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

// Copyright (c) 1995-1999 Matra Datavision
// Copyright (c) 1999-2014 OPEN CASCADE SAS
//
// This file is part of Open CASCADE Technology software library.
//
// This library is free software; you can redistribute it and / or modify it
// under the terms of the GNU Lesser General Public version 2.1 as published
// by the Free Software Foundation, with special exception defined in the file
// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
// distribution for complete text of the license and disclaimer of any warranty.
//
// Alternatively, this file may be used under the terms of Open CASCADE
// commercial license or contractual agreement.

#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>

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

//=======================================================================
//function : Extrema_ExtPElC
//purpose  : 
//=======================================================================
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);
}
//=======================================================================
//function : Perform
//purpose  : 
//=======================================================================
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 (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;
  //Standard_Real TolU = Tol*C.Radius();
  Standard_Real TolU, aR;
  aR=C.Radius();
  TolU=Precision::Infinite();
  if (aR > gp::Resolution()) {
    TolU= Tol/aR;
  }
  //
  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);
    myPoint[myNbExt] = Extrema_POnCurv(Us,Cu);
    Cu = ElCLib::Value(Us + 0.1, C);
    myIsMin[myNbExt] = mySqDist[myNbExt] < Cu.SquareDistance(P);
    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];
}
//=============================================================================

const 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
973c2be1	2	// Copyright (c) 1999-2014 OPEN CASCADE SAS
b311480e	3	//
973c2be1	4	// This file is part of Open CASCADE Technology software library.
b311480e	5	//
973c2be1	6	// This library is free software; you can redistribute it and / or modify it
	7	// under the terms of the GNU Lesser General Public version 2.1 as published
	8	// by the Free Software Foundation, with special exception defined in the file
	9	// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
	10	// distribution for complete text of the license and disclaimer of any warranty.
b311480e	11	//
973c2be1	12	// Alternatively, this file may be used under the terms of Open CASCADE
973c2be1	13	// commercial license or contractual agreement.
b311480e	14
7fd59977	15	#include <Extrema_ExtPElC.ixx>
	16	#include <StdFail_NotDone.hxx>
	17	#include <math_DirectPolynomialRoots.hxx>
	18	#include <math_TrigonometricFunctionRoots.hxx>
	19	#include <ElCLib.hxx>
	20	#include <Standard_OutOfRange.hxx>
	21	#include <Standard_NotImplemented.hxx>
	22	#include <Precision.hxx>
	23
42ff8f5b	24	//=======================================================================
	25	//function : Extrema_ExtPElC
	26	//purpose :
	27	//=======================================================================
7fd59977	28	Extrema_ExtPElC::Extrema_ExtPElC () { myDone = Standard_False; }
7fd59977	29
42ff8f5b	30	//=======================================================================
	31	//function : Extrema_ExtPElC
	32	//purpose :
	33	//=======================================================================
7fd59977	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	}
42ff8f5b	42	//=======================================================================
	43	//function : Perform
	44	//purpose :
	45	//=======================================================================
7fd59977	46	void Extrema_ExtPElC::Perform(const gp_Pnt& P,
	47	const gp_Lin& L,
	48	const Standard_Real Tol,
	49	const Standard_Real Uinf,
	50	const Standard_Real Usup)
	51	{
	52	myDone = Standard_False;
	53	myNbExt = 0;
42ff8f5b	54	gp_Vec V1 (L.Direction());
7fd59977	55	gp_Pnt OR = L.Location();
	56	gp_Vec V(OR, P);
	57	Standard_Real Mydist = V1.Dot(V);
	58	if ((Mydist >= Uinf-Tol) &&
	59	(Mydist <= Usup+Tol)){
	60
	61	gp_Pnt MyP = OR.Translated(Mydist*V1);
	62	Extrema_POnCurv MyPOnCurve(Mydist, MyP);
	63	mySqDist[0] = P.SquareDistance(MyP);
	64	myPoint[0] = MyPOnCurve;
	65	myIsMin[0] = Standard_True;
	66	myNbExt = 1;
	67	myDone = Standard_True;
	68	}
	69
	70	}
	71
	72
	73
	74	Extrema_ExtPElC::Extrema_ExtPElC (const gp_Pnt& P,
	75	const gp_Circ& C,
	76	const Standard_Real Tol,
	77	const Standard_Real Uinf,
	78	const Standard_Real Usup)
	79	{
	80	Perform(P, C, Tol, Uinf, Usup);
	81	}
	82
	83	void Extrema_ExtPElC::Perform(const gp_Pnt& P,
	84	const gp_Circ& C,
	85	const Standard_Real Tol,
	86	const Standard_Real Uinf,
	87	const Standard_Real Usup)
	88	/*-----------------------------------------------------------------------------
0d969553 Y	89	Function:
	90	Find values of parameter u such as:
	91	- dist(P,C(u)) pass by an extrema,
7fd59977	92	- Uinf <= u <= Usup.
7fd59977	93
0d969553 Y	94	Method:
	95	Pass 3 stages:
	96	1- Projection of point P in the plane of the circle,
c6541a0c	97	2- Calculation of u solutions in [0.,2.*M_PI]:
0d969553 Y	98	Let Pp, the projected point and
	99	O, the center of the circle;
	100	2 cases:
	101	- if Pp is mixed with 0, there is an infinite number of solutions;
7fd59977	102	IsDone() renvoie Standard_False.
0d969553 Y	103	- otherwise, 2 points are solutions for the complete circle:
0d969553 Y	104	. Us1 = angle(OPp,OX) corresponds to the minimum,
c6541a0c D	105	. let Us2 = ( Us1 + M_PI if Us1 < M_PI,
c6541a0c D	106	( Us1 - M_PI otherwise;
0d969553 Y	107	Us2 corresponds to the maximum.
0d969553 Y	108	3- Calculate the extrema in [Uinf,Usup].
7fd59977	109	-----------------------------------------------------------------------------*/
	110	{
	111	myDone = Standard_False;
	112	myNbExt = 0;
	113
0d969553	114	// 1- Projection of the point P in the plane of circle -> Pp ...
7fd59977	115
	116	gp_Pnt O = C.Location();
	117	gp_Vec Axe (C.Axis().Direction());
	118	gp_Vec Trsl = Axe.Multiplied(-(gp_Vec(O,P).Dot(Axe)));
	119	gp_Pnt Pp = P.Translated(Trsl);
	120
0d969553	121	// 2- Calculate u solutions in [0.,2.*PI] ...
7fd59977	122
	123	gp_Vec OPp (O,Pp);
	124	if (OPp.Magnitude() < Tol) { return; }
	125	Standard_Real Usol[2];
c6541a0c D	126	Usol[0] = C.XAxis().Direction().AngleWithRef(OPp,Axe); // -M_PI<U1<M_PI
c6541a0c D	127	Usol[1] = Usol[0] + M_PI;
7fd59977	128
7fd59977	129	Standard_Real myuinf = Uinf;
7fd59977	130	//Standard_Real TolU = Tol*C.Radius();
	131	Standard_Real TolU, aR;
	132	aR=C.Radius();
	133	TolU=Precision::Infinite();
	134	if (aR > gp::Resolution()) {
	135	TolU= Tol/aR;
	136	}
42ff8f5b	137	//
c6541a0c D	138	ElCLib::AdjustPeriodic(Uinf, Uinf+2*M_PI, TolU, myuinf, Usol[0]);
	139	ElCLib::AdjustPeriodic(Uinf, Uinf+2*M_PI, TolU, myuinf, Usol[1]);
	140	if (((Usol[0]-2M_PI-Uinf) < TolU) && ((Usol[0]-2M_PI-Uinf) > -TolU)) Usol[0] = Uinf;
	141	if (((Usol[1]-2M_PI-Uinf) < TolU) && ((Usol[1]-2M_PI-Uinf) > -TolU)) Usol[1] = Uinf;
7fd59977	142
7fd59977	143
0d969553	144	// 3- Calculate extrema in [Umin,Umax] ...
7fd59977	145
	146	gp_Pnt Cu;
	147	Standard_Real Us;
	148	for (Standard_Integer NoSol = 0; NoSol <= 1; NoSol++) {
	149	Us = Usol[NoSol];
	150	if (((Uinf-Us) < TolU) && ((Us-Usup) < TolU)) {
	151	Cu = ElCLib::Value(Us,C);
	152	mySqDist[myNbExt] = Cu.SquareDistance(P);
	153	myIsMin[myNbExt] = (NoSol == 0);
	154	myPoint[myNbExt] = Extrema_POnCurv(Us,Cu);
	155	myNbExt++;
	156	}
	157	}
	158	myDone = Standard_True;
	159	}
	160	//=============================================================================
	161
	162	Extrema_ExtPElC::Extrema_ExtPElC (const gp_Pnt& P,
	163	const gp_Elips& C,
	164	const Standard_Real Tol,
	165	const Standard_Real Uinf,
	166	const Standard_Real Usup)
	167	{
	168	Perform(P, C, Tol, Uinf, Usup);
	169	}
	170
	171
	172
	173	void Extrema_ExtPElC::Perform (const gp_Pnt& P,
	174	const gp_Elips& C,
	175	const Standard_Real Tol,
	176	const Standard_Real Uinf,
	177	const Standard_Real Usup)
	178	/*-----------------------------------------------------------------------------
0d969553 Y	179	Function:
	180	Find values of parameter u so that:
	181	- dist(P,C(u)) passes by an extremum,
7fd59977	182	- Uinf <= u <= Usup.
7fd59977	183
0d969553 Y	184	Method:
	185	Takes 2 steps:
	186	1- Projection of point P in the plane of the ellipse,
	187	2- Calculation of the solutions:
	188	Let Pp, the projected point; find values u so that:
7fd59977	189	(C(u)-Pp).C'(u) = 0. (1)
0d969553 Y	190	Let Cos = cos(u) and Sin = sin(u),
	191	C(u) = (ACos,BSin) and Pp = (X,Y);
	192	Then, (1) <=> (ACos-X,BSin-Y).(-ASin,BCos) = 0.
7fd59977	193	(B2-A2)CosSin - BYCos + AXSin = 0.
0d969553	194	Use algorithm math_TrigonometricFunctionRoots to solve this equation.
7fd59977	195	-----------------------------------------------------------------------------*/
	196	{
	197	myDone = Standard_False;
	198	myNbExt = 0;
	199
0d969553	200	// 1- Projection of point P in the plane of the ellipse -> Pp ...
7fd59977	201
	202	gp_Pnt O = C.Location();
	203	gp_Vec Axe (C.Axis().Direction());
	204	gp_Vec Trsl = Axe.Multiplied(-(gp_Vec(O,P).Dot(Axe)));
	205	gp_Pnt Pp = P.Translated(Trsl);
	206
0d969553	207	// 2- Calculation of solutions ...
7fd59977	208
	209	Standard_Integer NoSol, NbSol;
	210	Standard_Real A = C.MajorRadius();
	211	Standard_Real B = C.MinorRadius();
	212	gp_Vec OPp (O,Pp);
	213	Standard_Real OPpMagn = OPp.Magnitude();
	214	if (OPpMagn < Tol) { if (Abs(A-B) < Tol) { return; } }
	215	Standard_Real X = OPp.Dot(gp_Vec(C.XAxis().Direction()));
	216	Standard_Real Y = OPp.Dot(gp_Vec(C.YAxis().Direction()));
	217	// Standard_Real Y = Sqrt(OPpMagnOPpMagn-XX);
	218
	219	Standard_Real ko2 = (BB-AA)/2., ko3 = -BY, ko4 = AX;
	220	if(Abs(ko3) < 1.e-16*Max(Abs(ko2), Abs(ko3))) ko3 = 0.0;
	221
	222	// math_TrigonometricFunctionRoots Sol(0.,(BB-AA)/2.,-BY,AX,0.,Uinf,Usup);
	223	math_TrigonometricFunctionRoots Sol(0.,ko2, ko3, ko4, 0.,Uinf,Usup);
	224
	225	if (!Sol.IsDone()) { return; }
	226	gp_Pnt Cu;
	227	Standard_Real Us;
	228	NbSol = Sol.NbSolutions();
	229	for (NoSol = 1; NoSol <= NbSol; NoSol++) {
	230	Us = Sol.Value(NoSol);
	231	Cu = ElCLib::Value(Us,C);
	232	mySqDist[myNbExt] = Cu.SquareDistance(P);
7fd59977	233	myPoint[myNbExt] = Extrema_POnCurv(Us,Cu);
a20400b3	234	Cu = ElCLib::Value(Us + 0.1, C);
a20400b3	235	myIsMin[myNbExt] = mySqDist[myNbExt] < Cu.SquareDistance(P);
7fd59977	236	myNbExt++;
	237	}
	238	myDone = Standard_True;
	239	}
	240	//=============================================================================
	241
	242	Extrema_ExtPElC::Extrema_ExtPElC (const gp_Pnt& P,
	243	const gp_Hypr& C,
	244	const Standard_Real Tol,
	245	const Standard_Real Uinf,
	246	const Standard_Real Usup)
	247	{
	248	Perform(P, C, Tol, Uinf, Usup);
	249	}
	250
	251
	252	void Extrema_ExtPElC::Perform(const gp_Pnt& P,
	253	const gp_Hypr& C,
	254	const Standard_Real Tol,
	255	const Standard_Real Uinf,
	256	const Standard_Real Usup)
	257	/*-----------------------------------------------------------------------------
0d969553 Y	258	Function:
	259	Find values of parameter u so that:
	260	- dist(P,C(u)) passes by an extremum,
7fd59977	261	- Uinf <= u <= Usup.
7fd59977	262
0d969553 Y	263	Method:
	264	Takes 2 steps:
	265	1- Projection of point P in the plane of the hyperbola,
	266	2- Calculation of solutions:
	267	Let Pp, le point projete; on recherche les valeurs u telles que:
7fd59977	268	(C(u)-Pp).C'(u) = 0. (1)
0d969553 Y	269	Let R and r be the radiuses of the hyperbola,
	270	Chu = Cosh(u) and Shu = Sinh(u),
	271	C(u) = (RChu,rShu) and Pp = (X,Y);
	272	Then, (1) <=> (RChu-X,rShu-Y).(RShu,rChu) = 0.
7fd59977	273	(R2+r2)ChuShu - XRShu - YrChu = 0. (2)
0d969553 Y	274	Let v = e**u;
0d969553 Y	275	Then, by using Chu = (eu+e(-u))/2. and Sh = (eu-e(-u)))/2.
7fd59977	276	(2) <=> ((R2+r2)/4.) * (v2-v(-2)) -
	277	((XR+Yr)/2.) * v +
	278	((XR-Yr)/2.) * v**(-1) = 0.
	279	(2)* v2 <=> ((R2+r*2)/4.) v**4 -
	280	((XR+Yr)/2.) * v**3 +
	281	((XR-Yr)/2.) * v -
	282	((R2+r2)/4.) = 0.
0d969553	283	Use algorithm math_DirectPolynomialRoots to solve this equation by v.
7fd59977	284	-----------------------------------------------------------------------------*/
	285	{
	286	myDone = Standard_False;
	287	myNbExt = 0;
	288
0d969553	289	// 1- Projection of point P in the plane of hyperbola -> Pp ...
7fd59977	290
	291	gp_Pnt O = C.Location();
	292	gp_Vec Axe (C.Axis().Direction());
	293	gp_Vec Trsl = Axe.Multiplied(-(gp_Vec(O,P).Dot(Axe)));
	294	gp_Pnt Pp = P.Translated(Trsl);
	295
0d969553	296	// 2- Calculation of solutions ...
7fd59977	297
	298	Standard_Real Tol2 = Tol * Tol;
	299	Standard_Real R = C.MajorRadius();
	300	Standard_Real r = C.MinorRadius();
	301	gp_Vec OPp (O,Pp);
7fd59977	302	Standard_Real X = OPp.Dot(gp_Vec(C.XAxis().Direction()));
	303	Standard_Real Y = OPp.Dot(gp_Vec(C.YAxis().Direction()));
	304
	305	Standard_Real C1 = (RR+rr)/4.;
	306	math_DirectPolynomialRoots Sol(C1,-(XR+Yr)/2.,0.,(XR-Yr)/2.,-C1);
	307	if (!Sol.IsDone()) { return; }
	308	gp_Pnt Cu;
	309	Standard_Real Us, Vs;
	310	Standard_Integer NbSol = Sol.NbSolutions();
	311	Standard_Boolean DejaEnr;
	312	Standard_Integer NoExt;
	313	gp_Pnt TbExt[4];
	314	for (Standard_Integer NoSol = 1; NoSol <= NbSol; NoSol++) {
	315	Vs = Sol.Value(NoSol);
	316	if (Vs > 0.) {
	317	Us = Log(Vs);
	318	if ((Us >= Uinf) && (Us <= Usup)) {
	319	Cu = ElCLib::Value(Us,C);
	320	DejaEnr = Standard_False;
	321	for (NoExt = 0; NoExt < myNbExt; NoExt++) {
	322	if (TbExt[NoExt].SquareDistance(Cu) < Tol2) {
	323	DejaEnr = Standard_True;
	324	break;
	325	}
	326	}
	327	if (!DejaEnr) {
	328	TbExt[myNbExt] = Cu;
	329	mySqDist[myNbExt] = Cu.SquareDistance(P);
	330	myIsMin[myNbExt] = mySqDist[myNbExt] < P.SquareDistance(ElCLib::Value(Us+1,C));
	331	myPoint[myNbExt] = Extrema_POnCurv(Us,Cu);
	332	myNbExt++;
	333	}
	334	} // if ((Us >= Uinf) && (Us <= Usup))
	335	} // if (Vs > 0.)
	336	} // for (Standard_Integer NoSol = 1; ...
	337	myDone = Standard_True;
	338	}
	339	//=============================================================================
	340
	341	Extrema_ExtPElC::Extrema_ExtPElC (const gp_Pnt& P,
	342	const gp_Parab& C,
	343	const Standard_Real Tol,
	344	const Standard_Real Uinf,
	345	const Standard_Real Usup)
	346	{
	347	Perform(P, C, Tol, Uinf, Usup);
	348	}
	349
	350
	351	void Extrema_ExtPElC::Perform(const gp_Pnt& P,
	352	const gp_Parab& C,
	353	// const Standard_Real Tol,
	354	const Standard_Real ,
	355	const Standard_Real Uinf,
	356	const Standard_Real Usup)
	357	/*-----------------------------------------------------------------------------
0d969553 Y	358	Function:
	359	Find values of parameter u so that:
	360	- dist(P,C(u)) pass by an extremum,
7fd59977	361	- Uinf <= u <= Usup.
7fd59977	362
0d969553 Y	363	Method:
	364	Takes 2 steps:
	365	1- Projection of point P in the plane of the parabola,
	366	2- Calculation of solutions:
	367	Let Pp, the projected point; find values u so that:
7fd59977	368	(C(u)-Pp).C'(u) = 0. (1)
0d969553 Y	369	Let F the focus of the parabola,
0d969553 Y	370	C(u) = ((uu)/(4.F),u) and Pp = (X,Y);
7fd59977	371	Alors, (1) <=> ((uu)/(4.F)-X,u-Y).(u/(2.*F),1) = 0.
7fd59977	372	(1./(4.F)) U*3 + (2.F-X) * U - 2FY = 0.
0d969553	373	Use algorithm math_DirectPolynomialRoots to solve this equation by U.
7fd59977	374	-----------------------------------------------------------------------------*/
	375	{
	376	myDone = Standard_False;
	377	myNbExt = 0;
	378
0d969553	379	// 1- Projection of point P in the plane of the parabola -> Pp ...
7fd59977	380
	381	gp_Pnt O = C.Location();
	382	gp_Vec Axe (C.Axis().Direction());
	383	gp_Vec Trsl = Axe.Multiplied(-(gp_Vec(O,P).Dot(Axe)));
	384	gp_Pnt Pp = P.Translated(Trsl);
	385
0d969553	386	// 2- Calculation of solutions ...
7fd59977	387
	388	Standard_Real F = C.Focal();
	389	gp_Vec OPp (O,Pp);
7fd59977	390	Standard_Real X = OPp.Dot(gp_Vec(C.XAxis().Direction()));
	391	// Standard_Real Y = Sqrt(OPpMagnOPpMagn-XX);
	392	Standard_Real Y = OPp.Dot(gp_Vec(C.YAxis().Direction()));
	393	math_DirectPolynomialRoots Sol(1./(4.F),0.,2.F-X,-2.FY);
	394	if (!Sol.IsDone()) { return; }
	395	gp_Pnt Cu;
	396	Standard_Real Us;
	397	Standard_Integer NbSol = Sol.NbSolutions();
	398	Standard_Boolean DejaEnr;
	399	Standard_Integer NoExt;
	400	gp_Pnt TbExt[3];
	401	for (Standard_Integer NoSol = 1; NoSol <= NbSol; NoSol++) {
	402	Us = Sol.Value(NoSol);
	403	if ((Us >= Uinf) && (Us <= Usup)) {
	404	Cu = ElCLib::Value(Us,C);
	405	DejaEnr = Standard_False;
	406	for (NoExt = 0; NoExt < myNbExt; NoExt++) {
08cd2f6b	407	if (TbExt[NoExt].SquareDistance(Cu) < Precision::SquareConfusion()) {
7fd59977	408	DejaEnr = Standard_True;
	409	break;
	410	}
	411	}
	412	if (!DejaEnr) {
	413	TbExt[myNbExt] = Cu;
	414	mySqDist[myNbExt] = Cu.SquareDistance(P);
	415	myIsMin[myNbExt] = mySqDist[myNbExt] < P.SquareDistance(ElCLib::Value(Us+1,C));
	416	myPoint[myNbExt] = Extrema_POnCurv(Us,Cu);
	417	myNbExt++;
	418	}
	419	} // if ((Us >= Uinf) && (Us <= Usup))
	420	} // for (Standard_Integer NoSol = 1; ...
	421	myDone = Standard_True;
	422	}
	423	//=============================================================================
	424
	425	Standard_Boolean Extrema_ExtPElC::IsDone () const { return myDone; }
	426	//=============================================================================
	427
	428	Standard_Integer Extrema_ExtPElC::NbExt () const
	429	{
	430	if (!IsDone()) { StdFail_NotDone::Raise(); }
	431	return myNbExt;
	432	}
	433	//=============================================================================
	434
	435	Standard_Real Extrema_ExtPElC::SquareDistance (const Standard_Integer N) const
	436	{
	437	if ((N < 1) \|\| (N > NbExt())) { Standard_OutOfRange::Raise(); }
	438	return mySqDist[N-1];
	439	}
	440	//=============================================================================
	441
	442	Standard_Boolean Extrema_ExtPElC::IsMin (const Standard_Integer N) const
	443	{
	444	if ((N < 1) \|\| (N > NbExt())) { Standard_OutOfRange::Raise(); }
	445	return myIsMin[N-1];
	446	}
	447	//=============================================================================
	448
5d99f2c8	449	const Extrema_POnCurv& Extrema_ExtPElC::Point (const Standard_Integer N) const
7fd59977	450	{
	451	if ((N < 1) \|\| (N > NbExt())) { Standard_OutOfRange::Raise(); }
	452	return myPoint[N-1];
	453	}
	454	//=============================================================================