20d87d93c5
This will allow us in future to accept `const T &` anywhere it's necessary to reduce the amount of copying. This commit is quite conservative: it does not attempt very hard to refactor code that performs incidental mutation. In particular dogd and caches are not marked with the `mutable` keyword. dogd will be eliminated later, opening up more opportunities to add const qualifiers. This commit also doesn't introduce any uses of the newly added const qualifers. This will be done later.
506 lines
15 KiB
C++
506 lines
15 KiB
C++
//-----------------------------------------------------------------------------
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// Triangulate a surface. If the surface is curved, then we first superimpose
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// a grid of quads, with spacing to achieve our chord tolerance. We then
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// proceed by ear-clipping; the resulting mesh should be watertight and not
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// awful numerically, but has no special properties (Delaunay, etc.).
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//
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// Copyright 2008-2013 Jonathan Westhues.
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//-----------------------------------------------------------------------------
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#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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//int64_t 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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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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top->MakeEdgesInto(&el);
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List<Vector> 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", (int)(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", (int)(GetMilliseconds() - in));
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scmin->tag = 3;
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}
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// dbp("finished merging holes: %d ms", (int)(GetMilliseconds() - in));
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merged.UvTriangulateInto(m, srf);
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// dbp("finished ear clippping: %d ms", (int)(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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// Careful, need to free the points within the contours, and not just
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// the contours themselves. This was a tricky memory leak.
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for(sc = l.First(); sc; sc = l.NextAfter(sc)) {
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if(sc->tag) {
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sc->l.Clear();
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}
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}
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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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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) const {
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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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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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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) const {
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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) const {
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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) const
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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.GetMaxSegments();
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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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MakeEdgesInto(&orig);
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SEdgeList 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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li = {};
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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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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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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);
|
|
}
|
|
|
|
orig.Clear();
|
|
holes.Clear();
|
|
li.Clear();
|
|
lj.Clear();
|
|
hp.l.Clear();
|
|
|
|
UvTriangulateInto(mesh, srf);
|
|
}
|
|
|
|
|