public bool Project(Bez2D bez, out Param par, out VecD pnt)
{
/*
* MEANING: the NEAREST point in the RANGE [0,1]
* ASSUMPTION: - bezier can be non-reduced
* - bezier is NOT self-intersecting
*/
par = null;
pnt = null;
Param parM;
if (bez.IsSelfInters(out parM))
{
throw new ExceptionGMath("VecD", "Project(bez)", null);
//return false;
}
if (bez.IsDegen)
{
par = new Param(Param.Degen);
pnt = bez.Middle;
return(true);
}
if (bez.IsSeg(out parM))
{
SegD seg = bez.Reduced as SegD;
this.Project(seg, out par, out pnt);
bez.ParamFromSeg(par);
return(true);
}
// case of non-flat Bezier
Param[] parsPerp;
if (!this.Perp(bez, out parsPerp))
{
return(false);
}
double distS = this.Dist(bez.Start);
double distE = this.Dist(bez.End);
double distMin = Math.Min(distS, distE);
double parMin = (distS <= distE)? 0.0: 1.0;
if (parsPerp != null)
{
for (int iPerp = 0; iPerp < parsPerp.Length; iPerp++)
{
if (bez.IsEvaluableStrict(parsPerp[iPerp]))
{
double distPerp = this.Dist(bez.Evaluate(parsPerp[iPerp]));
if (distPerp < distMin)
{
distMin = distPerp;
parMin = parsPerp[iPerp];
}
}
}
}
par = parMin;
pnt = bez.Evaluate(parMin);
return(true);
}
public bool Inverse(Bez2D bez, out Param par)
{
/*
* MEANING:
* - Parameter of the nearest point in range
* [-Infinity, Infinity]
* ASSUMPTIONS:
* - Bezier is REDUCED
* - Works for any bezier if the nearest point belongs
* to support
* - Works for non S/I bezier if the nearest point lies
* without the support
*/
par = null;
Param parM;
if (!bez.IsSelfInters(out parM))
{
Param[] parsPerp;
if (!this.Perp(bez, out parsPerp))
{
return(false);
}
double distMin = MConsts.Infinity;
for (int iPar = 0; iPar < parsPerp.Length; iPar++)
{
double distCur = this.Dist(bez.Evaluate(parsPerp[iPar]));
if (distCur < distMin)
{
distMin = distCur;
par = parsPerp[iPar];
}
}
return(true);
}
// bezier is s/i
Param[] parsProj;
VecD pnt;
if (!this.ProjectGeneral(bez, out parsProj, out pnt))
{
return(false);
}
if (this.Dist(pnt) > MConsts.EPS_DEC)
{
throw new ExceptionGMath("VecD", "Inverse(bez)", null);
//return false;
}
par = parsProj[0];
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);
}
bool InverseOn(Bez2D bez, out bool isOn, out Param par)
{
/*
* MEANING: inverse point which is known to lie on the
* bezier in range [-Infinity, Infinity]
*
* ASSUMPTIONS: bez is IRREDUCABLE && NOT S/I
*
*/
isOn = false;
par = null;
Param parM;
if ((bez.IsDegen) || (bez.IsSeg(out parM)) || (bez.IsSelfInters(out parM)))
{
throw new ExceptionGMath("VecD", "InverseOn(bez)", null);
//return false;
}
VecD[] cfBez;
bez.PowerCoeff(out cfBez);
double dev = (cfBez[2].Cross(this - cfBez[0])) *
(cfBez[2].Cross(this - cfBez[0])) -
(cfBez[2].Cross(cfBez[1])) *
((this - cfBez[0]).Cross(cfBez[1]));
if (Math.Abs(dev) < MConsts.EPS_DEC)
{
isOn = true;
par = (cfBez[2].Cross(this - cfBez[0])) / (cfBez[2].Cross(cfBez[1]));
}
return(true);
}
bool Perp(Bez2D bez, out Param[] pars)
{
/*
* MEANING: perpendicular to the parametric range
* [-Infinity, Infinity] for NON-DEGENERATED,
* NON-FLAT bezier
*/
pars = null;
Param parM;
if (bez.IsDegen)
{
throw new ExceptionGMath("VecD", "Perp", null);
//return false;
}
if (bez.IsSeg(out parM) || bez.IsSelfInters(out parM))
{
throw new ExceptionGMath("VecD", "Perp", null);
//return false;
}
VecD[] pcf;
bez.PowerCoeff(out pcf);
double a = 2 * (pcf[2].Dot(pcf[2]));
double b = 3 * (pcf[2].Dot(pcf[1]));
double c = pcf[1].Dot(pcf[1]) + 2 * ((pcf[0] - (this)).Dot(pcf[2]));
double d = (pcf[0] - (this)).Dot(pcf[1]);
int numRootReal;
double[] root;
Equation.RootsReal(a, b, c, d, out numRootReal, out root);
pars = new Param[root.Length];
for (int iRoot = 0; iRoot < root.Length; iRoot++)
{
pars[iRoot] = new Param(root[iRoot]);
}
return(true);
}
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 bool Inverse(Bez2D bez, out Param par)
{
/*
* MEANING:
* - Parameter of the nearest point in range
* [-Infinity, Infinity]
* ASSUMPTIONS:
* - Bezier is REDUCED
* - Works for any bezier if the nearest point belongs
* to support
* - Works for non S/I bezier if the nearest point lies
* without the support
*/
par=null;
Param parM;
if (!bez.IsSelfInters(out parM))
{
Param[] parsPerp;
if (!this.Perp(bez, out parsPerp))
return false;
double distMin=MConsts.Infinity;
for (int iPar=0; iPar<parsPerp.Length; iPar++)
{
double distCur=this.Dist(bez.Evaluate(parsPerp[iPar]));
if (distCur<distMin)
{
distMin=distCur;
par=parsPerp[iPar];
}
}
return true;
}
// bezier is s/i
Param[] parsProj;
VecD pnt;
if (!this.ProjectGeneral(bez, out parsProj, out pnt))
return false;
if (this.Dist(pnt)>MConsts.EPS_DEC)
{
throw new ExceptionGMath("VecD","Inverse(bez)",null);
//return false;
}
par=parsProj[0];
return true;
}
bool InverseOn(Bez2D bez, out bool isOn, out Param par)
{
/*
* MEANING: inverse point which is known to lie on the
* bezier in range [-Infinity, Infinity]
*
* ASSUMPTIONS: bez is IRREDUCABLE && NOT S/I
*
*/
isOn=false;
par=null;
Param parM;
if ((bez.IsDegen)||(bez.IsSeg(out parM))||(bez.IsSelfInters(out parM)))
{
throw new ExceptionGMath("VecD","InverseOn(bez)",null);
//return false;
}
VecD[] cfBez;
bez.PowerCoeff(out cfBez);
double dev=(cfBez[2].Cross(this-cfBez[0]))*
(cfBez[2].Cross(this-cfBez[0]))-
(cfBez[2].Cross(cfBez[1]))*
((this-cfBez[0]).Cross(cfBez[1]));
if (Math.Abs(dev)<MConsts.EPS_DEC)
{
isOn=true;
par=(cfBez[2].Cross(this-cfBez[0]))/(cfBez[2].Cross(cfBez[1]));
}
return true;
}
public bool Project(Bez2D bez, out Param par, out VecD pnt)
{
/*
* MEANING: the NEAREST point in the RANGE [0,1]
* ASSUMPTION: - bezier can be non-reduced
* - bezier is NOT self-intersecting
*/
par=null;
pnt=null;
Param parM;
if (bez.IsSelfInters(out parM))
{
throw new ExceptionGMath("VecD","Project(bez)",null);
//return false;
}
if (bez.IsDegen)
{
par=new Param(Param.Degen);
pnt=bez.Middle;
return true;
}
if (bez.IsSeg(out parM))
{
SegD seg=bez.Reduced as SegD;
this.Project(seg,out par,out pnt);
bez.ParamFromSeg(par);
return true;
}
// case of non-flat Bezier
Param[] parsPerp;
if (!this.Perp(bez, out parsPerp))
return false;
double distS=this.Dist(bez.Start);
double distE=this.Dist(bez.End);
double distMin=Math.Min(distS,distE);
double parMin=(distS<=distE)? 0.0: 1.0;
if (parsPerp!=null)
{
for (int iPerp=0; iPerp<parsPerp.Length; iPerp++)
{
if (bez.IsEvaluableStrict(parsPerp[iPerp]))
{
double distPerp=this.Dist(bez.Evaluate(parsPerp[iPerp]));
if (distPerp<distMin)
{
distMin=distPerp;
parMin=parsPerp[iPerp];
}
}
}
}
par=parMin;
pnt=bez.Evaluate(parMin);
return true;
}
public bool ProjectGeneral(Bez2D bez, out Param[] pars, out VecD pnt)
{
/*
* MEANING: parameter (or parameters) of the nearest point
* in range [0,1]
*
* ASSUMPTIONS: bezier can be non-reduced
* bezier can be self-intersecting
*
*/
pars=null;
pnt=null;
Param parM;
if (!bez.IsSelfInters(out parM))
{
Param par;
if (!this.Project(bez,out par,out pnt))
return false;
if (par!=null)
{
pars=new Param[1];
pars[0]=par;
}
return true;
}
double valM=parM.Val;
if (parM<0)
{
Bez2D bezRev=new Bez2D(bez);
bezRev.Reverse();
if (!this.ProjectGeneral(bezRev,out pars,out pnt))
return false;
if (pars!=null)
{
for (int iPar=0; iPar<pars.Length; iPar++)
{
pars[iPar].Reverse(1);
}
}
return true;
}
SegD support=bez.SupportFlat();
Param parSupport;
if (!this.Project(support,out parSupport, out pnt))
return false;
if (!bez.ParamFromSupport(parSupport,out pars))
return false;
return true;
}
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 bool ProjectGeneral(Bez2D bez, out Param[] pars, out VecD pnt)
{
/*
* MEANING: parameter (or parameters) of the nearest point
* in range [0,1]
*
* ASSUMPTIONS: bezier can be non-reduced
* bezier can be self-intersecting
*
*/
pars = null;
pnt = null;
Param parM;
if (!bez.IsSelfInters(out parM))
{
Param par;
if (!this.Project(bez, out par, out pnt))
{
return(false);
}
if (par != null)
{
pars = new Param[1];
pars[0] = par;
}
return(true);
}
double valM = parM.Val;
if (parM < 0)
{
Bez2D bezRev = new Bez2D(bez);
bezRev.Reverse();
if (!this.ProjectGeneral(bezRev, out pars, out pnt))
{
return(false);
}
if (pars != null)
{
for (int iPar = 0; iPar < pars.Length; iPar++)
{
pars[iPar].Reverse(1);
}
}
return(true);
}
SegD support = bez.SupportFlat();
Param parSupport;
if (!this.Project(support, out parSupport, out pnt))
{
return(false);
}
if (!bez.ParamFromSupport(parSupport, out pars))
{
return(false);
}
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 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 Perp(Bez2D bez, out Param[] pars)
{
/*
* MEANING: perpendicular to the parametric range
* [-Infinity, Infinity] for NON-DEGENERATED,
* NON-FLAT bezier
*/
pars=null;
Param parM;
if (bez.IsDegen)
{
throw new ExceptionGMath("VecD","Perp",null);
//return false;
}
if (bez.IsSeg(out parM)||bez.IsSelfInters(out parM))
{
throw new ExceptionGMath("VecD","Perp",null);
//return false;
}
VecD[] pcf;
bez.PowerCoeff(out pcf);
double a = 2*(pcf[2].Dot(pcf[2]));
double b = 3*(pcf[2].Dot(pcf[1]));
double c = pcf[1].Dot(pcf[1])+2*((pcf[0]-(this)).Dot(pcf[2]));
double d = (pcf[0]-(this)).Dot(pcf[1]);
int numRootReal;
double[] root;
Equation.RootsReal(a,b,c,d,out numRootReal,out root);
pars=new Param[root.Length];
for (int iRoot=0; iRoot<root.Length; iRoot++)
{
pars[iRoot]=new Param(root[iRoot]);
}
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);
}
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;
}