#include "solvespace.h" int I, N, FLAG; void SShell::MakeFromUnionOf(SShell *a, SShell *b) { MakeFromBoolean(a, b, AS_UNION); } void SShell::MakeFromDifferenceOf(SShell *a, SShell *b) { MakeFromBoolean(a, b, AS_DIFFERENCE); } //----------------------------------------------------------------------------- // Take our original pwl curve. Wherever an edge intersects a surface within // either agnstA or agnstB, split the piecewise linear element. Then refine // the intersection so that it lies on all three relevant surfaces: the // intersecting surface, srfA, and srfB. (So the pwl curve should lie at // the intersection of srfA and srfB.) Return a new pwl curve with everything // split. //----------------------------------------------------------------------------- static Vector LineStart, LineDirection; static int ByTAlongLine(const void *av, const void *bv) { SInter *a = (SInter *)av, *b = (SInter *)bv; double ta = (a->p.Minus(LineStart)).DivPivoting(LineDirection), tb = (b->p.Minus(LineStart)).DivPivoting(LineDirection); return (ta > tb) ? 1 : -1; } SCurve SCurve::MakeCopySplitAgainst(SShell *agnstA, SShell *agnstB, SSurface *srfA, SSurface *srfB) { SCurve ret; ret = *this; ZERO(&(ret.pts)); 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 il; ZERO(&il); // Find all the intersections with the two passed shells if(agnstA) agnstA->AllPointsIntersecting(prev, *p, &il, true,true,true); if(agnstB) agnstB->AllPointsIntersecting(prev, *p, &il, true,true,true); if(il.n > 0) { // The intersections were generated by intersecting the pwl // edge against a surface; so they must be refined to lie // exactly on the original curve. SInter *pi; for(pi = il.First(); pi; pi = il.NextAfter(pi)) { double u, v; (pi->srf)->ClosestPointTo(pi->p, &u, &v, false); (pi->srf)->PointOnSurfaces(srfA, srfB, &u, &v); pi->p = (pi->srf)->PointAt(u, v); } // And now sort them in order along the line. Note that we must // do that after refining, in case the refining would make two // points switch places. LineStart = prev; LineDirection = p->Minus(prev); qsort(il.elem, il.n, sizeof(il.elem[0]), ByTAlongLine); // And now uses the intersections to generate our split pwl edge(s) Vector prev = Vector::From(VERY_POSITIVE, 0, 0); for(pi = il.First(); pi; pi = il.NextAfter(pi)) { double t = (pi->p.Minus(LineStart)).DivPivoting(LineDirection); // On-edge intersection will generate same split point for // both surfaces, so don't create zero-length edge. if(!prev.Equals(pi->p)) { ret.pts.Add(&(pi->p)); } prev = pi->p; } } il.Clear(); ret.pts.Add(p); prev = *p; } return ret; } void SShell::CopyCurvesSplitAgainst(bool opA, SShell *agnst, SShell *into) { SCurve *sc; for(sc = curve.First(); sc; sc = curve.NextAfter(sc)) { SCurve scn = sc->MakeCopySplitAgainst(agnst, NULL, surface.FindById(sc->surfA), surface.FindById(sc->surfB)); scn.source = opA ? SCurve::FROM_A : SCurve::FROM_B; hSCurve hsc = into->curve.AddAndAssignId(&scn); // And note the new ID so that we can rewrite the trims appropriately sc->newH = hsc; } } void SSurface::TrimFromEdgeList(SEdgeList *el) { el->l.ClearTags(); STrimBy stb; ZERO(&stb); for(;;) { // Find an edge, any edge; we'll start from there. SEdge *se; for(se = el->l.First(); se; se = el->l.NextAfter(se)) { if(se->tag) continue; break; } if(!se) break; se->tag = 1; stb.start = se->a; stb.finish = se->b; stb.curve.v = se->auxA; stb.backwards = se->auxB ? true : false; // Find adjoining edges from the same curve; those should be // merged into a single trim. bool merged; do { merged = false; for(se = el->l.First(); se; se = el->l.NextAfter(se)) { if(se->tag) continue; if(se->auxA != stb.curve.v) continue; if(( se->auxB && !stb.backwards) || (!se->auxB && stb.backwards)) continue; if((se->a).Equals(stb.finish)) { stb.finish = se->b; se->tag = 1; merged = true; } else if((se->b).Equals(stb.start)) { stb.start = se->a; se->tag = 1; merged = true; } } } while(merged); // And add the merged trim, with xyz (not uv like the polygon) pts stb.start = PointAt(stb.start.x, stb.start.y); stb.finish = PointAt(stb.finish.x, stb.finish.y); trim.Add(&stb); } } // For each edge, we record the membership of the regions to its left and // right, which we call the "in direction" and "out direction" (wrt its // outer normal) #define INDIR (0) #define OUTDIR (8) // Regions of interest are the other shell itself, the coincident faces of the // shell (same or opposite normal) and the original surface. #define SHELL (0) #define COINCIDENT_SAME (1) #define COINCIDENT_OPPOSITE (2) #define ORIG (3) // Macro for building bit to test #define INSIDE(reg, dir) (1 << ((reg)+(dir))) static bool KeepRegion(int type, bool opA, int tag, int dir) { bool inShell = (tag & INSIDE(SHELL, dir)) != 0, inSame = (tag & INSIDE(COINCIDENT_SAME, dir)) != 0, inOpp = (tag & INSIDE(COINCIDENT_OPPOSITE, dir)) != 0, inOrig = (tag & INSIDE(ORIG, dir)) != 0; bool inFace = inSame || inOpp; // If these are correct, then they should be independent of inShell // if inFace is true. if(!inOrig) return false; switch(type) { case SShell::AS_UNION: if(opA) { return (!inShell && !inFace); } else { return (!inShell && !inFace) || inSame; } break; case SShell::AS_DIFFERENCE: if(opA) { return (!inShell && !inFace); } else { return (inShell && !inFace) || inSame; } break; default: oops(); } } static bool KeepEdge(int type, bool opA, int tag) { bool keepIn = KeepRegion(type, opA, tag, INDIR), keepOut = KeepRegion(type, opA, tag, OUTDIR); // If the regions to the left and right of this edge are both in or both // out, then this edge is not useful and should be discarded. if(keepIn && !keepOut) return true; return false; } static int TagByClassifiedEdge(int bspclass, int reg) { switch(bspclass) { case SBspUv::INSIDE: return INSIDE(reg, OUTDIR) | INSIDE(reg, INDIR); case SBspUv::OUTSIDE: return 0; case SBspUv::EDGE_PARALLEL: return INSIDE(reg, INDIR); case SBspUv::EDGE_ANTIPARALLEL: return INSIDE(reg, OUTDIR); default: oops(); } } void DBPEDGE(int tag) { dbp("edge: indir %s %s %s %s ; outdir %s %s %s %s", (tag & INSIDE(SHELL, INDIR)) ? "shell" : "", (tag & INSIDE(COINCIDENT_SAME, INDIR)) ? "coinc-same" : "", (tag & INSIDE(COINCIDENT_OPPOSITE, INDIR)) ? "coinc-opp" : "", (tag & INSIDE(ORIG, INDIR)) ? "orig" : "", (tag & INSIDE(SHELL, OUTDIR)) ? "shell" : "", (tag & INSIDE(COINCIDENT_SAME, OUTDIR)) ? "coinc-same" : "", (tag & INSIDE(COINCIDENT_OPPOSITE, OUTDIR)) ? "coinc-opp" : "", (tag & INSIDE(ORIG, OUTDIR)) ? "orig" : ""); } void DEBUGEDGELIST(SEdgeList *sel, SSurface *surf) { dbp("print %d edges", sel->l.n); SEdge *se; for(se = sel->l.First(); se; se = sel->l.NextAfter(se)) { 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(surf->PointAt(se->a.x, se->a.y), surf->PointAt(se->b.x, se->b.y)); SS.nakedEdges.AddEdge(surf->PointAt(mid.x, mid.y), surf->PointAt(arrow.x, arrow.y)); } } //----------------------------------------------------------------------------- // Trim this surface against the specified shell, in the way that's appropriate // for the specified Boolean operation type (and which operand we are). We // also need a pointer to the shell that contains our own surface, since that // contains our original trim curves. //----------------------------------------------------------------------------- SSurface SSurface::MakeCopyTrimAgainst(SShell *agnst, SShell *parent, SShell *into, int type, bool opA) { SSurface ret; // The returned surface is identical, just the trim curves change ret = *this; ZERO(&(ret.trim)); // 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); } if(type == SShell::AS_DIFFERENCE && !opA) { // The second operand of a Boolean difference gets turned inside out ret.Reverse(); } // Build up our original trim polygon; remember the coordinates could // be changed if we just flipped the surface normal. SEdgeList orig; ZERO(&orig); ret.MakeEdgesInto(into, &orig, true); ret.trim.Clear(); // which means that we can't necessarily use the old BSP... SBspUv *origBsp = SBspUv::From(&orig); // Find any surfaces from the other shell that are coincident with ours, // and get the intersection polygons, grouping surfaces with the same // and with opposite normal separately. SEdgeList sameNormal, oppositeNormal; ZERO(&sameNormal); ZERO(&oppositeNormal); agnst->MakeCoincidentEdgesInto(&ret, true, &sameNormal, into); agnst->MakeCoincidentEdgesInto(&ret, false, &oppositeNormal, into); // and cull parallel or anti-parallel pairs, which may occur if multiple // surfaces are coincident with ours sameNormal.CullExtraneousEdges(); oppositeNormal.CullExtraneousEdges(); // and build the trees for quick in-polygon testing SBspUv *sameBsp = SBspUv::From(&sameNormal); SBspUv *oppositeBsp = SBspUv::From(&oppositeNormal); // 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->source != SCurve::FROM_INTERSECTION) continue; if(opA) { if(sc->surfA.v != h.v || sc->surfB.v != ss->h.v) continue; } else { if(sc->surfB.v != h.v || sc->surfA.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::OUTSIDE) { Vector ta = Vector::From(0, 0, 0); Vector tb = Vector::From(0, 0, 0); ret.ClosestPointTo(a, &(ta.x), &(ta.y)); ret.ClosestPointTo(b, &(tb.x), &(tb.y)); Vector tn = ret.NormalAt(ta.x, ta.y); Vector sn = ss->NormalAt(auv.x, auv.y); // We are subtracting the portion of our surface that // lies in the shell, so the in-plane edge normal should // point opposite to the surface normal. bool bkwds = true; if((tn.Cross(b.Minus(a))).Dot(sn) < 0) bkwds = !bkwds; if(type == SShell::AS_DIFFERENCE && !opA) bkwds = !bkwds; if(bkwds) { inter.AddEdge(tb, ta, sc->h.v, 1); } else { inter.AddEdge(ta, tb, sc->h.v, 0); } } } } } SEdgeList final; ZERO(&final); SEdge *se; for(se = orig.l.First(); se; se = orig.l.NextAfter(se)) { Point2d auv = (se->a).ProjectXy(), buv = (se->b).ProjectXy(); int c_same = sameBsp->ClassifyEdge(auv, buv); int c_opp = oppositeBsp->ClassifyEdge(auv, buv); // Get the midpoint of this edge Point2d am = (auv.Plus(buv)).ScaledBy(0.5); Vector pt = ret.PointAt(am.x, am.y); // and the outer normal from the trim polygon (within the surface) Vector surf_n = ret.NormalAt(am.x, am.y); Vector ea = ret.PointAt(auv.x, auv.y), eb = ret.PointAt(buv.x, buv.y); Vector edge_n = surf_n.Cross((eb.Minus(ea))); int c_shell = agnst->ClassifyPoint(pt, edge_n, surf_n); int tag = 0; tag |= INSIDE(ORIG, INDIR); tag |= TagByClassifiedEdge(c_same, COINCIDENT_SAME); tag |= TagByClassifiedEdge(c_opp, COINCIDENT_OPPOSITE); if(c_shell == SShell::INSIDE) { tag |= INSIDE(SHELL, INDIR) | INSIDE(SHELL, OUTDIR); } else if(c_shell == SShell::OUTSIDE) { tag |= 0; } else if(c_shell == SShell::SURF_PARALLEL) { tag |= INSIDE(SHELL, INDIR); } else if(c_shell == SShell::SURF_ANTIPARALLEL) { tag |= INSIDE(SHELL, OUTDIR); } else if(c_shell == SShell::EDGE_PARALLEL) { tag |= INSIDE(SHELL, INDIR); } else if(c_shell == SShell::EDGE_ANTIPARALLEL) { tag |= INSIDE(SHELL, OUTDIR); } else if(c_shell == SShell::EDGE_TANGENT) { continue; } if(KeepEdge(type, opA, tag)) { final.AddEdge(se->a, se->b, se->auxA, se->auxB); } } for(se = inter.l.First(); se; se = inter.l.NextAfter(se)) { Point2d auv = (se->a).ProjectXy(), buv = (se->b).ProjectXy(); int c_this = origBsp->ClassifyEdge(auv, buv); int c_same = sameBsp->ClassifyEdge(auv, buv); int c_opp = oppositeBsp->ClassifyEdge(auv, buv); int tag = 0; tag |= TagByClassifiedEdge(c_this, ORIG); tag |= TagByClassifiedEdge(c_same, COINCIDENT_SAME); tag |= TagByClassifiedEdge(c_opp, COINCIDENT_OPPOSITE); if(type == SShell::AS_DIFFERENCE && !opA) { // The second operand of a difference gets turned inside out tag |= INSIDE(SHELL, INDIR); } else { tag |= INSIDE(SHELL, OUTDIR); } if(KeepEdge(type, opA, tag)) { final.AddEdge(se->a, se->b, se->auxA, se->auxB); } } // Cull extraneous edges; duplicates or anti-parallel pairs. In particular, // we can get duplicate edges if our surface intersects the other shell // at an edge, so that both surfaces intersect coincident (and both // generate an intersection edge). final.CullExtraneousEdges(); // Use our reassembled edges to trim the new surface. ret.TrimFromEdgeList(&final); SPolygon poly; ZERO(&poly); final.l.ClearTags(); if(!final.AssemblePolygon(&poly, NULL, true)) { DEBUGEDGELIST(&final, &ret); } poly.Clear(); sameNormal.Clear(); oppositeNormal.Clear(); final.Clear(); inter.Clear(); orig.Clear(); return ret; } void SShell::CopySurfacesTrimAgainst(SShell *against, SShell *into, int type, bool opA) { SSurface *ss; for(ss = surface.First(); ss; ss = surface.NextAfter(ss)) { SSurface ssn; ssn = ss->MakeCopyTrimAgainst(against, this, into, type, opA); ss->newH = into->surface.AddAndAssignId(&ssn); I++; } } void SShell::MakeIntersectionCurvesAgainst(SShell *agnst, SShell *into) { SSurface *sa; for(sa = surface.First(); sa; sa = surface.NextAfter(sa)) { SSurface *sb; for(sb = agnst->surface.First(); sb; sb = agnst->surface.NextAfter(sb)){ // 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, this, agnst, into); } FLAG++; } } void SShell::CleanupAfterBoolean(void) { SSurface *ss; for(ss = surface.First(); ss; ss = surface.NextAfter(ss)) { } } 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(true, b, this); b->CopyCurvesSplitAgainst(false, a, this); // Generate the intersection curves for each surface in A against all // the surfaces in B (which is all of the intersection curves). a->MakeIntersectionCurvesAgainst(b, this); if(b->surface.n == 0 || a->surface.n == 0) { // Then trim and copy the surfaces a->CopySurfacesTrimAgainst(b, this, type, true); b->CopySurfacesTrimAgainst(a, this, type, false); } else { a->CopySurfacesTrimAgainst(b, this, type, true); b->CopySurfacesTrimAgainst(a, this, type, false); } // Now that we've copied the surfaces, we know their new hSurfaces, so // rewrite the curves to refer to the surfaces by their handles in the // result. SCurve *sc; for(sc = curve.First(); sc; sc = curve.NextAfter(sc)) { if(sc->source == SCurve::FROM_A) { sc->surfA = a->surface.FindById(sc->surfA)->newH; sc->surfB = a->surface.FindById(sc->surfB)->newH; } else if(sc->source == SCurve::FROM_B) { sc->surfA = b->surface.FindById(sc->surfA)->newH; sc->surfB = b->surface.FindById(sc->surfB)->newH; } else if(sc->source == SCurve::FROM_INTERSECTION) { sc->surfA = a->surface.FindById(sc->surfA)->newH; sc->surfB = b->surface.FindById(sc->surfB)->newH; } else { oops(); } } // 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(!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(fabs(dp) < LENGTH_EPS) { 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 int c1 = neg ? neg->ClassifyPoint(p, eb) : OUTSIDE; int c2 = pos ? pos->ClassifyPoint(p, eb) : INSIDE; if(c1 != c2) { dbp("MISMATCH: %d %d %08x %08x", c1, c2, neg, pos); } return c1; } else if(dp > 0) { return pos ? pos->ClassifyPoint(p, eb) : INSIDE; } else { return neg ? neg->ClassifyPoint(p, eb) : OUTSIDE; } } int SBspUv::ClassifyEdge(Point2d ea, Point2d eb) { int ret = ClassifyPoint((ea.Plus(eb)).ScaledBy(0.5), eb); if(ret == EDGE_OTHER) { // Perhaps the edge is tangent at its midpoint (and we screwed up // somewhere earlier and failed to split it); try a different // point on the edge. ret = ClassifyPoint(ea.Plus((eb.Minus(ea)).ScaledBy(0.294)), eb); } return ret; }