public bool IsSelfInters(out InfoInters inters)
{
/*
* RETURN VALUE: true if Self-Intersecting; false otherwise
*/
inters = null;
Param parM;
if (!IsSelfInters(out parM))
{
return(false);
}
if (parM.Val == Param.Infinity)
{
inters = new IntersD1(0, null, 1, null, this, true);
}
else if (parM > 1)
{
Param paramStart = 1.0 / (2.0 * parM.Val - 1.0);
BCurve curveInters = this.SubCurve(paramStart, 1);
if (curveInters == null)
{
throw new ExceptionGMath("Bez2D", "IsSelfInters", "");
}
inters = new IntersD1(paramStart, null, 1.0, null, curveInters, true);
}
else if (parM < 0)
{
Param paramEnd = (-2.0 * parM.Val) / (1.0 - 2.0 * parM.Val);
BCurve curveInters = this.SubCurve(0, paramEnd);
if (curveInters == null)
{
throw new ExceptionGMath("Bez2D", "IsSelfInters", "");
}
inters = new IntersD1(0.0, null, paramEnd, null, curveInters, true);
}
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 bool IsSelfInters(out InfoInters inters)
{
/*
* RETURN VALUE: true if Self-Intersecting; false otherwise
*/
inters=null;
Param parM;
if (!IsSelfInters(out parM))
return false;
if (parM.Val==Param.Infinity)
{
inters=new IntersD1(0,null,1,null,this,true);
}
else if (parM>1)
{
Param paramStart=1.0/(2.0*parM.Val-1.0);
BCurve curveInters=this.SubCurve(paramStart,1);
if (curveInters==null)
{
throw new ExceptionGMath("Bez2D","IsSelfInters","");
}
inters=new IntersD1(paramStart,null,1.0,null,curveInters,true);
}
else if (parM<0)
{
Param paramEnd=(-2.0*parM.Val)/(1.0-2.0*parM.Val);
BCurve curveInters=this.SubCurve(0,paramEnd);
if (curveInters==null)
{
throw new ExceptionGMath("Bez2D","IsSelfInters","");
}
inters=new IntersD1(0.0,null,paramEnd,null,curveInters,true);
}
return true;
}
public static bool RefineIntersLLD1(LCurve lrsA, LCurve lrsB,
out InfoInters inters)
{
inters = null;
if ((lrsA is SegD) && (lrsB is SegD))
{
BCurve curveA = lrsA as BCurve;
BCurve curveB = lrsB as BCurve;
return(Inters.RefineIntersBBD1(curveA, curveB, out inters));
}
if (lrsA.LComplexity > lrsB.LComplexity)
{
bool res = Inters.RefineIntersLLD1(lrsB, lrsA, out inters);
if (inters != null)
{
inters.ParamSwap();
}
return(res);
}
VecD a0 = lrsA.Start;
VecD a1 = lrsA.End;
VecD b0 = lrsB.Start;
VecD b1 = lrsB.End;
Param paramBInvA0, paramBInvA1;
bool isOn;
if ((!a0.InverseOn(lrsB, out isOn, out paramBInvA0)) || (!isOn))
{
return(false);
}
if ((!a1.InverseOn(lrsB, out isOn, out paramBInvA1)) || (!isOn))
{
return(false);
}
Param paramAInvB0, paramAInvB1;
if ((!b0.InverseOn(lrsA, out isOn, out paramAInvB0)) || (!isOn))
{
return(false);
}
if ((!b1.InverseOn(lrsA, out isOn, out paramAInvB1)) || (!isOn))
{
return(false);
}
bool areCoDirected = (paramBInvA1.Val >= paramBInvA0.Val);
if (!areCoDirected)
{
if (lrsA is LineD)
{
if (lrsB is LineD)
{
paramAInvB0 = (areCoDirected)? -Param.Infinity: Param.Infinity;
paramAInvB1 = (areCoDirected)? Param.Infinity: -Param.Infinity;
inters = new IntersD1(paramAInvB0, -Param.Infinity,
paramAInvB1, Param.Infinity, lrsB, false);
return(true);
}
if (lrsB is RayD)
{
paramAInvB1 = (areCoDirected)? Param.Infinity: -Param.Infinity;
inters = new IntersD1(paramAInvB0, 0,
paramAInvB1, Param.Infinity, lrsB, false);
return(true);
}
if (lrsB is SegD)
{
inters = new IntersD1(paramAInvB0, 0,
paramAInvB1, 1, lrsB, false);
return(true);
}
}
if (lrsA is RayD)
{
if (lrsB is RayD)
{
if (areCoDirected)
{
if (paramAInvB0 > 0)
{
inters = new IntersD1(paramAInvB0, 0,
Param.Infinity, Param.Infinity, lrsB, false);
return(true);
}
else
{
inters = new IntersD1(0, paramBInvA0,
Param.Infinity, Param.Infinity, lrsA, false);
return(true);
}
}
else
{
if (paramAInvB0 > 0)
{
inters = new IntersD1(0, paramBInvA0,
paramAInvB0, 0, new SegD(a0, b0), false);
return(true);
}
}
}
if (lrsB is SegD)
{
// intersection is known to have dimension D1 !!!
if ((paramBInvA0 >= 1) || (paramBInvA0 <= 0))
{
inters = new IntersD1(paramAInvB0, 0,
paramAInvB1, 1, new SegD(b0, b1), false);
return(true);
}
if ((0 < paramBInvA0) && (paramBInvA1 < 1))
{
if (areCoDirected)
{
inters = new IntersD1(0, paramBInvA0,
paramAInvB1, 1, new SegD(a0, b1), false);
return(true);
}
else
{
inters = new IntersD1(0, paramBInvA0,
paramAInvB0, 0, new SegD(a0, b0), false);
return(true);
}
}
}
}
}
throw new ExceptionGMath("Intersect", "RefineIntersLLD1", null);
//return false;
}
/*
* REFINE INTERSECTION D1
*/
public static bool RefineIntersBBD1(BCurve curveA, BCurve curveB,
out InfoInters inters)
{
/*
* ASSUMPTIONS:
* - curveA & curveB are MAXIMALLY REDUCED
* - intersection is KNOWN to have dimension D1
* - does not work in case of SI beziers
* => OR: both curveA & curveB are SEGMENTS
* OR: both curveA & curveB are BEZIER
*/
inters = null;
InfoInters selfinters;
if (curveA.IsSelfInters(out selfinters) || curveB.IsSelfInters(out selfinters))
{
throw new ExceptionGMath("Intersect", "RefineIntersBBD1", null);
//return false;
}
VecD a0 = curveA.Start;
VecD a1 = curveA.End;
Param paramBInvA0, paramBInvA1;
bool isOn;
if (!a0.InverseOn(curveB, out isOn, out paramBInvA0) || (!isOn))
{
return(false);
}
if (!a1.InverseOn(curveB, out isOn, out paramBInvA1) || (!isOn))
{
return(false);
}
paramBInvA0.Round(0, 1);
paramBInvA1.Round(0, 1);
bool areCoDirected = (paramBInvA1 >= paramBInvA0);
if (!areCoDirected)
{
BCurve revB = curveB.Reversed as BCurve;
if (!Inters.RefineIntersBBD1(curveA, revB, out inters))
{
return(false);
}
if (inters != null)
{
inters.ParamReverse(1, 1);
}
return(true);
}
VecD b0 = curveB.Start;
VecD b1 = curveB.End;
Param paramAInvB0, paramAInvB1;
if (!b0.InverseOn(curveA, out isOn, out paramAInvB0) || (!isOn))
{
return(false);
}
if (!b1.InverseOn(curveA, out isOn, out paramAInvB1) || (!isOn))
{
return(false);
}
paramAInvB0.Round(0, 1);
paramAInvB1.Round(0, 1);
Param paramInA = null, paramInB = null, paramOutA = null, paramOutB = null;
VecD pntIn = null, pntOut = null;
if (paramBInvA0 <= 0) // before or start
{
paramInA = paramAInvB0;
paramInB = 0;
pntIn = b0;
}
else if (paramBInvA0 < 1) // inner
{
paramInA = 0;
paramInB = paramBInvA0;
pntIn = a0;
}
if ((paramBInvA1 >= 0) && (paramBInvA1 <= 1)) // inner or end
{
paramOutA = 1;
paramOutB = paramBInvA1;
pntOut = a1;
}
else if (paramBInvA1 > 1) // after
{
paramOutA = paramAInvB1;
paramOutB = 1;
pntOut = b1;
}
if ((pntIn == null) || (pntOut == null))
{
throw new ExceptionGMath("Intersect", "RefineIntersBBD1", null);
//return false;
}
Curve curveInters = curveA.SubCurve(paramInA, paramOutA);
inters = new IntersD1(paramInA, paramInB,
paramOutA, paramOutB, curveInters, false);
return(true);
}
/*
* REFINE INTERSECTION D1
*/
public static bool RefineIntersBBD1(BCurve curveA, BCurve curveB,
out InfoInters inters)
{
/*
* ASSUMPTIONS:
* - curveA & curveB are MAXIMALLY REDUCED
* - intersection is KNOWN to have dimension D1
* - does not work in case of SI beziers
* => OR: both curveA & curveB are SEGMENTS
* OR: both curveA & curveB are BEZIER
*/
inters=null;
InfoInters selfinters;
if (curveA.IsSelfInters(out selfinters)||curveB.IsSelfInters(out selfinters))
{
throw new ExceptionGMath("Intersect","RefineIntersBBD1",null);
//return false;
}
VecD a0=curveA.Start;
VecD a1=curveA.End;
Param paramBInvA0, paramBInvA1;
bool isOn;
if (!a0.InverseOn(curveB, out isOn, out paramBInvA0)||(!isOn))
return false;
if (!a1.InverseOn(curveB, out isOn, out paramBInvA1)||(!isOn))
return false;
paramBInvA0.Round(0,1);
paramBInvA1.Round(0,1);
bool areCoDirected=(paramBInvA1>=paramBInvA0);
if (!areCoDirected)
{
BCurve revB=curveB.Reversed as BCurve;
if (!Inters.RefineIntersBBD1(curveA,revB,out inters))
return false;
if (inters!=null)
{
inters.ParamReverse(1,1);
}
return true;
}
VecD b0=curveB.Start;
VecD b1=curveB.End;
Param paramAInvB0, paramAInvB1;
if (!b0.InverseOn(curveA, out isOn, out paramAInvB0)||(!isOn))
return false;
if (!b1.InverseOn(curveA, out isOn, out paramAInvB1)||(!isOn))
return false;
paramAInvB0.Round(0,1);
paramAInvB1.Round(0,1);
Param paramInA=null, paramInB=null, paramOutA=null, paramOutB=null;
VecD pntIn=null, pntOut=null;
if (paramBInvA0<=0) // before or start
{
paramInA=paramAInvB0;
paramInB=0;
pntIn=b0;
}
else if (paramBInvA0<1) // inner
{
paramInA=0;
paramInB=paramBInvA0;
pntIn=a0;
}
if ((paramBInvA1>=0)&&(paramBInvA1<=1)) // inner or end
{
paramOutA=1;
paramOutB=paramBInvA1;
pntOut=a1;
}
else if (paramBInvA1>1) // after
{
paramOutA=paramAInvB1;
paramOutB=1;
pntOut=b1;
}
if ((pntIn==null)||(pntOut==null))
{
throw new ExceptionGMath("Intersect","RefineIntersBBD1",null);
//return false;
}
Curve curveInters=curveA.SubCurve(paramInA,paramOutA);
inters=new IntersD1(paramInA,paramInB,
paramOutA,paramOutB,curveInters,false);
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 RefineIntersLLD1(LCurve lrsA, LCurve lrsB,
out InfoInters inters)
{
inters=null;
if ((lrsA is SegD) && (lrsB is SegD))
{
BCurve curveA=lrsA as BCurve;
BCurve curveB=lrsB as BCurve;
return Inters.RefineIntersBBD1(curveA, curveB, out inters);
}
if (lrsA.LComplexity>lrsB.LComplexity)
{
bool res=Inters.RefineIntersLLD1(lrsB,lrsA,out inters);
if (inters!=null)
{
inters.ParamSwap();
}
return res;
}
VecD a0=lrsA.Start;
VecD a1=lrsA.End;
VecD b0=lrsB.Start;
VecD b1=lrsB.End;
Param paramBInvA0, paramBInvA1;
bool isOn;
if ((!a0.InverseOn(lrsB, out isOn, out paramBInvA0))||(!isOn))
return false;
if ((!a1.InverseOn(lrsB, out isOn, out paramBInvA1))||(!isOn))
return false;
Param paramAInvB0, paramAInvB1;
if ((!b0.InverseOn(lrsA, out isOn, out paramAInvB0))||(!isOn))
return false;
if ((!b1.InverseOn(lrsA, out isOn, out paramAInvB1))||(!isOn))
return false;
bool areCoDirected=(paramBInvA1.Val>=paramBInvA0.Val);
if (!areCoDirected)
{
if (lrsA is LineD)
{
if (lrsB is LineD)
{
paramAInvB0=(areCoDirected)? -Param.Infinity: Param.Infinity;
paramAInvB1=(areCoDirected)? Param.Infinity: -Param.Infinity;
inters=new IntersD1(paramAInvB0,-Param.Infinity,
paramAInvB1,Param.Infinity,lrsB,false);
return true;
}
if (lrsB is RayD)
{
paramAInvB1=(areCoDirected)? Param.Infinity: -Param.Infinity;
inters=new IntersD1(paramAInvB0,0,
paramAInvB1,Param.Infinity,lrsB,false);
return true;
}
if (lrsB is SegD)
{
inters=new IntersD1(paramAInvB0,0,
paramAInvB1,1,lrsB,false);
return true;
}
}
if (lrsA is RayD)
{
if (lrsB is RayD)
{
if (areCoDirected)
{
if (paramAInvB0>0)
{
inters=new IntersD1(paramAInvB0,0,
Param.Infinity,Param.Infinity,lrsB,false);
return true;
}
else
{
inters=new IntersD1(0,paramBInvA0,
Param.Infinity,Param.Infinity,lrsA,false);
return true;
}
}
else
{
if (paramAInvB0>0)
{
inters=new IntersD1(0,paramBInvA0,
paramAInvB0,0,new SegD(a0,b0),false);
return true;
}
}
}
if (lrsB is SegD)
{
// intersection is known to have dimension D1 !!!
if ((paramBInvA0>=1)||(paramBInvA0<=0))
{
inters=new IntersD1(paramAInvB0,0,
paramAInvB1,1,new SegD(b0,b1),false);
return true;
}
if ((0<paramBInvA0)&&(paramBInvA1<1))
{
if (areCoDirected)
{
inters=new IntersD1(0,paramBInvA0,
paramAInvB1,1,new SegD(a0,b1),false);
return true;
}
else
{
inters=new IntersD1(0,paramBInvA0,
paramAInvB0,0,new SegD(a0,b0),false);
return true;
}
}
}
}
}
throw new ExceptionGMath("Intersect","RefineIntersLLD1",null);
//return false;
}