src/IntAna/IntAna_Curve.cxx

// Created on: 1992-06-30
// Created by: Laurent BUCHARD
// Copyright (c) 1992-1999 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 License 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.

#ifndef OCCT_DEBUG
#define No_Standard_RangeError
#define No_Standard_OutOfRange
#endif

//----------------------------------------------------------------------
//-- Differents constructeurs sont proposes qui correspondent aux
//-- polynomes en Z :
//--    A(Sin(Theta),Cos(Theta)) Z**2
//--  + B(Sin(Theta),Cos(Theta)) Z
//--  + C(Sin(Theta),Cos(Theta))
//--
//-- Une Courbe est definie sur un domaine
//--
//-- Value retourne le point de parametre U(Theta),V(Theta)
//--       ou V est la solution du polynome A V**2 + B V + C
//--       (Selon les cas, on prend V+ ou V-)
//--
//-- D1u   calcule le vecteur tangent a la courbe
//--       et retourne le booleen Standard_False si ce calcul ne peut
//--       pas etre mene a bien.
//----------------------------------------------------------------------

#include <algorithm>

#include <ElSLib.hxx>
#include <gp_Cone.hxx>
#include <gp_Cylinder.hxx>
#include <gp_Pnt.hxx>
#include <gp_Vec.hxx>
#include <gp_XYZ.hxx>
#include <IntAna_Curve.hxx>
#include <math_DirectPolynomialRoots.hxx>
#include <Precision.hxx>
#include <Standard_DomainError.hxx>

//=======================================================================
//function : IntAna_Curve
//purpose  :
//=======================================================================
IntAna_Curve::IntAna_Curve()
: Z0Cte(0.0),
  Z0Sin(0.0),
  Z0Cos(0.0),
  Z0SinSin(0.0),
  Z0CosCos(0.0),
  Z0CosSin(0.0),
  Z1Cte(0.0),
  Z1Sin(0.0),
  Z1Cos(0.0),
  Z1SinSin(0.0),
  Z1CosCos(0.0),
  Z1CosSin(0.0),
  Z2Cte(0.0),
  Z2Sin(0.0),
  Z2Cos(0.0),
  Z2SinSin(0.0),
  Z2CosCos(0.0),
  Z2CosSin(0.0),
  TwoCurves(Standard_False),
  TakeZPositive(Standard_False),
  Tolerance(0.0),
  DomainInf(0.0),
  DomainSup(0.0),
  RestrictedInf(Standard_False),
  RestrictedSup(Standard_False),
  firstbounded(Standard_False),
  lastbounded(Standard_False),
  typequadric(GeomAbs_OtherSurface),
  RCyl(0.0),
  Angle(0.0),
  myFirstParameter(0.0),
  myLastParameter(0.0)
{
}
//=======================================================================
//function : SetConeQuadValues
//purpose  : Description de l intersection Cone Quadrique
//=======================================================================
void IntAna_Curve::SetConeQuadValues(const gp_Cone& Cone,
                                     const Standard_Real Qxx,
                                     const Standard_Real Qyy,
                                     const Standard_Real Qzz,
                                     const Standard_Real Qxy,
                                     const Standard_Real Qxz,
                                     const Standard_Real Qyz,
                                     const Standard_Real Qx,
                                     const Standard_Real Qy,
                                     const Standard_Real Qz,
                                     const Standard_Real Q1,
                                     const Standard_Real TOL,
                                     const Standard_Real DomInf,
                                     const Standard_Real DomSup,
                                     const Standard_Boolean twocurves,
                                     const Standard_Boolean takezpositive)
{

  Ax3        = Cone.Position();
  RCyl       = Cone.RefRadius();

  Angle      = Cone.SemiAngle();
  Standard_Real UnSurTgAngle = 1.0/(Tan(Cone.SemiAngle()));

  typequadric= GeomAbs_Cone;

  TwoCurves     = twocurves;         //-- deux  Z pour un meme parametre
  TakeZPositive = takezpositive;     //-- Prendre sur la courbe le Z Positif
                                     //--   ( -B + Sqrt()) et non (-B - Sqrt())


  Z0Cte      = Q1;                   //-- Attention On a    Z?Cos Cos(t)
  Z0Sin      = 0.0;                  //-- et Non          2 Z?Cos Cos(t) !!!
  Z0Cos      = 0.0;                  //-- Ce pour tous les Parametres
  Z0CosCos   = 0.0;                  //--  ie pas de Coefficient 2
  Z0SinSin   = 0.0;                  //--     devant les termes CS C S
  Z0CosSin   = 0.0;

  Z1Cte      = 2.0*(UnSurTgAngle)*Qz;
  Z1Sin      = Qy+Qy;
  Z1Cos      = Qx+Qx;
  Z1CosCos   = 0.0;
  Z1SinSin   = 0.0;
  Z1CosSin   = 0.0;

  Z2Cte      = Qzz * UnSurTgAngle*UnSurTgAngle;
  Z2Sin      = (UnSurTgAngle+UnSurTgAngle)*Qyz;
  Z2Cos      = (UnSurTgAngle+UnSurTgAngle)*Qxz;
  Z2CosCos   = Qxx;
  Z2SinSin   = Qyy;
  Z2CosSin   = Qxy;

  Tolerance  = TOL;
  DomainInf = DomInf;
  DomainSup = DomSup;

  RestrictedInf = RestrictedSup = Standard_True;   //-- Le Domaine est Borne
  firstbounded = lastbounded = Standard_False;

  myFirstParameter = DomainInf;
  myLastParameter = (TwoCurves) ? DomainSup + DomainSup - DomainInf :
                                  DomainSup;
}

//=======================================================================
//function : SetCylinderQuadValues
//purpose  : Description de l intersection Cylindre Quadrique
//=======================================================================
void IntAna_Curve::SetCylinderQuadValues(const gp_Cylinder& Cyl,
                                         const Standard_Real Qxx,
                                         const Standard_Real Qyy,
                                         const Standard_Real Qzz,
                                         const Standard_Real Qxy,
                                         const Standard_Real Qxz,
                                         const Standard_Real Qyz,
                                         const Standard_Real Qx,
                                         const Standard_Real Qy,
                                         const Standard_Real Qz,
                                         const Standard_Real Q1,
                                         const Standard_Real TOL,
                                         const Standard_Real DomInf,
                                         const Standard_Real DomSup,
                                         const Standard_Boolean twocurves,
                                         const Standard_Boolean takezpositive)
{

  Ax3        = Cyl.Position();
  RCyl       = Cyl.Radius();
  typequadric= GeomAbs_Cylinder;

  TwoCurves     = twocurves;         //-- deux  Z pour un meme parametre
  TakeZPositive = takezpositive;     //-- Prendre sur la courbe le Z Positif
  Standard_Real RCylmul2 = RCyl+RCyl;         //--   ( -B + Sqrt())

  Z0Cte      = Q1;
  Z0Sin      = RCylmul2*Qy;
  Z0Cos      = RCylmul2*Qx;
  Z0CosCos   = Qxx*RCyl*RCyl;
  Z0SinSin   = Qyy*RCyl*RCyl;
  Z0CosSin   = RCyl*RCyl*Qxy;

  Z1Cte      = Qz+Qz;
  Z1Sin      = RCylmul2*Qyz;
  Z1Cos      = RCylmul2*Qxz;
  Z1CosCos   = 0.0;
  Z1SinSin   = 0.0;
  Z1CosSin   = 0.0;

  Z2Cte      = Qzz;
  Z2Sin      = 0.0;
  Z2Cos      = 0.0;
  Z2CosCos   = 0.0;
  Z2SinSin   = 0.0;
  Z2CosSin   = 0.0;

  Tolerance  = TOL;
  DomainInf = DomInf;
  DomainSup = DomSup;

  RestrictedInf = RestrictedSup = Standard_True;
  firstbounded = lastbounded = Standard_False;

  myFirstParameter = DomainInf;
  myLastParameter  = (TwoCurves) ? DomainSup + DomainSup - DomainInf :
                                   DomainSup;
}

//=======================================================================
//function : IsOpen
//purpose  :
//=======================================================================
Standard_Boolean IntAna_Curve::IsOpen() const
{
  return(RestrictedInf && RestrictedSup);
}

//=======================================================================
//function : Domain
//purpose  :
//=======================================================================
void IntAna_Curve::Domain(Standard_Real& theFirst,
                          Standard_Real& theLast) const
{
  if (RestrictedInf && RestrictedSup)
  {
    theFirst = myFirstParameter;
    theLast = myLastParameter;
  }
  else
  {
    throw Standard_DomainError("IntAna_Curve::Domain");
  }
}
//=======================================================================
//function : IsConstant
//purpose  :
//=======================================================================
Standard_Boolean IntAna_Curve::IsConstant() const
{
  //-- ???  Pas facile de decider a la seule vue des Param.
  return(Standard_False);
}

//=======================================================================
//function : IsFirstOpen
//purpose  :
//=======================================================================
Standard_Boolean IntAna_Curve::IsFirstOpen() const
{
  return(firstbounded);
}

//=======================================================================
//function : IsLastOpen
//purpose  :
//=======================================================================
Standard_Boolean IntAna_Curve::IsLastOpen() const
{
  return(lastbounded);
}
//=======================================================================
//function : SetIsFirstOpen
//purpose  :
//=======================================================================
void IntAna_Curve::SetIsFirstOpen(const Standard_Boolean Flag)
{
  firstbounded = Flag;
}

//=======================================================================
//function : SetIsLastOpen
//purpose  :
//=======================================================================
void IntAna_Curve::SetIsLastOpen(const Standard_Boolean Flag)
{
  lastbounded = Flag;
}

//=======================================================================
//function : InternalUVValue
//purpose  :
//=======================================================================
void IntAna_Curve::InternalUVValue(const Standard_Real theta,
                                   Standard_Real& Param1,
                                   Standard_Real& Param2,
                                   Standard_Real& A,
                                   Standard_Real& B,
                                   Standard_Real& C,
                                   Standard_Real& cost,
                                   Standard_Real& sint,
                                   Standard_Real& SigneSqrtDis) const
{
  const Standard_Real aRelTolp = 1.0+Epsilon(1.0), aRelTolm = 1.0-Epsilon(1.0);

  // Infinitesimal step of increasing curve parameter. See comment below.
  const Standard_Real aDT = 100.0*Epsilon(DomainSup + DomainSup - DomainInf);

  Standard_Real Theta=theta;
  Standard_Boolean SecondSolution=Standard_False;

  if ((Theta<DomainInf*aRelTolm) ||
      ((Theta>DomainSup*aRelTolp) && (!TwoCurves)) ||
      (Theta>(DomainSup + DomainSup - DomainInf)*aRelTolp))
  {
    SigneSqrtDis = 0.;
    throw Standard_DomainError("IntAna_Curve::Domain");
  }

  if (Abs(Theta - DomainSup) < aDT)
  {
    // Point of Null-discriminant.
    Theta = DomainSup;
  }
  else if (Theta>DomainSup)
  {
    Theta = DomainSup + DomainSup - Theta;
    SecondSolution=Standard_True;
  }

  Param1=Theta;

  if(!TwoCurves) {
    SecondSolution=TakeZPositive;
  }
  //
  cost = Cos(Theta);
  sint = Sin(Theta);
  const Standard_Real aSin2t = Sin(Theta + Theta);
  const Standard_Real aCos2t = Cos(Theta + Theta);

  A=Z2Cte+sint*(Z2Sin+sint*Z2SinSin)+cost*(Z2Cos+cost*Z2CosCos)
    + Z2CosSin*aSin2t;

  const Standard_Real aDA = cost*Z2Sin - sint*Z2Cos +
                            aSin2t*(Z2SinSin - Z2CosCos) +
                            aCos2t*(Z2CosSin * Z2CosSin);

  B=Z1Cte+sint*(Z1Sin+sint*Z1SinSin)+cost*(Z1Cos+cost*Z1CosCos)
    + Z1CosSin*aSin2t;

  const Standard_Real aDB = Z1Sin*cost - Z1Cos*sint +
                            aSin2t*(Z1SinSin - Z1CosCos) +
                            aCos2t*(Z1CosSin + Z1CosSin);

  C=Z0Cte+sint*(Z0Sin+sint*Z0SinSin)+cost*(Z0Cos+cost*Z0CosCos)
    + Z0CosSin*aSin2t;

  const Standard_Real aDC = Z0Sin*cost - Z0Cos*sint +
                            aSin2t*(Z0SinSin - Z0CosCos) +
                            aCos2t*(Z0CosSin + Z0CosSin);

  Standard_Real aDiscriminant = B*B-4.0*A*C;

  // We consider that infinitesimal dt = aDT.
  // Error of discriminant computation is equal to
  // (d(Disc)/dt)*dt, where 1st derivative d(Disc)/dt = 2*B*aDB - 4*(A*aDC + C*aDA).

  const Standard_Real aTolD = 2.0*aDT*Abs(B*aDB - 2.0*(A*aDC + C*aDA));

  if (aDiscriminant < aTolD)
    aDiscriminant = 0.0;

  if (Abs(A) <= Precision::PConfusion())
  {
    if (Abs(B) <= Precision::PConfusion())
    {
      Param2 = 0.0;
    }
    else
    {
      Param2 = -C / B;
    }
  }
  else
  {
    SigneSqrtDis = (SecondSolution) ? Sqrt(aDiscriminant) : -Sqrt(aDiscriminant);
    Param2 = (-B + SigneSqrtDis) / (A + A);
  }
}

//=======================================================================
//function : Value
//purpose  :
//=======================================================================
gp_Pnt IntAna_Curve::Value(const Standard_Real theta)
{
  Standard_Real A, B, C, U, V, sint, cost, SigneSqrtDis;
  //
  A=0.0;  B=0.0;   C=0.0;
  U=0.0;  V=0.0;
  sint=0.0;  cost=0.0;
  SigneSqrtDis=0.0;
  InternalUVValue(theta,U,V,A,B,C,cost,sint,SigneSqrtDis);
  //-- checked the parameter U and Raises Domain Error if Error
  return(InternalValue(U,V));
}
//=======================================================================
//function : D1u
//purpose  :
//=======================================================================
Standard_Boolean IntAna_Curve::D1u(const Standard_Real theta,
                                   gp_Pnt& Pt,
                                   gp_Vec& Vec)
{
  //-- Pour detecter le cas ou le calcul est impossible
  Standard_Real A, B, C, U, V, sint, cost, SigneSqrtDis;
  A=0.0;  B=0.0;   C=0.0;
  U=0.0;  V=0.0;
  sint=0.0;  cost=0.0;
  //
  InternalUVValue(theta,U,V,A,B,C,cost,sint,SigneSqrtDis);
  //
  Pt = Value(theta);
  if (Abs(A)<1.0e-7 || Abs(SigneSqrtDis)<1.0e-10) return(Standard_False);


  //-- Approximation de la derivee (mieux que le calcul mathematique!)
  Standard_Real dtheta = (DomainSup - DomainInf)*1.0e-6;
  Standard_Real theta2 = theta+dtheta;
  if ((theta2<DomainInf) || ((theta2>DomainSup) && (!TwoCurves))
      || (theta2>(DomainSup + DomainSup - DomainInf + 1.0e-14)))
  {
    dtheta = -dtheta;
    theta2 = theta+dtheta;
  }
  gp_Pnt P2 = Value(theta2);
  dtheta = 1.0/dtheta;
  Vec.SetCoord((P2.X()-Pt.X())*dtheta,
	       (P2.Y()-Pt.Y())*dtheta,
	       (P2.Z()-Pt.Z())*dtheta);

  return(Standard_True);
}
//=======================================================================
//function : FindParameter
//purpose  : Projects P to the ALine. Returns the list of parameters as a results
//            of projection.
//           Sometimes aline can be self-intersected line (see bug #29807 where
//            ALine goes through the cone apex).
//=======================================================================
void IntAna_Curve::FindParameter(const gp_Pnt& theP,
                                 TColStd_ListOfReal& theParams) const
{
  const Standard_Real aPIpPI = M_PI + M_PI,
    anEpsAng = 1.e-8,
    InternalPrecision = 1.e-8, //precision of internal algorithm of values computation
    aSqTolPrecision = Precision::SquareConfusion(); //for boundary points to check their coincidence with others

  Standard_Real aTheta = 0.0;
  //
  switch (typequadric)
  {
    case GeomAbs_Cylinder:
    {
      Standard_Real aZ;
      ElSLib::CylinderParameters(Ax3, RCyl, theP, aTheta, aZ);
    }
    break;

    case GeomAbs_Cone:
    {
      Standard_Real aZ;
      ElSLib::ConeParameters(Ax3, RCyl, Angle, theP, aTheta, aZ);
    }
    break;

    default:
      return;
  }
  //
  if (!firstbounded && (DomainInf > aTheta) && ((DomainInf - aTheta) <= anEpsAng))
  {
    aTheta = DomainInf;
  }
  else if (!lastbounded && (aTheta > DomainSup) && ((aTheta - DomainSup) <= anEpsAng))
  {
    aTheta = DomainSup;
  }
  //
  if (aTheta < DomainInf)
  {
    aTheta = aTheta + aPIpPI;
  }
  else if (aTheta > DomainSup)
  {
    aTheta = aTheta - aPIpPI;
  }

  const Standard_Integer aMaxPar = 5;
  Standard_Real aParams[aMaxPar] = {DomainInf, DomainSup, aTheta,
                                    (TwoCurves)? DomainSup + DomainSup - aTheta : RealLast(),
                                    (TwoCurves) ? DomainSup + DomainSup - DomainInf : RealLast()};

  std::sort(aParams, aParams + aMaxPar - 1);

  for (Standard_Integer i = 0; i < aMaxPar; i++)
  {
    if (aParams[i] > myLastParameter)
      break;

    if (aParams[i] < myFirstParameter)
      continue;

    if (i && (aParams[i] - aParams[i - 1]) < Precision::PConfusion())
      continue;

    Standard_Real U = 0.0, V= 0.0,
                  A = 0.0, B = 0.0, C = 0.0,
                  sint = 0.0, cost = 0.0, SigneSqrtDis = 0.0;
    InternalUVValue(aParams[i], U, V, A, B, C,
                    cost, sint, SigneSqrtDis);
    const gp_Pnt aP(InternalValue(U, V));

    Standard_Real aSqTol;
    if (aParams[i] == aTheta ||
        (TwoCurves && aParams[i] == DomainSup + DomainSup - aTheta))
      aSqTol = InternalPrecision;
    else
      aSqTol = aSqTolPrecision;

    if (aP.SquareDistance(theP) < aSqTol)
    {
      theParams.Append(aParams[i]);
    }
  }
}
//=======================================================================
//function : InternalValue
//purpose  :
//=======================================================================
gp_Pnt IntAna_Curve::InternalValue(const Standard_Real U,
                                   const Standard_Real _V) const
{
  //-- std::cout<<" ["<<U<<","<<V<<"]";
  Standard_Real V = _V;
  if(V > 100000.0 )   {   V= 100000.0; }
  if(V < -100000.0 )  {   V=-100000.0; }

  switch(typequadric) {
  case GeomAbs_Cone:
    {
      //------------------------------------------------
      //-- Parametrage : X = V * Cos(U)              ---
      //--               Y = V * Sin(U)              ---
      //--               Z = (V-RCyl) / Tan(SemiAngle)--
      //------------------------------------------------
      //-- Angle Vaut Cone.SemiAngle()
      return(ElSLib::ConeValue(U,(V-RCyl)/Sin(Angle),Ax3,RCyl,Angle));
    }
    break;

  case GeomAbs_Cylinder:
    return(ElSLib::CylinderValue(U,V,Ax3,RCyl));
  case GeomAbs_Sphere:
    return(ElSLib::SphereValue(U,V,Ax3,RCyl));
  default:
    return(gp_Pnt(0.0,0.0,0.0));
  }
}

//
//=======================================================================
//function : SetDomain
//purpose  :
//=======================================================================
void IntAna_Curve::SetDomain(const Standard_Real theFirst,
                             const Standard_Real theLast)
{
  if (theLast <= theFirst)
  {
    throw Standard_DomainError("IntAna_Curve::Domain");
  }
  //
  myFirstParameter = theFirst;
  myLastParameter = theLast;
}