u, vf, swapped);
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double vm1 = (2*vs + vf) / 3,
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vm2 = (vs + 2*vf) / 3;
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Vector pm1 = PointAtMaybeSwapped(u, vm1, swapped),
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pm2 = PointAtMaybeSwapped(u, vm2, swapped);
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worst = max(worst, pm1.DistanceToLine(ps, pf.Minus(ps)));
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worst = max(worst, pm2.DistanceToLine(ps, pf.Minus(ps)));
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}
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double step = 1.0/SS.maxSegments;
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if((vf - vs) < step || worst < SS.ChordTolMm()) {
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l->Add(&vf);
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} else {
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MakeTriangulationGridInto(l, vs, (vs+vf)/2, swapped);
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MakeTriangulationGridInto(l, (vs+vf)/2, vf, swapped);
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}
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}
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void SPolygon::UvGridTriangulateInto(SMesh *mesh, SSurface *srf) {
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SEdgeList orig;
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ZERO(&orig);
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MakeEdgesInto(&orig);
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SEdgeList holes;
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ZERO(&holes);
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normal = Vector::From(0, 0, 1);
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FixContourDirections();
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// Build a rectangular grid, with horizontal and vertical lines in the
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// uv plane. The spacing of these lines is adaptive, so calculate that.
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List<double> li, lj;
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ZERO(&li);
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ZERO(&lj);
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double v = 0;
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li.Add(&v);
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srf->MakeTriangulationGridInto(&li, 0, 1, true);
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lj.Add(&v);
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srf->MakeTriangulationGridInto(&lj, 0, 1, false);
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// Now iterate over each quad in the grid. If it's outside the polygon,
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// or if it intersects the polygon, then we discard it. Otherwise we
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// generate two triangles in the mesh, and cut it out of our polygon.
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int i, j;
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for(i = 0; i < (li.n - 1); i++) {
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for(j = 0; j < (lj.n - 1); j++) {
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double us = li.elem[i], uf = li.elem[i+1],
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vs = lj.elem[j], vf = lj.elem[j+1];
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Vector a = Vector::From(us, vs, 0),
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b = Vector::From(us, vf, 0),
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c = Vector::From(uf, vf, 0),
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d = Vector::From(uf, vs, 0);
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if(orig.AnyEdgeCrossings(a, b, NULL) ||
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orig.AnyEdgeCrossings(b, c, NULL) ||
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orig.AnyEdgeCrossings(c, d, NULL) ||
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orig.AnyEdgeCrossings(d, a, NULL))
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{
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continue;
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}
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// There's no intersections, so it doesn't matter which point
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// we decide to test.
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if(!this->ContainsPoint(a)) {
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continue;
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}
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// Add the quad to our mesh
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STriangle tr;
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ZERO(&tr);
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tr.a = a;
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tr.b = b;
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tr.c = c;
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mesh->AddTriangle(&tr);
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tr.a = a;
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tr.b = c;
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tr.c = d;
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mesh->AddTriangle(&tr);
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holes.AddEdge(a, b);
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holes.AddEdge(b, c);
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holes.AddEdge(c, d);
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holes.AddEdge(d, a);
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}
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}
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holes.CullExtraneousEdges();
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SPolygon hp;
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ZERO(&hp);
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holes.AssemblePolygon(&hp, NULL, true);
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SContour *sc;
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for(sc = hp.l.First(); sc; sc = hp.l.NextAfter(sc)) {
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l.Add(sc);
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}
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orig.Clear();
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holes.Clear();
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li.Clear();
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lj.Clear();
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hp.l.Clear();
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UvTriangulateInto(mesh, srf);
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}
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