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 void FromReduced(BCurve bcurve)
{
// parameter of the (reduced)curve may be invalidated if
// the curve intersects the self-intersecting Bezier
if (this.val == Param.Invalid)
{
return;
}
if (bcurve.IsDegen)
{
return;
}
if (bcurve is Bez2D)
{
Bez2D bez = bcurve as Bez2D;
Param parM;
if (bez.IsSeg(out parM))
{
bez.ParamFromSeg(this);
}
}
}
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);
}
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;
}
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;
}