bool InverseOn(LCurve lrs, out bool isOn, out Param par)
{
/*
* MEANING: inverse point which is known to lie on the
* lrs in range [-Infinity, Infinity]
*
* ASSUMPTIONS: lrs is non-degenerated
*
*/
isOn = false;
par = null;
if (lrs.IsDegen)
{
throw new ExceptionGMath("VecD", "InverseOn(lrs)", null);
//return false;
}
this.Inverse(lrs, out par);
if (this.Dist(lrs.Evaluate(par)) < MConsts.EPS_DEC)
{
isOn = true;
}
else
{
par = null;
}
return(true);
}
public bool Project(LCurve lcurve, out Param param, out VecD pnt)
{
/*
* MEANING: the NEAREST point in the PARAMETRIC RANGE
* of the curve
*
* ASSUMPTIONS: the curve may be not reduced
*/
param = null;
pnt = null;
if (lcurve.IsDegen)
{
SegD seg = lcurve as SegD;
if (seg == null)
{
throw new ExceptionGMath("VecD", "Project", null);
//return false;
}
param = new Param(Param.Degen);
pnt = seg.Middle;
return(true);
}
this.Perp(lcurve, out param);
param.Clip(lcurve.ParamStart, lcurve.ParamEnd);
pnt = lcurve.Evaluate(param);
return(true);
}
/*
* INTERSECT: (LCurve, LCurve)
* - both curves are supposed to be NON-DEGENERATED
*/
public static bool IntersectLL(LCurve lrsA, LCurve lrsB,
out InfoInters inters)
{
inters = null;
if ((lrsA.IsDegen) || (lrsB.IsDegen))
{
throw new ExceptionGMath("Intersect", "IntersectLL(lrs,lrs)", null);
}
VecD a0 = lrsA.Start;
VecD a1 = lrsA.End;
VecD b0 = lrsB.Start;
VecD b1 = lrsB.End;
VecD dirA = lrsA.DirTang;
VecD dirB = lrsB.DirTang;
double det = dirA.Cross(dirB);
// lrsA and lrsB are not parallel
if (Math.Abs(det) > MConsts.EPS_DEC)
{
double lenA = (a1 - a0).Norm;
double lenB = (b1 - b0).Norm;
VecD diff = b0 - a0;
Param parA = (diff.Cross(dirB)) / (det * lenA);
Param parB = (diff.Cross(dirA)) / (det * lenB);
if (lrsA.IsEvaluableStrict(parA) && lrsB.IsEvaluableStrict(parB))
{
VecD pnt = 0.5 * (lrsA.Evaluate(parA) + lrsB.Evaluate(parB));
inters = new IntersD0(parA, parB, pnt, false);
}
return(true);
}
// lrsA and lrsB are parallel
LineD lineB = new LineD(lrsB);
Param paramBInvA0, paramBInvA1;
VecD pntProjA0, pntProjA1;
a0.Project(lineB, out paramBInvA0, out pntProjA0);
a1.Project(lineB, out paramBInvA1, out pntProjA1);
double distA0 = a0.Dist(pntProjA0);
double distA1 = a1.Dist(pntProjA1);
if ((distA0 < MConsts.EPS_DEC) || (distA1 < MConsts.EPS_DEC))
{
// lrsA and lrsB are colinear
Param.TypeParam typeA0 = lrsB.ParamClassify(paramBInvA0);
Param.TypeParam typeA1 = lrsB.ParamClassify(paramBInvA1);
int mult = (int)typeA0 * (int)typeA1;
if (mult == 4)
{
return(true);
}
else if (mult == 1)
{
throw new ExceptionGMath("Intersect", "IntersectLL(lrs,lrs)", null); // lrsA is degenerated
//return false;
}
else if (mult == 2)
{
if ((typeA0 == Param.TypeParam.Start) &&
(typeA1 == Param.TypeParam.Before))
{
inters = new IntersD0(0, 0, a0, false);
}
if ((typeA0 == Param.TypeParam.Before) &&
(typeA1 == Param.TypeParam.Start))
{
inters = new IntersD0(1, 0, a1, false);
}
if ((typeA0 == Param.TypeParam.End) &&
(typeA1 == Param.TypeParam.After))
{
inters = new IntersD0(0, 1, a0, false);
}
if ((typeA0 == Param.TypeParam.After) &&
(typeA1 == Param.TypeParam.End))
{
inters = new IntersD0(1, 1, a1, false);
}
return(true);
}
else if (mult <= 0)
{
return(Inters.RefineIntersLLD1(lrsA, lrsB, out inters));
}
}
return(true);
}
public static bool AuxIntersectBL(Bez2D bez, LCurve lrs, ListInfoInters linters)
{
// bezier is irreducable !!!
if (linters == null)
{
throw new ExceptionGMath("Intersect", "AuxIntersectBL(bez,lrs)", "Null argument");
}
if (lrs.IsDegen)
{
throw new ExceptionGMath("Intersect", "AuxIntersectBL(bez,lrs)", null);
}
Param parM;
if (bez.IsSelfInters(out parM))
{
if (parM.Val < 0)
{
Bez2D bezRev = bez.Reversed as Bez2D;
int numIntersBefore = linters.Count;
if (!Inters.AuxIntersectBL(bezRev, lrs, linters))
{
return(false);
}
linters.ParamReverse(1, 0, numIntersBefore);
return(true);
}
SegD support = bez.SupportFlat();
InfoInters intersSup;
if (!Inters.IntersectLL(support, lrs, out intersSup))
{
return(false);
}
if (intersSup == null)
{
return(true);
}
/*
* convert parameters from support to Bezier
*/
// invalidate in case of D1 intersection
if (intersSup.Dim == InfoInters.TypeDim.Dim1)
{
(intersSup as IntersD1).ParamInvalidateBezSI();
linters.Add(intersSup);
return(true);
}
// write as 1 or 2 intersections with different parameters
// in case of D0 intersections
InfoInters[] intersBez;
if (!bez.IntersFromSupport(intersSup, 0, out intersBez))
{
return(false);
}
for (int iIntersBez = 0; iIntersBez < intersBez.Length; iIntersBez++)
{
linters.Add(intersBez[iIntersBez]);
}
return(true);
}
// bezier is NOT self/intersecting
VecD[] cfLrs, cfBez;
lrs.PowerCoeff(out cfLrs);
bez.PowerCoeff(out cfBez);
VecD norm = lrs.DirNorm;
VecD tang = lrs.DirTang;
double[] roots;
int numRootBez;
Equation.RootsReal(cfBez[2].Dot(norm),
cfBez[1].Dot(norm), (cfBez[0] - cfLrs[0]).Dot(norm),
out numRootBez, out roots);
if (numRootBez == Equation.NumRootInfinite)
{
// bezier is irreducable,=> only D0 intersections are possible
throw new ExceptionGMath("Intersect", "AuxIntersectBL(bez,lrs)", null);
//return false;
}
for (int iRoot = 0; iRoot < numRootBez; iRoot++)
{
Param parBez = roots[iRoot];
if (bez.IsEvaluableStrict(parBez))
{
Param parLrs = Equation.Evaluate(parBez.Val,
cfBez[2].Dot(tang), cfBez[1].Dot(tang),
(cfBez[0] - cfLrs[0]).Dot(tang)) / (cfLrs[1].Dot(tang));
if (lrs.IsEvaluableStrict(parLrs))
{
IntersD0 inters = new IntersD0(parBez, parLrs,
0.5 * (lrs.Evaluate(parLrs.Val) + bez.Evaluate(parBez.Val)),
false);
linters.Add(inters);
}
}
}
return(true);
}
bool InverseOn(LCurve lrs, out bool isOn, out Param par)
{
/*
* MEANING: inverse point which is known to lie on the
* lrs in range [-Infinity, Infinity]
*
* ASSUMPTIONS: lrs is non-degenerated
*
*/
isOn=false;
par=null;
if (lrs.IsDegen)
{
throw new ExceptionGMath("VecD","InverseOn(lrs)",null);
//return false;
}
this.Inverse(lrs, out par);
if (this.Dist(lrs.Evaluate(par))<MConsts.EPS_DEC)
{
isOn=true;
}
else
{
par=null;
}
return true;
}
public bool Project(LCurve lcurve, out Param param, out VecD pnt)
{
/*
* MEANING: the NEAREST point in the PARAMETRIC RANGE
* of the curve
*
* ASSUMPTIONS: the curve may be not reduced
*/
param=null;
pnt=null;
if (lcurve.IsDegen)
{
SegD seg=lcurve as SegD;
if (seg==null)
{
throw new ExceptionGMath("VecD","Project",null);
//return false;
}
param=new Param(Param.Degen);
pnt=seg.Middle;
return true;
}
this.Perp(lcurve, out param);
param.Clip(lcurve.ParamStart,lcurve.ParamEnd);
pnt=lcurve.Evaluate(param);
return true;
}
/*
* INTERSECT: (LCurve, LCurve)
* - both curves are supposed to be NON-DEGENERATED
*/
public static bool IntersectLL(LCurve lrsA, LCurve lrsB,
out InfoInters inters)
{
inters=null;
if ((lrsA.IsDegen)||(lrsB.IsDegen))
{
throw new ExceptionGMath("Intersect","IntersectLL(lrs,lrs)",null);
}
VecD a0=lrsA.Start;
VecD a1=lrsA.End;
VecD b0=lrsB.Start;
VecD b1=lrsB.End;
VecD dirA=lrsA.DirTang;
VecD dirB=lrsB.DirTang;
double det = dirA.Cross(dirB);
// lrsA and lrsB are not parallel
if (Math.Abs(det)>MConsts.EPS_DEC)
{
double lenA = (a1-a0).Norm;
double lenB = (b1-b0).Norm;
VecD diff = b0-a0;
Param parA = (diff.Cross(dirB))/(det*lenA);
Param parB = (diff.Cross(dirA))/(det*lenB);
if (lrsA.IsEvaluableStrict(parA)&&lrsB.IsEvaluableStrict(parB))
{
VecD pnt = 0.5*(lrsA.Evaluate(parA)+lrsB.Evaluate(parB));
inters=new IntersD0(parA,parB,pnt,false);
}
return true;
}
// lrsA and lrsB are parallel
LineD lineB=new LineD(lrsB);
Param paramBInvA0, paramBInvA1;
VecD pntProjA0, pntProjA1;
a0.Project(lineB, out paramBInvA0, out pntProjA0);
a1.Project(lineB, out paramBInvA1, out pntProjA1);
double distA0=a0.Dist(pntProjA0);
double distA1=a1.Dist(pntProjA1);
if ((distA0<MConsts.EPS_DEC)||(distA1<MConsts.EPS_DEC))
{
// lrsA and lrsB are colinear
Param.TypeParam typeA0=lrsB.ParamClassify(paramBInvA0);
Param.TypeParam typeA1=lrsB.ParamClassify(paramBInvA1);
int mult=(int)typeA0*(int)typeA1;
if (mult==4)
{
return true;
}
else if (mult==1)
{
throw new ExceptionGMath("Intersect","IntersectLL(lrs,lrs)",null); // lrsA is degenerated
//return false;
}
else if (mult==2)
{
if ((typeA0==Param.TypeParam.Start)&&
(typeA1==Param.TypeParam.Before))
{
inters=new IntersD0(0,0,a0,false);
}
if ((typeA0==Param.TypeParam.Before)&&
(typeA1==Param.TypeParam.Start))
{
inters=new IntersD0(1,0,a1,false);
}
if ((typeA0==Param.TypeParam.End)&&
(typeA1==Param.TypeParam.After))
{
inters=new IntersD0(0,1,a0,false);
}
if ((typeA0==Param.TypeParam.After)&&
(typeA1==Param.TypeParam.End))
{
inters=new IntersD0(1,1,a1,false);
}
return true;
}
else if (mult<=0)
{
return (Inters.RefineIntersLLD1(lrsA,lrsB,out inters));
}
}
return true;
}
public static bool AuxIntersectBL(Bez2D bez, LCurve lrs, ListInfoInters linters)
{
// bezier is irreducable !!!
if (linters==null)
{
throw new ExceptionGMath("Intersect","AuxIntersectBL(bez,lrs)","Null argument");
}
if (lrs.IsDegen)
{
throw new ExceptionGMath("Intersect","AuxIntersectBL(bez,lrs)",null);
}
Param parM;
if (bez.IsSelfInters(out parM))
{
if (parM.Val<0)
{
Bez2D bezRev=bez.Reversed as Bez2D;
int numIntersBefore=linters.Count;
if (!Inters.AuxIntersectBL(bezRev,lrs,linters))
return false;
linters.ParamReverse(1,0,numIntersBefore);
return true;
}
SegD support=bez.SupportFlat();
InfoInters intersSup;
if (!Inters.IntersectLL(support, lrs, out intersSup))
return false;
if (intersSup==null)
return true;
/*
* convert parameters from support to Bezier
*/
// invalidate in case of D1 intersection
if (intersSup.Dim==InfoInters.TypeDim.Dim1)
{
(intersSup as IntersD1).ParamInvalidateBezSI();
linters.Add(intersSup);
return true;
}
// write as 1 or 2 intersections with different parameters
// in case of D0 intersections
InfoInters[] intersBez;
if (!bez.IntersFromSupport(intersSup,0,out intersBez))
return false;
for (int iIntersBez=0; iIntersBez<intersBez.Length; iIntersBez++)
{
linters.Add(intersBez[iIntersBez]);
}
return true;
}
// bezier is NOT self/intersecting
VecD[] cfLrs, cfBez;
lrs.PowerCoeff(out cfLrs);
bez.PowerCoeff(out cfBez);
VecD norm=lrs.DirNorm;
VecD tang=lrs.DirTang;
double[] roots;
int numRootBez;
Equation.RootsReal(cfBez[2].Dot(norm),
cfBez[1].Dot(norm),(cfBez[0]-cfLrs[0]).Dot(norm),
out numRootBez, out roots);
if (numRootBez==Equation.NumRootInfinite)
{
// bezier is irreducable,=> only D0 intersections are possible
throw new ExceptionGMath("Intersect","AuxIntersectBL(bez,lrs)",null);
//return false;
}
for (int iRoot=0; iRoot<numRootBez; iRoot++)
{
Param parBez=roots[iRoot];
if (bez.IsEvaluableStrict(parBez))
{
Param parLrs=Equation.Evaluate(parBez.Val,
cfBez[2].Dot(tang), cfBez[1].Dot(tang),
(cfBez[0]-cfLrs[0]).Dot(tang))/(cfLrs[1].Dot(tang));
if (lrs.IsEvaluableStrict(parLrs))
{
IntersD0 inters=new IntersD0(parBez,parLrs,
0.5*(lrs.Evaluate(parLrs.Val)+bez.Evaluate(parBez.Val)),
false);
linters.Add(inters);
}
}
}
return true;
}