solvespace/src/srf/triangulate.cpp at master · solvespace/solvespace · GitHub

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//-----------------------------------------------------------------------------

// Triangulate a surface. If the surface is curved, then we first superimpose

// a grid of quads, with spacing to achieve our chord tolerance. We then

// proceed by ear-clipping; the resulting mesh should be watertight and not

// awful numerically, but has no special properties (Delaunay, etc.).

//-----------------------------------------------------------------------------

#include "solvespace.h"

namespace SolveSpace {

void SPolygon::UvTriangulateInto(SMesh *m, SSurface *srf) {

if(l.n <= 0) return;

//int64_t in = GetMilliseconds();

normal = {0, 0, 1};

while(l.n > 0) {

FixContourDirections();

l.ClearTags();

// Find a top-level contour, and start with that. Then build bridges

// in order to merge all its islands into a single contour.

SContour *top;

for(top = l.First(); top; top = l.NextAfter(top)) {

if(top->timesEnclosed == 0) {

break;

}

if(!top) {

dbp("polygon has no top-level contours?");

return;

}

// Start with the outer contour

SContour merged = {};

top->tag = 1;

top->CopyInto(&merged);

merged.l.RemoveLast(1);

// List all of the edges, for testing whether bridges work.

SEdgeList el = {};

top->MakeEdgesInto(&el);

List<Vector> vl = {};

// And now find all of its holes. Note that we will also find any

// outer contours that lie entirely within this contour, and any

// holes for those contours. But that's okay, because we can merge

// those too.

SContour *sc;

for(sc = l.First(); sc; sc = l.NextAfter(sc)) {

if(sc->timesEnclosed != 1) continue;

if(sc->l.n < 2) continue;

// Test the midpoint of an edge. Our polygon may not be self-

// intersecting, but two contours may share a vertex; so a

// vertex could be on the edge of another polygon, in which

// case ContainsPointProjdToNormal returns indeterminate.

Vector tp = sc->AnyEdgeMidpoint();

if(top->ContainsPointProjdToNormal(normal, tp)) {

sc->tag = 2;

sc->MakeEdgesInto(&el);

sc->FindPointWithMinX();

}

// dbp("finished finding holes: %d ms", (int)(GetMilliseconds() - in));

for(;;) {

double xmin = 1e10;

SContour *scmin = NULL;

for(sc = l.First(); sc; sc = l.NextAfter(sc)) {

if(sc->tag != 2) continue;

if(sc->xminPt.x < xmin) {

xmin = sc->xminPt.x;

scmin = sc;

}

if(!scmin) break;

if(!merged.BridgeToContour(scmin, &el, &vl)) {

dbp("couldn't merge our hole");

return;

}

// dbp(" bridged to contour: %d ms", (int)(GetMilliseconds() - in));

scmin->tag = 3;

}

// dbp("finished merging holes: %d ms", (int)(GetMilliseconds() - in));

merged.UvTriangulateInto(m, srf);

// dbp("finished ear clippping: %d ms", (int)(GetMilliseconds() - in));

merged.l.Clear();

el.Clear();

vl.Clear();

// Careful, need to free the points within the contours, and not just

// the contours themselves. This was a tricky memory leak.

for(sc = l.First(); sc; sc = l.NextAfter(sc)) {

if(sc->tag) {

sc->l.Clear();

}

l.RemoveTagged();

}

bool SContour::BridgeToContour(SContour *sc,

SEdgeList *avoidEdges, List<Vector> *avoidPts)

{

int i, j;

bool withbridge = true;

// Start looking for a bridge on our new hole near its leftmost (min x)

// point.

int sco = 0;

for(i = 0; i < (sc->l.n - 1); i++) {

if((sc->l[i].p).EqualsExactly(sc->xminPt)) {

sco = i;

}

// And start looking on our merged contour at whichever point is nearest

// to the leftmost point of the new segment.

int thiso = 0;

double dmin = 1e10;

for(i = 0; i < l.n-1; i++) {

Vector p = l[i].p;

double d = (p.Minus(sc->xminPt)).MagSquared();

if(d < dmin) {

dmin = d;

thiso = i;

}

int thisp, scp;

Vector a, b, *f;

// First check if the contours share a point; in that case we should

// merge them there, without a bridge.

for(i = 0; i < l.n; i++) {

thisp = WRAP(i+thiso, l.n-1);

a = l[thisp].p;

for(f = avoidPts->First(); f; f = avoidPts->NextAfter(f)) {

if(f->Equals(a)) break;

}

if(f) continue;

for(j = 0; j < (sc->l.n - 1); j++) {

scp = WRAP(j+sco, (sc->l.n - 1));

b = sc->l[scp].p;

if(a.Equals(b)) {

withbridge = false;

goto haveEdge;

}

// If that fails, look for a bridge that does not intersect any edges.

for(i = 0; i < l.n; i++) {

thisp = WRAP(i+thiso, l.n);

a = l[thisp].p;

for(f = avoidPts->First(); f; f = avoidPts->NextAfter(f)) {

if(f->Equals(a)) break;

}

if(f) continue;

for(j = 0; j < (sc->l.n - 1); j++) {

scp = WRAP(j+sco, (sc->l.n - 1));

b = sc->l[scp].p;

for(f = avoidPts->First(); f; f = avoidPts->NextAfter(f)) {

if(f->Equals(b)) break;

}

if(f) continue;

if(avoidEdges->AnyEdgeCrossings(a, b) > 0) {

// doesn't work, bridge crosses an existing edge

} else {

goto haveEdge;

}

// Tried all the possibilities, didn't find an edge

return false;

haveEdge:

SContour merged = {};

for(i = 0; i < l.n; i++) {

if(withbridge || (i != thisp)) {

merged.AddPoint(l[i].p);

}

if(i == thisp) {

// less than or equal; need to duplicate the join point

for(j = 0; j <= (sc->l.n - 1); j++) {

int jp = WRAP(j + scp, (sc->l.n - 1));

merged.AddPoint((sc->l[jp]).p);

}

// and likewise duplicate join point for the outer curve

if(withbridge) {

merged.AddPoint(l[i].p);

}

// and future bridges mustn't cross our bridge, and it's tricky to get

// things right if two bridges come from the same point

if(withbridge) {

avoidEdges->AddEdge(a, b);

avoidPts->Add(&a);

}

avoidPts->Add(&b);

l.Clear();

l = merged.l;

return true;

}

bool SContour::IsEmptyTriangle(int ap, int bp, int cp, double scaledEPS) const {

STriangle tr = {};

tr.a = l[ap].p;

tr.b = l[bp].p;

tr.c = l[cp].p;

// Accelerate with an axis-aligned bounding box test

Vector maxv = tr.a, minv = tr.a;

(tr.b).MakeMaxMin(&maxv, &minv);

(tr.c).MakeMaxMin(&maxv, &minv);

Vector n = {0, 0, -1};

int i;

for(i = 0; i < l.n; i++) {

if(i == ap || i == bp || i == cp) continue;

Vector p = l[i].p;

if(p.OutsideAndNotOn(maxv, minv)) continue;

// A point on the edge of the triangle is considered to be inside,

// and therefore makes it a non-ear; but a point on the vertex is

// "outside", since that's necessary to make bridges work.

if(p.EqualsExactly(tr.a)) continue;

if(p.EqualsExactly(tr.b)) continue;

if(p.EqualsExactly(tr.c)) continue;

if(tr.ContainsPointProjd(n, p)) {

return false;

}

return true;

}

// Test if ray b->d passes through triangle a,b,c

static bool RayIsInside(Vector a, Vector c, Vector b, Vector d) {

// coincident edges are not considered to intersect the triangle

if (d.Equals(a)) return false;

if (d.Equals(c)) return false;

// if d and c are on opposite sides of ba, we are ok

// likewise if d and a are on opposite sides of bc

Vector ba = a.Minus(b);

Vector bc = c.Minus(b);

Vector bd = d.Minus(b);

// perpendicular to (x,y) is (x,-y) so dot that with the two points. If they

// have opposite signs their product will be negative. If bd and bc are on

// opposite sides of ba the ray does not intersect. Likewise for bd,ba and bc.

if ( (bd.x*(ba.y) + (bd.y * (-ba.x))) * ( bc.x*(ba.y) + (bc.y * (-ba.x))) < LENGTH_EPS)

return false;

if ( (bd.x*(bc.y) + (bd.y * (-bc.x))) * ( ba.x*(bc.y) + (ba.y * (-bc.x))) < LENGTH_EPS)

return false;

return true;

}

bool SContour::IsEar(int bp, double scaledEps) const {

int ap = WRAP(bp-1, l.n),

cp = WRAP(bp+1, l.n);

STriangle tr = {};

tr.a = l[ap].p;

tr.b = l[bp].p;

tr.c = l[cp].p;

if((tr.a).Equals(tr.c)) {

// This is two coincident and anti-parallel edges. Zero-area, so

// won't generate a real triangle, but we certainly can clip it.

return true;

}

Vector n = {0, 0, -1};

if((tr.Normal()).Dot(n) < scaledEps) {

// This vertex is reflex, or between two collinear edges; either way,

// it's not an ear.

return false;

}

// Accelerate with an axis-aligned bounding box test

Vector maxv = tr.a, minv = tr.a;

(tr.b).MakeMaxMin(&maxv, &minv);

(tr.c).MakeMaxMin(&maxv, &minv);

int i;

for(i = 0; i < l.n; i++) {

if(i == ap || i == bp || i == cp) continue;

Vector p = l[i].p;

if(p.OutsideAndNotOn(maxv, minv)) continue;

// A point on the edge of the triangle is considered to be inside,

// and therefore makes it a non-ear; but a point on the vertex is

// "outside", since that's necessary to make bridges work.

if(p.EqualsExactly(tr.a)) continue;

if(p.EqualsExactly(tr.c)) continue;

// points coincident with bp have to be allowed for bridges but edges

// from that other point must not cross through our triangle.

if(p.EqualsExactly(tr.b)) {

int j = WRAP(i-1, l.n);

int k = WRAP(i+1, l.n);

Vector jp = l[j].p;

Vector kp = l[k].p;

// two consecutive bridges (A,B,C) and later (C,B,A) are not an ear

if (jp.Equals(tr.c) && kp.Equals(tr.a)) return false;

// check both edges from the point in question

if (!RayIsInside(tr.a, tr.c, p,jp) && !RayIsInside(tr.a, tr.c, p,kp))

continue;

}

if(tr.ContainsPointProjd(n, p)) {

return false;

}

return true;

}

void SContour::ClipEarInto(SMesh *m, int bp, double scaledEps) {

int ap = WRAP(bp-1, l.n),

cp = WRAP(bp+1, l.n);

STriangle tr = {};

tr.a = l[ap].p;

tr.b = l[bp].p;

tr.c = l[cp].p;

if(tr.Normal().MagSquared() < scaledEps*scaledEps) {

// A vertex with more than two edges will cause us to generate

// zero-area triangles, which must be culled.

} else {

m->AddTriangle(&tr);

}

// By deleting the point at bp, we may change the ear-ness of the points

// on either side.

l[ap].ear = EarType::UNKNOWN;

l[cp].ear = EarType::UNKNOWN;

l.ClearTags();

l[bp].tag = 1;

l.RemoveTagged();

}

void SContour::UvTriangulateInto(SMesh *m, SSurface *srf) {

Vector tu, tv;

srf->TangentsAt(0.5, 0.5, &tu, &tv);

double s = sqrt(tu.MagSquared() + tv.MagSquared());

// We would like to apply our tolerances in xyz; but that would be a lot

// of work, so at least scale the epsilon semi-reasonably. That's

// perfect for square planes, less perfect for anything else.

double scaledEps = LENGTH_EPS / s;

int i;

// Clean the original contour by removing any zero-length edges.

// initialize eartypes to unknown while we're going over them.

l.ClearTags();

l[0].ear = EarType::UNKNOWN;

for(i = 1; i < l.n; i++) {

l[i].ear = EarType::UNKNOWN;

if((l[i].p).Equals(l[i-1].p)) {

l[i].tag = 1;

}

if( (l[0].p).Equals(l[l.n-1].p) ) {

l[l.n-1].tag = 1;

}

l.RemoveTagged();

// Handle simple triangle fans all at once. This pass is optional.

if(srf->degm == 1 && srf->degn == 1) {

l.ClearTags();

int j=0;

int pstart = 0;

double elen = -1.0;

double oldspan = 0.0;

for(i = 1; i < l.n; i++) {

Vector ab = l[i].p.Minus(l[i-1].p);

// first time just measure the segment

if (elen < 0.0) {

elen = ab.Dot(ab);

oldspan = elen;

j = 1;

continue;

}

// check for consecutive segments of similar size which are also

// ears and where the group forms a convex ear

bool end = false;

double ratio = ab.Dot(ab) / elen;

if ((ratio < 0.25) || (ratio > 4.0)) end = true;

double slen = l[pstart].p.Minus(l[i].p).MagSquared();

if (slen < oldspan) end = true;

if (!IsEar(i-1, scaledEps) ) end = true;

// if ((j>0) && !IsEar(pstart, i-1, i, scaledEps)) end = true;

if ((j>0) && !IsEmptyTriangle(pstart, i-1, i, scaledEps)) end = true;

// the new segment is valid so add to the fan

if (!end) {

j++;

oldspan = slen;

}

// we need to stop at the end of polygon but may still

if (i == l.n-1) {

end = true;

}

if (end) { // triangulate the fan and tag the vertices

if (j > 3) {

Vector center = l[pstart+1].p.Plus(l[pstart+j-1].p).ScaledBy(0.5);

for (int x=0; x<j; x++) {

STriangle tr = {};

tr.a = center;

tr.b = l[pstart+x].p;

tr.c = l[pstart+x+1].p;

m->AddTriangle(&tr);

}

for (int x=1; x<j; x++) {

l[pstart+x].tag = 1;

}

STriangle tr = {};

tr.a = center;

tr.b = l[pstart+j].p;

tr.c = l[pstart].p;

m->AddTriangle(&tr);

}

pstart = i-1;

elen = ab.Dot(ab);

oldspan = elen;

j = 1;

}

l.RemoveTagged();

} // end optional fan creation pass

bool toggle = false;

while(l.n > 3) {

int bestEar = -1;

double bestChordTol = VERY_POSITIVE;

// Alternate the starting position so we generate strip-like

// triangulations instead of fan-like

toggle = !toggle;

int offset = toggle ? -1 : 0;

for(i = 0; i < l.n; i++) {

int ear = WRAP(i+offset, l.n);

if(l[ear].ear == EarType::UNKNOWN) {

(l[ear]).ear = IsEar(ear, scaledEps) ? EarType::EAR : EarType::NOT_EAR;

}

if(l[ear].ear == EarType::EAR) {

if(srf->degm == 1 && srf->degn == 1) {

// This is a plane; any ear is a good ear.

bestEar = ear;

break;

}

// If we are triangulating a curved surface, then try to

// clip ears that have a small chord tolerance from the

// surface.

Vector prev = l[WRAP((i+offset-1), l.n)].p,

next = l[WRAP((i+offset+1), l.n)].p;

double tol = srf->ChordToleranceForEdge(prev, next);

if(tol < bestChordTol - scaledEps) {

bestEar = ear;

bestChordTol = tol;

}

if(bestChordTol < 0.1*SS.ChordTolMm()) {

break;

}

if(bestEar < 0) {

dbp("couldn't find an ear! fail");

return;

}

ClipEarInto(m, bestEar, scaledEps);

}

ClipEarInto(m, 0, scaledEps); // add the last triangle

}

double SSurface::ChordToleranceForEdge(Vector a, Vector b) const {

Vector as = PointAt(a.x, a.y), bs = PointAt(b.x, b.y);

double worst = VERY_NEGATIVE;

int i;

for(i = 1; i <= 3; i++) {

Vector p = a. Plus((b. Minus(a )).ScaledBy(i/4.0)),

ps = as.Plus((bs.Minus(as)).ScaledBy(i/4.0));

Vector pps = PointAt(p.x, p.y);

worst = max(worst, (pps.Minus(ps)).MagSquared());

}

return sqrt(worst);

}

Vector SSurface::PointAtMaybeSwapped(double u, double v, bool swapped) const {

if(swapped) {

return PointAt(v, u);

} else {

return PointAt(u, v);

}

Vector SSurface::NormalAtMaybeSwapped(double u, double v, bool swapped) const {

Vector du, dv;

if(swapped) {

TangentsAt(v, u, &dv, &du);

} else {

TangentsAt(u, v, &du, &dv);

}

return du.Cross(dv).WithMagnitude(1.0);

}

void SSurface::MakeTriangulationGridInto(List<double> *l, double vs, double vf,

bool swapped, int depth) const

{

double worst = 0;

// Try piecewise linearizing four curves, at u = 0, 1/3, 2/3, 1; choose

// the worst chord tolerance of any of those.

double worst_twist = 1.0;

int i;

for(i = 0; i <= 3; i++) {

double u = i/3.0;

// This chord test should be identical to the one in SBezier::MakePwl

// to make the piecewise linear edges line up with the grid more or

// less.

Vector ps = PointAtMaybeSwapped(u, vs, swapped),

pf = PointAtMaybeSwapped(u, vf, swapped);

double vm1 = (2*vs + vf) / 3,

vm2 = (vs + 2*vf) / 3;

Vector pm1 = PointAtMaybeSwapped(u, vm1, swapped),

pm2 = PointAtMaybeSwapped(u, vm2, swapped);

// 0.999 is about 2.5 degrees of twist over the middle 1/3 V-span.

// we don't check at the ends because the derivative may not be valid there.

double twist = 1.0;

if (degm == 1) twist = NormalAtMaybeSwapped(u, vm1, swapped).Dot(

NormalAtMaybeSwapped(u, vm2, swapped) );

if (twist < worst_twist) worst_twist = twist;

worst = max(worst, pm1.DistanceToLine(ps, pf.Minus(ps)));

worst = max(worst, pm2.DistanceToLine(ps, pf.Minus(ps)));

}

double step = 1.0/SS.GetMaxSegments();

if( ((vf - vs) < step || worst < SS.ChordTolMm())

&& ((worst_twist > 0.999) || (depth > 3)) ) {

l->Add(&vf);

} else {

MakeTriangulationGridInto(l, vs, (vs+vf)/2, swapped, depth+1);

MakeTriangulationGridInto(l, (vs+vf)/2, vf, swapped, depth+1);

}

void SPolygon::UvGridTriangulateInto(SMesh *mesh, SSurface *srf) {

SEdgeList orig = {};

MakeEdgesInto(&orig);

SEdgeList holes = {};

normal = {0, 0, 1};

FixContourDirections();

// Build a rectangular grid, with horizontal and vertical lines in the

// uv plane. The spacing of these lines is adaptive, so calculate that.

List<double> li, lj;

li = {};

lj = {};

double v[5] = {0.0, 0.25, 0.5, 0.75, 1.0};

li.Add(&v[0]);

srf->MakeTriangulationGridInto(&li, 0, 1, /*swapped=*/true, 0);

lj.Add(&v[0]);

srf->MakeTriangulationGridInto(&lj, 0, 1, /*swapped=*/false, 0);

// force 2nd order grid to have at least 4 segments in each direction

if ((li.n < 5) && (srf->degm>1)) { // 4 segments minimum

li.Clear();

li.Add(&v[0]);li.Add(&v[1]);li.Add(&v[2]);li.Add(&v[3]);li.Add(&v[4]);

}

if ((lj.n < 5) && (srf->degn>1)) { // 4 segments minimum

lj.Clear();

lj.Add(&v[0]);lj.Add(&v[1]);lj.Add(&v[2]);lj.Add(&v[3]);lj.Add(&v[4]);

}

if ((li.n > 3) && (lj.n > 3)) {

// Now iterate over each quad in the grid. If it's outside the polygon,

// or if it intersects the polygon, then we discard it. Otherwise we

// generate two triangles in the mesh, and cut it out of our polygon.

// Quads around the perimeter would be rejected by AnyEdgeCrossings.

std::vector<bool> bottom(lj.n, false); // did we use this quad?

Vector tu = {}, tv = {};

int i, j;

for(i = 1; i < (li.n-1); i++) {

bool prev_flag = false;

for(j = 1; j < (lj.n-1); j++) {

bool this_flag = true;

double us = li[i], uf = li[i+1],

vs = lj[j], vf = lj[j+1];

Vector a = {us, vs, 0},

b = {us, vf, 0},

c = {uf, vf, 0},

d = {uf, vs, 0};

// | d-----c

// | | |

// | a-----b

// |

// +-------------> j/v axis

if( (i==(li.n-2)) || (j==(lj.n-2)) ||

orig.AnyEdgeCrossings(a, b, NULL) ||

orig.AnyEdgeCrossings(b, c, NULL) ||

orig.AnyEdgeCrossings(c, d, NULL) ||

orig.AnyEdgeCrossings(d, a, NULL))

{

this_flag = false;

}

// There's no intersections, so it doesn't matter which point

// we decide to test.

if(!this->ContainsPoint(a)) {

this_flag = false;

}

if (this_flag) {

// Add the quad to our mesh

srf->TangentsAt(us,vs, &tu,&tv);

if(tu.Dot(tv) < LENGTH_EPS) {

/* Split "the other way" if angle>90

compare to LENGTH_EPS instead of zero to avoid alternating triangle

"orientations" when the tangents are orthogonal (revolve, lathe etc.)

this results in a higher quality mesh. */

STriangle tr = {};

tr.a = a;

tr.b = b;

tr.c = c;

mesh->AddTriangle(&tr);

tr.a = a;

tr.b = c;

tr.c = d;

mesh->AddTriangle(&tr);

} else{

STriangle tr = {};

tr.a = a;

tr.b = b;

tr.c = d;

mesh->AddTriangle(&tr);

tr.a = b;

tr.b = c;

tr.c = d;

mesh->AddTriangle(&tr);

}

if (!prev_flag) // add our own left edge

holes.AddEdge(d, a);

if (!bottom[j]) // add our own bottom edge

holes.AddEdge(a, b);

} else {

if (prev_flag) // add our left neighbors right edge

holes.AddEdge(a, d);

if (bottom[j]) // add our bottom neighbors top edge

holes.AddEdge(b, a);

}

prev_flag = this_flag;

bottom[j] = this_flag;

}

// Because no duplicate edges were created we do not need to cull them.

SPolygon hp = {};

holes.AssemblePolygon(&hp, NULL, /*keepDir=*/true);

SContour *sc;

for(sc = hp.l.First(); sc; sc = hp.l.NextAfter(sc)) {

l.Add(sc);

}

hp.l.Clear();

}

orig.Clear();

holes.Clear();

li.Clear();

lj.Clear();

UvTriangulateInto(mesh, srf);

}

void SPolygon::TriangulateInto(SMesh *m) const {

Vector n = normal;

if(n.Equals({0, 0, 0})) {

n = ComputeNormal();

}

Vector u = n.Normal(0);

Vector v = n.Normal(1);

SPolygon p = {};

this->InverseTransformInto(&p, u, v, n);

SSurface srf = SSurface::FromPlane({0.0, 0.0, 0.0},

{1.0, 0.0, 0.0},

{0.0, 1.0, 0.0});

SMesh pm = {};

p.UvTriangulateInto(&pm, &srf);

for(STriangle st : pm.l) {

st = st.Transform(u, v, n);

m->AddTriangle(&st);

}

p.Clear();

pm.Clear();

}

} // namespace SolveSpace

solvespace/src/srf/triangulate.cpp at master · solvespace/solvespace · GitHub

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