OCCT

// Created on: 1997-02-10
// Created by: Jacques GOUSSARD
// Copyright (c) 1997-1999 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.

#include <BRepBlend_RstRstConstRad.hxx>

#include <Adaptor2d_Curve2d.hxx>
#include <Adaptor3d_Curve.hxx>
#include <Adaptor3d_Surface.hxx>
#include <Blend_Point.hxx>
#include <BlendFunc.hxx>
#include <ElCLib.hxx>
#include <GeomFill.hxx>
#include <gp_Circ.hxx>
#include <gp_Pnt.hxx>
#include <gp_Pnt2d.hxx>
#include <gp_Vec.hxx>
#include <gp_Vec2d.hxx>
#include <math_Gauss.hxx>
#include <math_Matrix.hxx>
#include <math_SVD.hxx>
#include <Precision.hxx>
#include <Standard_DomainError.hxx>
#include <Standard_NotImplemented.hxx>

#define Eps 1.e-15

static void t3dto2d(double& a, double& b, const gp_Vec& A, const gp_Vec& B, const gp_Vec& C)
{
  double AB   = A.Dot(B);
  double AC   = A.Dot(C);
  double BC   = B.Dot(C);
  double BB   = B.Dot(B);
  double CC   = C.Dot(C);
  double deno = (BB * CC - BC * BC);
  a           = (AB * CC - AC * BC) / deno;
  b           = (AC * BB - AB * BC) / deno;
}

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

BRepBlend_RstRstConstRad::BRepBlend_RstRstConstRad(const occ::handle<Adaptor3d_Surface>& Surf1,
                                                   const occ::handle<Adaptor2d_Curve2d>& Rst1,
                                                   const occ::handle<Adaptor3d_Surface>& Surf2,
                                                   const occ::handle<Adaptor2d_Curve2d>& Rst2,
                                                   const occ::handle<Adaptor3d_Curve>&   CGuide)
    : surf1(Surf1),
      surf2(Surf2),
      rst1(Rst1),
      rst2(Rst2),
      cons1(Rst1, Surf1),
      cons2(Rst2, Surf2),
      guide(CGuide),
      tguide(CGuide),
      prmrst1(0.0),
      prmrst2(0.0),
      istangent(true),
      ray(0.0),
      choix(0),
      normtg(0.0),
      theD(0.0),
      maxang(RealFirst()),
      minang(RealLast()),
      distmin(RealLast()),
      mySShape(BlendFunc_Rational)
{
}

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

int BRepBlend_RstRstConstRad::NbVariables() const
{
  return 2;
}

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

int BRepBlend_RstRstConstRad::NbEquations() const
{
  return 2;
}

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

bool BRepBlend_RstRstConstRad::Value(const math_Vector& X, math_Vector& F)
{
  ptrst1 = cons1.Value(X(1));
  ptrst2 = cons2.Value(X(2));

  F(1) = nplan.XYZ().Dot(ptrst1.XYZ()) + theD;
  F(2) = nplan.XYZ().Dot(ptrst2.XYZ()) + theD;

  return true;
}

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

bool BRepBlend_RstRstConstRad::Derivatives(const math_Vector& X, math_Matrix& D)
{
  gp_Vec d11, d21;

  cons1.D1(X(1), ptrst1, d11);
  cons2.D1(X(2), ptrst2, d21);

  D(1, 1) = nplan.Dot(d11);
  D(1, 2) = 0.;

  D(2, 1) = 0.;
  D(2, 2) = nplan.Dot(d21);

  return true;
}

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

bool BRepBlend_RstRstConstRad::Values(const math_Vector& X, math_Vector& F, math_Matrix& D)
{
  Value(X, F);
  Derivatives(X, D);

  return true;
}

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

void BRepBlend_RstRstConstRad::Set(const occ::handle<Adaptor3d_Surface>& SurfRef1,
                                   const occ::handle<Adaptor2d_Curve2d>& RstRef1,
                                   const occ::handle<Adaptor3d_Surface>& SurfRef2,
                                   const occ::handle<Adaptor2d_Curve2d>& RstRef2)
{
  surfref1 = SurfRef1;
  surfref2 = SurfRef2;
  rstref1  = RstRef1;
  rstref2  = RstRef2;
}

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

void BRepBlend_RstRstConstRad::Set(const double Param)
{
  tguide->D2(Param, ptgui, d1gui, d2gui);
  normtg = d1gui.Magnitude();
  nplan  = d1gui.Normalized();
  theD   = -(nplan.XYZ().Dot(ptgui.XYZ()));
}

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

void BRepBlend_RstRstConstRad::Set(const double First, const double Last)
{
  tguide = guide->Trim(First, Last, 1.e-12);
}

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

void BRepBlend_RstRstConstRad::GetTolerance(math_Vector& Tolerance, const double Tol) const
{
  Tolerance(1) = cons1.Resolution(Tol);
  Tolerance(2) = cons2.Resolution(Tol);
}

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

void BRepBlend_RstRstConstRad::GetBounds(math_Vector& InfBound, math_Vector& SupBound) const
{
  InfBound(1) = cons1.FirstParameter();
  InfBound(2) = cons2.FirstParameter();
  SupBound(1) = cons1.LastParameter();
  SupBound(2) = cons2.LastParameter();
}

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

bool BRepBlend_RstRstConstRad::IsSolution(const math_Vector& Sol, const double Tol)

{
  math_Vector valsol(1, 2), secmember(1, 2);
  math_Matrix gradsol(1, 2, 1, 2);

  gp_Vec dnplan, d1urst1, d1vrst1, d1urst2, d1vrst2, d11, d21, temp;
  gp_Pnt bid;

  double Cosa, Sina, Angle;

  Values(Sol, valsol, gradsol);

  if (std::abs(valsol(1)) <= Tol && std::abs(valsol(2)) <= Tol)
  {

    // Calculation of tangents
    prmrst1  = Sol(1);
    pt2drst1 = rst1->Value(prmrst1);
    prmrst2  = Sol(2);
    pt2drst2 = rst2->Value(prmrst2);

    cons1.D1(Sol(1), ptrst1, d11);
    cons2.D1(Sol(2), ptrst2, d21);

    dnplan.SetLinearForm(1. / normtg, d2gui, -1. / normtg * (nplan.Dot(d2gui)), nplan);

    temp.SetXYZ(ptrst1.XYZ() - ptgui.XYZ());
    secmember(1) = normtg - dnplan.Dot(temp);

    temp.SetXYZ(ptrst2.XYZ() - ptgui.XYZ());
    secmember(2) = normtg - dnplan.Dot(temp);

    math_Gauss Resol(gradsol);

    if (Resol.IsDone())
    {
      Resol.Solve(secmember);
      istangent = false;
    }
    else
    {
      math_SVD SingRS(gradsol);
      if (SingRS.IsDone())
      {
        math_Vector DEDT(1, 3);
        DEDT = secmember;
        SingRS.Solve(DEDT, secmember, 1.e-6);
        istangent = false;
      }
      else
      {
        istangent = true;
      }
    }

    if (!istangent)
    {
      tgrst1 = secmember(1) * d11;
      tgrst2 = secmember(2) * d21;

      double a, b;
      surf1->D1(pt2drst1.X(), pt2drst1.Y(), bid, d1urst1, d1vrst1);
      t3dto2d(a, b, tgrst1, d1urst1, d1vrst1);
      tg2drst1.SetCoord(a, b);
      surf2->D1(pt2drst2.X(), pt2drst2.Y(), bid, d1urst2, d1vrst2);
      t3dto2d(a, b, tgrst1, d1urst2, d1vrst2);
      tg2drst2.SetCoord(a, b);
    }

    gp_Pnt Center;
    gp_Vec NotUsed;
    bool   IsCenter;

    IsCenter = CenterCircleRst1Rst2(ptrst1, ptrst2, nplan, Center, NotUsed);

    if (!IsCenter)
    {
      return false;
    }

    gp_Vec n1(Center, ptrst1), n2(Center, ptrst2);

    n1.Normalize();
    n2.Normalize();

    Cosa = n1.Dot(n2);
    Sina = nplan.Dot(n1.Crossed(n2));

    if (choix % 2 != 0)
    {
      Sina = -Sina; // nplan is changed into -nplan
    }

    Angle = std::acos(Cosa);
    if (Sina < 0.)
    {
      Angle = 2. * M_PI - Angle;
    }

    if (Angle > maxang)
    {
      maxang = Angle;
    }
    if (Angle < minang)
    {
      minang = Angle;
    }
    distmin = std::min(distmin, ptrst1.Distance(ptrst2));

    return true;
  }
  istangent = true;
  return false;
}

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

double BRepBlend_RstRstConstRad::GetMinimalDistance() const
{
  return distmin;
}

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

const gp_Pnt& BRepBlend_RstRstConstRad::PointOnRst1() const
{
  return ptrst1;
}

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

const gp_Pnt& BRepBlend_RstRstConstRad::PointOnRst2() const
{
  return ptrst2;
}

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

const gp_Pnt2d& BRepBlend_RstRstConstRad::Pnt2dOnRst1() const
{
  return pt2drst1;
}

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

const gp_Pnt2d& BRepBlend_RstRstConstRad::Pnt2dOnRst2() const
{
  return pt2drst2;
}

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

double BRepBlend_RstRstConstRad::ParameterOnRst1() const
{
  return prmrst1;
}

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

double BRepBlend_RstRstConstRad::ParameterOnRst2() const
{
  return prmrst2;
}

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

bool BRepBlend_RstRstConstRad::IsTangencyPoint() const
{
  return istangent;
}

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

const gp_Vec& BRepBlend_RstRstConstRad::TangentOnRst1() const
{
  if (istangent)
  {
    throw Standard_DomainError();
  }
  return tgrst1;
}

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

const gp_Vec2d& BRepBlend_RstRstConstRad::Tangent2dOnRst1() const
{
  if (istangent)
  {
    throw Standard_DomainError();
  }
  return tg2drst1;
}

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

const gp_Vec& BRepBlend_RstRstConstRad::TangentOnRst2() const
{
  if (istangent)
  {
    throw Standard_DomainError();
  }
  return tgrst2;
}

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

const gp_Vec2d& BRepBlend_RstRstConstRad::Tangent2dOnRst2() const
{
  if (istangent)
  {
    throw Standard_DomainError();
  }
  return tg2drst2;
}

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

Blend_DecrochStatus BRepBlend_RstRstConstRad::Decroch(const math_Vector& Sol,
                                                      gp_Vec&            NRst1,
                                                      gp_Vec&            TgRst1,
                                                      gp_Vec&            NRst2,
                                                      gp_Vec&            TgRst2) const
{
  gp_Vec NRst1InPlane, NRst2InPlane;
  gp_Pnt PtTmp1, PtTmp2, Center;
  gp_Vec d1u, d1v, centptrst, NotUsed;
  double norm, unsurnorm;
  double u, v;

  rstref1->Value(Sol(1)).Coord(u, v);
  surfref1->D1(u, v, PtTmp1, d1u, d1v);
  // Normal to the reference surface 1
  NRst1 = d1u.Crossed(d1v);
  rstref2->Value(Sol(2)).Coord(u, v);
  surfref2->D1(u, v, PtTmp2, d1u, d1v);
  // Normal to the reference surface 2
  NRst2 = d1u.Crossed(d1v);

  CenterCircleRst1Rst2(PtTmp1, PtTmp2, nplan, Center, NotUsed);

  norm      = nplan.Crossed(NRst1).Magnitude();
  unsurnorm = 1. / norm;

  NRst1InPlane.SetLinearForm(nplan.Dot(NRst1) * unsurnorm, nplan, -unsurnorm, NRst1);

  centptrst.SetXYZ(PtTmp1.XYZ() - Center.XYZ());

  if (centptrst.Dot(NRst1InPlane) < 0.)
  {
    NRst1InPlane.Reverse();
  }

  TgRst1 = nplan.Crossed(centptrst);

  norm      = nplan.Crossed(NRst2).Magnitude();
  unsurnorm = 1. / norm;
  NRst2InPlane.SetLinearForm(nplan.Dot(NRst2) * unsurnorm, nplan, -unsurnorm, NRst2);
  centptrst.SetXYZ(PtTmp2.XYZ() - Center.XYZ());

  if (centptrst.Dot(NRst2InPlane) < 0.)
  {
    NRst2InPlane.Reverse();
  }

  TgRst2 = nplan.Crossed(centptrst);

  if (choix % 2 != 0)
  {
    TgRst1.Reverse();
    TgRst2.Reverse();
  }

  // The vectors are returned
  if (NRst1InPlane.Dot(TgRst1) > -1.e-10)
  {
    if (NRst2InPlane.Dot(TgRst2) < 1.e-10)
    {
      return Blend_DecrochBoth;
    }
    else
    {
      return Blend_DecrochRst1;
    }
  }
  else
  {
    if (NRst2InPlane.Dot(TgRst2) < 1.e-10)
    {
      return Blend_DecrochRst2;
    }
    else
    {
      return Blend_NoDecroch;
    }
  }
}

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

void BRepBlend_RstRstConstRad::Set(const double Radius, const int Choix)
{
  choix = Choix;
  ray   = std::abs(Radius);
}

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

void BRepBlend_RstRstConstRad::Set(const BlendFunc_SectionShape TypeSection)
{
  mySShape = TypeSection;
}

//=======================================================================
// function : CenterCircleRst1Rst2
// purpose  : Calculate the center of the circle passing by two points of restrictions
//=======================================================================
bool BRepBlend_RstRstConstRad::CenterCircleRst1Rst2(const gp_Pnt& PtRst1,
                                                    const gp_Pnt& PtRst2,
                                                    const gp_Vec& np,
                                                    gp_Pnt&       Center,
                                                    gp_Vec&       VdMed) const
{

  gp_Vec rst1rst2(PtRst1, PtRst2);
  gp_Vec vdmedNor; //,NRst1;    vdmedNor directong vector of the perpendicular bisector
  double norm2;
  double Dist; // distance between the middle of PtRst1,PtRst2 and Center

  // Calculate the center of the circle
  VdMed = rst1rst2.Crossed(np);
  norm2 = rst1rst2.SquareMagnitude();
  Dist  = ray * ray - 0.25 * norm2;

  if (choix > 2)
  {
    VdMed.Reverse();
  }

  if (Dist < -1.E-07)
  {
    return false;
  }

  if (Dist > 1.E-07)
  {
    Dist     = sqrt(Dist);
    vdmedNor = VdMed.Normalized();
    Center.SetXYZ(0.5 * rst1rst2.XYZ() + PtRst1.XYZ() + Dist * vdmedNor.XYZ());
  }
  else
  {
    Center.SetXYZ(0.5 * rst1rst2.XYZ() + PtRst1.XYZ());
  }

  return true;
}

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

void BRepBlend_RstRstConstRad::Section(const double Param,
                                       const double U,
                                       const double V,
                                       double&      Pdeb,
                                       double&      Pfin,
                                       gp_Circ&     C)
{
  gp_Vec ns, np, NotUsed;
  gp_Pnt Center;

  tguide->D1(Param, ptgui, d1gui);
  np     = d1gui.Normalized();
  ptrst1 = cons1.Value(U);
  ptrst2 = cons2.Value(V);

  CenterCircleRst1Rst2(ptrst1, ptrst2, np, Center, NotUsed);

  C.SetRadius(std::abs(ray));
  ns = gp_Vec(Center, ptrst1).Normalized();

  if (choix % 2 != 0)
  {
    np.Reverse();
  }

  C.SetPosition(gp_Ax2(Center, np, ns));
  Pdeb = 0; // ElCLib::Parameter(C, pts);
  Pfin = ElCLib::Parameter(C, ptrst2);

  // Test of angles negative and almost null : Special Case
  if (Pfin > 1.5 * M_PI)
  {
    np.Reverse();
    C.SetPosition(gp_Ax2(Center, np, ns));
    Pfin = ElCLib::Parameter(C, ptrst2);
  }
  if (Pfin < Precision::PConfusion())
  {
    Pfin += Precision::PConfusion();
  }
}

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

bool BRepBlend_RstRstConstRad::IsRational() const
{
  return (mySShape == BlendFunc_Rational || mySShape == BlendFunc_QuasiAngular);
}

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

double BRepBlend_RstRstConstRad::GetSectionSize() const
{
  return maxang * std::abs(ray);
}

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

void BRepBlend_RstRstConstRad::GetMinimalWeight(NCollection_Array1<double>& Weights) const
{
  BlendFunc::GetMinimalWeights(mySShape, myTConv, minang, maxang, Weights);
  // It is supposed that it does not depend on the Radius!
}

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

int BRepBlend_RstRstConstRad::NbIntervals(const GeomAbs_Shape S) const
{
  return guide->NbIntervals(BlendFunc::NextShape(S));
}

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

void BRepBlend_RstRstConstRad::Intervals(NCollection_Array1<double>& T, const GeomAbs_Shape S) const
{
  guide->Intervals(T, BlendFunc::NextShape(S));
}

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

void BRepBlend_RstRstConstRad::GetShape(int& NbPoles, int& NbKnots, int& Degree, int& NbPoles2d)
{
  NbPoles2d = 2;
  BlendFunc::GetShape(mySShape, maxang, NbPoles, NbKnots, Degree, myTConv);
}

//=======================================================================
// function : GetTolerance
// purpose  : Determine Tolerances to be used in approximations.
//=======================================================================

void BRepBlend_RstRstConstRad::GetTolerance(const double BoundTol,
                                            const double SurfTol,
                                            const double AngleTol,
                                            math_Vector& Tol3d,
                                            math_Vector& Tol1d) const
{
  int    low = Tol3d.Lower(), up = Tol3d.Upper();
  double Tol;
  Tol = GeomFill::GetTolerance(myTConv, minang, std::abs(ray), AngleTol, SurfTol);
  Tol1d.Init(SurfTol);
  Tol3d.Init(SurfTol);
  Tol3d(low + 1) = Tol3d(up - 1) = std::min(Tol, SurfTol);
  Tol3d(low) = Tol3d(up) = std::min(Tol, BoundTol);
}

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

void BRepBlend_RstRstConstRad::Knots(NCollection_Array1<double>& TKnots)
{
  GeomFill::Knots(myTConv, TKnots);
}

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

void BRepBlend_RstRstConstRad::Mults(NCollection_Array1<int>& TMults)
{
  GeomFill::Mults(myTConv, TMults);
}

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

void BRepBlend_RstRstConstRad::Section(const Blend_Point&            P,
                                       NCollection_Array1<gp_Pnt>&   Poles,
                                       NCollection_Array1<gp_Pnt2d>& Poles2d,
                                       NCollection_Array1<double>&   Weights)
{
  gp_Vec ns, ns2, NotUsed;
  gp_Pnt Center;
  double u, v;

  double prm = P.Parameter();
  int    low = Poles.Lower();
  int    upp = Poles.Upper();

  tguide->D1(prm, ptgui, d1gui);
  nplan = d1gui.Normalized();

  u = P.ParameterOnC1();
  v = P.ParameterOnC2();

  gp_Pnt2d pt2d1 = rst1->Value(u);
  gp_Pnt2d pt2d2 = rst2->Value(v);

  ptrst1  = cons1.Value(u);
  ptrst2  = cons2.Value(v);
  distmin = std::min(distmin, ptrst1.Distance(ptrst2));

  Poles2d(Poles2d.Lower()).SetCoord(pt2d1.X(), pt2d1.Y());
  Poles2d(Poles2d.Upper()).SetCoord(pt2d2.X(), pt2d2.Y());

  // Linear case
  if (mySShape == BlendFunc_Linear)
  {
    Poles(low)   = ptrst1;
    Poles(upp)   = ptrst2;
    Weights(low) = 1.0;
    Weights(upp) = 1.0;
    return;
  }

  // Calculate the center of the circle
  CenterCircleRst1Rst2(ptrst1, ptrst2, nplan, Center, NotUsed);

  // normals to the section with points
  ns  = gp_Vec(Center, ptrst1).Normalized();
  ns2 = gp_Vec(Center, ptrst2).Normalized();

  if (choix % 2 != 0)
  {
    nplan.Reverse();
  }

  GeomFill::GetCircle(myTConv,
                      ns,
                      ns2,
                      nplan,
                      ptrst1,
                      ptrst2,
                      std::abs(ray),
                      Center,
                      Poles,
                      Weights);
}

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

bool BRepBlend_RstRstConstRad::Section(const Blend_Point&            P,
                                       NCollection_Array1<gp_Pnt>&   Poles,
                                       NCollection_Array1<gp_Vec>&   DPoles,
                                       NCollection_Array1<gp_Pnt2d>& Poles2d,
                                       NCollection_Array1<gp_Vec2d>& DPoles2d,
                                       NCollection_Array1<double>&   Weights,
                                       NCollection_Array1<double>&   DWeights)
{

  gp_Vec d11, d21;
  gp_Vec dnplan, d1n1, d1n2; //,np2, dnp2;
  gp_Vec temp, tgct;
  gp_Vec d1urst, d1vrst;
  gp_Pnt Center, NotUsed;

  double norm2, normmed, Dist;

  math_Vector sol(1, 2), valsol(1, 2), secmember(1, 2);
  math_Matrix gradsol(1, 2, 1, 2);

  double prm = P.Parameter();
  int    low = Poles.Lower();
  int    upp = Poles.Upper();
  bool   istgt;

  tguide->D2(prm, ptgui, d1gui, d2gui);
  normtg = d1gui.Magnitude();
  nplan  = d1gui.Normalized();
  dnplan.SetLinearForm(1. / normtg, d2gui, -1. / normtg * (nplan.Dot(d2gui)), nplan);

  sol(1) = prmrst1 = P.ParameterOnC1();
  sol(2) = prmrst2 = P.ParameterOnC2();
  pt2drst1         = rst1->Value(prmrst1);
  pt2drst2         = rst2->Value(prmrst2);

  Values(sol, valsol, gradsol);

  cons1.D1(sol(1), ptrst1, d11);
  cons2.D1(sol(2), ptrst2, d21);

  temp.SetXYZ(ptrst1.XYZ() - ptgui.XYZ());
  secmember(1) = normtg - dnplan.Dot(temp);

  temp.SetXYZ(ptrst2.XYZ() - ptgui.XYZ());
  secmember(2) = normtg - dnplan.Dot(temp);

  math_Gauss Resol(gradsol, 1.e-9);

  if (Resol.IsDone())
  {
    istgt = false;
    Resol.Solve(secmember);
  }
  else
  {
    math_SVD SingRS(gradsol);
    if (SingRS.IsDone())
    {
      math_Vector DEDT(1, 2);
      DEDT = secmember;
      SingRS.Solve(DEDT, secmember, 1.e-6);
      istgt = false;
    }
    else
    {
      istgt = true;
    }
  }

  gp_Vec med;
  gp_Vec rst1rst2(ptrst1, ptrst2);
  bool   IsCenter;

  IsCenter = CenterCircleRst1Rst2(ptrst1, ptrst2, nplan, Center, med);
  if (!IsCenter)
  {
    return false;
  }

  normmed = med.Magnitude();
  med.Normalize();
  gp_Vec n1(Center, ptrst1), n2(Center, ptrst2);
  n1.Normalize();
  n2.Normalize();

  if (!istgt)
  {
    // secmember contains derivatives of parameters on curves
    // compared to t
    tgrst1 = secmember(1) * d11;
    tgrst2 = secmember(2) * d21;

    gp_Vec d1rst1rst2;

    norm2      = rst1rst2.SquareMagnitude();
    d1rst1rst2 = tgrst2 - tgrst1;
    Dist       = ray * ray - 0.25 * norm2;

    if (Dist > 1.E-07)
    {
      gp_Vec d1P1P2CrosNp, dmed;
      d1P1P2CrosNp = d1rst1rst2.Crossed(nplan) + rst1rst2.Crossed(dnplan);
      // derivative of the perpendicular bisector
      dmed = d1P1P2CrosNp - med.Dot(d1P1P2CrosNp) * med;
      dmed /= normmed;
      Dist          = sqrt(Dist);
      double d1Dist = -(0.25 / Dist) * rst1rst2.Dot(d1rst1rst2);

      if (choix > 2)
      {
        dmed.Reverse();
      }

      // the derivative of coefficient Dist is located in dmed
      dmed.SetLinearForm(Dist, dmed, d1Dist, med);
      d1rst1rst2 *= 0.5;
      // derivative of the Normal to the curve in P1
      d1n1 = -(dmed + d1rst1rst2) / ray;

      // derivative of the Normal to the curve in P2
      d1n2 = (d1rst1rst2 - dmed) / ray;
    }
    else
    {
      d1rst1rst2 *= 0.5;
      // Normal to the curve in P1
      d1n1 = -d1rst1rst2 / ray;

      // Normal to the curve in P2
      d1n2 = d1rst1rst2 / ray;
    }
  }

  // Tops 2d

  Poles2d(Poles2d.Lower()).SetCoord(pt2drst1.X(), pt2drst1.Y());
  Poles2d(Poles2d.Upper()).SetCoord(pt2drst2.X(), pt2drst2.Y());
  if (!istgt)
  {
    double a, b;
    surf1->D1(pt2drst1.X(), pt2drst1.Y(), NotUsed, d1urst, d1vrst);
    t3dto2d(a, b, tgrst1, d1urst, d1vrst);
    DPoles2d(Poles2d.Lower()).SetCoord(a, b);

    surf2->D1(pt2drst2.X(), pt2drst2.Y(), NotUsed, d1urst, d1vrst);
    t3dto2d(a, b, tgrst2, d1urst, d1vrst);
    DPoles2d(Poles2d.Upper()).SetCoord(a, b);
  }

  // Linear case
  if (mySShape == BlendFunc_Linear)
  {
    Poles(low)   = ptrst1;
    Poles(upp)   = ptrst2;
    Weights(low) = 1.0;
    Weights(upp) = 1.0;
    if (!istgt)
    {
      DPoles(low)   = tgrst1;
      DPoles(upp)   = tgrst2;
      DWeights(low) = 0.0;
      DWeights(upp) = 0.0;
    }
    return (!istgt);
  }

  // Case of the circle
  // tangent to the center of the circle
  if (!istgt)
  {
    tgct.SetLinearForm(-ray, d1n1, tgrst1);
  }

  if (choix % 2 != 0)
  {
    nplan.Reverse();
    dnplan.Reverse();
  }

  if (!istgt)
  {
    return GeomFill::GetCircle(myTConv,
                               n1,
                               n2,
                               d1n1,
                               d1n2,
                               nplan,
                               dnplan,
                               ptrst1,
                               ptrst2,
                               tgrst1,
                               tgrst2,
                               std::abs(ray),
                               0,
                               Center,
                               tgct,
                               Poles,
                               DPoles,
                               Weights,
                               DWeights);
  }
  else
  {
    GeomFill::GetCircle(myTConv,
                        n1,
                        n2,
                        nplan,
                        ptrst1,
                        ptrst2,
                        std::abs(ray),
                        Center,
                        Poles,
                        Weights);
    return false;
  }
}

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

bool BRepBlend_RstRstConstRad::Section(const Blend_Point&,
                                       NCollection_Array1<gp_Pnt>&,
                                       NCollection_Array1<gp_Vec>&,
                                       NCollection_Array1<gp_Vec>&,
                                       NCollection_Array1<gp_Pnt2d>&,
                                       NCollection_Array1<gp_Vec2d>&,
                                       NCollection_Array1<gp_Vec2d>&,
                                       NCollection_Array1<double>&,
                                       NCollection_Array1<double>&,
                                       NCollection_Array1<double>&)
{
  return false;
}

void BRepBlend_RstRstConstRad::Resolution(const int    IC2d,
                                          const double Tol,
                                          double&      TolU,
                                          double&      TolV) const
{
  if (IC2d == 1)
  {
    TolU = surf1->UResolution(Tol);
    TolV = surf1->VResolution(Tol);
  }
  else
  {
    TolU = surf2->UResolution(Tol);
    TolV = surf2->VResolution(Tol);
  }
}