void SContour::ClipEarInto(SMesh *m, int bp, double scaledEps) { int ap = WRAP(bp-1, l.n), cp = WRAP(bp+1, l.n); STriangle tr; ZERO(&tr); tr.a = l.elem[ap].p; tr.b = l.elem[bp].p; tr.c = l.elem[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.elem[ap].ear = SPoint::UNKNOWN; l.elem[cp].ear = SPoint::UNKNOWN; l.ClearTags(); l.elem[bp].tag = 1; l.RemoveTagged(); }
//----------------------------------------------------------------------------- // Export the mesh as an STL file; it should always be vertex-to-vertex and // not self-intersecting, so not much to do. //----------------------------------------------------------------------------- void SolveSpace::ExportMeshAsStlTo(FILE *f, SMesh *sm) { char str[80]; memset(str, 0, sizeof(str)); strcpy(str, "STL exported mesh"); fwrite(str, 1, 80, f); DWORD n = sm->l.n; fwrite(&n, 4, 1, f); double s = SS.exportScale; int i; for(i = 0; i < sm->l.n; i++) { STriangle *tr = &(sm->l.elem[i]); Vector n = tr->Normal().WithMagnitude(1); float w; w = (float)n.x; fwrite(&w, 4, 1, f); w = (float)n.y; fwrite(&w, 4, 1, f); w = (float)n.z; fwrite(&w, 4, 1, f); w = (float)((tr->a.x)/s); fwrite(&w, 4, 1, f); w = (float)((tr->a.y)/s); fwrite(&w, 4, 1, f); w = (float)((tr->a.z)/s); fwrite(&w, 4, 1, f); w = (float)((tr->b.x)/s); fwrite(&w, 4, 1, f); w = (float)((tr->b.y)/s); fwrite(&w, 4, 1, f); w = (float)((tr->b.z)/s); fwrite(&w, 4, 1, f); w = (float)((tr->c.x)/s); fwrite(&w, 4, 1, f); w = (float)((tr->c.y)/s); fwrite(&w, 4, 1, f); w = (float)((tr->c.z)/s); fwrite(&w, 4, 1, f); fputc(0, f); fputc(0, f); } }
bool SContour::IsEar(int bp, double scaledEps) { int ap = WRAP(bp-1, l.n), cp = WRAP(bp+1, l.n); STriangle tr; ZERO(&tr); tr.a = l.elem[ap].p; tr.b = l.elem[bp].p; tr.c = l.elem[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 = Vector::From(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.elem[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; }
void SSurface::TriangulateInto(SShell *shell, SMesh *sm) { SEdgeList el = {}; MakeEdgesInto(shell, &el, AS_UV); SPolygon poly = {}; if(el.AssemblePolygon(&poly, NULL, true)) { int i, start = sm->l.n; if(degm == 1 && degn == 1) { // A surface with curvature along one direction only; so // choose the triangulation with chords that lie as much // as possible within the surface. And since the trim curves // have been pwl'd to within the desired chord tol, that will // produce a surface good to within roughly that tol. // // If this is just a plane (degree (1, 1)) then the triangulation // code will notice that, and not bother checking chord tols. poly.UvTriangulateInto(sm, this); } else { // A surface with compound curvature. So we must overlay a // two-dimensional grid, and triangulate around that. poly.UvGridTriangulateInto(sm, this); } STriMeta meta = { face, color }; for(i = start; i < sm->l.n; i++) { STriangle *st = &(sm->l.elem[i]); st->meta = meta; st->an = NormalAt(st->a.x, st->a.y); st->bn = NormalAt(st->b.x, st->b.y); st->cn = NormalAt(st->c.x, st->c.y); st->a = PointAt(st->a.x, st->a.y); st->b = PointAt(st->b.x, st->b.y); st->c = PointAt(st->c.x, st->c.y); // Works out that my chosen contour direction is inconsistent with // the triangle direction, sigh. st->FlipNormal(); } } else { dbp("failed to assemble polygon to trim nurbs surface in uv space"); } el.Clear(); poly.Clear(); }
void SolveSpaceUI::MenuAnalyze(int id) { SS.GW.GroupSelection(); #define gs (SS.GW.gs) switch(id) { case GraphicsWindow::MNU_STEP_DIM: if(gs.constraints == 1 && gs.n == 0) { Constraint *c = SK.GetConstraint(gs.constraint[0]); if(c->HasLabel() && !c->reference) { SS.TW.shown.dimFinish = c->valA; SS.TW.shown.dimSteps = 10; SS.TW.shown.dimIsDistance = (c->type != Constraint::ANGLE) && (c->type != Constraint::LENGTH_RATIO) && (c->type != Constraint::LENGTH_DIFFERENCE); SS.TW.shown.constraint = c->h; SS.TW.shown.screen = TextWindow::SCREEN_STEP_DIMENSION; // The step params are specified in the text window, // so force that to be shown. SS.GW.ForceTextWindowShown(); SS.ScheduleShowTW(); SS.GW.ClearSelection(); } else { Error("Constraint must have a label, and must not be " "a reference dimension."); } } else { Error("Bad selection for step dimension; select a constraint."); } break; case GraphicsWindow::MNU_NAKED_EDGES: { SS.nakedEdges.Clear(); Group *g = SK.GetGroup(SS.GW.activeGroup); SMesh *m = &(g->displayMesh); SKdNode *root = SKdNode::From(m); bool inters, leaks; root->MakeCertainEdgesInto(&(SS.nakedEdges), SKdNode::NAKED_OR_SELF_INTER_EDGES, true, &inters, &leaks); InvalidateGraphics(); const char *intersMsg = inters ? "The mesh is self-intersecting (NOT okay, invalid)." : "The mesh is not self-intersecting (okay, valid)."; const char *leaksMsg = leaks ? "The mesh has naked edges (NOT okay, invalid)." : "The mesh is watertight (okay, valid)."; std::string cntMsg = ssprintf("\n\nThe model contains %d triangles, from " "%d surfaces.", g->displayMesh.l.n, g->runningShell.surface.n); if(SS.nakedEdges.l.n == 0) { Message("%s\n\n%s\n\nZero problematic edges, good.%s", intersMsg, leaksMsg, cntMsg.c_str()); } else { Error("%s\n\n%s\n\n%d problematic edges, bad.%s", intersMsg, leaksMsg, SS.nakedEdges.l.n, cntMsg.c_str()); } break; } case GraphicsWindow::MNU_INTERFERENCE: { SS.nakedEdges.Clear(); SMesh *m = &(SK.GetGroup(SS.GW.activeGroup)->displayMesh); SKdNode *root = SKdNode::From(m); bool inters, leaks; root->MakeCertainEdgesInto(&(SS.nakedEdges), SKdNode::SELF_INTER_EDGES, false, &inters, &leaks); InvalidateGraphics(); if(inters) { Error("%d edges interfere with other triangles, bad.", SS.nakedEdges.l.n); } else { Message("The assembly does not interfere, good."); } break; } case GraphicsWindow::MNU_VOLUME: { SMesh *m = &(SK.GetGroup(SS.GW.activeGroup)->displayMesh); double vol = 0; int i; for(i = 0; i < m->l.n; i++) { STriangle tr = m->l.elem[i]; // Translate to place vertex A at (x, y, 0) Vector trans = Vector::From(tr.a.x, tr.a.y, 0); tr.a = (tr.a).Minus(trans); tr.b = (tr.b).Minus(trans); tr.c = (tr.c).Minus(trans); // Rotate to place vertex B on the y-axis. Depending on // whether the triangle is CW or CCW, C is either to the // right or to the left of the y-axis. This handles the // sign of our normal. Vector u = Vector::From(-tr.b.y, tr.b.x, 0); u = u.WithMagnitude(1); Vector v = Vector::From(tr.b.x, tr.b.y, 0); v = v.WithMagnitude(1); Vector n = Vector::From(0, 0, 1); tr.a = (tr.a).DotInToCsys(u, v, n); tr.b = (tr.b).DotInToCsys(u, v, n); tr.c = (tr.c).DotInToCsys(u, v, n); n = tr.Normal().WithMagnitude(1); // Triangles on edge don't contribute if(fabs(n.z) < LENGTH_EPS) continue; // The plane has equation p dot n = a dot n double d = (tr.a).Dot(n); // nx*x + ny*y + nz*z = d // nz*z = d - nx*x - ny*y double A = -n.x/n.z, B = -n.y/n.z, C = d/n.z; double mac = tr.c.y/tr.c.x, mbc = (tr.c.y - tr.b.y)/tr.c.x; double xc = tr.c.x, yb = tr.b.y; // I asked Maple for // int(int(A*x + B*y +C, y=mac*x..(mbc*x + yb)), x=0..xc); double integral = (1.0/3)*( A*(mbc-mac)+ (1.0/2)*B*(mbc*mbc-mac*mac) )*(xc*xc*xc)+ (1.0/2)*(A*yb+B*yb*mbc+C*(mbc-mac))*xc*xc+ C*yb*xc+ (1.0/2)*B*yb*yb*xc; vol += integral; } std::string msg = ssprintf("The volume of the solid model is:\n\n"" %.3f %s^3", vol / pow(SS.MmPerUnit(), 3), SS.UnitName()); if(SS.viewUnits == SolveSpaceUI::UNIT_MM) { msg += ssprintf("\n %.2f mL", vol/(10*10*10)); } msg += "\n\nCurved surfaces have been approximated as triangles.\n" "This introduces error, typically of around 1%."; Message("%s", msg.c_str()); break; } case GraphicsWindow::MNU_AREA: { Group *g = SK.GetGroup(SS.GW.activeGroup); if(g->polyError.how != Group::POLY_GOOD) { Error("This group does not contain a correctly-formed " "2d closed area. It is open, not coplanar, or self-" "intersecting."); break; } SEdgeList sel = {}; g->polyLoops.MakeEdgesInto(&sel); SPolygon sp = {}; sel.AssemblePolygon(&sp, NULL, true); sp.normal = sp.ComputeNormal(); sp.FixContourDirections(); double area = sp.SignedArea(); double scale = SS.MmPerUnit(); Message("The area of the region sketched in this group is:\n\n" " %.3f %s^2\n\n" "Curves have been approximated as piecewise linear.\n" "This introduces error, typically of around 1%%.", area / (scale*scale), SS.UnitName()); sel.Clear(); sp.Clear(); break; } case GraphicsWindow::MNU_SHOW_DOF: // This works like a normal solve, except that it calculates // which variables are free/bound at the same time. SS.GenerateAll(SolveSpaceUI::GENERATE_ALL, true); break; case GraphicsWindow::MNU_TRACE_PT: if(gs.points == 1 && gs.n == 1) { SS.traced.point = gs.point[0]; SS.GW.ClearSelection(); } else { Error("Bad selection for trace; select a single point."); } break; case GraphicsWindow::MNU_STOP_TRACING: { std::string exportFile; if(GetSaveFile(&exportFile, "", CsvFileFilter)) { FILE *f = ssfopen(exportFile, "wb"); if(f) { int i; SContour *sc = &(SS.traced.path); for(i = 0; i < sc->l.n; i++) { Vector p = sc->l.elem[i].p; double s = SS.exportScale; fprintf(f, "%.10f, %.10f, %.10f\r\n", p.x/s, p.y/s, p.z/s); } fclose(f); } else { Error("Couldn't write to '%s'", exportFile.c_str()); } } // Clear the trace, and stop tracing SS.traced.point = Entity::NO_ENTITY; SS.traced.path.l.Clear(); InvalidateGraphics(); break; } default: oops(); } }
SBsp3 *SBsp3::Insert(STriangle *tr, SMesh *instead) { if(!this) { 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; } double dt[3] = { (tr->a).Dot(n), (tr->b).Dot(n), (tr->c).Dot(n) }; int inc = 0, posc = 0, negc = 0; bool isPos[3], isNeg[3], isOn[3]; ZERO(&isPos); ZERO(&isNeg); ZERO(&isOn); // Count vertices in the plane for(int i = 0; i < 3; i++) { if(fabs(dt[i] - d) < LENGTH_EPS) { inc++; isOn[i] = true; } else if(dt[i] > d) { posc++; isPos[i] = true; } else { negc++; isNeg[i] = true; } } // All vertices in-plane if(inc == 3) { InsertHow(COPLANAR, tr, instead); return this; } // No split required if(posc == 0 || negc == 0) { if(inc == 2) { 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 oops(); if(!instead) { SEdge se = SEdge::From(a, b); edges = edges->InsertEdge(&se, n, tr->Normal()); } } if(posc > 0) { InsertHow(POS, tr, instead); } else { InsertHow(NEG, tr, instead); } return this; } // 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 oops(); 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) { InsertHow(POS, &btri, instead); InsertHow(NEG, &ctri, instead); } else { InsertHow(POS, &ctri, instead); InsertHow(NEG, &btri, instead); } if(!instead) { SEdge se = SEdge::From(a, bPc); edges = edges->InsertEdge(&se, n, tr->Normal()); } return this; } 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 oops(); } 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 oops(); } else oops(); Vector aPb = IntersectionWith(a, b); Vector cPa = IntersectionWith(c, a); STriangle alone = STriangle::From(tr->meta, a, aPb, cPa); Vector quad[4] = { aPb, b, c, cPa }; if(posc == 2 && negc == 1) { InsertConvexHow(POS, tr->meta, quad, 4, instead); InsertHow(NEG, &alone, instead); } else { InsertConvexHow(NEG, tr->meta, quad, 4, instead); InsertHow(POS, &alone, instead); } if(!instead) { SEdge se = SEdge::From(aPb, cPa); edges = edges->InsertEdge(&se, n, alone.Normal()); } return this; }
void Group::GenerateDisplayItems(void) { // This is potentially slow (since we've got to triangulate a shell, or // to find the emphasized edges for a mesh), so we will run it only // if its inputs have changed. if(displayDirty) { Group *pg = RunningMeshGroup(); if(pg && thisMesh.IsEmpty() && thisShell.IsEmpty()) { // We don't contribute any new solid model in this group, so our // display items are identical to the previous group's; which means // that we can just display those, and stop ourselves from // recalculating for those every time we get a change in this group. // // Note that this can end up recursing multiple times (if multiple // groups that contribute no solid model exist in sequence), but // that's okay. pg->GenerateDisplayItems(); displayMesh.Clear(); displayMesh.MakeFromCopyOf(&(pg->displayMesh)); displayEdges.Clear(); displayOutlines.Clear(); if(SS.GW.showEdges) { SEdge *se; SEdgeList *src = &(pg->displayEdges); for(se = src->l.First(); se; se = src->l.NextAfter(se)) { displayEdges.l.Add(se); } displayOutlines.MakeFromCopyOf(&pg->displayOutlines); } } else { // We do contribute new solid model, so we have to triangulate the // shell, and edge-find the mesh. displayMesh.Clear(); runningShell.TriangulateInto(&displayMesh); STriangle *t; for(t = runningMesh.l.First(); t; t = runningMesh.l.NextAfter(t)) { STriangle trn = *t; Vector n = trn.Normal(); trn.an = n; trn.bn = n; trn.cn = n; displayMesh.AddTriangle(&trn); } displayEdges.Clear(); displayOutlines.Clear(); if(SS.GW.showEdges) { if(runningMesh.l.n > 0) { // Triangle mesh only; no shell or emphasized edges. runningMesh.MakeCertainEdgesAndOutlinesInto( &displayEdges, &displayOutlines, SKdNode::EMPHASIZED_EDGES); } else { displayMesh.MakeCertainEdgesAndOutlinesInto( &displayEdges, &displayOutlines, SKdNode::SHARP_EDGES); } } } displayDirty = false; } }
void SolveSpace::ExportLinesAndMesh(SEdgeList *sel, SBezierList *sbl, SMesh *sm, Vector u, Vector v, Vector n, Vector origin, double cameraTan, VectorFileWriter *out) { double s = 1.0 / SS.exportScale; // Project into the export plane; so when we're done, z doesn't matter, // and x and y are what goes in the DXF. SEdge *e; for(e = sel->l.First(); e; e = sel->l.NextAfter(e)) { // project into the specified csys, and apply export scale (e->a) = e->a.InPerspective(u, v, n, origin, cameraTan).ScaledBy(s); (e->b) = e->b.InPerspective(u, v, n, origin, cameraTan).ScaledBy(s); } SBezier *b; if(sbl) { for(b = sbl->l.First(); b; b = sbl->l.NextAfter(b)) { *b = b->InPerspective(u, v, n, origin, cameraTan); int i; for(i = 0; i <= b->deg; i++) { b->ctrl[i] = (b->ctrl[i]).ScaledBy(s); } } } // If cutter radius compensation is requested, then perform it now if(fabs(SS.exportOffset) > LENGTH_EPS) { // assemble those edges into a polygon, and clear the edge list SPolygon sp; ZERO(&sp); sel->AssemblePolygon(&sp, NULL); sel->Clear(); SPolygon compd; ZERO(&compd); sp.normal = Vector::From(0, 0, -1); sp.FixContourDirections(); sp.OffsetInto(&compd, SS.exportOffset*s); sp.Clear(); compd.MakeEdgesInto(sel); compd.Clear(); } // Now the triangle mesh; project, then build a BSP to perform // occlusion testing and generated the shaded surfaces. SMesh smp; ZERO(&smp); if(sm) { Vector l0 = (SS.lightDir[0]).WithMagnitude(1), l1 = (SS.lightDir[1]).WithMagnitude(1); STriangle *tr; for(tr = sm->l.First(); tr; tr = sm->l.NextAfter(tr)) { STriangle tt = *tr; tt.a = (tt.a).InPerspective(u, v, n, origin, cameraTan).ScaledBy(s); tt.b = (tt.b).InPerspective(u, v, n, origin, cameraTan).ScaledBy(s); tt.c = (tt.c).InPerspective(u, v, n, origin, cameraTan).ScaledBy(s); // And calculate lighting for the triangle Vector n = tt.Normal().WithMagnitude(1); double lighting = SS.ambientIntensity + max(0, (SS.lightIntensity[0])*(n.Dot(l0))) + max(0, (SS.lightIntensity[1])*(n.Dot(l1))); double r = min(1, REDf (tt.meta.color)*lighting), g = min(1, GREENf(tt.meta.color)*lighting), b = min(1, BLUEf (tt.meta.color)*lighting); tt.meta.color = RGBf(r, g, b); smp.AddTriangle(&tt); } } // Use the BSP routines to generate the split triangles in paint order. SBsp3 *bsp = SBsp3::FromMesh(&smp); SMesh sms; ZERO(&sms); bsp->GenerateInPaintOrder(&sms); // And cull the back-facing triangles STriangle *tr; sms.l.ClearTags(); for(tr = sms.l.First(); tr; tr = sms.l.NextAfter(tr)) { Vector n = tr->Normal(); if(n.z < 0) { tr->tag = 1; } } sms.l.RemoveTagged(); // And now we perform hidden line removal if requested SEdgeList hlrd; ZERO(&hlrd); if(sm && !SS.GW.showHdnLines) { SKdNode *root = SKdNode::From(&smp); // Generate the edges where a curved surface turns from front-facing // to back-facing. if(SS.GW.showEdges) { root->MakeCertainEdgesInto(sel, SKdNode::TURNING_EDGES, false, NULL, NULL); } root->ClearTags(); int cnt = 1234; SEdge *se; for(se = sel->l.First(); se; se = sel->l.NextAfter(se)) { if(se->auxA == Style::CONSTRAINT) { // Constraints should not get hidden line removed; they're // always on top. hlrd.AddEdge(se->a, se->b, se->auxA); continue; } SEdgeList out; ZERO(&out); // Split the original edge against the mesh out.AddEdge(se->a, se->b, se->auxA); root->OcclusionTestLine(*se, &out, cnt); // the occlusion test splits unnecessarily; so fix those out.MergeCollinearSegments(se->a, se->b); cnt++; // And add the results to our output SEdge *sen; for(sen = out.l.First(); sen; sen = out.l.NextAfter(sen)) { hlrd.AddEdge(sen->a, sen->b, sen->auxA); } out.Clear(); } sel = &hlrd; } // We kept the line segments and Beziers separate until now; but put them // all together, and also project everything into the xy plane, since not // all export targets ignore the z component of the points. for(e = sel->l.First(); e; e = sel->l.NextAfter(e)) { SBezier sb = SBezier::From(e->a, e->b); sb.auxA = e->auxA; sbl->l.Add(&sb); } for(b = sbl->l.First(); b; b = sbl->l.NextAfter(b)) { for(int i = 0; i <= b->deg; i++) { b->ctrl[i].z = 0; } } // If possible, then we will assemble these output curves into loops. They // will then get exported as closed paths. SBezierLoopSetSet sblss; ZERO(&sblss); SBezierList leftovers; ZERO(&leftovers); SSurface srf = SSurface::FromPlane(Vector::From(0, 0, 0), Vector::From(1, 0, 0), Vector::From(0, 1, 0)); SPolygon spxyz; ZERO(&spxyz); bool allClosed; SEdge notClosedAt; sbl->l.ClearTags(); sblss.FindOuterFacesFrom(sbl, &spxyz, &srf, SS.ChordTolMm()*s, &allClosed, ¬ClosedAt, NULL, NULL, &leftovers); for(b = leftovers.l.First(); b; b = leftovers.l.NextAfter(b)) { sblss.AddOpenPath(b); } // Now write the lines and triangles to the output file out->Output(&sblss, &sms); leftovers.Clear(); spxyz.Clear(); sblss.Clear(); smp.Clear(); sms.Clear(); hlrd.Clear(); }