[occt.git] / src / Extrema / Extrema_ExtPElC.cxx

// Copyright (c) 1995-1999 Matra Datavision
// Copyright (c) 1999-2012 OPEN CASCADE SAS
//
// The content of this file is subject to the Open CASCADE Technology Public
// License Version 6.5 (the "License"). You may not use the content of this file
// except in compliance with the License. Please obtain a copy of the License
// at http://www.opencascade.org and read it completely before using this file.
//
// The Initial Developer of the Original Code is Open CASCADE S.A.S., having its
// main offices at: 1, place des Freres Montgolfier, 78280 Guyancourt, France.
//
// The Original Code and all software distributed under the License is
// distributed on an "AS IS" basis, without warranty of any kind, and the
// Initial Developer hereby disclaims all such warranties, including without
// limitation, any warranties of merchantability, fitness for a particular
// purpose or non-infringement. Please see the License for the specific terms
// and conditions governing the rights and limitations under the License.

#include <Extrema_ExtPElC.ixx>
#include <StdFail_NotDone.hxx>
#include <math_DirectPolynomialRoots.hxx>
#include <math_TrigonometricFunctionRoots.hxx>
#include <ElCLib.hxx>
#include <Standard_OutOfRange.hxx>
#include <Standard_NotImplemented.hxx>
#include <Precision.hxx>


//=============================================================================

Extrema_ExtPElC::Extrema_ExtPElC () { myDone = Standard_False; }
//=============================================================================

Extrema_ExtPElC::Extrema_ExtPElC (const gp_Pnt&       P, 
				  const gp_Lin&       L,
				  const Standard_Real Tol,
				  const Standard_Real Uinf, 
				  const Standard_Real Usup)
{
  Perform(P, L, Tol, Uinf, Usup);
}

void Extrema_ExtPElC::Perform(const gp_Pnt&       P, 
			      const gp_Lin&       L,
			      const Standard_Real Tol,
			      const Standard_Real Uinf, 
			      const Standard_Real Usup)
{
  myDone = Standard_False;
  myNbExt = 0;
  gp_Vec V1 = gp_Vec(L.Direction());
  gp_Pnt OR = L.Location();
  gp_Vec V(OR, P);
  Standard_Real Mydist = V1.Dot(V);
  if ((Mydist >= Uinf-Tol) && 
      (Mydist <= Usup+Tol)){ 
    
    gp_Pnt MyP = OR.Translated(Mydist*V1);
    Extrema_POnCurv MyPOnCurve(Mydist, MyP);
    mySqDist[0] = P.SquareDistance(MyP);
    myPoint[0] = MyPOnCurve;
    myIsMin[0] = Standard_True;
    myNbExt = 1;
    myDone = Standard_True;
  }

}


Extrema_ExtPElC::Extrema_ExtPElC (const gp_Pnt&       P,
				  const gp_Circ&      C,
				  const Standard_Real Tol,
				  const Standard_Real Uinf,
				  const Standard_Real Usup)
{
  Perform(P, C, Tol, Uinf, Usup);
}

void Extrema_ExtPElC::Perform(const gp_Pnt&       P, 
			      const gp_Circ&      C,
			      const Standard_Real Tol,
			      const Standard_Real Uinf,
			      const Standard_Real Usup)
/*-----------------------------------------------------------------------------
Function:
  Find values of parameter u such as:
   - dist(P,C(u)) pass by an extrema,
   - Uinf <= u <= Usup.

Method:
  Pass 3 stages:
  1- Projection of point P in the plane of the circle,
  2- Calculation of u solutions in [0.,2.*M_PI]:
      Let Pp, the projected point and 
           O, the center of the circle;
     2 cases:
     - if Pp is mixed with 0, there is an infinite number of solutions;
       IsDone() renvoie Standard_False.
     - otherwise, 2 points are solutions for the complete circle:
       . Us1 = angle(OPp,OX) corresponds to the minimum,
       . let Us2 = ( Us1 + M_PI if Us1 < M_PI,
                    ( Us1 - M_PI otherwise;
         Us2 corresponds to the maximum.
  3- Calculate the extrema in [Uinf,Usup].
-----------------------------------------------------------------------------*/
{
  myDone = Standard_False;
  myNbExt = 0;

// 1- Projection of the point P in the plane of circle -> Pp ...

  gp_Pnt O = C.Location();
  gp_Vec Axe (C.Axis().Direction());
  gp_Vec Trsl = Axe.Multiplied(-(gp_Vec(O,P).Dot(Axe)));
  gp_Pnt Pp = P.Translated(Trsl);

// 2- Calculate u solutions in [0.,2.*PI] ...

  gp_Vec OPp (O,Pp);
  if (OPp.Magnitude() < Tol) { return; }
  Standard_Real Usol[2];
  Usol[0] = C.XAxis().Direction().AngleWithRef(OPp,Axe); // -M_PI<U1<M_PI
  Usol[1] = Usol[0] + M_PI;

  Standard_Real myuinf = Uinf;
  //modified by NIZNHY-PKV Fri Apr 20 15:03:28 2001 f
  //Standard_Real TolU = Tol*C.Radius();
  Standard_Real TolU, aR;
  aR=C.Radius();
  TolU=Precision::Infinite();
  if (aR > gp::Resolution()) {
    TolU= Tol/aR;
  }
  //modified by NIZNHY-PKV Fri Apr 20 15:03:32 2001 t
  ElCLib::AdjustPeriodic(Uinf, Uinf+2*M_PI, TolU, myuinf, Usol[0]);
  ElCLib::AdjustPeriodic(Uinf, Uinf+2*M_PI, TolU, myuinf, Usol[1]);
  if (((Usol[0]-2*M_PI-Uinf) < TolU) && ((Usol[0]-2*M_PI-Uinf) > -TolU)) Usol[0] = Uinf;
  if (((Usol[1]-2*M_PI-Uinf) < TolU) && ((Usol[1]-2*M_PI-Uinf) > -TolU)) Usol[1] = Uinf;


// 3- Calculate extrema in [Umin,Umax] ...

  gp_Pnt Cu;
  Standard_Real Us;
  for (Standard_Integer NoSol = 0; NoSol <= 1; NoSol++) {
    Us = Usol[NoSol];
    if (((Uinf-Us) < TolU) && ((Us-Usup) < TolU)) {
      Cu = ElCLib::Value(Us,C);
      mySqDist[myNbExt] = Cu.SquareDistance(P);
      myIsMin[myNbExt] = (NoSol == 0);
      myPoint[myNbExt] = Extrema_POnCurv(Us,Cu);
      myNbExt++;
    }
  }
  myDone = Standard_True;
}
//=============================================================================

Extrema_ExtPElC::Extrema_ExtPElC (const gp_Pnt&       P,
				  const gp_Elips&     C,
				  const Standard_Real Tol,
				  const Standard_Real Uinf, 
				  const Standard_Real Usup)
{
  Perform(P, C, Tol, Uinf, Usup);
}


void Extrema_ExtPElC::Perform (const gp_Pnt&       P, 
			       const gp_Elips&     C,
			       const Standard_Real Tol,
			       const Standard_Real Uinf, 
			       const Standard_Real Usup)
/*-----------------------------------------------------------------------------
Function:
  Find values of parameter u so that:
   - dist(P,C(u)) passes by an extremum,
   - Uinf <= u <= Usup.

Method:
  Takes 2 steps:
  1- Projection of point P in the plane of the ellipse,
  2- Calculation of the solutions:
     Let Pp, the projected point; find values u so that:
       (C(u)-Pp).C'(u) = 0. (1)
     Let Cos = cos(u) and Sin = sin(u),
          C(u) = (A*Cos,B*Sin) and Pp = (X,Y);
     Then, (1) <=> (A*Cos-X,B*Sin-Y).(-A*Sin,B*Cos) = 0.
                    (B**2-A**2)*Cos*Sin - B*Y*Cos + A*X*Sin = 0.
     Use algorithm math_TrigonometricFunctionRoots to solve this equation.
-----------------------------------------------------------------------------*/
{
  myDone = Standard_False;
  myNbExt = 0;

// 1- Projection of point P in the plane of the ellipse -> Pp ...

  gp_Pnt O = C.Location();
  gp_Vec Axe (C.Axis().Direction());
  gp_Vec Trsl = Axe.Multiplied(-(gp_Vec(O,P).Dot(Axe)));
  gp_Pnt Pp = P.Translated(Trsl);

// 2- Calculation of solutions ...

  Standard_Integer NoSol, NbSol;
  Standard_Real A = C.MajorRadius();
  Standard_Real B = C.MinorRadius();
  gp_Vec OPp (O,Pp);
  Standard_Real OPpMagn = OPp.Magnitude();
  if (OPpMagn < Tol) { if (Abs(A-B) < Tol) { return; } }
  Standard_Real X = OPp.Dot(gp_Vec(C.XAxis().Direction()));
  Standard_Real Y = OPp.Dot(gp_Vec(C.YAxis().Direction()));
  //  Standard_Real Y = Sqrt(OPpMagn*OPpMagn-X*X);

  Standard_Real ko2 = (B*B-A*A)/2., ko3 = -B*Y, ko4 = A*X;
  if(Abs(ko3) < 1.e-16*Max(Abs(ko2), Abs(ko3))) ko3 = 0.0;

//  math_TrigonometricFunctionRoots Sol(0.,(B*B-A*A)/2.,-B*Y,A*X,0.,Uinf,Usup);
  math_TrigonometricFunctionRoots Sol(0.,ko2, ko3, ko4, 0.,Uinf,Usup);

  if (!Sol.IsDone()) { return; }
  gp_Pnt Cu;
  Standard_Real Us;
  NbSol = Sol.NbSolutions();
  for (NoSol = 1; NoSol <= NbSol; NoSol++) {
    Us = Sol.Value(NoSol);
    Cu = ElCLib::Value(Us,C);
    mySqDist[myNbExt] = Cu.SquareDistance(P);
    myIsMin[myNbExt] = (NoSol == 1);
    myPoint[myNbExt] = Extrema_POnCurv(Us,Cu);
    myNbExt++;
  }
  myDone = Standard_True;
}
//=============================================================================

Extrema_ExtPElC::Extrema_ExtPElC (const gp_Pnt&       P, 
				  const gp_Hypr&      C,
				  const Standard_Real Tol,
				  const Standard_Real Uinf,
				  const Standard_Real Usup)
{
  Perform(P, C, Tol, Uinf, Usup);
}


void Extrema_ExtPElC::Perform(const gp_Pnt&       P, 
			      const gp_Hypr&      C,
			      const Standard_Real Tol,
			      const Standard_Real Uinf,
			      const Standard_Real Usup)
/*-----------------------------------------------------------------------------
Function:
  Find values of parameter u so that:
   - dist(P,C(u)) passes by an extremum,
   - Uinf <= u <= Usup.

Method:
  Takes 2 steps:
  1- Projection of point P in the plane of the hyperbola,
  2- Calculation of solutions:
      Let Pp, le point projete; on recherche les valeurs u telles que:
       (C(u)-Pp).C'(u) = 0. (1)
      Let R and r be the radiuses of the hyperbola,
          Chu = Cosh(u) and Shu = Sinh(u),
          C(u) = (R*Chu,r*Shu) and Pp = (X,Y);
     Then, (1) <=> (R*Chu-X,r*Shu-Y).(R*Shu,r*Chu) = 0.
                    (R**2+r**2)*Chu*Shu - X*R*Shu - Y*r*Chu = 0. (2)
     Let v = e**u;
     Then, by using Chu = (e**u+e**(-u))/2. and Sh = (e**u-e**(-u)))/2.
            (2) <=> ((R**2+r**2)/4.) * (v**2-v**(-2)) -
	            ((X*R+Y*r)/2.) * v +
	            ((X*R-Y*r)/2.) * v**(-1) = 0.
      (2)* v**2	<=> ((R**2+r**2)/4.) * v**4 -
                     ((X*R+Y*r)/2.)  * v**3 +
		     ((X*R-Y*r)/2.)  * v    -
		    ((R**2+r**2)/4.)        = 0.
  Use algorithm math_DirectPolynomialRoots to solve this equation by v.
-----------------------------------------------------------------------------*/
{
  myDone = Standard_False;
  myNbExt = 0;

// 1- Projection of point P in the plane of hyperbola -> Pp ...

  gp_Pnt O = C.Location();
  gp_Vec Axe (C.Axis().Direction());
  gp_Vec Trsl = Axe.Multiplied(-(gp_Vec(O,P).Dot(Axe)));
  gp_Pnt Pp = P.Translated(Trsl);

// 2- Calculation of solutions ...

  Standard_Real Tol2 = Tol * Tol;
  Standard_Real R = C.MajorRadius();
  Standard_Real r = C.MinorRadius();
  gp_Vec OPp (O,Pp);
  Standard_Real X = OPp.Dot(gp_Vec(C.XAxis().Direction()));
  Standard_Real Y = OPp.Dot(gp_Vec(C.YAxis().Direction()));

  Standard_Real C1 = (R*R+r*r)/4.;
  math_DirectPolynomialRoots Sol(C1,-(X*R+Y*r)/2.,0.,(X*R-Y*r)/2.,-C1);
  if (!Sol.IsDone()) { return; }
  gp_Pnt Cu;
  Standard_Real Us, Vs;
  Standard_Integer NbSol = Sol.NbSolutions();
  Standard_Boolean DejaEnr;
  Standard_Integer NoExt;
  gp_Pnt TbExt[4];
  for (Standard_Integer NoSol = 1; NoSol <= NbSol; NoSol++) {
    Vs = Sol.Value(NoSol);
    if (Vs > 0.) {
      Us = Log(Vs);
      if ((Us >= Uinf) && (Us <= Usup)) {
	Cu = ElCLib::Value(Us,C);
	DejaEnr = Standard_False;
	for (NoExt = 0; NoExt < myNbExt; NoExt++) {
	  if (TbExt[NoExt].SquareDistance(Cu) < Tol2) {
	    DejaEnr = Standard_True;
	    break;
	  }
	}
	if (!DejaEnr) {
	  TbExt[myNbExt] = Cu;
	  mySqDist[myNbExt] = Cu.SquareDistance(P);
	  myIsMin[myNbExt] = mySqDist[myNbExt] < P.SquareDistance(ElCLib::Value(Us+1,C));
	  myPoint[myNbExt] = Extrema_POnCurv(Us,Cu);
	  myNbExt++;
	}
      } // if ((Us >= Uinf) && (Us <= Usup))
    } // if (Vs > 0.)
  } // for (Standard_Integer NoSol = 1; ...
  myDone = Standard_True;
}
//=============================================================================

Extrema_ExtPElC::Extrema_ExtPElC (const gp_Pnt&       P,
				  const gp_Parab&     C,
				  const Standard_Real Tol,
				  const Standard_Real Uinf,
				  const Standard_Real Usup)
{
  Perform(P, C, Tol, Uinf, Usup);
}


void Extrema_ExtPElC::Perform(const gp_Pnt&       P, 
			      const gp_Parab&     C,
//			      const Standard_Real Tol,
			      const Standard_Real ,
			      const Standard_Real Uinf,
			      const Standard_Real Usup)
/*-----------------------------------------------------------------------------
Function:
  Find values of parameter u so that:
   - dist(P,C(u)) pass by an extremum,
   - Uinf <= u <= Usup.

Method:
  Takes 2 steps:
  1- Projection of point P in the plane of the parabola,
  2- Calculation of solutions:
     Let Pp, the projected point; find values u so that:
       (C(u)-Pp).C'(u) = 0. (1)
     Let F the focus of the parabola,
          C(u) = ((u*u)/(4.*F),u) and Pp = (X,Y);
     Alors, (1) <=> ((u*u)/(4.*F)-X,u-Y).(u/(2.*F),1) = 0.
                    (1./(4.*F)) * U**3 + (2.*F-X) * U - 2*F*Y = 0.
    Use algorithm math_DirectPolynomialRoots to solve this equation by U.
-----------------------------------------------------------------------------*/
{
  myDone = Standard_False;
  myNbExt = 0;

// 1- Projection of point P in the plane of the parabola -> Pp ...

  gp_Pnt O = C.Location();
  gp_Vec Axe (C.Axis().Direction());
  gp_Vec Trsl = Axe.Multiplied(-(gp_Vec(O,P).Dot(Axe)));
  gp_Pnt Pp = P.Translated(Trsl);

// 2- Calculation of solutions ...

  Standard_Real F = C.Focal();
  gp_Vec OPp (O,Pp);
  Standard_Real X = OPp.Dot(gp_Vec(C.XAxis().Direction()));
//  Standard_Real Y = Sqrt(OPpMagn*OPpMagn-X*X);
  Standard_Real Y = OPp.Dot(gp_Vec(C.YAxis().Direction()));
  math_DirectPolynomialRoots Sol(1./(4.*F),0.,2.*F-X,-2.*F*Y);
  if (!Sol.IsDone()) { return; }
  gp_Pnt Cu;
  Standard_Real Us;
  Standard_Integer NbSol = Sol.NbSolutions();
  Standard_Boolean DejaEnr;
  Standard_Integer NoExt;
  gp_Pnt TbExt[3];
  for (Standard_Integer NoSol = 1; NoSol <= NbSol; NoSol++) {
    Us = Sol.Value(NoSol);
    if ((Us >= Uinf) && (Us <= Usup)) {
      Cu = ElCLib::Value(Us,C);
      DejaEnr = Standard_False;
      for (NoExt = 0; NoExt < myNbExt; NoExt++) {
    if (TbExt[NoExt].SquareDistance(Cu) < Precision::SquareConfusion()) {
	  DejaEnr = Standard_True;
	  break;
	}
      }
      if (!DejaEnr) {
	TbExt[myNbExt] = Cu;
	mySqDist[myNbExt] = Cu.SquareDistance(P);
	myIsMin[myNbExt] = mySqDist[myNbExt] < P.SquareDistance(ElCLib::Value(Us+1,C));
	myPoint[myNbExt] = Extrema_POnCurv(Us,Cu);
	myNbExt++;
      }
    } // if ((Us >= Uinf) && (Us <= Usup))
  } // for (Standard_Integer NoSol = 1; ...
  myDone = Standard_True;
}
//=============================================================================

Standard_Boolean Extrema_ExtPElC::IsDone () const { return myDone; }
//=============================================================================

Standard_Integer Extrema_ExtPElC::NbExt () const
{
  if (!IsDone()) { StdFail_NotDone::Raise(); }
  return myNbExt;
}
//=============================================================================

Standard_Real Extrema_ExtPElC::SquareDistance (const Standard_Integer N) const
{
  if ((N < 1) || (N > NbExt())) { Standard_OutOfRange::Raise(); }
  return mySqDist[N-1];
}
//=============================================================================

Standard_Boolean Extrema_ExtPElC::IsMin (const Standard_Integer N) const
{
  if ((N < 1) || (N > NbExt())) { Standard_OutOfRange::Raise(); }
  return myIsMin[N-1];
}
//=============================================================================

Extrema_POnCurv Extrema_ExtPElC::Point (const Standard_Integer N) const
{
  if ((N < 1) || (N > NbExt())) { Standard_OutOfRange::Raise(); }
  return myPoint[N-1];
}
//=============================================================================
Commit	Line	Data
b311480e	1	// Copyright (c) 1995-1999 Matra Datavision
	2	// Copyright (c) 1999-2012 OPEN CASCADE SAS
	3	//
	4	// The content of this file is subject to the Open CASCADE Technology Public
	5	// License Version 6.5 (the "License"). You may not use the content of this file
	6	// except in compliance with the License. Please obtain a copy of the License
	7	// at http://www.opencascade.org and read it completely before using this file.
	8	//
	9	// The Initial Developer of the Original Code is Open CASCADE S.A.S., having its
	10	// main offices at: 1, place des Freres Montgolfier, 78280 Guyancourt, France.
	11	//
	12	// The Original Code and all software distributed under the License is
	13	// distributed on an "AS IS" basis, without warranty of any kind, and the
	14	// Initial Developer hereby disclaims all such warranties, including without
	15	// limitation, any warranties of merchantability, fitness for a particular
	16	// purpose or non-infringement. Please see the License for the specific terms
	17	// and conditions governing the rights and limitations under the License.
	18
7fd59977	19	#include <Extrema_ExtPElC.ixx>
	20	#include <StdFail_NotDone.hxx>
	21	#include <math_DirectPolynomialRoots.hxx>
	22	#include <math_TrigonometricFunctionRoots.hxx>
	23	#include <ElCLib.hxx>
	24	#include <Standard_OutOfRange.hxx>
	25	#include <Standard_NotImplemented.hxx>
	26	#include <Precision.hxx>
	27
	28
	29	//=============================================================================
	30
	31	Extrema_ExtPElC::Extrema_ExtPElC () { myDone = Standard_False; }
	32	//=============================================================================
	33
	34	Extrema_ExtPElC::Extrema_ExtPElC (const gp_Pnt& P,
	35	const gp_Lin& L,
	36	const Standard_Real Tol,
	37	const Standard_Real Uinf,
	38	const Standard_Real Usup)
	39	{
	40	Perform(P, L, Tol, Uinf, Usup);
	41	}
	42
	43	void Extrema_ExtPElC::Perform(const gp_Pnt& P,
	44	const gp_Lin& L,
	45	const Standard_Real Tol,
	46	const Standard_Real Uinf,
	47	const Standard_Real Usup)
	48	{
	49	myDone = Standard_False;
	50	myNbExt = 0;
	51	gp_Vec V1 = gp_Vec(L.Direction());
	52	gp_Pnt OR = L.Location();
	53	gp_Vec V(OR, P);
	54	Standard_Real Mydist = V1.Dot(V);
	55	if ((Mydist >= Uinf-Tol) &&
	56	(Mydist <= Usup+Tol)){
	57
	58	gp_Pnt MyP = OR.Translated(Mydist*V1);
	59	Extrema_POnCurv MyPOnCurve(Mydist, MyP);
	60	mySqDist[0] = P.SquareDistance(MyP);
	61	myPoint[0] = MyPOnCurve;
	62	myIsMin[0] = Standard_True;
	63	myNbExt = 1;
	64	myDone = Standard_True;
	65	}
	66
	67	}
	68
	69
	70
	71	Extrema_ExtPElC::Extrema_ExtPElC (const gp_Pnt& P,
	72	const gp_Circ& C,
	73	const Standard_Real Tol,
	74	const Standard_Real Uinf,
	75	const Standard_Real Usup)
	76	{
	77	Perform(P, C, Tol, Uinf, Usup);
	78	}
	79
	80	void Extrema_ExtPElC::Perform(const gp_Pnt& P,
	81	const gp_Circ& C,
	82	const Standard_Real Tol,
83	const Standard_Real Uinf,
84	const Standard_Real Usup)
85	/*-----------------------------------------------------------------------------
0d969553 Y	86	Function:
	87	Find values of parameter u such as:
	88	- dist(P,C(u)) pass by an extrema,
7fd59977	89	- Uinf <= u <= Usup.
7fd59977	90
0d969553 Y	91	Method:
	92	Pass 3 stages:
	93	1- Projection of point P in the plane of the circle,
c6541a0c	94	2- Calculation of u solutions in [0.,2.*M_PI]:
0d969553 Y	95	Let Pp, the projected point and
	96	O, the center of the circle;
	97	2 cases:
	98	- if Pp is mixed with 0, there is an infinite number of solutions;
7fd59977	99	IsDone() renvoie Standard_False.
0d969553 Y	100	- otherwise, 2 points are solutions for the complete circle:
0d969553 Y	101	. Us1 = angle(OPp,OX) corresponds to the minimum,
c6541a0c D	102	. let Us2 = ( Us1 + M_PI if Us1 < M_PI,
c6541a0c D	103	( Us1 - M_PI otherwise;
0d969553 Y	104	Us2 corresponds to the maximum.
0d969553 Y	105	3- Calculate the extrema in [Uinf,Usup].
7fd59977	106	-----------------------------------------------------------------------------*/
	107	{
	108	myDone = Standard_False;
	109	myNbExt = 0;
	110
0d969553	111	// 1- Projection of the point P in the plane of circle -> Pp ...
7fd59977	112
	113	gp_Pnt O = C.Location();
	114	gp_Vec Axe (C.Axis().Direction());
	115	gp_Vec Trsl = Axe.Multiplied(-(gp_Vec(O,P).Dot(Axe)));
	116	gp_Pnt Pp = P.Translated(Trsl);
	117
0d969553	118	// 2- Calculate u solutions in [0.,2.*PI] ...
7fd59977	119
	120	gp_Vec OPp (O,Pp);
	121	if (OPp.Magnitude() < Tol) { return; }
	122	Standard_Real Usol[2];
c6541a0c D	123	Usol[0] = C.XAxis().Direction().AngleWithRef(OPp,Axe); // -M_PI<U1<M_PI
c6541a0c D	124	Usol[1] = Usol[0] + M_PI;
7fd59977	125
	126	Standard_Real myuinf = Uinf;
	127	//modified by NIZNHY-PKV Fri Apr 20 15:03:28 2001 f
	128	//Standard_Real TolU = Tol*C.Radius();
	129	Standard_Real TolU, aR;
	130	aR=C.Radius();
	131	TolU=Precision::Infinite();
	132	if (aR > gp::Resolution()) {
	133	TolU= Tol/aR;
	134	}
	135	//modified by NIZNHY-PKV Fri Apr 20 15:03:32 2001 t
c6541a0c D	136	ElCLib::AdjustPeriodic(Uinf, Uinf+2*M_PI, TolU, myuinf, Usol[0]);
	137	ElCLib::AdjustPeriodic(Uinf, Uinf+2*M_PI, TolU, myuinf, Usol[1]);
	138	if (((Usol[0]-2M_PI-Uinf) < TolU) && ((Usol[0]-2M_PI-Uinf) > -TolU)) Usol[0] = Uinf;
	139	if (((Usol[1]-2M_PI-Uinf) < TolU) && ((Usol[1]-2M_PI-Uinf) > -TolU)) Usol[1] = Uinf;
7fd59977	140
7fd59977	141
0d969553	142	// 3- Calculate extrema in [Umin,Umax] ...
7fd59977	143
	144	gp_Pnt Cu;
	145	Standard_Real Us;
	146	for (Standard_Integer NoSol = 0; NoSol <= 1; NoSol++) {
	147	Us = Usol[NoSol];
	148	if (((Uinf-Us) < TolU) && ((Us-Usup) < TolU)) {
	149	Cu = ElCLib::Value(Us,C);
	150	mySqDist[myNbExt] = Cu.SquareDistance(P);
	151	myIsMin[myNbExt] = (NoSol == 0);
	152	myPoint[myNbExt] = Extrema_POnCurv(Us,Cu);
	153	myNbExt++;
	154	}
	155	}
	156	myDone = Standard_True;
	157	}
	158	//=============================================================================
	159
	160	Extrema_ExtPElC::Extrema_ExtPElC (const gp_Pnt& P,
	161	const gp_Elips& C,
	162	const Standard_Real Tol,
	163	const Standard_Real Uinf,
	164	const Standard_Real Usup)
	165	{
	166	Perform(P, C, Tol, Uinf, Usup);
	167	}
	168
	169
	170
	171	void Extrema_ExtPElC::Perform (const gp_Pnt& P,
	172	const gp_Elips& C,
	173	const Standard_Real Tol,
	174	const Standard_Real Uinf,
	175	const Standard_Real Usup)
	176	/*-----------------------------------------------------------------------------
0d969553 Y	177	Function:
	178	Find values of parameter u so that:
	179	- dist(P,C(u)) passes by an extremum,
7fd59977	180	- Uinf <= u <= Usup.
7fd59977	181
0d969553 Y	182	Method:
	183	Takes 2 steps:
	184	1- Projection of point P in the plane of the ellipse,
	185	2- Calculation of the solutions:
	186	Let Pp, the projected point; find values u so that:
7fd59977	187	(C(u)-Pp).C'(u) = 0. (1)
0d969553 Y	188	Let Cos = cos(u) and Sin = sin(u),
	189	C(u) = (ACos,BSin) and Pp = (X,Y);
	190	Then, (1) <=> (ACos-X,BSin-Y).(-ASin,BCos) = 0.
7fd59977	191	(B2-A2)CosSin - BYCos + AXSin = 0.
0d969553	192	Use algorithm math_TrigonometricFunctionRoots to solve this equation.
7fd59977	193	-----------------------------------------------------------------------------*/
	194	{
	195	myDone = Standard_False;
	196	myNbExt = 0;
	197
0d969553	198	// 1- Projection of point P in the plane of the ellipse -> Pp ...
7fd59977	199
	200	gp_Pnt O = C.Location();
	201	gp_Vec Axe (C.Axis().Direction());
	202	gp_Vec Trsl = Axe.Multiplied(-(gp_Vec(O,P).Dot(Axe)));
	203	gp_Pnt Pp = P.Translated(Trsl);
	204
0d969553	205	// 2- Calculation of solutions ...
7fd59977	206
	207	Standard_Integer NoSol, NbSol;
	208	Standard_Real A = C.MajorRadius();
	209	Standard_Real B = C.MinorRadius();
	210	gp_Vec OPp (O,Pp);
	211	Standard_Real OPpMagn = OPp.Magnitude();
	212	if (OPpMagn < Tol) { if (Abs(A-B) < Tol) { return; } }
	213	Standard_Real X = OPp.Dot(gp_Vec(C.XAxis().Direction()));
	214	Standard_Real Y = OPp.Dot(gp_Vec(C.YAxis().Direction()));
	215	// Standard_Real Y = Sqrt(OPpMagnOPpMagn-XX);
	216
	217	Standard_Real ko2 = (BB-AA)/2., ko3 = -BY, ko4 = AX;
	218	if(Abs(ko3) < 1.e-16*Max(Abs(ko2), Abs(ko3))) ko3 = 0.0;
	219
	220	// math_TrigonometricFunctionRoots Sol(0.,(BB-AA)/2.,-BY,AX,0.,Uinf,Usup);
	221	math_TrigonometricFunctionRoots Sol(0.,ko2, ko3, ko4, 0.,Uinf,Usup);
	222
	223	if (!Sol.IsDone()) { return; }
	224	gp_Pnt Cu;
	225	Standard_Real Us;
	226	NbSol = Sol.NbSolutions();
	227	for (NoSol = 1; NoSol <= NbSol; NoSol++) {
	228	Us = Sol.Value(NoSol);
	229	Cu = ElCLib::Value(Us,C);
	230	mySqDist[myNbExt] = Cu.SquareDistance(P);
	231	myIsMin[myNbExt] = (NoSol == 1);
	232	myPoint[myNbExt] = Extrema_POnCurv(Us,Cu);
	233	myNbExt++;
	234	}
	235	myDone = Standard_True;
	236	}
	237	//=============================================================================
	238
	239	Extrema_ExtPElC::Extrema_ExtPElC (const gp_Pnt& P,
	240	const gp_Hypr& C,
	241	const Standard_Real Tol,
	242	const Standard_Real Uinf,
	243	const Standard_Real Usup)
	244	{
	245	Perform(P, C, Tol, Uinf, Usup);
	246	}
	247
	248
	249	void Extrema_ExtPElC::Perform(const gp_Pnt& P,
	250	const gp_Hypr& C,
	251	const Standard_Real Tol,
	252	const Standard_Real Uinf,
	253	const Standard_Real Usup)
	254	/*-----------------------------------------------------------------------------
0d969553 Y	255	Function:
	256	Find values of parameter u so that:
	257	- dist(P,C(u)) passes by an extremum,
7fd59977	258	- Uinf <= u <= Usup.
7fd59977	259
0d969553 Y	260	Method:
	261	Takes 2 steps:
	262	1- Projection of point P in the plane of the hyperbola,
	263	2- Calculation of solutions:
	264	Let Pp, le point projete; on recherche les valeurs u telles que:
7fd59977	265	(C(u)-Pp).C'(u) = 0. (1)
0d969553 Y	266	Let R and r be the radiuses of the hyperbola,
	267	Chu = Cosh(u) and Shu = Sinh(u),
	268	C(u) = (RChu,rShu) and Pp = (X,Y);
	269	Then, (1) <=> (RChu-X,rShu-Y).(RShu,rChu) = 0.
7fd59977	270	(R2+r2)ChuShu - XRShu - YrChu = 0. (2)
0d969553 Y	271	Let v = e**u;
0d969553 Y	272	Then, by using Chu = (eu+e(-u))/2. and Sh = (eu-e(-u)))/2.
7fd59977	273	(2) <=> ((R2+r2)/4.) * (v2-v(-2)) -
	274	((XR+Yr)/2.) * v +
	275	((XR-Yr)/2.) * v**(-1) = 0.
	276	(2)* v2 <=> ((R2+r*2)/4.) v**4 -
	277	((XR+Yr)/2.) * v**3 +
	278	((XR-Yr)/2.) * v -
	279	((R2+r2)/4.) = 0.
0d969553	280	Use algorithm math_DirectPolynomialRoots to solve this equation by v.
7fd59977	281	-----------------------------------------------------------------------------*/
	282	{
	283	myDone = Standard_False;
	284	myNbExt = 0;
	285
0d969553	286	// 1- Projection of point P in the plane of hyperbola -> Pp ...
7fd59977	287
	288	gp_Pnt O = C.Location();
	289	gp_Vec Axe (C.Axis().Direction());
	290	gp_Vec Trsl = Axe.Multiplied(-(gp_Vec(O,P).Dot(Axe)));
	291	gp_Pnt Pp = P.Translated(Trsl);
	292
0d969553	293	// 2- Calculation of solutions ...
7fd59977	294
	295	Standard_Real Tol2 = Tol * Tol;
	296	Standard_Real R = C.MajorRadius();
	297	Standard_Real r = C.MinorRadius();
	298	gp_Vec OPp (O,Pp);
7fd59977	299	Standard_Real X = OPp.Dot(gp_Vec(C.XAxis().Direction()));
	300	Standard_Real Y = OPp.Dot(gp_Vec(C.YAxis().Direction()));
	301
	302	Standard_Real C1 = (RR+rr)/4.;
	303	math_DirectPolynomialRoots Sol(C1,-(XR+Yr)/2.,0.,(XR-Yr)/2.,-C1);
	304	if (!Sol.IsDone()) { return; }
	305	gp_Pnt Cu;
	306	Standard_Real Us, Vs;
	307	Standard_Integer NbSol = Sol.NbSolutions();
	308	Standard_Boolean DejaEnr;
	309	Standard_Integer NoExt;
	310	gp_Pnt TbExt[4];
	311	for (Standard_Integer NoSol = 1; NoSol <= NbSol; NoSol++) {
	312	Vs = Sol.Value(NoSol);
	313	if (Vs > 0.) {
	314	Us = Log(Vs);
	315	if ((Us >= Uinf) && (Us <= Usup)) {
	316	Cu = ElCLib::Value(Us,C);
	317	DejaEnr = Standard_False;
	318	for (NoExt = 0; NoExt < myNbExt; NoExt++) {
	319	if (TbExt[NoExt].SquareDistance(Cu) < Tol2) {
	320	DejaEnr = Standard_True;
	321	break;
	322	}
	323	}
	324	if (!DejaEnr) {
	325	TbExt[myNbExt] = Cu;
	326	mySqDist[myNbExt] = Cu.SquareDistance(P);
	327	myIsMin[myNbExt] = mySqDist[myNbExt] < P.SquareDistance(ElCLib::Value(Us+1,C));
	328	myPoint[myNbExt] = Extrema_POnCurv(Us,Cu);
	329	myNbExt++;
	330	}
	331	} // if ((Us >= Uinf) && (Us <= Usup))
	332	} // if (Vs > 0.)
	333	} // for (Standard_Integer NoSol = 1; ...
	334	myDone = Standard_True;
	335	}
	336	//=============================================================================
	337
	338	Extrema_ExtPElC::Extrema_ExtPElC (const gp_Pnt& P,
	339	const gp_Parab& C,
	340	const Standard_Real Tol,
	341	const Standard_Real Uinf,
	342	const Standard_Real Usup)
	343	{
	344	Perform(P, C, Tol, Uinf, Usup);
	345	}
	346
	347
	348	void Extrema_ExtPElC::Perform(const gp_Pnt& P,
	349	const gp_Parab& C,
	350	// const Standard_Real Tol,
	351	const Standard_Real ,
	352	const Standard_Real Uinf,
	353	const Standard_Real Usup)
	354	/*-----------------------------------------------------------------------------
0d969553 Y	355	Function:
	356	Find values of parameter u so that:
	357	- dist(P,C(u)) pass by an extremum,
7fd59977	358	- Uinf <= u <= Usup.
7fd59977	359
0d969553 Y	360	Method:
	361	Takes 2 steps:
	362	1- Projection of point P in the plane of the parabola,
	363	2- Calculation of solutions:
	364	Let Pp, the projected point; find values u so that:
7fd59977	365	(C(u)-Pp).C'(u) = 0. (1)
0d969553 Y	366	Let F the focus of the parabola,
0d969553 Y	367	C(u) = ((uu)/(4.F),u) and Pp = (X,Y);
7fd59977	368	Alors, (1) <=> ((uu)/(4.F)-X,u-Y).(u/(2.*F),1) = 0.
7fd59977	369	(1./(4.F)) U*3 + (2.F-X) * U - 2FY = 0.
0d969553	370	Use algorithm math_DirectPolynomialRoots to solve this equation by U.
7fd59977	371	-----------------------------------------------------------------------------*/
	372	{
	373	myDone = Standard_False;
	374	myNbExt = 0;
	375
0d969553	376	// 1- Projection of point P in the plane of the parabola -> Pp ...
7fd59977	377
	378	gp_Pnt O = C.Location();
	379	gp_Vec Axe (C.Axis().Direction());
	380	gp_Vec Trsl = Axe.Multiplied(-(gp_Vec(O,P).Dot(Axe)));
	381	gp_Pnt Pp = P.Translated(Trsl);
	382
0d969553	383	// 2- Calculation of solutions ...
7fd59977	384
	385	Standard_Real F = C.Focal();
	386	gp_Vec OPp (O,Pp);
7fd59977	387	Standard_Real X = OPp.Dot(gp_Vec(C.XAxis().Direction()));
	388	// Standard_Real Y = Sqrt(OPpMagnOPpMagn-XX);
	389	Standard_Real Y = OPp.Dot(gp_Vec(C.YAxis().Direction()));
	390	math_DirectPolynomialRoots Sol(1./(4.F),0.,2.F-X,-2.FY);
	391	if (!Sol.IsDone()) { return; }
	392	gp_Pnt Cu;
	393	Standard_Real Us;
	394	Standard_Integer NbSol = Sol.NbSolutions();
	395	Standard_Boolean DejaEnr;
	396	Standard_Integer NoExt;
	397	gp_Pnt TbExt[3];
	398	for (Standard_Integer NoSol = 1; NoSol <= NbSol; NoSol++) {
	399	Us = Sol.Value(NoSol);
	400	if ((Us >= Uinf) && (Us <= Usup)) {
	401	Cu = ElCLib::Value(Us,C);
	402	DejaEnr = Standard_False;
	403	for (NoExt = 0; NoExt < myNbExt; NoExt++) {
08cd2f6b	404	if (TbExt[NoExt].SquareDistance(Cu) < Precision::SquareConfusion()) {
7fd59977	405	DejaEnr = Standard_True;
	406	break;
	407	}
	408	}
	409	if (!DejaEnr) {
	410	TbExt[myNbExt] = Cu;
	411	mySqDist[myNbExt] = Cu.SquareDistance(P);
	412	myIsMin[myNbExt] = mySqDist[myNbExt] < P.SquareDistance(ElCLib::Value(Us+1,C));
	413	myPoint[myNbExt] = Extrema_POnCurv(Us,Cu);
	414	myNbExt++;
	415	}
	416	} // if ((Us >= Uinf) && (Us <= Usup))
	417	} // for (Standard_Integer NoSol = 1; ...
	418	myDone = Standard_True;
	419	}
	420	//=============================================================================
	421
	422	Standard_Boolean Extrema_ExtPElC::IsDone () const { return myDone; }
	423	//=============================================================================
	424
	425	Standard_Integer Extrema_ExtPElC::NbExt () const
	426	{
	427	if (!IsDone()) { StdFail_NotDone::Raise(); }
	428	return myNbExt;
	429	}
	430	//=============================================================================
	431
	432	Standard_Real Extrema_ExtPElC::SquareDistance (const Standard_Integer N) const
	433	{
	434	if ((N < 1) \|\| (N > NbExt())) { Standard_OutOfRange::Raise(); }
	435	return mySqDist[N-1];
	436	}
	437	//=============================================================================
	438
	439	Standard_Boolean Extrema_ExtPElC::IsMin (const Standard_Integer N) const
	440	{
	441	if ((N < 1) \|\| (N > NbExt())) { Standard_OutOfRange::Raise(); }
	442	return myIsMin[N-1];
	443	}
	444	//=============================================================================
	445
	446	Extrema_POnCurv Extrema_ExtPElC::Point (const Standard_Integer N) const
	447	{
	448	if ((N < 1) \|\| (N > NbExt())) { Standard_OutOfRange::Raise(); }
	449	return myPoint[N-1];
	450	}
	451	//=============================================================================