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solvespace/mesh.cpp

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#include "solvespace.h"
void SMesh::Clear(void) {
l.Clear();
}
void SMesh::AddTriangle(STriMeta meta, Vector n, Vector a, Vector b, Vector c) {
Vector ab = b.Minus(a), bc = c.Minus(b);
Vector np = ab.Cross(bc);
if(np.Magnitude() < 1e-10) {
// ugh; gl sometimes tesselates to collinear triangles
return;
}
if(np.Dot(n) > 0) {
AddTriangle(meta, a, b, c);
} else {
AddTriangle(meta, c, b, a);
}
}
void SMesh::AddTriangle(STriMeta meta, Vector a, Vector b, Vector c) {
STriangle t; ZERO(&t);
t.meta = meta;
t.a = a;
t.b = b;
t.c = c;
AddTriangle(&t);
}
void SMesh::AddTriangle(STriangle *st) {
l.Add(st);
}
void SMesh::DoBounding(Vector v, Vector *vmax, Vector *vmin) {
vmax->x = max(vmax->x, v.x);
vmax->y = max(vmax->y, v.y);
vmax->z = max(vmax->z, v.z);
vmin->x = min(vmin->x, v.x);
vmin->y = min(vmin->y, v.y);
vmin->z = min(vmin->z, v.z);
}
void SMesh::GetBounding(Vector *vmax, Vector *vmin) {
int i;
*vmin = Vector::From( 1e12, 1e12, 1e12);
*vmax = Vector::From(-1e12, -1e12, -1e12);
for(i = 0; i < l.n; i++) {
STriangle *st = &(l.elem[i]);
DoBounding(st->a, vmax, vmin);
DoBounding(st->b, vmax, vmin);
DoBounding(st->c, vmax, vmin);
}
}
void SMesh::Simplify(int start) {
int maxTriangles = (l.n - start) + 10;
STriMeta meta = l.elem[start].meta;
STriangle *tout = (STriangle *)AllocTemporary(maxTriangles*sizeof(*tout));
int toutc = 0;
Vector n, *conv = (Vector *)AllocTemporary(maxTriangles*3*sizeof(*conv));
int convc = 0;
int start0 = start;
int i, j;
for(i = start; i < l.n; i++) {
STriangle *tr = &(l.elem[i]);
if(tr->MinAltitude() < LENGTH_EPS) {
tr->tag = 1;
} else {
tr->tag = 0;
}
}
for(;;) {
bool didAdd;
convc = 0;
for(i = start; i < l.n; i++) {
STriangle *tr = &(l.elem[i]);
if(tr->tag) continue;
tr->tag = 1;
n = (tr->Normal()).WithMagnitude(1);
conv[convc++] = tr->a;
conv[convc++] = tr->b;
conv[convc++] = tr->c;
start = i+1;
break;
}
if(i >= l.n) break;
do {
didAdd = false;
for(j = 0; j < convc; j++) {
Vector a = conv[WRAP((j-1), convc)],
b = conv[j],
d = conv[WRAP((j+1), convc)],
e = conv[WRAP((j+2), convc)];
Vector c;
for(i = start; i < l.n; i++) {
STriangle *tr = &(l.elem[i]);
if(tr->tag) continue;
if((tr->a).Equals(d) && (tr->b).Equals(b)) {
c = tr->c;
} else if((tr->b).Equals(d) && (tr->c).Equals(b)) {
c = tr->a;
} else if((tr->c).Equals(d) && (tr->a).Equals(b)) {
c = tr->b;
} else {
continue;
}
// The vertex at C must be convex; but the others must
// be tested
Vector ab = b.Minus(a);
Vector bc = c.Minus(b);
Vector cd = d.Minus(c);
Vector de = e.Minus(d);
double bDot = (ab.Cross(bc)).Dot(n);
double dDot = (cd.Cross(de)).Dot(n);
bDot /= min(ab.Magnitude(), bc.Magnitude());
dDot /= min(cd.Magnitude(), de.Magnitude());
if(fabs(bDot) < LENGTH_EPS && fabs(dDot) < LENGTH_EPS) {
conv[WRAP((j+1), convc)] = c;
// and remove the vertex at j, which is a dup
memmove(conv+j, conv+j+1,
(convc - j - 1)*sizeof(conv[0]));
convc--;
} else if(fabs(bDot) < LENGTH_EPS && dDot > 0) {
conv[j] = c;
} else if(fabs(dDot) < LENGTH_EPS && bDot > 0) {
conv[WRAP((j+1), convc)] = c;
} else if(bDot > 0 && dDot > 0) {
// conv[j] is unchanged, conv[j+1] goes to [j+2]
memmove(conv+j+2, conv+j+1,
(convc - j - 1)*sizeof(conv[0]));
conv[j+1] = c;
convc++;
} else {
continue;
}
didAdd = true;
tr->tag = 1;
break;
}
}
} while(didAdd);
// I need to debug why this is required; sometimes the above code
// still generates a convex polygon
for(i = 0; i < convc; i++) {
Vector a = conv[WRAP((i-1), convc)],
b = conv[i],
c = conv[WRAP((i+1), convc)];
Vector ab = b.Minus(a);
Vector bc = c.Minus(b);
double bDot = (ab.Cross(bc)).Dot(n);
bDot /= min(ab.Magnitude(), bc.Magnitude());
if(bDot < 0) return; // XXX, shouldn't happen
}
for(i = 0; i < convc - 2; i++) {
STriangle tr = STriangle::From(meta, conv[0], conv[i+1], conv[i+2]);
if(tr.MinAltitude() > LENGTH_EPS) {
tout[toutc++] = tr;
}
}
}
l.n = start0;
for(i = 0; i < toutc; i++) {
AddTriangle(&(tout[i]));
}
FreeTemporary(tout);
FreeTemporary(conv);
}
void SMesh::AddAgainstBsp(SMesh *srcm, SBsp3 *bsp3) {
int i;
for(i = 0; i < srcm->l.n; i++) {
STriangle *st = &(srcm->l.elem[i]);
int pn = l.n;
atLeastOneDiscarded = false;
bsp3->Insert(st, this);
if(!atLeastOneDiscarded && (l.n != (pn+1))) {
l.n = pn;
if(flipNormal) {
AddTriangle(st->meta, st->c, st->b, st->a);
} else {
AddTriangle(st->meta, st->a, st->b, st->c);
}
}
if(l.n - pn > 1) {
Simplify(pn);
}
}
}
void SMesh::MakeFromUnionOf(SMesh *a, SMesh *b) {
SBsp3 *bspa = SBsp3::FromMesh(a);
SBsp3 *bspb = SBsp3::FromMesh(b);
flipNormal = false;
keepCoplanar = false;
AddAgainstBsp(b, bspa);
flipNormal = false;
keepCoplanar = true;
AddAgainstBsp(a, bspb);
}
void SMesh::MakeFromDifferenceOf(SMesh *a, SMesh *b) {
SBsp3 *bspa = SBsp3::FromMesh(a);
SBsp3 *bspb = SBsp3::FromMesh(b);
flipNormal = true;
keepCoplanar = true;
AddAgainstBsp(b, bspa);
flipNormal = false;
keepCoplanar = false;
AddAgainstBsp(a, bspb);
}
void SMesh::MakeFromCopyOf(SMesh *a) {
int i;
for(i = 0; i < a->l.n; i++) {
AddTriangle(&(a->l.elem[i]));
}
}
void SMesh::MakeFromAssemblyOf(SMesh *a, SMesh *b) {
MakeFromCopyOf(a);
MakeFromCopyOf(b);
}
void SMesh::MakeFromTransformationOf(SMesh *a, Vector trans, Quaternion q) {
STriangle *tr;
for(tr = a->l.First(); tr; tr = a->l.NextAfter(tr)) {
STriangle tt = *tr;
tt.a = (q.Rotate(tt.a)).Plus(trans);
tt.b = (q.Rotate(tt.b)).Plus(trans);
tt.c = (q.Rotate(tt.c)).Plus(trans);
AddTriangle(&tt);
}
}
bool SMesh::IsEmpty(void) {
return (l.n == 0);
}
DWORD SMesh::FirstIntersectionWith(Point2d mp) {
Vector p0 = Vector::From(mp.x, mp.y, 0);
Vector gn = Vector::From(0, 0, 1);
double maxT = -1e12;
DWORD face = 0;
int i;
for(i = 0; i < l.n; i++) {
STriangle tr = l.elem[i];
tr.a = SS.GW.ProjectPoint3(tr.a);
tr.b = SS.GW.ProjectPoint3(tr.b);
tr.c = SS.GW.ProjectPoint3(tr.c);
Vector n = tr.Normal();
if(n.Dot(gn) < LENGTH_EPS) continue; // back-facing or on edge
if(tr.ContainsPointProjd(gn, p0)) {
// Let our line have the form r(t) = p0 + gn*t
double t = -(n.Dot((tr.a).Minus(p0)))/(n.Dot(gn));
if(t > maxT) {
maxT = t;
face = tr.meta.face;
}
}
}
return face;
}
#define KDTREE_EPS (20*LENGTH_EPS) // nice and sloppy
STriangleLl *STriangleLl::Alloc(void)
{ return (STriangleLl *)AllocTemporary(sizeof(STriangleLl)); }
SKdNode *SKdNode::Alloc(void)
{ return (SKdNode *)AllocTemporary(sizeof(SKdNode)); }
SKdNode *SKdNode::From(SMesh *m) {
int i;
STriangle *tra = (STriangle *)AllocTemporary((m->l.n) * sizeof(*tra));
for(i = 0; i < m->l.n; i++) {
tra[i] = m->l.elem[i];
}
srand(0);
int n = m->l.n;
while(n > 1) {
int k = rand() % n;
n--;
SWAP(STriangle, tra[k], tra[n]);
}
STriangleLl *tll = NULL;
for(i = 0; i < m->l.n; i++) {
STriangleLl *tn = STriangleLl::Alloc();
tn->tri = &(tra[i]);
tn->next = tll;
tll = tn;
}
return SKdNode::From(tll, 0);
}
SKdNode *SKdNode::From(STriangleLl *tll, int which) {
SKdNode *ret = Alloc();
if(!tll) goto leaf;
int i;
int gtc[3] = { 0, 0, 0 }, ltc[3] = { 0, 0, 0 }, allc = 0;
double badness[3];
double split[3];
for(i = 0; i < 3; i++) {
int tcnt = 0;
STriangleLl *ll;
for(ll = tll; ll; ll = ll->next) {
STriangle *tr = ll->tri;
split[i] += (ll->tri->a).Element(i);
split[i] += (ll->tri->b).Element(i);
split[i] += (ll->tri->c).Element(i);
tcnt++;
}
split[i] /= (tcnt*3);
for(ll = tll; ll; ll = ll->next) {
STriangle *tr = ll->tri;
double a = (tr->a).Element(i),
b = (tr->b).Element(i),
c = (tr->c).Element(i);
if(a < split[i] + KDTREE_EPS ||
b < split[i] + KDTREE_EPS ||
c < split[i] + KDTREE_EPS)
{
ltc[i]++;
}
if(a > split[i] - KDTREE_EPS ||
b > split[i] - KDTREE_EPS ||
c > split[i] - KDTREE_EPS)
{
gtc[i]++;
}
if(i == 0) allc++;
}
badness[i] = pow((double)ltc[i], 4) + pow((double)gtc[i], 4);
}
if(badness[0] < badness[1] && badness[0] < badness[2]) {
which = 0;
} else if(badness[1] < badness[2]) {
which = 1;
} else {
which = 2;
}
if(allc < 10) goto leaf;
if(allc == gtc[which] || allc == ltc[which]) goto leaf;
STriangleLl *ll;
STriangleLl *lgt = NULL, *llt = NULL;
for(ll = tll; ll; ll = ll->next) {
STriangle *tr = ll->tri;
double a = (tr->a).Element(which),
b = (tr->b).Element(which),
c = (tr->c).Element(which);
if(a < split[which] + KDTREE_EPS ||
b < split[which] + KDTREE_EPS ||
c < split[which] + KDTREE_EPS)
{
STriangleLl *n = STriangleLl::Alloc();
*n = *ll;
n->next = llt;
llt = n;
}
if(a > split[which] - KDTREE_EPS ||
b > split[which] - KDTREE_EPS ||
c > split[which] - KDTREE_EPS)
{
STriangleLl *n = STriangleLl::Alloc();
*n = *ll;
n->next = lgt;
lgt = n;
}
}
ret->which = which;
ret->c = split[which];
ret->gt = SKdNode::From(lgt, (which + 1) % 3);
ret->lt = SKdNode::From(llt, (which + 1) % 3);
return ret;
leaf:
// dbp("leaf: allc=%d gtc=%d ltc=%d which=%d", allc, gtc[which], ltc[which], which);
ret->tris = tll;
return ret;
}
void SKdNode::ClearTags(void) {
if(gt && lt) {
gt->ClearTags();
lt->ClearTags();
} else {
STriangleLl *ll;
for(ll = tris; ll; ll = ll->next) {
ll->tri->tag = 0;
}
}
}
void SKdNode::AddTriangle(STriangle *tr) {
if(gt && lt) {
double ta = (tr->a).Element(which),
tb = (tr->b).Element(which),
tc = (tr->c).Element(which);
if(ta < c + KDTREE_EPS ||
tb < c + KDTREE_EPS ||
tc < c + KDTREE_EPS)
{
lt->AddTriangle(tr);
}
if(ta > c - KDTREE_EPS ||
tb > c - KDTREE_EPS ||
tc > c - KDTREE_EPS)
{
gt->AddTriangle(tr);
}
} else {
STriangleLl *tn = STriangleLl::Alloc();
tn->tri = tr;
tn->next = tris;
tris = tn;
}
}
void SKdNode::MakeMeshInto(SMesh *m) {
if(gt) gt->MakeMeshInto(m);
if(lt) lt->MakeMeshInto(m);
STriangleLl *ll;
for(ll = tris; ll; ll = ll->next) {
if(ll->tri->tag) continue;
m->AddTriangle(ll->tri);
ll->tri->tag = 1;
}
}
void SKdNode::FindEdgeOn(Vector a, Vector b, int *n, int cnt,
bool coplanarIsInter, bool *inter, bool *fwd)
{
if(gt && lt) {
double ac = a.Element(which),
bc = b.Element(which);
if(ac < c + KDTREE_EPS ||
bc < c + KDTREE_EPS)
{
lt->FindEdgeOn(a, b, n, cnt, coplanarIsInter, inter, fwd);
}
if(ac > c - KDTREE_EPS ||
bc > c - KDTREE_EPS)
{
gt->FindEdgeOn(a, b, n, cnt, coplanarIsInter, inter, fwd);
}
return;
}
// We are a leaf node; so we iterate over all the triangles in our
// linked list.
STriangleLl *ll;
for(ll = tris; ll; ll = ll->next) {
STriangle *tr = ll->tri;
if(tr->tag == cnt) continue;
// Test if this triangle matches up with the given edge
if((a.Equals(tr->b) && b.Equals(tr->a)) ||
(a.Equals(tr->c) && b.Equals(tr->b)) ||
(a.Equals(tr->a) && b.Equals(tr->c)))
{
(*n)++;
// Record whether this triangle is front- or back-facing.
if(tr->Normal().z > LENGTH_EPS) {
*fwd = true;
} else {
*fwd = false;
}
} else if(((a.Equals(tr->a) && b.Equals(tr->b)) ||
(a.Equals(tr->b) && b.Equals(tr->c)) ||
(a.Equals(tr->c) && b.Equals(tr->a))))
{
// It's an edge of this triangle, okay.
} else {
// Check for self-intersection
Vector n = (tr->Normal()).WithMagnitude(1);
double d = (tr->a).Dot(n);
double pa = a.Dot(n) - d, pb = b.Dot(n) - d;
// It's an intersection if neither point lies in-plane,
// and the edge crosses the plane (should handle in-plane
// intersections separately but don't yet).
if((pa < -LENGTH_EPS || pa > LENGTH_EPS) &&
(pb < -LENGTH_EPS || pb > LENGTH_EPS) &&
(pa*pb < 0))
{
// The edge crosses the plane of the triangle; now see if
// it crosses inside the triangle.
if(tr->ContainsPointProjd(b.Minus(a), a)) {
if(coplanarIsInter) {
*inter = true;
} else {
Vector p = Vector::AtIntersectionOfPlaneAndLine(
n, d, a, b, NULL);
Vector ta = tr->a,
tb = tr->b,
tc = tr->c;
if((p.DistanceToLine(ta, tb.Minus(ta)) < LENGTH_EPS) ||
(p.DistanceToLine(tb, tc.Minus(tb)) < LENGTH_EPS) ||
(p.DistanceToLine(tc, ta.Minus(tc)) < LENGTH_EPS))
{
// Intersection lies on edge. This happens when
// our edge is from a triangle coplanar with
// another triangle in the mesh. We don't test
// the edge against triangles whose plane contains
// that edge, but we do end up testing against
// the coplanar triangle's neighbours, which we
// will intersect on their edges.
} else {
*inter = true;
}
}
}
}
}
// Ensure that we don't count this triangle twice if it appears
// in two buckets of the kd tree.
tr->tag = cnt;
}
}
void SKdNode::SplitLinesAgainstTriangle(SEdgeList *sel, STriangle *tr) {
SEdgeList seln;
ZERO(&seln);
Vector tn = tr->Normal().WithMagnitude(1);
double td = tn.Dot(tr->a);
// Consider front-facing triangles only
if(tn.z > LENGTH_EPS) {
// If the edge crosses our triangle's plane, then split into above
// and below parts.
SEdge *se;
for(se = sel->l.First(); se; se = sel->l.NextAfter(se)) {
double da = (se->a).Dot(tn) - td,
db = (se->b).Dot(tn) - td;
if((da < -LENGTH_EPS && db > LENGTH_EPS) ||
(db < -LENGTH_EPS && da > LENGTH_EPS))
{
Vector m = Vector::AtIntersectionOfPlaneAndLine(
tn, td,
se->a, se->b, NULL);
seln.AddEdge(m, se->b);
se->b = m;
}
}
for(se = seln.l.First(); se; se = seln.l.NextAfter(se)) {
sel->AddEdge(se->a, se->b);
}
seln.Clear();
for(se = sel->l.First(); se; se = sel->l.NextAfter(se)) {
Vector pt = ((se->a).Plus(se->b)).ScaledBy(0.5);
double dt = pt.Dot(tn) - td;
if(pt.Dot(tn) - td > -LENGTH_EPS) {
// Edge is in front of or on our plane (remember, tn.z > 0)
// so it is exempt from further splitting
se->auxA = 1;
} else {
// Edge is behind our plane, needs further splitting
se->auxA = 0;
}
}
// Considering only the (x, y) coordinates, split the edge against our
// triangle.
Point2d a = (tr->a).ProjectXy(),
b = (tr->b).ProjectXy(),
c = (tr->c).ProjectXy();
Point2d n[3] = { (b.Minus(a)).Normal().WithMagnitude(1),
(c.Minus(b)).Normal().WithMagnitude(1),
(a.Minus(c)).Normal().WithMagnitude(1) };
double d[3] = { n[0].Dot(b),
n[1].Dot(c),
n[2].Dot(a) };
// Split all of the edges where they intersect the triangle edges
int i;
for(i = 0; i < 3; i++) {
for(se = sel->l.First(); se; se = sel->l.NextAfter(se)) {
if(se->auxA) continue;
Point2d ap = (se->a).ProjectXy(),
bp = (se->b).ProjectXy();
double da = n[i].Dot(ap) - d[i],
db = n[i].Dot(bp) - d[i];
if((da < -LENGTH_EPS && db > LENGTH_EPS) ||
(db < -LENGTH_EPS && da > LENGTH_EPS))
{
double dab = (db - da);
Vector spl = ((se->a).ScaledBy( db/dab)).Plus(
(se->b).ScaledBy(-da/dab));
seln.AddEdge(spl, se->b);
se->b = spl;
}
}
for(se = seln.l.First(); se; se = seln.l.NextAfter(se)) {
sel->AddEdge(se->a, se->b, 0);
}
seln.Clear();
}
for(se = sel->l.First(); se; se = sel->l.NextAfter(se)) {
if(se->auxA) {
// Lies above or on the triangle plane, so triangle doesn't
// occlude it.
se->tag = 0;
} else {
// Test the segment to see if it lies outside the triangle
// (i.e., outside wrt at least one edge), and keep it only
// then.
Point2d pt = ((se->a).Plus(se->b).ScaledBy(0.5)).ProjectXy();
se->tag = 1;
for(i = 0; i < 3; i++) {
// If the test point lies on the boundary of our triangle,
// then we still discard the edge.
if(n[i].Dot(pt) - d[i] > LENGTH_EPS) se->tag = 0;
}
}
}
sel->l.RemoveTagged();
}
}
void SKdNode::OcclusionTestLine(SEdge orig, SEdgeList *sel, int cnt) {
if(gt && lt) {
double ac = (orig.a).Element(which),
bc = (orig.b).Element(which);
// We can ignore triangles that are separated in x or y, but triangles
// that are separated in z may still contribute
if(ac < c + KDTREE_EPS ||
bc < c + KDTREE_EPS ||
which == 2)
{
lt->OcclusionTestLine(orig, sel, cnt);
}
if(ac > c - KDTREE_EPS ||
bc > c - KDTREE_EPS ||
which == 2)
{
gt->OcclusionTestLine(orig, sel, cnt);
}
} else {
STriangleLl *ll;
for(ll = tris; ll; ll = ll->next) {
STriangle *tr = ll->tri;
if(tr->tag == cnt) continue;
SplitLinesAgainstTriangle(sel, tr);
tr->tag = cnt;
}
}
}
//-----------------------------------------------------------------------------
// Report all naked edges of the mesh (i.e., edges that don't join up to
// a single anti-parallel edge of another triangle), and all edges that
// intersect another triangle. If coplanarIsInter, then edges coplanar with
// another triangle and within it are reported, otherwise not. We report
// in *inter and *leaky whether the mesh is self-intersecting or leaky
// (having naked edges) respectively.
//-----------------------------------------------------------------------------
void SKdNode::MakeNakedEdgesInto(SEdgeList *sel, bool coplanarIsInter,
bool *inter, bool *leaky)
{
if(inter) *inter = false;
if(leaky) *leaky = false;
SMesh m;
ZERO(&m);
ClearTags();
MakeMeshInto(&m);
int cnt = 1234;
int i, j;
for(i = 0; i < m.l.n; i++) {
STriangle *tr = &(m.l.elem[i]);
for(j = 0; j < 3; j++) {
Vector a = (j == 0) ? tr->a : ((j == 1) ? tr->b : tr->c);
Vector b = (j == 0) ? tr->b : ((j == 1) ? tr->c : tr->a);
int n = 0, nOther = 0;
bool thisIntersects = false, fwd;
FindEdgeOn(a, b, &n, cnt, coplanarIsInter, &thisIntersects, &fwd);
if(n != 1) {
sel->AddEdge(a, b);
if(leaky) *leaky = true;
}
if(thisIntersects) {
sel->AddEdge(a, b);
if(inter) *inter = true;
}
cnt++;
}
}
m.Clear();
}
void SKdNode::MakeTurningEdgesInto(SEdgeList *sel) {
SMesh m;
ZERO(&m);
ClearTags();
MakeMeshInto(&m);
int cnt = 1234;
int i, j;
for(i = 0; i < m.l.n; i++) {
STriangle *tr = &(m.l.elem[i]);
if(tr->Normal().z > LENGTH_EPS) continue;
// So this is a back-facing triangle
for(j = 0; j < 3; j++) {
Vector a = (j == 0) ? tr->a : ((j == 1) ? tr->b : tr->c);
Vector b = (j == 0) ? tr->b : ((j == 1) ? tr->c : tr->a);
int n = 0;
bool inter, fwd;
FindEdgeOn(a, b, &n, cnt, true, &inter, &fwd);
if(n == 1) {
// and its neighbour is front-facing, so generate the edge.
if(fwd) sel->AddEdge(a, b);
}
cnt++;
}
}
m.Clear();
}
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