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//-----------------------------------------------------------------------------
// Binary space partitioning tree, used to represent a volume in 3-space
// bounded by a triangle mesh. These are used to compute Boolean operations
// on meshes. These aren't used for anything relating to an SShell of
// ratpoly surfaces.
//
// Copyright 2008-2013 Jonathan Westhues.
//-----------------------------------------------------------------------------
#include "solvespace.h"
SBsp2 *SBsp2::Alloc() { return (SBsp2 *)AllocTemporary(sizeof(SBsp2)); }
SBsp3 *SBsp3::Alloc() { return (SBsp3 *)AllocTemporary(sizeof(SBsp3)); }
SBsp3 *SBsp3::FromMesh(const SMesh *m) {
SBsp3 *bsp3 = NULL;
int i;
SMesh mc = {};
for(i = 0; i < m->l.n; i++) {
mc.AddTriangle(&(m->l.elem[i]));
}
srand(0); // Let's be deterministic, at least!
int n = mc.l.n;
while(n > 1) {
int k = rand() % n;
n--;
swap(mc.l.elem[k], mc.l.elem[n]);
}
for(i = 0; i < mc.l.n; i++) {
bsp3 = InsertOrCreate(bsp3, &(mc.l.elem[i]), NULL);
}
mc.Clear();
return bsp3;
}
Vector SBsp3::IntersectionWith(Vector a, Vector b) const {
double da = a.Dot(n) - d;
double db = b.Dot(n) - d;
ssassert(da*db < 0, "Expected segment to intersect BSP node");
double dab = (db - da);
return (a.ScaledBy(db/dab)).Plus(b.ScaledBy(-da/dab));
}
void SBsp3::InsertInPlane(bool pos2, STriangle *tr, SMesh *m) {
Vector tc = ((tr->a).Plus(tr->b).Plus(tr->c)).ScaledBy(1.0/3);
bool onFace = false;
bool sameNormal = false;
double maxNormalMag = -1;
Vector lln, trn = tr->Normal();
SBsp3 *ll = this;
while(ll) {
if((ll->tri).ContainsPoint(tc)) {
onFace = true;
// If the mesh contains almost-zero-area triangles, and we're
// just on the edge of one of those, then don't trust its normal.
lln = (ll->tri).Normal();
if(lln.Magnitude() > maxNormalMag) {
sameNormal = trn.Dot(lln) > 0;
maxNormalMag = lln.Magnitude();
}
}
ll = ll->more;
}
if(m->flipNormal && ((!pos2 && !onFace) ||
(onFace && !sameNormal && m->keepCoplanar)))
{
m->AddTriangle(tr->meta, tr->c, tr->b, tr->a);
} else if(!(m->flipNormal) && ((pos2 && !onFace) ||
(onFace && sameNormal && m->keepCoplanar)))
{
m->AddTriangle(tr->meta, tr->a, tr->b, tr->c);
} else {
m->atLeastOneDiscarded = true;
}
}
void SBsp3::InsertHow(BspClass how, STriangle *tr, SMesh *instead) {
switch(how) {
case BspClass::POS:
if(instead && !pos) goto alt;
pos = InsertOrCreate(pos, tr, instead);
break;
case BspClass::NEG:
if(instead && !neg) goto alt;
neg = InsertOrCreate(neg, tr, instead);
break;
case BspClass::COPLANAR: {
if(instead) goto alt;
SBsp3 *m = Alloc();
m->n = n;
m->d = d;
m->tri = *tr;
m->more = more;
more = m;
break;
}
}
return;
alt:
if(how == BspClass::POS && !(instead->flipNormal)) {
instead->AddTriangle(tr->meta, tr->a, tr->b, tr->c);
} else if(how == BspClass::NEG && instead->flipNormal) {
instead->AddTriangle(tr->meta, tr->c, tr->b, tr->a);
} else if(how == BspClass::COPLANAR) {
if(edges) {
edges->InsertTriangle(tr, instead, this);
} else {
// I suppose this actually is allowed to happen, if the coplanar
// face is the leaf, and all of its neighbors are earlier in tree?
InsertInPlane(/*pos2=*/false, tr, instead);
}
} else {
instead->atLeastOneDiscarded = true;
}
}
class BspUtil {
public:
SBsp3 *bsp;
size_t onc;
size_t posc;
size_t negc;
bool *isPos;
bool *isNeg;
bool *isOn;
// triangle operations
STriangle *tr;
STriangle *btri; // also as alone
STriangle *ctri;
// convex operations
Vector *on;
size_t npos;
size_t nneg;
Vector *vpos; // also as quad
Vector *vneg;
static BspUtil *Alloc() {
return (BspUtil *)AllocTemporary(sizeof(BspUtil));
}
void AllocOn() {
on = (Vector *)AllocTemporary(sizeof(Vector) * 2);
}
void AllocTriangle() {
btri = (STriangle *)AllocTemporary(sizeof(STriangle));
}
void AllocTriangles() {
btri = (STriangle *)AllocTemporary(sizeof(STriangle) * 2);
ctri = &btri[1];
}
void AllocQuad() {
vpos = (Vector *)AllocTemporary(sizeof(Vector) * 4);
}
void AllocClassify(size_t size) {
// Allocate a one big piece is faster than a small ones.
isPos = (bool *)AllocTemporary(sizeof(bool) * size * 3);
isNeg = &isPos[size];
isOn = &isNeg[size];
}
void AllocVertices(size_t size) {
vpos = (Vector *)AllocTemporary(sizeof(Vector) * size * 2);
vneg = &vpos[size];
}
void ClassifyTriangle(STriangle *tri, SBsp3 *node) {
tr = tri;
bsp = node;
onc = 0;
posc = 0;
negc = 0;
AllocClassify(3);
double dt[3] = { (tr->a).Dot(bsp->n), (tr->b).Dot(bsp->n), (tr->c).Dot(bsp->n) };
double d = bsp->d;
// Count vertices in the plane
for(int i = 0; i < 3; i++) {
if(dt[i] > d + LENGTH_EPS) {
posc++;
isPos[i] = true;
} else if(dt[i] < d - LENGTH_EPS) {
negc++;
isNeg[i] = true;
} else {
onc++;
isOn[i] = true;
}
}
}
bool ClassifyConvex(Vector *vertex, size_t cnt, SBsp3 *node, bool insertEdge) {
bsp = node;
onc = 0;
posc = 0;
negc = 0;
AllocClassify(cnt);
AllocOn();
for(size_t i = 0; i < cnt; i++) {
double dt = bsp->n.Dot(vertex[i]);
isPos[i] = isNeg[i] = isOn[i] = false;
if(fabs(dt - bsp->d) < LENGTH_EPS) {
isOn[i] = true;
if(onc < 2) {
on[onc] = vertex[i];
}
onc++;
} else if(dt > bsp->d) {
isPos[i] = true;
posc++;
} else {
isNeg[i] = true;
negc++;
}
}
if(onc != 2 && onc != 1 && onc != 0) return false;
if(onc == 2) {
if(insertEdge) {
Vector e01 = (vertex[1]).Minus(vertex[0]);
Vector e12 = (vertex[2]).Minus(vertex[1]);
Vector out = e01.Cross(e12);
SEdge se = SEdge::From(on[0], on[1]);
bsp->edges = SBsp2::InsertOrCreateEdge(bsp->edges, &se, bsp->n, out);
}
}
return true;
}
bool ClassifyConvexVertices(Vector *vertex, size_t cnt, bool insertEdges) {
Vector inter[2];
int inters = 0;
npos = 0;
nneg = 0;
// Enlarge vertices list to consider two intersections
AllocVertices(cnt + 4);
for(size_t i = 0; i < cnt; i++) {
size_t ip = WRAP((i + 1), cnt);
if(isPos[i]) {
vpos[npos++] = vertex[i];
}
if(isNeg[i]) {
vneg[nneg++] = vertex[i];
}
if(isOn[i]) {
vneg[nneg++] = vertex[i];
vpos[npos++] = vertex[i];
}
if((isPos[i] && isNeg[ip]) || (isNeg[i] && isPos[ip])) {
Vector vi = bsp->IntersectionWith(vertex[i], vertex[ip]);
vpos[npos++] = vi;
vneg[nneg++] = vi;
if(inters >= 2) return false; // triangulate: XXX shouldn't happen but does
inter[inters++] = vi;
}
}
ssassert(npos <= cnt + 1 && nneg <= cnt + 1, "Impossible");
if(insertEdges) {
Vector e01 = (vertex[1]).Minus(vertex[0]);
Vector e12 = (vertex[2]).Minus(vertex[1]);
Vector out = e01.Cross(e12);
if(inters == 2) {
SEdge se = SEdge::From(inter[0], inter[1]);
bsp->edges = SBsp2::InsertOrCreateEdge(bsp->edges, &se, bsp->n, out);
} else if(inters == 1 && onc == 1) {
SEdge se = SEdge::From(inter[0], on[0]);
bsp->edges = SBsp2::InsertOrCreateEdge(bsp->edges, &se, bsp->n, out);
} else if(inters == 0 && onc == 2) {
// We already handled this on-plane existing edge
} else {
return false; //triangulate;
}
}
if(nneg < 3 || npos < 3) return false; // triangulate; // XXX
return true;
}
void ProcessEdgeInsert() {
ssassert(onc == 2, "Impossible");
Vector a, b;
if (!isOn[0]) { a = tr->b; b = tr->c; }
else if(!isOn[1]) { a = tr->c; b = tr->a; }
else if(!isOn[2]) { a = tr->a; b = tr->b; }
else ssassert(false, "Impossible");
SEdge se = SEdge::From(a, b);
bsp->edges = SBsp2::InsertOrCreateEdge(bsp->edges, &se, bsp->n, tr->Normal());
}
bool SplitIntoTwoTriangles(bool insertEdge) {
ssassert(posc == 1 && negc == 1 && onc == 1, "Impossible");
bool bpos;
Vector a, b, c;
// Standardize so that a is on the plane
if (isOn[0]) { a = tr->a; b = tr->b; c = tr->c; bpos = isPos[1];
} else if(isOn[1]) { a = tr->b; b = tr->c; c = tr->a; bpos = isPos[2];
} else if(isOn[2]) { a = tr->c; b = tr->a; c = tr->b; bpos = isPos[0];
} else ssassert(false, "Impossible");
AllocTriangles();
Vector bPc = bsp->IntersectionWith(b, c);
*btri = STriangle::From(tr->meta, a, b, bPc);
*ctri = STriangle::From(tr->meta, c, a, bPc);
if(insertEdge) {
SEdge se = SEdge::From(a, bPc);
bsp->edges = SBsp2::InsertOrCreateEdge(bsp->edges, &se, bsp->n, tr->Normal());
}
return bpos;
}
bool SplitIntoTwoPieces(bool insertEdge) {
Vector a, b, c;
if(posc == 2 && negc == 1) {
// Standardize so that a is on one side, and b and c are on the other.
if (isNeg[0]) { a = tr->a; b = tr->b; c = tr->c;
} else if(isNeg[1]) { a = tr->b; b = tr->c; c = tr->a;
} else if(isNeg[2]) { a = tr->c; b = tr->a; c = tr->b;
} else ssassert(false, "Impossible");
} else if(posc == 1 && negc == 2) {
if (isPos[0]) { a = tr->a; b = tr->b; c = tr->c;
} else if(isPos[1]) { a = tr->b; b = tr->c; c = tr->a;
} else if(isPos[2]) { a = tr->c; b = tr->a; c = tr->b;
} else ssassert(false, "Impossible");
} else ssassert(false, "Impossible");
Vector aPb = bsp->IntersectionWith(a, b);
Vector cPa = bsp->IntersectionWith(c, a);
AllocTriangle();
AllocQuad();
*btri = STriangle::From(tr->meta, a, aPb, cPa);
vpos[0] = aPb;
vpos[1] = b;
vpos[2] = c;
vpos[3] = cPa;
if(insertEdge) {
SEdge se = SEdge::From(aPb, cPa);
bsp->edges = SBsp2::InsertOrCreateEdge(bsp->edges, &se, bsp->n, btri->Normal());
}
return posc == 2 && negc == 1;
}
static SBsp3 *Triangulate(SBsp3 *bsp, const STriMeta &meta, Vector *vertex,
size_t cnt, SMesh *instead) {
for(size_t i = 0; i < cnt - 2; i++) {
STriangle tr = STriangle::From(meta, vertex[0], vertex[i + 1], vertex[i + 2]);
bsp = SBsp3::InsertOrCreate(bsp, &tr, instead);
}
return bsp;
}
};
void SBsp3::InsertConvexHow(BspClass how, STriMeta meta, Vector *vertex, size_t n,
SMesh *instead) {
switch(how) {
case BspClass::POS:
if(pos) {
pos = pos->InsertConvex(meta, vertex, n, instead);
return;
}
break;
case BspClass::NEG:
if(neg) {
neg = neg->InsertConvex(meta, vertex, n, instead);
return;
}
break;
default: ssassert(false, "Unexpected BSP insert type");
}
for(size_t i = 0; i < n - 2; i++) {
STriangle tr = STriangle::From(meta,
vertex[0], vertex[i+1], vertex[i+2]);
InsertHow(how, &tr, instead);
}
}
SBsp3 *SBsp3::InsertConvex(STriMeta meta, Vector *vertex, size_t cnt, SMesh *instead) {
BspUtil *u = BspUtil::Alloc();
if(u->ClassifyConvex(vertex, cnt, this, !instead)) {
if(u->posc == 0) {
InsertConvexHow(BspClass::NEG, meta, vertex, cnt, instead);
return this;
}
if(u->negc == 0) {
InsertConvexHow(BspClass::POS, meta, vertex, cnt, instead);
return this;
}
if(u->ClassifyConvexVertices(vertex, cnt, !instead)) {
InsertConvexHow(BspClass::NEG, meta, u->vneg, u->nneg, instead);
InsertConvexHow(BspClass::POS, meta, u->vpos, u->npos, instead);
return this;
}
}
// We don't handle the special case for this; do it as triangles
return BspUtil::Triangulate(this, meta, vertex, cnt, instead);
}
SBsp3 *SBsp3::InsertOrCreate(SBsp3 *where, STriangle *tr, SMesh *instead) {
if(where == NULL) {
if(instead) {
if(instead->flipNormal) {
instead->atLeastOneDiscarded = true;
} else {
instead->AddTriangle(tr->meta, tr->a, tr->b, tr->c);
}
return NULL;
}
// Brand new node; so allocate for it, and fill us in.
SBsp3 *r = Alloc();
r->n = (tr->Normal()).WithMagnitude(1);
r->d = (tr->a).Dot(r->n);
r->tri = *tr;
return r;
}
where->Insert(tr, instead);
return where;
}
void SBsp3::Insert(STriangle *tr, SMesh *instead) {
BspUtil *u = BspUtil::Alloc();
u->ClassifyTriangle(tr, this);
// All vertices in-plane
if(u->onc == 3) {
InsertHow(BspClass::COPLANAR, tr, instead);
return;
}
// No split required
if(u->posc == 0 || u->negc == 0) {
if(!instead && u->onc == 2) {
u->ProcessEdgeInsert();
}
if(u->posc > 0) {
InsertHow(BspClass::POS, tr, instead);
} else {
InsertHow(BspClass::NEG, tr, instead);
}
return;
}
// The polygon must be split into two triangles, one above, one below.
if(u->posc == 1 && u->negc == 1 && u->onc == 1) {
if(u->SplitIntoTwoTriangles(!instead)) {
InsertHow(BspClass::POS, u->btri, instead);
InsertHow(BspClass::NEG, u->ctri, instead);
} else {
InsertHow(BspClass::POS, u->ctri, instead);
InsertHow(BspClass::NEG, u->btri, instead);
}
return;
}
// The polygon must be split into two pieces: a triangle and a quad.
if(u->SplitIntoTwoPieces(!instead)) {
InsertConvexHow(BspClass::POS, tr->meta, u->vpos, 4, instead);
InsertHow(BspClass::NEG, u->btri, instead);
} else {
InsertConvexHow(BspClass::NEG, tr->meta, u->vpos, 4, instead);
InsertHow(BspClass::POS, u->btri, instead);
}
}
void SBsp3::GenerateInPaintOrder(SMesh *m) const {
// Doesn't matter which branch we take if the normal has zero z
// component, so don't need a separate case for that.
if(n.z < 0) {
if(pos) pos->GenerateInPaintOrder(m);
} else {
if(neg) neg->GenerateInPaintOrder(m);
}
const SBsp3 *flip = this;
while(flip) {
m->AddTriangle(&(flip->tri));
flip = flip->more;
}
if(n.z < 0) {
if(neg) neg->GenerateInPaintOrder(m);
} else {
if(pos) pos->GenerateInPaintOrder(m);
}
}
/////////////////////////////////
Vector SBsp2::IntersectionWith(Vector a, Vector b) const {
double da = a.Dot(no) - d;
double db = b.Dot(no) - d;
ssassert(da*db < 0, "Expected segment to intersect BSP node");
double dab = (db - da);
return (a.ScaledBy(db/dab)).Plus(b.ScaledBy(-da/dab));
}
SBsp2 *SBsp2::InsertOrCreateEdge(SBsp2 *where, SEdge *nedge, Vector nnp, Vector out) {
if(where == NULL) {
// Brand new node; so allocate for it, and fill us in.
SBsp2 *r = Alloc();
r->np = nnp;
r->no = ((r->np).Cross((nedge->b).Minus(nedge->a))).WithMagnitude(1);
if(out.Dot(r->no) < 0) {
r->no = (r->no).ScaledBy(-1);
}
r->d = (nedge->a).Dot(r->no);
r->edge = *nedge;
return r;
}
where->InsertEdge(nedge, nnp, out);
return where;
}
void SBsp2::InsertEdge(SEdge *nedge, Vector nnp, Vector out) {
double dt[2] = { (nedge->a).Dot(no), (nedge->b).Dot(no) };
bool isPos[2] = {}, isNeg[2] = {}, isOn[2] = {};
for(int i = 0; i < 2; i++) {
if(fabs(dt[i] - d) < LENGTH_EPS) {
isOn[i] = true;
} else if(dt[i] > d) {
isPos[i] = true;
} else {
isNeg[i] = true;
}
}
if((isPos[0] && isPos[1])||(isPos[0] && isOn[1])||(isOn[0] && isPos[1])) {
pos = InsertOrCreateEdge(pos, nedge, nnp, out);
return;
}
if((isNeg[0] && isNeg[1])||(isNeg[0] && isOn[1])||(isOn[0] && isNeg[1])) {
neg = InsertOrCreateEdge(neg, nedge, nnp, out);
return;
}
if(isOn[0] && isOn[1]) {
SBsp2 *m = Alloc();
m->np = nnp;
m->no = ((m->np).Cross((nedge->b).Minus(nedge->a))).WithMagnitude(1);
if(out.Dot(m->no) < 0) {
m->no = (m->no).ScaledBy(-1);
}
m->d = (nedge->a).Dot(m->no);
m->edge = *nedge;
m->more = more;
more = m;
return;
}
if((isPos[0] && isNeg[1]) || (isNeg[0] && isPos[1])) {
Vector aPb = IntersectionWith(nedge->a, nedge->b);
SEdge ea = SEdge::From(nedge->a, aPb);
SEdge eb = SEdge::From(aPb, nedge->b);
if(isPos[0]) {
pos = InsertOrCreateEdge(pos, &ea, nnp, out);
neg = InsertOrCreateEdge(neg, &eb, nnp, out);
} else {
neg = InsertOrCreateEdge(neg, &ea, nnp, out);
pos = InsertOrCreateEdge(pos, &eb, nnp, out);
}
return;
}
ssassert(false, "Impossible");
}
void SBsp2::InsertTriangleHow(BspClass how, STriangle *tr, SMesh *m, SBsp3 *bsp3) {
switch(how) {
case BspClass::POS:
if(pos) {
pos->InsertTriangle(tr, m, bsp3);
} else {
bsp3->InsertInPlane(/*pos2=*/true, tr, m);
}
break;
case BspClass::NEG:
if(neg) {
neg->InsertTriangle(tr, m, bsp3);
} else {
bsp3->InsertInPlane(/*pos2=*/false, tr, m);
}
break;
default: ssassert(false, "Unexpected BSP insert type");
}
}
void SBsp2::InsertTriangle(STriangle *tr, SMesh *m, SBsp3 *bsp3) {
double dt[3] = { (tr->a).Dot(no), (tr->b).Dot(no), (tr->c).Dot(no) };
bool isPos[3] = {}, isNeg[3] = {}, isOn[3] = {};
int inc = 0, posc = 0, negc = 0;
for(int i = 0; i < 3; i++) {
if(fabs(dt[i] - d) < LENGTH_EPS) {
isOn[i] = true;
inc++;
} else if(dt[i] > d) {
isPos[i] = true;
posc++;
} else {
isNeg[i] = true;
negc++;
}
}
if(inc == 3) {
// All vertices on-line; so it's a degenerate triangle, to ignore.
return;
}
// No split required
if(posc == 0 || negc == 0) {
if(posc > 0) {
InsertTriangleHow(BspClass::POS, tr, m, bsp3);
} else {
InsertTriangleHow(BspClass::NEG, tr, m, bsp3);
}
return;
}
// The polygon must be split into two pieces, one above, one below.
Vector a, b, c;
if(posc == 1 && negc == 1 && inc == 1) {
bool bpos;
// Standardize so that a is on the plane
if (isOn[0]) { a = tr->a; b = tr->b; c = tr->c; bpos = isPos[1];
} else if(isOn[1]) { a = tr->b; b = tr->c; c = tr->a; bpos = isPos[2];
} else if(isOn[2]) { a = tr->c; b = tr->a; c = tr->b; bpos = isPos[0];
} else ssassert(false, "Impossible");
Vector bPc = IntersectionWith(b, c);
STriangle btri = STriangle::From(tr->meta, a, b, bPc);
STriangle ctri = STriangle::From(tr->meta, c, a, bPc);
if(bpos) {
InsertTriangleHow(BspClass::POS, &btri, m, bsp3);
InsertTriangleHow(BspClass::NEG, &ctri, m, bsp3);
} else {
InsertTriangleHow(BspClass::POS, &ctri, m, bsp3);
InsertTriangleHow(BspClass::NEG, &btri, m, bsp3);
}
return;
}
if(posc == 2 && negc == 1) {
// Standardize so that a is on one side, and b and c are on the other.
if (isNeg[0]) { a = tr->a; b = tr->b; c = tr->c;
} else if(isNeg[1]) { a = tr->b; b = tr->c; c = tr->a;
} else if(isNeg[2]) { a = tr->c; b = tr->a; c = tr->b;
} else ssassert(false, "Impossible");
} else if(posc == 1 && negc == 2) {
if (isPos[0]) { a = tr->a; b = tr->b; c = tr->c;
} else if(isPos[1]) { a = tr->b; b = tr->c; c = tr->a;
} else if(isPos[2]) { a = tr->c; b = tr->a; c = tr->b;
} else ssassert(false, "Impossible");
} else ssassert(false, "Impossible");
Vector aPb = IntersectionWith(a, b);
Vector cPa = IntersectionWith(c, a);
STriangle alone = STriangle::From(tr->meta, a, aPb, cPa);
STriangle quad1 = STriangle::From(tr->meta, aPb, b, c );
STriangle quad2 = STriangle::From(tr->meta, aPb, c, cPa);
if(posc == 2 && negc == 1) {
InsertTriangleHow(BspClass::POS, &quad1, m, bsp3);
InsertTriangleHow(BspClass::POS, &quad2, m, bsp3);
InsertTriangleHow(BspClass::NEG, &alone, m, bsp3);
} else {
InsertTriangleHow(BspClass::NEG, &quad1, m, bsp3);
InsertTriangleHow(BspClass::NEG, &quad2, m, bsp3);
InsertTriangleHow(BspClass::POS, &alone, m, bsp3);
}
return;
}
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