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More work on Booleans. This works only for planes, and only for 

non-coincident faces. There's also a problem when I don't generate
the full intersection polygon of shell B against a given surface in
shell A; I need to modify the code to not require that.

[git-p4: depot-paths = "//depot/solvespace/": change = 1910]
solver
Jonathan Westhues 2009-01-31 21:13:43 -08:00
parent db8859ec31
commit 9ffe95ea65
6 changed files with 437 additions and 51 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

3
dsc.h
View File

@ -79,6 +79,7 @@ public:
Vector bmax, Vector bmin);
bool OutsideAndNotOn(Vector maxv, Vector minv);
Point2d Project2d(Vector u, Vector v);
Point2d ProjectXy(void);
};
class Point2d {
@ -88,10 +89,12 @@ public:
Point2d Plus(Point2d b);
Point2d Minus(Point2d b);
Point2d ScaledBy(double s);
double Dot(Point2d p);
double DistanceTo(Point2d p);
double DistanceToLine(Point2d p0, Point2d dp, bool segment);
double Magnitude(void);
Point2d WithMagnitude(double v);
Point2d Normal(void);
};
// A simple list

365
srf/boolean.cpp
View File

@ -1,5 +1,7 @@
#include "solvespace.h"
static int I, N;
void SShell::MakeFromUnionOf(SShell *a, SShell *b) {
MakeFromBoolean(a, b, AS_UNION);
}
@ -8,38 +10,66 @@ void SShell::MakeFromDifferenceOf(SShell *a, SShell *b) {
MakeFromBoolean(a, b, AS_DIFFERENCE);
}
SCurve SCurve::MakeCopySplitAgainst(SShell *against) {
static Vector LineStart, LineDirection;
static int ByTAlongLine(const void *av, const void *bv)
{
Vector *a = (Vector *)av,
*b = (Vector *)bv;
double ta = (a->Minus(LineStart)).DivPivoting(LineDirection),
tb = (b->Minus(LineStart)).DivPivoting(LineDirection);
return (ta > tb) ? 1 : -1;
}
SCurve SCurve::MakeCopySplitAgainst(SShell *agnstA, SShell *agnstB) {
SCurve ret;
ret = *this;
ret.interCurve = false;
ZERO(&(ret.pts));
Vector *p;
for(p = pts.First(); p; p = pts.NextAfter(p)) {
Vector *p = pts.First();
if(!p) oops();
Vector prev = *p;
ret.pts.Add(p);
p = pts.NextAfter(p);
for(; p; p = pts.NextAfter(p)) {
List<Vector> il;
ZERO(&il);
// Find all the intersections with the two passed shells
if(agnstA) agnstA->AllPointsIntersecting(prev, *p, &il);
if(agnstB) agnstB->AllPointsIntersecting(prev, *p, &il);
// If any intersections exist, sort them in order along the
// line and add them to the curve.
if(il.n > 0) {
LineStart = prev;
LineDirection = p->Minus(prev);
qsort(il.elem, il.n, sizeof(il.elem[0]), ByTAlongLine);
Vector *pi;
for(pi = il.First(); pi; pi = il.NextAfter(pi)) {
ret.pts.Add(pi);
}
}
ret.pts.Add(p);
prev = *p;
}
return ret;
}
void SShell::CopyCurvesSplitAgainst(SShell *against, SShell *into) {
void SShell::CopyCurvesSplitAgainst(SShell *aga, SShell *agb, SShell *into) {
SCurve *sc;
for(sc = curve.First(); sc; sc = curve.NextAfter(sc)) {
SCurve scn = sc->MakeCopySplitAgainst(against);
SCurve scn = sc->MakeCopySplitAgainst(aga, agb);
hSCurve hsc = into->curve.AddAndAssignId(&scn);
// And note the new ID so that we can rewrite the trims appropriately
sc->newH = hsc;
}
}
void SShell::MakeEdgeListUseNewCurveIds(SEdgeList *el) {
SEdge *se;
for(se = el->l.First(); se; se = el->l.NextAfter(se)) {
hSCurve oldh = { se->auxA };
SCurve *osc = curve.FindById(oldh);
se->auxA = osc->newH.v;
// auxB is the direction, which is unchanged
}
}
void SSurface::TrimFromEdgeList(SEdgeList *el) {
el->l.ClearTags();
@ -95,7 +125,8 @@ void SSurface::TrimFromEdgeList(SEdgeList *el) {
// also need a pointer to the shell that contains our own surface, since that
// contains our original trim curves.
//-----------------------------------------------------------------------------
SSurface SSurface::MakeCopyTrimAgainst(SShell *against, SShell *shell,
SSurface SSurface::MakeCopyTrimAgainst(SShell *agnst, SShell *parent,
SShell *into,
int type, bool opA)
{
SSurface ret;
@ -103,14 +134,121 @@ SSurface SSurface::MakeCopyTrimAgainst(SShell *against, SShell *shell,
ret = *this;
ZERO(&(ret.trim));
SEdgeList el;
ZERO(&el);
MakeEdgesInto(shell, &el, true);
shell->MakeEdgeListUseNewCurveIds(&el);
// First, build a list of the existing trim curves; update them to use
// the split curves.
STrimBy *stb;
for(stb = trim.First(); stb; stb = trim.NextAfter(stb)) {
STrimBy stn = *stb;
stn.curve = (parent->curve.FindById(stn.curve))->newH;
ret.trim.Add(&stn);
}
ret.TrimFromEdgeList(&el);
// Build up our original trim polygon
SEdgeList orig;
ZERO(&orig);
ret.MakeEdgesInto(into, &orig, true);
ret.trim.Clear();
el.Clear();
// And now intersect the other shell against us
SEdgeList inter;
ZERO(&inter);
SSurface *ss;
for(ss = agnst->surface.First(); ss; ss = agnst->surface.NextAfter(ss)) {
SCurve *sc;
for(sc = into->curve.First(); sc; sc = into->curve.NextAfter(sc)) {
if(!(sc->interCurve)) continue;
if(opA) {
if(sc->surfB.v != h.v || sc->surfA.v != ss->h.v) continue;
} else {
if(sc->surfA.v != h.v || sc->surfB.v != ss->h.v) continue;
}
int i;
for(i = 1; i < sc->pts.n; i++) {
Vector a = sc->pts.elem[i-1],
b = sc->pts.elem[i];
Point2d auv, buv;
ss->ClosestPointTo(a, &(auv.x), &(auv.y));
ss->ClosestPointTo(b, &(buv.x), &(buv.y));
int c = ss->bsp->ClassifyEdge(auv, buv);
if(c == SBspUv::INSIDE) {
Vector ta = Vector::From(0, 0, 0);
Vector tb = Vector::From(0, 0, 0);
ClosestPointTo(a, &(ta.x), &(ta.y));
ClosestPointTo(b, &(tb.x), &(tb.y));
Vector tn = NormalAt(ta.x, ta.y);
Vector sn = ss->NormalAt(auv.x, auv.y);
if((tn.Cross(b.Minus(a))).Dot(sn) > 0) {
inter.AddEdge(ta, tb, sc->h.v, 0);
} else {
inter.AddEdge(tb, ta, sc->h.v, 1);
}
}
}
}
}
SEdgeList final;
ZERO(&final);
if(I == 2) dbp("INTERBSP: %d", inter.l.n);
SBspUv *interbsp = SBspUv::From(&inter);
if(I == 2) dbp("INTEROVER");
SEdge *se;
N = 0;
for(se = orig.l.First(); se; se = orig.l.NextAfter(se)) {
int c = interbsp->ClassifyEdge(se->a.ProjectXy(), se->b.ProjectXy());
if(I == 2) dbp("edge from %.3f %.3f %.3f to %.3f %.3f %.3f",
CO(PointAt(se->a.x, se->a.y)), CO(PointAt(se->b.x, se->b.y)));
if(c == SBspUv::OUTSIDE) {
if(I == 2) dbp(" keep");
final.AddEdge(se->a, se->b, se->auxA, se->auxB);
} else {
if(I == 2) dbp(" don't keep, %d", c);
}
N++;
}
for(se = inter.l.First(); se; se = inter.l.NextAfter(se)) {
if(I == 2) {
Vector mid = (se->a).Plus(se->b).ScaledBy(0.5);
Vector arrow = (se->b).Minus(se->a);
SWAP(double, arrow.x, arrow.y);
arrow.x *= -1;
arrow = arrow.WithMagnitude(0.03);
arrow = arrow.Plus(mid);
SS.nakedEdges.AddEdge(PointAt(se->a.x, se->a.y),
PointAt(se->b.x, se->b.y));
SS.nakedEdges.AddEdge(PointAt(mid.x, mid.y),
PointAt(arrow.x, arrow.y));
}
int c = bsp->ClassifyEdge(se->a.ProjectXy(), se->b.ProjectXy());
if(c == SBspUv::INSIDE) {
final.AddEdge(se->b, se->a, se->auxA, !se->auxB);
}
}
for(se = final.l.First(); se; se = final.l.NextAfter(se)) {
}
ret.TrimFromEdgeList(&final);
final.Clear();
inter.Clear();
orig.Clear();
return ret;
}
@ -120,8 +258,9 @@ void SShell::CopySurfacesTrimAgainst(SShell *against, SShell *into,
SSurface *ss;
for(ss = surface.First(); ss; ss = surface.NextAfter(ss)) {
SSurface ssn;
ssn = ss->MakeCopyTrimAgainst(against, this, type, opA);
ssn = ss->MakeCopyTrimAgainst(against, this, into, type, opA);
into->surface.AddAndAssignId(&ssn);
I++;
}
}
@ -133,7 +272,7 @@ void SShell::MakeIntersectionCurvesAgainst(SShell *agnst, SShell *into) {
// Intersect every surface from our shell against every surface
// from agnst; this will add zero or more curves to the curve
// list for into.
sa->IntersectAgainst(sb, into);
sa->IntersectAgainst(sb, agnst, this, into);
}
}
}
@ -141,30 +280,194 @@ void SShell::MakeIntersectionCurvesAgainst(SShell *agnst, SShell *into) {
void SShell::CleanupAfterBoolean(void) {
SSurface *ss;
for(ss = surface.First(); ss; ss = surface.NextAfter(ss)) {
(ss->orig).Clear();
(ss->inside).Clear();
(ss->onSameNormal).Clear();
(ss->onFlipNormal).Clear();
}
}
void SShell::MakeFromBoolean(SShell *a, SShell *b, int type) {
a->MakeClassifyingBsps();
b->MakeClassifyingBsps();
// Copy over all the original curves, splitting them so that a
// piecwise linear segment never crosses a surface from the other
// shell.
a->CopyCurvesSplitAgainst(b, this);
b->CopyCurvesSplitAgainst(a, this);
a->CopyCurvesSplitAgainst(b, NULL, this);
b->CopyCurvesSplitAgainst(a, NULL, this);
// Generate the intersection curves for each surface in A against all
// the surfaces in B
// the surfaces in B (which is all of the intersection curves).
a->MakeIntersectionCurvesAgainst(b, this);
if(a->surface.n == 0 || b->surface.n == 0) {
// Then trim and copy the surfaces
I = 100;
a->CopySurfacesTrimAgainst(b, this, type, true);
b->CopySurfacesTrimAgainst(a, this, type, false);
} else {
I = -1;
a->CopySurfacesTrimAgainst(b, this, type, true);
b->CopySurfacesTrimAgainst(a, this, type, false);
}
// And clean up the piecewise linear things we made as a calculation aid
a->CleanupAfterBoolean();
b->CleanupAfterBoolean();
}
//-----------------------------------------------------------------------------
// All of the BSP routines that we use to perform and accelerate polygon ops.
//-----------------------------------------------------------------------------
void SShell::MakeClassifyingBsps(void) {
SSurface *ss;
for(ss = surface.First(); ss; ss = surface.NextAfter(ss)) {
ss->MakeClassifyingBsp(this);
}
}
void SSurface::MakeClassifyingBsp(SShell *shell) {
SEdgeList el;
ZERO(&el);
MakeEdgesInto(shell, &el, true);
bsp = SBspUv::From(&el);
el.Clear();
}
SBspUv *SBspUv::Alloc(void) {
return (SBspUv *)AllocTemporary(sizeof(SBspUv));
}
static int ByLength(const void *av, const void *bv)
{
SEdge *a = (SEdge *)av,
*b = (SEdge *)bv;
double la = (a->a).Minus(a->b).Magnitude(),
lb = (b->a).Minus(b->b).Magnitude();
// Sort in descending order, longest first. This improves numerical
// stability for the normals.
return (la < lb) ? 1 : -1;
}
SBspUv *SBspUv::From(SEdgeList *el) {
SEdgeList work;
ZERO(&work);
SEdge *se;
for(se = el->l.First(); se; se = el->l.NextAfter(se)) {
work.AddEdge(se->a, se->b, se->auxA, se->auxB);
}
qsort(work.l.elem, work.l.n, sizeof(work.l.elem[0]), ByLength);
SBspUv *bsp = NULL;
for(se = work.l.First(); se; se = work.l.NextAfter(se)) {
bsp = bsp->InsertEdge((se->a).ProjectXy(), (se->b).ProjectXy());
}
work.Clear();
return bsp;
}
SBspUv *SBspUv::InsertEdge(Point2d ea, Point2d eb) {
if(I == 2) {
dbp("insert edge %.3f %.3f to %.3f %.3f", ea.x, ea.y, eb.x, eb.y);
}
if(!this) {
SBspUv *ret = Alloc();
ret->a = ea;
ret->b = eb;
return ret;
}
Point2d n = ((b.Minus(a)).Normal()).WithMagnitude(1);
double d = a.Dot(n);
double dea = ea.Dot(n) - d,
deb = eb.Dot(n) - d;
if(fabs(dea) < LENGTH_EPS && fabs(deb) < LENGTH_EPS) {
// Line segment is coincident with this one, store in same node
SBspUv *m = Alloc();
m->a = ea;
m->b = eb;
m->more = more;
more = m;
} else if(fabs(dea) < LENGTH_EPS) {
// Point A lies on this lie, but point B does not
if(deb > 0) {
pos = pos->InsertEdge(ea, eb);
} else {
neg = neg->InsertEdge(ea, eb);
}
} else if(fabs(deb) < LENGTH_EPS) {
// Point B lies on this lie, but point A does not
if(dea > 0) {
pos = pos->InsertEdge(ea, eb);
} else {
neg = neg->InsertEdge(ea, eb);
}
} else if(dea > 0 && deb > 0) {
pos = pos->InsertEdge(ea, eb);
} else if(dea < 0 && deb < 0) {
neg = neg->InsertEdge(ea, eb);
} else {
// New edge crosses this one; we need to split.
double t = (d - n.Dot(ea)) / (n.Dot(eb.Minus(ea)));
Point2d pi = ea.Plus((eb.Minus(ea)).ScaledBy(t));
if(dea > 0) {
pos = pos->InsertEdge(ea, pi);
neg = neg->InsertEdge(pi, eb);
} else {
neg = neg->InsertEdge(ea, pi);
pos = pos->InsertEdge(pi, eb);
}
}
return this;
}
int SBspUv::ClassifyPoint(Point2d p, Point2d eb) {
if(!this) return OUTSIDE;
Point2d n = ((b.Minus(a)).Normal()).WithMagnitude(1);
double d = a.Dot(n);
double dp = p.Dot(n) - d;
if(I == 2 && N == 5) {
dbp("point %.3f %.3f has d=%.3f", p.x, p.y, dp);
}
if(fabs(dp) < LENGTH_EPS) {
if(I == 2 && N == 5) dbp(" on line");
SBspUv *f = this;
while(f) {
Point2d ba = (f->b).Minus(f->a);
if(p.DistanceToLine(f->a, ba, true) < LENGTH_EPS) {
if(eb.DistanceToLine(f->a, ba, false) < LENGTH_EPS) {
if(ba.Dot(eb.Minus(p)) > 0) {
return EDGE_PARALLEL;
} else {
return EDGE_ANTIPARALLEL;
}
} else {
return EDGE_OTHER;
}
}
f = f->more;
}
// Pick arbitrarily which side to send it down, doesn't matter
return neg ? neg->ClassifyPoint(p, eb) : OUTSIDE;
} else if(dp > 0) {
if(I == 2 && N == 5) dbp(" pos");
return pos ? pos->ClassifyPoint(p, eb) : INSIDE;
} else {
if(I == 2 && N == 5) dbp(" neg");
return neg ? neg->ClassifyPoint(p, eb) : OUTSIDE;
}
}
int SBspUv::ClassifyEdge(Point2d ea, Point2d eb) {
return ClassifyPoint((ea.Plus(eb)).ScaledBy(0.5), eb);
}

2
srf/ratpoly.cpp
View File

@ -522,7 +522,7 @@ void SSurface::ClosestPointTo(Vector p, double *u, double *v) {
// independently projected into uv and back, to end up equal with
// the LENGTH_EPS. Best case that requires LENGTH_EPS/2, but more
// is better and convergence should be fast by now.
if(p0.Equals(p, LENGTH_EPS/100)) {
if(p0.Equals(p, LENGTH_EPS/1e3)) {
return;
}

50
srf/surface.h
View File

@ -6,6 +6,35 @@
double Bernstein(int k, int deg, double t);
double BernsteinDerivative(int k, int deg, double t);
// Utility data structure, a two-dimensional BSP to accelerate polygon
// operations.
class SBspUv {
public:
Point2d a, b;
SBspUv *pos;
SBspUv *neg;
SBspUv *more;
static const int INSIDE = 100;
static const int OUTSIDE = 200;
static const int EDGE_PARALLEL = 300;
static const int EDGE_ANTIPARALLEL = 400;
static const int EDGE_OTHER = 500;
static SBspUv *Alloc(void);
static SBspUv *From(SEdgeList *el);
Point2d IntersectionWith(Point2d a, Point2d b);
SBspUv *InsertEdge(Point2d a, Point2d b);
int ClassifyPoint(Point2d p, Point2d eb);
int ClassifyEdge(Point2d ea, Point2d eb);
};
// Now the data structures to represent a shell of trimmed rational polynomial
// surfaces.
class SShell;
class hSSurface {
@ -94,7 +123,7 @@ public:
hSSurface surfB;
static SCurve FromTransformationOf(SCurve *a, Vector t, Quaternion q);
SCurve MakeCopySplitAgainst(SShell *against);
SCurve MakeCopySplitAgainst(SShell *agnstA, SShell *agnstB);
void Clear(void);
};
@ -130,21 +159,20 @@ public:
List<STrimBy> trim;
// The trims broken down into piecewise linear segments.
SEdgeList orig;
SEdgeList inside;
SEdgeList onSameNormal;
SEdgeList onFlipNormal;
// For testing whether a point (u, v) on the surface lies inside the trim
SBspUv *bsp;
static SSurface FromExtrusionOf(SBezier *spc, Vector t0, Vector t1);
static SSurface FromPlane(Vector pt, Vector u, Vector v);
static SSurface FromTransformationOf(SSurface *a, Vector t, Quaternion q,
bool includingTrims);
SSurface MakeCopyTrimAgainst(SShell *against, SShell *shell,
SSurface MakeCopyTrimAgainst(SShell *against, SShell *parent, SShell *into,
int type, bool opA);
void TrimFromEdgeList(SEdgeList *el);
void IntersectAgainst(SSurface *b, SShell *into);
void IntersectAgainst(SSurface *b, SShell *agnstA, SShell *agnstB,
SShell *into);
void AllPointsIntersecting(Vector a, Vector b, List<Vector> *l);
void ClosestPointTo(Vector p, double *u, double *v);
Vector PointAt(double u, double v);
@ -154,6 +182,7 @@ public:
void TriangulateInto(SShell *shell, SMesh *sm);
void MakeEdgesInto(SShell *shell, SEdgeList *sel, bool asUv);
void MakeClassifyingBsp(SShell *shell);
void Clear(void);
};
@ -172,10 +201,11 @@ public:
static const int AS_DIFFERENCE = 11;
static const int AS_INTERSECT = 12;
void MakeFromBoolean(SShell *a, SShell *b, int type);
void CopyCurvesSplitAgainst(SShell *against, SShell *into);
void CopyCurvesSplitAgainst(SShell *agnstA, SShell *agnstB, SShell *into);
void CopySurfacesTrimAgainst(SShell *against, SShell *into, int t, bool a);
void MakeIntersectionCurvesAgainst(SShell *against, SShell *into);
void MakeEdgeListUseNewCurveIds(SEdgeList *el);
void MakeClassifyingBsps(void);
void AllPointsIntersecting(Vector a, Vector b, List<Vector> *il);
void CleanupAfterBoolean(void);
void MakeFromCopyOf(SShell *a);

43
srf/surfinter.cpp
View File

@ -1,6 +1,8 @@
#include "solvespace.h"
void SSurface::IntersectAgainst(SSurface *b, SShell *into) {
void SSurface::IntersectAgainst(SSurface *b, SShell *agnstA, SShell *agnstB,
SShell *into)
{
Vector amax, amin, bmax, bmin;
GetAxisAlignedBounding(&amax, &amin);
b->GetAxisAlignedBounding(&bmax, &bmin);
@ -37,16 +39,16 @@ void SSurface::IntersectAgainst(SSurface *b, SShell *into) {
ZERO(&sc);
sc.surfA = h;
sc.surfB = b->h;
v = inter.Minus(d.WithMagnitude(2*maxl));
v = inter.Minus(d.WithMagnitude(5*maxl));
sc.pts.Add(&v);
v = inter.Plus(d.WithMagnitude(2*maxl));
v = inter.Plus(d.WithMagnitude(5*maxl));
sc.pts.Add(&v);
sc.interCurve = true;
// Now split the line where it intersects our existing surfaces
SCurve split = sc.MakeCopySplitAgainst(into);
SCurve split = sc.MakeCopySplitAgainst(agnstA, agnstB);
sc.Clear();
split.interCurve = true;
into->curve.AddAndAssignId(&split);
}
@ -54,3 +56,34 @@ void SSurface::IntersectAgainst(SSurface *b, SShell *into) {
// cases, just giving up for now
}
void SSurface::AllPointsIntersecting(Vector a, Vector b, List<Vector> *l) {
if(degm == 1 && degn == 1) {
// line-plane intersection
Vector p = ctrl[0][0];
Vector n = NormalAt(0, 0).WithMagnitude(1);
double d = n.Dot(p);
if((n.Dot(a) - d < -LENGTH_EPS && n.Dot(b) - d > LENGTH_EPS) ||
(n.Dot(b) - d < -LENGTH_EPS && n.Dot(a) - d > LENGTH_EPS))
{
// It crosses the plane, one point of intersection
// (a + t*(b - a)) dot n = d
// (a dot n) + t*((b - a) dot n) = d
// t = (d - (a dot n))/((b - a) dot n)
double t = (d - a.Dot(n)) / ((b.Minus(a)).Dot(n));
Vector pi = a.Plus((b.Minus(a)).ScaledBy(t));
Point2d puv, dummy = { 0, 0 };
ClosestPointTo(pi, &(puv.x), &(puv.y));
if(bsp->ClassifyPoint(puv, dummy) != SBspUv::OUTSIDE) {
l->Add(&pi);
}
}
}
}
void SShell::AllPointsIntersecting(Vector a, Vector b, List<Vector> *il) {
SSurface *ss;
for(ss = surface.First(); ss; ss = surface.NextAfter(ss)) {
ss->AllPointsIntersecting(a, b, il);
}
}

17
util.cpp
View File

@ -515,6 +515,13 @@ Point2d Vector::Project2d(Vector u, Vector v) {
return p;
}
Point2d Vector::ProjectXy(void) {
Point2d p;
p.x = x;
p.y = y;
return p;
}
double Vector::DivPivoting(Vector delta) {
double mx = fabs(delta.x), my = fabs(delta.y), mz = fabs(delta.z);
@ -654,6 +661,10 @@ double Point2d::DistanceTo(Point2d p) {
return sqrt(dx*dx + dy*dy);
}
double Point2d::Dot(Point2d p) {
return x*p.x + y*p.y;
}
double Point2d::DistanceToLine(Point2d p0, Point2d dp, bool segment) {
double m = dp.x*dp.x + dp.y*dp.y;
if(m < 0.05) return 1e12;
@ -673,4 +684,10 @@ double Point2d::DistanceToLine(Point2d p0, Point2d dp, bool segment) {
}
}
Point2d Point2d::Normal(void) {
Point2d ret;
ret.x = y;
ret.y = -x;
return ret;
}