public static bool AuxIntersectBB(DegenD degen, SegD seg, InfoConnect icAB, InfoConnect icBA, ListInfoInters linters) { if (linters == null) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(degen,seg)", "Null argument"); } // no reduction bool connectAB = ((icAB != null) && (icAB.IsConnect)); if (connectAB) { return(true); } Param param; VecD pnt; degen.Cp.Project(seg, out param, out pnt); if (degen.Cp.Dist(pnt) < MConsts.EPS_DEC) { IntersD0 inters = new IntersD0(Param.Degen, param, pnt, false); linters.Add(inters); } return(true); }
public static bool AuxIntersectBB(DegenD degen, Bez2D bez, InfoConnect icAB, InfoConnect icBA, ListInfoInters linters) { if (linters == null) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(degen,bez)", "Null argument"); } // no reduction !! bool connectAB = ((icAB != null) && (icAB.IsConnect)); bool connectBA = ((icBA != null) && (icBA.IsConnect)); bool connect = connectAB || connectBA; if (connect) { return(true); } // bbox check if (!bez.BBox.Contains(degen.Cp)) { return(true); } Param[] pars; VecD pnt; if (!degen.Cp.ProjectGeneral(bez, out pars, out pnt)) { return(false); } if (degen.Cp.Dist(pnt) < MConsts.EPS_DEC) { Param parM; bool isSelfInters = bez.IsSelfInters(out parM); for (int iPar = 0; iPar < pars.Length; iPar++) { IntersD0 inters = new IntersD0(Param.Degen, pars[iPar], pnt, isSelfInters); linters.Add(inters); } } return(true); }
public bool InfoConnectByPozPoz(int pozA, int pozB, out InfoConnect icAB) { /* curveA and curveB are connected if * - they follow one another or * - they are separated by a sequence of degenerated curves * * ASSUMPTIONS: * pozA!=pozB */ icAB = null; bool areConj; if (!this.AreConjByPozPoz(pozA, pozB, out areConj)) { return(false); } if (!areConj) { return(true); } // are conjunctive int pozNextA; if (!this.PozStartNextByPoz(pozA, out pozNextA)) { return(false); } if (pozNextA != pozB) { icAB = new InfoConnect(true, false); } // curveB is next after curveA Knot knotNextA = this.KnotByPoz(this.PozNext(pozA)); Knot knotNextNextA = this.KnotByPoz(this.PozNext(this.PozNext(pozA))); bool isTang = ((!knotNextA.On) && (!knotNextNextA.On)); icAB = new InfoConnect(true, isTang); return(true); }
/* * INTERSECTIONS: (BCurve,BCurve) * - ORDER is IMPORTANT * order: if infoConnect are not nulls, => * it is supposed that curveA(1)=curveB(0) * * NOTES: - InfoConnect are supposed to be CORRECT * - Curves are maximally reduced in AuxIntersectBB * - Self/intersecting Bezier is NOT a reduction * from bezier */ public static bool AuxIntersectBB(DegenD degenA, DegenD degenB, InfoConnect icAB, InfoConnect icBA, ListInfoInters linters) { if (linters==null) { throw new ExceptionGMath("Intersect","AuxIntersectBB(degen,degen)","Null argument"); } bool connectAB = ((icAB!=null)&&(icAB.IsConnect)); bool connectBA = ((icBA!=null)&&(icBA.IsConnect)); bool connect = connectAB||connectBA; if (connect) // connect,=> no "real" intersections { return true; } if (degenA.Cp==degenB.Cp) // coincide but are not known to be connected { IntersD0 inters=new IntersD0(Param.Degen,Param.Degen, 0.5*(degenA.Cp+degenB.Cp),false); linters.Add(inters); } return true; }
public static bool AuxIntersectBB(DegenD degen, Bez2D bez, InfoConnect icAB, InfoConnect icBA, ListInfoInters linters) { if (linters==null) { throw new ExceptionGMath("Intersect","AuxIntersectBB(degen,bez)","Null argument"); } // no reduction !! bool connectAB = ((icAB!=null)&&(icAB.IsConnect)); bool connectBA = ((icBA!=null)&&(icBA.IsConnect)); bool connect=connectAB||connectBA; if (connect) { return true; } // bbox check if (!bez.BBox.Contains(degen.Cp)) return true; Param[] pars; VecD pnt; if (!degen.Cp.ProjectGeneral(bez,out pars, out pnt)) return false; if (degen.Cp.Dist(pnt)<MConsts.EPS_DEC) { Param parM; bool isSelfInters=bez.IsSelfInters(out parM); for (int iPar=0; iPar<pars.Length; iPar++) { IntersD0 inters=new IntersD0(Param.Degen,pars[iPar],pnt,isSelfInters); linters.Add(inters); } } return true; }
/* * INTERSECTIONS: (BCurve,BCurve) * - ORDER is IMPORTANT * order: if infoConnect are not nulls, => * it is supposed that curveA(1)=curveB(0) * * NOTES: - InfoConnect are supposed to be CORRECT * - Curves are maximally reduced in AuxIntersectBB * - Self/intersecting Bezier is NOT a reduction * from bezier */ public static bool AuxIntersectBB(DegenD degenA, DegenD degenB, InfoConnect icAB, InfoConnect icBA, ListInfoInters linters) { if (linters == null) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(degen,degen)", "Null argument"); } bool connectAB = ((icAB != null) && (icAB.IsConnect)); bool connectBA = ((icBA != null) && (icBA.IsConnect)); bool connect = connectAB || connectBA; if (connect) // connect,=> no "real" intersections { return(true); } if (degenA.Cp == degenB.Cp) // coincide but are not known to be connected { IntersD0 inters = new IntersD0(Param.Degen, Param.Degen, 0.5 * (degenA.Cp + degenB.Cp), false); linters.Add(inters); } return(true); }
public static bool AuxIntersectBB(DegenD degen, SegD seg, InfoConnect icAB, InfoConnect icBA, ListInfoInters linters) { if (linters==null) { throw new ExceptionGMath("Intersect","AuxIntersectBB(degen,seg)","Null argument"); } // no reduction bool connectAB = ((icAB!=null)&&(icAB.IsConnect)); if (connectAB) { return true; } Param param; VecD pnt; degen.Cp.Project(seg,out param, out pnt); if (degen.Cp.Dist(pnt)<MConsts.EPS_DEC) { IntersD0 inters=new IntersD0(Param.Degen,param,pnt,false); linters.Add(inters); } return true; }
public static bool AuxIntersectBB(SegD segA, SegD segB, InfoConnect icAB, InfoConnect icBA, ListInfoInters linters) { bool connectAB = ((icAB != null) && (icAB.IsConnect)); bool connectBA = ((icBA != null) && (icBA.IsConnect)); bool connect = connectAB || connectBA; InfoInters inters; if (!Inters.IntersectLL(segA, segB, out inters)) { return(false); } if (inters != null) { if ((!connect) || ((connect) && (inters.Dim == InfoInters.TypeDim.Dim1))) { linters.Add(inters); } } return(true); }
public static bool IntersectBB(BCurve curveA, BCurve curveB, InfoConnect icAB, InfoConnect icBA, ListInfoInters linters) { BoxD bboxA = curveA.BBox; BoxD bboxB = curveB.BBox; if (!bboxA.HasInters(bboxB)) { return(true); } int numIntersBefore = linters.Count; bool connectAB = (icAB != null) && (icAB.IsConnect); bool connectBA = (icBA != null) && (icBA.IsConnect); bool toReverseByConnection = (connectBA) && (!connectAB); if (toReverseByConnection) { if (!Inters.IntersectBB(curveB, curveA, icBA, icAB, linters)) { return(false); } linters.ParamSwap(numIntersBefore); return(false); } BCurve redA = curveA.Reduced; BCurve redB = curveB.Reduced; bool toReverseByComplexity = (redA.BComplexity > redB.BComplexity); object[] pars = { redA, redB, icAB, icBA, linters }; if (toReverseByComplexity) { // TODO: check !!! // TODO: what happens with connection info ??? pars[0] = redB.Reversed; pars[1] = redA.Reversed; } Type[] types = { pars[0].GetType(), pars[1].GetType(), typeof(InfoConnect), typeof(InfoConnect), typeof(ListInfoInters) }; MethodInfo infoMethod = typeof(Inters).GetMethod("AuxIntersectBB", types); bool res; try { res = (bool)infoMethod.Invoke(null, pars); } catch (System.Reflection.TargetInvocationException TIException) { throw TIException.InnerException; } if (toReverseByComplexity) { linters.ParamReverse(1, 0, numIntersBefore); linters.ParamReverse(1, 1, numIntersBefore); linters.ParamSwap(numIntersBefore); } if ((object)redA != (object)curveA) { linters.ParamFromReduced(curveA, 0, numIntersBefore); } if ((object)redB != (object)curveB) { linters.ParamFromReduced(curveB, 1, numIntersBefore); } // clean-up end-point intersections linters.CleanEndPointInters(connectAB, connectBA, numIntersBefore); return(res); }
public static bool AuxIntersectBB(Bez2D bezA, Bez2D bezB, InfoConnect icAB, InfoConnect icBA, ListInfoInters linters) { // bezA and bezB are irreducable !!! bool connectAB = ((icAB != null) && (icAB.IsConnect)); bool connectBA = ((icBA != null) && (icBA.IsConnect)); if ((connectBA) && (!connectAB)) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(bez,bez)", null); } bool connect = connectAB || connectBA; Param parM; bool isSelfIntersA = bezA.IsSelfInters(out parM); bool isSelfIntersB = bezB.IsSelfInters(out parM); if (isSelfIntersA || isSelfIntersB) { BCurve curveA = bezA; if (isSelfIntersA) { curveA = bezA.SupportFlat(); } BCurve curveB = bezB; if (isSelfIntersB) { curveB = bezB.SupportFlat(); } int numIntersBefore = linters.Count; Inters.IntersectBB(curveA, curveB, null, null, linters); /* * CLEAN END-POINT if the curve does not return to it */ if ((connectAB) && (!connectBA)) { bool coversA1 = false; bool coversB0 = false; if (isSelfIntersA) { coversA1 = bezA.CoversEndPoint(false); } if (isSelfIntersB) { coversB0 = bezB.CoversEndPoint(true); } if ((!coversA1) && (!coversB0)) { linters.CleanEndPointBezSI(bezA.End, numIntersBefore); } } linters.ParamInvalidateBezSI(numIntersBefore); return(true); } // test for 1-dimensional intersection of supports bool isB0OnA, isB2OnA; Param paramAInvB0, paramAInvB2; if (!bezB.Cp(0).InverseOn(bezA, out isB0OnA, out paramAInvB0)) { return(false); } if (!bezB.Cp(2).InverseOn(bezA, out isB2OnA, out paramAInvB2)) { return(false); } if ((isB0OnA) && (isB2OnA)) { bool areCoincide = true; Param par; for (int i = 1; i <= 3; i++) { // evaluate bezB at paramaters 1/4, 1/2, 3/4 and check // whether the points lie on bezA [-Infinity,Infinity] VecD pnt = bezB.Evaluate(0.25 * i); if (!pnt.InverseOn(bezA, out areCoincide, out par)) { return(false); } if (!areCoincide) { break; } } if (areCoincide) { Param.TypeParam typeB0 = bezA.ParamClassify(paramAInvB0); Param.TypeParam typeB2 = bezA.ParamClassify(paramAInvB2); int mult = (int)typeB0 * (int)typeB2; if (mult == 4) { return(true); // no intersections } else if (mult == 1) { // bezB is degenerated throw new ExceptionGMath("Intersect", "AuxIntersectBB(bez,bez)", null); //return false; } else if (mult == 2) { // 0-dimentional connection at the end point if ((typeB0 == Param.TypeParam.Start) && (typeB2 == Param.TypeParam.Before)) { if (connect) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(bez,bez)", null); //return false; } IntersD0 inters = new IntersD0(0, 0, bezB.Start, false); linters.Add(inters); return(true); } if ((typeB0 == Param.TypeParam.Before) && (typeB2 == Param.TypeParam.Start)) { if (connect) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(bez,bez)", null); //return false; } IntersD0 inters = new IntersD0(1, 0, bezB.End, false); linters.Add(inters); return(true); } if ((typeB0 == Param.TypeParam.End) && (typeB2 == Param.TypeParam.After)) { if (!connect) { IntersD0 inters = new IntersD0(0, 1, bezB.Start, false); linters.Add(inters); return(true); } return(true); } if ((typeB0 == Param.TypeParam.After) && (typeB2 == Param.TypeParam.End)) { if (connect) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(bez,bez)", null); //return false; } IntersD0 inters = new IntersD0(1, 1, bezB.End, false); linters.Add(inters); return(true); } } else if (mult <= 0) { InfoInters inters; Inters.RefineIntersBBD1(bezA, bezB, out inters); linters.Add(inters); return(true); } throw new ExceptionGMath("Intersect", "AuxIntersectBB(bez,bez)", null); //return false; } } /* * INTERSECTION IS 0-DIMENTIONAL AT MOST */ VecD[] cfA, cfB; bezA.PowerCoeff(out cfA); bezB.PowerCoeff(out cfB); Param parA, parB; int numRootB; double[] rootsB; double kappa = cfA[2].Cross(cfA[1]); // bezA and bezB are non-degenerated and consequent if (connectAB) { if (bezA.End != bezB.Start) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(bez,bez)", null); //return false; } if (connectBA) { // both ends are connected if (bezA.Start != bezB.End) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(bez,bez)", null); //return false; } if (icAB.IsTangent || icBA.IsTangent) { // tangent connection - no additional intersections return(true); } double crossA2B2 = cfA[2].Cross(cfB[2]); double[] cfEqn = { kappa *(kappa + 2 * crossA2B2 + cfA[1].Cross(cfB[2])), -crossA2B2 * (2 * kappa + crossA2B2), crossA2B2 *crossA2B2 }; Equation.RootsReal(cfEqn[2], cfEqn[1], cfEqn[0], out numRootB, out rootsB); if (numRootB == Equation.NumRootInfinite) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(bez,bez)", null); //return false; } if (rootsB != null) { for (int iRoot = 0; iRoot < numRootB; iRoot++) { parB = rootsB[iRoot]; if (bezB.IsEvaluableStrict(parB)) { parA = 1.0 + parB.Val * (cfA[2].Cross(cfB[2]) * parB.Val + cfA[2].Cross(cfB[1])) / kappa; if (bezA.IsEvaluableStrict(parA) /*&& (parA!=1.)*/) { IntersD0 inters = new IntersD0(parA, parB, 0.5 * (bezA.Evaluate(parA) + bezB.Evaluate(parB)), false); linters.Add(inters); } } } } return(true); } // consequent Bezier with one connection if (icAB.IsTangent) { // tangent connection - at most 2 additional intersections double[] cfEqn = { kappa *(kappa - cfB[2].Cross(cfB[1])), 2 * cfA[2].Cross(cfB[2]) * kappa, cfA[2].Cross(cfB[2]) * cfA[2].Cross(cfB[2]) }; Equation.RootsReal(cfEqn[2], cfEqn[1], cfEqn[0], out numRootB, out rootsB); if (numRootB == Equation.NumRootInfinite) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(bez,bez)", null); //return false; } if (rootsB != null) { for (int iRoot = 0; iRoot < numRootB; iRoot++) { parB = rootsB[iRoot]; if (bezB.IsEvaluableStrict(parB)) { parA = 1 + parB.Val * (cfA[2].Cross(cfB[2]) * parB.Val + cfA[2].Cross(cfB[1])) / kappa; if (bezA.IsEvaluableStrict(parA) /*&&(parA!=1)*/) { IntersD0 inters = new IntersD0(parA, parB, 0.5 * (bezA.Evaluate(parA) + bezB.Evaluate(parB)), false); linters.Add(inters); } } } } return(true); } else { // non-tangent connection - at most 3 additional intersections double[] cfEqn = { kappa *(2 * cfA[2].Cross(cfB[1]) + cfA[1].Cross(cfB[1])), cfA[2].Cross(cfB[1]) * cfA[2].Cross(cfB[1]) + kappa * (2 * cfA[2].Cross(cfB[2]) + cfA[1].Cross(cfB[2])), 2 * cfA[2].Cross(cfB[2]) * cfA[2].Cross(cfB[1]), cfA[2].Cross(cfB[2]) * cfA[2].Cross(cfB[2]) }; Equation.RootsReal(cfEqn[3], cfEqn[2], cfEqn[1], cfEqn[0], out numRootB, out rootsB); if (numRootB == Equation.NumRootInfinite) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(bez,bez)", null); //return false; } if (rootsB != null) { for (int iRoot = 0; iRoot < numRootB; iRoot++) { parB = rootsB[iRoot]; if (bezB.IsEvaluableStrict(parB)) { parA = 1 + parB.Val * (cfA[2].Cross(cfB[2]) * parB + cfA[2].Cross(cfB[1])) / kappa; if (bezA.IsEvaluableStrict(parA) /*&&(parA!=1)*/) { IntersD0 inters = new IntersD0(parA, parB, 0.5 * (bezA.Evaluate(parA) + bezB.Evaluate(parB)), false); linters.Add(inters); } } } } return(true); } } // bezA and bezB are non-degenerated, non-consequent curves bool isSwappedAB = false; if (Math.Abs(cfA[2].Cross(cfA[1])) < Math.Abs(cfB[2].Cross(cfB[1]))) { kappa = cfB[2].Cross(cfB[1]); isSwappedAB = true; VecD tmp; for (int i = 0; i < 3; i++) { tmp = cfA[i]; cfA[i] = cfB[i]; cfB[i] = tmp; } } double[] e = { cfA[2].Cross(cfB[0] - cfA[0]), cfA[2].Cross(cfB[1]), cfA[2].Cross(cfB[2]) }; double[] f = { (cfB[0] - cfA[0]).Cross(cfA[1]), cfB[1].Cross(cfA[1]), cfB[2].Cross(cfA[1]) }; Equation.RootsReal(e[2] * e[2], 2 * e[2] * e[1], e[1] * e[1] + 2 * e[2] * e[0] - kappa * f[2], 2 * e[1] * e[0] - kappa * f[1], e[0] * e[0] - kappa * f[0], out numRootB, out rootsB); if (numRootB == Equation.NumRootInfinite) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(bez,bez)", null); //return false; } if (rootsB != null) { for (int iRoot = 0; iRoot < numRootB; iRoot++) { parB = rootsB[iRoot]; parA = Equation.Evaluate(parB.Val, e[2], e[1], e[0]) / kappa; if (isSwappedAB) { Param parTmp; parTmp = parA; parA = parB; parB = parTmp; } if (bezA.IsEvaluableStrict(parA) && bezB.IsEvaluableStrict(parB)) { IntersD0 inters = new IntersD0(parA, parB, 0.5 * (bezA.Evaluate(parA) + bezB.Evaluate(parB)), false); linters.Add(inters); } } } return(true); }
public static bool AuxIntersectBB(SegD seg, Bez2D bez, InfoConnect icAB, InfoConnect icBA, ListInfoInters linters) { // both seg & bez are irreducable !!! if (linters == null) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(seg,bez)", "Null argument"); } bool connectAB = ((icAB != null) && (icAB.IsConnect)); bool connectBA = ((icBA != null) && (icBA.IsConnect)); if ((connectBA) && (!connectAB)) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(seg,bez)", null); //return false; } bool connect = connectAB || connectBA; if (!connect) { int numIntersBefore = linters.Count; if (!Inters.AuxIntersectBL(bez, seg, linters)) { return(false); } linters.ParamSwap(numIntersBefore); return(true); } // bez and seg are connected, => connectAB=true Param parM; if (bez.IsSelfInters(out parM)) { if (connectBA) // both ends are connected { // parM!=Infinity - otherwise the seg is degenerated double valM = parM.Val; IntersD1 inters; if (valM > 1) { inters = new IntersD1(0, 1, 1, 1 / (2 * valM - 1), seg, true); } else { inters = new IntersD1(0, 1, 1, (2 * valM) / (2 * valM - 1), seg, true); } linters.Add(inters); return(true); } if (icAB.IsTangent) { return(true); // no additional intersections } else { SegD segSupp = bez.SupportFlat(); InfoInters inters; if (!Inters.IntersectLL(seg, segSupp, out inters)) { return(false); } if (inters == null) { return(true); } inters.ParamInvalidateBezSI(); int numIntersBefore = linters.Count; linters.Add(inters); /* * CLEAN END-POINT if the Bezier does not return to it */ bool coversBezStart = bez.CoversEndPoint(true); if (!coversBezStart) { linters.CleanEndPointBezSI(bez.Start, numIntersBefore); } return(true); } } // bezier is NOT self-intersecting if (connectBA) { return(true); // no additional intersections } if (icAB.IsTangent) { return(true); // no additional intersections } // seg & bez are connected and not-tangent,=> // at most one additional point of intersection VecD[] cfSeg, cfBez; seg.PowerCoeff(out cfSeg); bez.PowerCoeff(out cfBez); VecD tang = (seg as LCurve).DirTang; VecD norm = (seg as LCurve).DirNorm; // connected but not-tangent: one double[] rootsBez; int numRootBez; Equation.RootsReal(cfBez[2].Dot(norm), cfBez[1].Dot(norm), out numRootBez, out rootsBez); if (numRootBez == Equation.NumRootInfinite) { throw new ExceptionGMath("Intersect", "AuxIntersectBB(seg,bez)", null); //return false; } if (rootsBez == null) { return(true); } Param parBez = rootsBez[0]; if (bez.IsEvaluableStrict(parBez)) { double valBez = parBez.Val; Param parSeg = 1 + valBez * (cfBez[2].Dot(tang) * valBez + cfBez[1].Dot(tang)) / cfSeg[1].Dot(tang); if (seg.IsEvaluableStrict(parSeg)) // ??? && (parSeg!=1) { IntersD0 inters = new IntersD0(parSeg, parBez, 0.5 * (seg.Evaluate(parSeg) + bez.Evaluate(parBez)), false); linters.Add(inters); } } return(true); }
public static bool IntersectBB(BCurve curveA, BCurve curveB, InfoConnect icAB, InfoConnect icBA, ListInfoInters linters) { BoxD bboxA=curveA.BBox; BoxD bboxB=curveB.BBox; if (!bboxA.HasInters(bboxB)) return true; int numIntersBefore=linters.Count; bool connectAB=(icAB!=null)&&(icAB.IsConnect); bool connectBA=(icBA!=null)&&(icBA.IsConnect); bool toReverseByConnection=(connectBA)&&(!connectAB); if (toReverseByConnection) { if (!Inters.IntersectBB(curveB,curveA,icBA,icAB,linters)) return false; linters.ParamSwap(numIntersBefore); return false; } BCurve redA = curveA.Reduced; BCurve redB = curveB.Reduced; bool toReverseByComplexity=(redA.BComplexity>redB.BComplexity); object[] pars={redA,redB,icAB,icBA,linters}; if (toReverseByComplexity) { // TODO: check !!! // TODO: what happens with connection info ??? pars[0]=redB.Reversed; pars[1]=redA.Reversed; } Type[] types={pars[0].GetType(),pars[1].GetType(), typeof(InfoConnect),typeof(InfoConnect),typeof(ListInfoInters)}; MethodInfo infoMethod=typeof(Inters).GetMethod("AuxIntersectBB",types); bool res; try { res=(bool)infoMethod.Invoke(null,pars); } catch(System.Reflection.TargetInvocationException TIException) { throw TIException.InnerException; } if (toReverseByComplexity) { linters.ParamReverse(1,0,numIntersBefore); linters.ParamReverse(1,1,numIntersBefore); linters.ParamSwap(numIntersBefore); } if ((object)redA!=(object)curveA) { linters.ParamFromReduced(curveA,0,numIntersBefore); } if ((object)redB!=(object)curveB) { linters.ParamFromReduced(curveB,1,numIntersBefore); } // clean-up end-point intersections linters.CleanEndPointInters(connectAB,connectBA,numIntersBefore); return res; }
public static bool AuxIntersectBB(Bez2D bezA, Bez2D bezB, InfoConnect icAB, InfoConnect icBA, ListInfoInters linters) { // bezA and bezB are irreducable !!! bool connectAB = ((icAB!=null)&&(icAB.IsConnect)); bool connectBA = ((icBA!=null)&&(icBA.IsConnect)); if ((connectBA)&&(!connectAB)) { throw new ExceptionGMath("Intersect","AuxIntersectBB(bez,bez)",null); } bool connect = connectAB||connectBA; Param parM; bool isSelfIntersA=bezA.IsSelfInters(out parM); bool isSelfIntersB=bezB.IsSelfInters(out parM); if (isSelfIntersA||isSelfIntersB) { BCurve curveA=bezA; if (isSelfIntersA) curveA=bezA.SupportFlat(); BCurve curveB=bezB; if (isSelfIntersB) curveB=bezB.SupportFlat(); int numIntersBefore=linters.Count; Inters.IntersectBB(curveA,curveB,null,null,linters); /* * CLEAN END-POINT if the curve does not return to it */ if ((connectAB)&&(!connectBA)) { bool coversA1=false; bool coversB0=false; if (isSelfIntersA) { coversA1=bezA.CoversEndPoint(false); } if (isSelfIntersB) { coversB0=bezB.CoversEndPoint(true); } if ((!coversA1)&&(!coversB0)) { linters.CleanEndPointBezSI(bezA.End,numIntersBefore); } } linters.ParamInvalidateBezSI(numIntersBefore); return true; } // test for 1-dimensional intersection of supports bool isB0OnA, isB2OnA; Param paramAInvB0, paramAInvB2; if (!bezB.Cp(0).InverseOn(bezA,out isB0OnA,out paramAInvB0)) return false; if (!bezB.Cp(2).InverseOn(bezA,out isB2OnA,out paramAInvB2)) return false; if ((isB0OnA)&&(isB2OnA)) { bool areCoincide=true; Param par; for (int i=1;i<=3;i++) { // evaluate bezB at paramaters 1/4, 1/2, 3/4 and check // whether the points lie on bezA [-Infinity,Infinity] VecD pnt=bezB.Evaluate(0.25*i); if (!pnt.InverseOn(bezA,out areCoincide,out par)) return false; if (!areCoincide) break; } if (areCoincide) { Param.TypeParam typeB0 = bezA.ParamClassify(paramAInvB0); Param.TypeParam typeB2 = bezA.ParamClassify(paramAInvB2); int mult = (int)typeB0*(int)typeB2; if (mult==4) { return true; // no intersections } else if (mult==1) { // bezB is degenerated throw new ExceptionGMath("Intersect","AuxIntersectBB(bez,bez)",null); //return false; } else if (mult==2) { // 0-dimentional connection at the end point if ((typeB0==Param.TypeParam.Start)&& (typeB2==Param.TypeParam.Before)) { if (connect) { throw new ExceptionGMath("Intersect","AuxIntersectBB(bez,bez)",null); //return false; } IntersD0 inters=new IntersD0(0,0,bezB.Start,false); linters.Add(inters); return true; } if ((typeB0==Param.TypeParam.Before)&& (typeB2==Param.TypeParam.Start)) { if (connect) { throw new ExceptionGMath("Intersect","AuxIntersectBB(bez,bez)",null); //return false; } IntersD0 inters=new IntersD0(1,0,bezB.End,false); linters.Add(inters); return true; } if ((typeB0==Param.TypeParam.End)&& (typeB2==Param.TypeParam.After)) { if (!connect) { IntersD0 inters=new IntersD0(0,1,bezB.Start,false); linters.Add(inters); return true; } return true; } if ((typeB0==Param.TypeParam.After)&& (typeB2==Param.TypeParam.End)) { if (connect) { throw new ExceptionGMath("Intersect","AuxIntersectBB(bez,bez)",null); //return false; } IntersD0 inters=new IntersD0(1,1,bezB.End,false); linters.Add(inters); return true; } } else if (mult<=0) { InfoInters inters; Inters.RefineIntersBBD1(bezA,bezB,out inters); linters.Add(inters); return true; } throw new ExceptionGMath("Intersect","AuxIntersectBB(bez,bez)",null); //return false; } } /* * INTERSECTION IS 0-DIMENTIONAL AT MOST */ VecD[] cfA, cfB; bezA.PowerCoeff(out cfA); bezB.PowerCoeff(out cfB); Param parA, parB; int numRootB; double[] rootsB; double kappa=cfA[2].Cross(cfA[1]); // bezA and bezB are non-degenerated and consequent if (connectAB) { if (bezA.End!=bezB.Start) { throw new ExceptionGMath("Intersect","AuxIntersectBB(bez,bez)",null); //return false; } if (connectBA) { // both ends are connected if (bezA.Start!=bezB.End) { throw new ExceptionGMath("Intersect","AuxIntersectBB(bez,bez)",null); //return false; } if (icAB.IsTangent||icBA.IsTangent) { // tangent connection - no additional intersections return true; } double crossA2B2=cfA[2].Cross(cfB[2]); double[] cfEqn= { kappa*(kappa+2*crossA2B2+cfA[1].Cross(cfB[2])), -crossA2B2*(2*kappa+crossA2B2), crossA2B2*crossA2B2}; Equation.RootsReal(cfEqn[2],cfEqn[1],cfEqn[0], out numRootB, out rootsB); if (numRootB==Equation.NumRootInfinite) { throw new ExceptionGMath("Intersect","AuxIntersectBB(bez,bez)",null); //return false; } if (rootsB!=null) { for (int iRoot=0; iRoot<numRootB; iRoot++) { parB=rootsB[iRoot]; if (bezB.IsEvaluableStrict(parB)) { parA=1.0+ parB.Val*(cfA[2].Cross(cfB[2])*parB.Val+ cfA[2].Cross(cfB[1]))/kappa; if (bezA.IsEvaluableStrict(parA) /*&& (parA!=1.)*/) { IntersD0 inters=new IntersD0(parA,parB, 0.5*(bezA.Evaluate(parA)+bezB.Evaluate(parB)), false); linters.Add(inters); } } } } return true; } // consequent Bezier with one connection if (icAB.IsTangent) { // tangent connection - at most 2 additional intersections double[] cfEqn={kappa*(kappa-cfB[2].Cross(cfB[1])), 2*cfA[2].Cross(cfB[2])*kappa, cfA[2].Cross(cfB[2])*cfA[2].Cross(cfB[2])}; Equation.RootsReal(cfEqn[2],cfEqn[1],cfEqn[0], out numRootB, out rootsB); if (numRootB==Equation.NumRootInfinite) { throw new ExceptionGMath("Intersect","AuxIntersectBB(bez,bez)",null); //return false; } if (rootsB!=null) { for (int iRoot=0; iRoot<numRootB; iRoot++) { parB=rootsB[iRoot]; if (bezB.IsEvaluableStrict(parB)) { parA=1+ parB.Val*(cfA[2].Cross(cfB[2])*parB.Val+ cfA[2].Cross(cfB[1]))/kappa; if (bezA.IsEvaluableStrict(parA)/*&&(parA!=1)*/) { IntersD0 inters=new IntersD0(parA,parB, 0.5*(bezA.Evaluate(parA)+bezB.Evaluate(parB)), false); linters.Add(inters); } } } } return true; } else { // non-tangent connection - at most 3 additional intersections double[] cfEqn={kappa*(2*cfA[2].Cross(cfB[1])+cfA[1].Cross(cfB[1])), cfA[2].Cross(cfB[1])*cfA[2].Cross(cfB[1])+ kappa*(2*cfA[2].Cross(cfB[2])+cfA[1].Cross(cfB[2])), 2*cfA[2].Cross(cfB[2])*cfA[2].Cross(cfB[1]), cfA[2].Cross(cfB[2])*cfA[2].Cross(cfB[2])}; Equation.RootsReal(cfEqn[3],cfEqn[2],cfEqn[1],cfEqn[0], out numRootB, out rootsB); if (numRootB==Equation.NumRootInfinite) { throw new ExceptionGMath("Intersect","AuxIntersectBB(bez,bez)",null); //return false; } if (rootsB!=null) { for (int iRoot=0; iRoot<numRootB; iRoot++) { parB=rootsB[iRoot]; if (bezB.IsEvaluableStrict(parB)) { parA=1+ parB.Val*(cfA[2].Cross(cfB[2])*parB+ cfA[2].Cross(cfB[1]))/kappa; if (bezA.IsEvaluableStrict(parA)/*&&(parA!=1)*/) { IntersD0 inters=new IntersD0(parA,parB, 0.5*(bezA.Evaluate(parA)+bezB.Evaluate(parB)), false); linters.Add(inters); } } } } return true; } } // bezA and bezB are non-degenerated, non-consequent curves bool isSwappedAB=false; if (Math.Abs(cfA[2].Cross(cfA[1]))<Math.Abs(cfB[2].Cross(cfB[1]))) { kappa = cfB[2].Cross(cfB[1]); isSwappedAB = true; VecD tmp; for (int i=0; i<3; i++) { tmp=cfA[i]; cfA[i]=cfB[i]; cfB[i]=tmp; } } double[] e={cfA[2].Cross(cfB[0]-cfA[0]), cfA[2].Cross(cfB[1]), cfA[2].Cross(cfB[2])}; double[] f={(cfB[0]-cfA[0]).Cross(cfA[1]), cfB[1].Cross(cfA[1]), cfB[2].Cross(cfA[1])}; Equation.RootsReal(e[2]*e[2], 2*e[2]*e[1], e[1]*e[1]+2*e[2]*e[0]-kappa*f[2], 2*e[1]*e[0]-kappa*f[1], e[0]*e[0]-kappa*f[0], out numRootB, out rootsB); if (numRootB==Equation.NumRootInfinite) { throw new ExceptionGMath("Intersect","AuxIntersectBB(bez,bez)",null); //return false; } if (rootsB!=null) { for (int iRoot=0; iRoot<numRootB; iRoot++) { parB=rootsB[iRoot]; parA=Equation.Evaluate(parB.Val, e[2], e[1], e[0])/kappa; if (isSwappedAB) { Param parTmp; parTmp=parA; parA=parB; parB=parTmp; } if (bezA.IsEvaluableStrict(parA)&&bezB.IsEvaluableStrict(parB)) { IntersD0 inters=new IntersD0(parA,parB, 0.5*(bezA.Evaluate(parA)+bezB.Evaluate(parB)), false); linters.Add(inters); } } } return true; }
public static bool AuxIntersectBB(SegD seg, Bez2D bez, InfoConnect icAB, InfoConnect icBA, ListInfoInters linters) { // both seg & bez are irreducable !!! if (linters==null) { throw new ExceptionGMath("Intersect","AuxIntersectBB(seg,bez)","Null argument"); } bool connectAB = ((icAB!=null)&&(icAB.IsConnect)); bool connectBA = ((icBA!=null)&&(icBA.IsConnect)); if ((connectBA)&&(!connectAB)) { throw new ExceptionGMath("Intersect","AuxIntersectBB(seg,bez)",null); //return false; } bool connect=connectAB||connectBA; if (!connect) { int numIntersBefore=linters.Count; if (!Inters.AuxIntersectBL(bez,seg,linters)) return false; linters.ParamSwap(numIntersBefore); return true; } // bez and seg are connected, => connectAB=true Param parM; if (bez.IsSelfInters(out parM)) { if (connectBA) // both ends are connected { // parM!=Infinity - otherwise the seg is degenerated double valM=parM.Val; IntersD1 inters; if (valM>1) { inters=new IntersD1(0,1, 1,1/(2*valM-1),seg,true); } else { inters=new IntersD1(0,1, 1,(2*valM)/(2*valM-1),seg,true); } linters.Add(inters); return true; } if (icAB.IsTangent) { return true; // no additional intersections } else { SegD segSupp=bez.SupportFlat(); InfoInters inters; if (!Inters.IntersectLL(seg,segSupp,out inters)) return false; if (inters==null) return true; inters.ParamInvalidateBezSI(); int numIntersBefore=linters.Count; linters.Add(inters); /* * CLEAN END-POINT if the Bezier does not return to it */ bool coversBezStart=bez.CoversEndPoint(true); if (!coversBezStart) { linters.CleanEndPointBezSI(bez.Start,numIntersBefore); } return true; } } // bezier is NOT self-intersecting if (connectBA) return true; // no additional intersections if (icAB.IsTangent) return true; // no additional intersections // seg & bez are connected and not-tangent,=> // at most one additional point of intersection VecD[] cfSeg, cfBez; seg.PowerCoeff(out cfSeg); bez.PowerCoeff(out cfBez); VecD tang=(seg as LCurve).DirTang; VecD norm=(seg as LCurve).DirNorm; // connected but not-tangent: one double[] rootsBez; int numRootBez; Equation.RootsReal(cfBez[2].Dot(norm),cfBez[1].Dot(norm), out numRootBez, out rootsBez); if (numRootBez==Equation.NumRootInfinite) { throw new ExceptionGMath("Intersect","AuxIntersectBB(seg,bez)",null); //return false; } if (rootsBez==null) return true; Param parBez=rootsBez[0]; if (bez.IsEvaluableStrict(parBez)) { double valBez=parBez.Val; Param parSeg=1+valBez*(cfBez[2].Dot(tang)*valBez+cfBez[1].Dot(tang))/cfSeg[1].Dot(tang); if (seg.IsEvaluableStrict(parSeg)) // ??? && (parSeg!=1) { IntersD0 inters=new IntersD0(parSeg,parBez, 0.5*(seg.Evaluate(parSeg)+bez.Evaluate(parBez)),false); linters.Add(inters); } } return true; }
public static bool AuxIntersectBB(SegD segA, SegD segB, InfoConnect icAB, InfoConnect icBA, ListInfoInters linters) { bool connectAB = ((icAB!=null)&&(icAB.IsConnect)); bool connectBA = ((icBA!=null)&&(icBA.IsConnect)); bool connect=connectAB||connectBA; InfoInters inters; if (!Inters.IntersectLL(segA,segB,out inters)) return false; if (inters!=null) { if ((!connect)|| ((connect)&&(inters.Dim==InfoInters.TypeDim.Dim1))) { linters.Add(inters); } } return true; }
public InfoConnect(InfoConnect ic) { this.isConnect=ic.IsConnect; this.isTangent=ic.IsTangent; }
public bool InfoConnectByPozPoz(int pozA, int pozB, out InfoConnect icAB) { /* curveA and curveB are connected if * - they follow one another or * - they are separated by a sequence of degenerated curves * * ASSUMPTIONS: * pozA!=pozB */ icAB=null; bool areConj; if (!this.AreConjByPozPoz(pozA, pozB, out areConj)) return false; if (!areConj) return true; // are conjunctive int pozNextA; if (!this.PozStartNextByPoz(pozA,out pozNextA)) return false; if (pozNextA!=pozB) { icAB=new InfoConnect(true,false); } // curveB is next after curveA Knot knotNextA=this.KnotByPoz(this.PozNext(pozA)); Knot knotNextNextA=this.KnotByPoz(this.PozNext(this.PozNext(pozA))); bool isTang=((!knotNextA.On)&&(!knotNextNextA.On)); icAB=new InfoConnect(true,isTang); return true; }
public InfoConnect(InfoConnect ic) { this.isConnect = ic.IsConnect; this.isTangent = ic.IsTangent; }