// Created on: 1993-12-02
// Created by: Jacques GOUSSARD
// Copyright (c) 1993-1999 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 <Adaptor2d_Curve2d.hxx>
#include <BlendFunc.hxx>
#include <BlendFunc_ConstRadInv.hxx>
#include <math_Matrix.hxx>
#include <Precision.hxx>

#define Eps 1.e-15


BlendFunc_ConstRadInv::BlendFunc_ConstRadInv(const Handle(Adaptor3d_Surface)& S1,
					     const Handle(Adaptor3d_Surface)& S2,
					     const Handle(Adaptor3d_Curve)& C)
: surf1(S1),
  surf2(S2),
  curv(C),
  ray1(0.0),
  ray2(0.0),
  choix(0),
  first(Standard_False)
{
}

void BlendFunc_ConstRadInv::Set(const Standard_Real R,
				const Standard_Integer Choix)

{
  choix = Choix;
  switch (choix) {
  case 1:
  case 2:
    {
      ray1 = -R;
      ray2 = -R;
    }
    break;
  case 3:
  case 4:
    {
      ray1 = R;
      ray2 = -R;
    }
    break;
  case 5:
  case 6:
    {
      ray1 = R;
      ray2 = R;
    }
    break;
  case 7:
  case 8:
    {
      ray1 = -R;
      ray2 = R;
    }
    break;
  default:
    ray1 = ray2 = -R;
  }
}

void BlendFunc_ConstRadInv::Set(const Standard_Boolean OnFirst,
				const Handle(Adaptor2d_Curve2d)& C)
{
  first = OnFirst;
  csurf = C;
}

Standard_Integer BlendFunc_ConstRadInv::NbEquations () const
{
  return 4;
}


void BlendFunc_ConstRadInv::GetTolerance(math_Vector& Tolerance,
					 const Standard_Real Tol) const
{
  Tolerance(1) = csurf->Resolution(Tol);
  Tolerance(2) = curv->Resolution(Tol);
  if (first) {
    Tolerance(3) = surf2->UResolution(Tol);
    Tolerance(4) = surf2->VResolution(Tol);
  }
  else {
    Tolerance(3) = surf1->UResolution(Tol);
    Tolerance(4) = surf1->VResolution(Tol);
  }
}


void BlendFunc_ConstRadInv::GetBounds(math_Vector& InfBound,
				      math_Vector& SupBound) const
{
  InfBound(1) = csurf->FirstParameter();
  InfBound(2) = curv->FirstParameter();
  SupBound(1) = csurf->LastParameter();
  SupBound(2) = curv->LastParameter();

  if (first) {
    InfBound(3) = surf2->FirstUParameter();
    InfBound(4) = surf2->FirstVParameter();
    SupBound(3) = surf2->LastUParameter();
    SupBound(4) = surf2->LastVParameter();
    if(!Precision::IsInfinite(InfBound(3)) &&
       !Precision::IsInfinite(SupBound(3))) {
      Standard_Real range = (SupBound(3) - InfBound(3));
      InfBound(3) -= range;
      SupBound(3) += range;
    }
    if(!Precision::IsInfinite(InfBound(4)) &&
       !Precision::IsInfinite(SupBound(4))) {
      Standard_Real range = (SupBound(4) - InfBound(4));
      InfBound(4) -= range;
      SupBound(4) += range;
    }
  }
  else {
    InfBound(3) = surf1->FirstUParameter();
    InfBound(4) = surf1->FirstVParameter();
    SupBound(3) = surf1->LastUParameter();
    SupBound(4) = surf1->LastVParameter();
    if(!Precision::IsInfinite(InfBound(3)) &&
       !Precision::IsInfinite(SupBound(3))) {
      Standard_Real range = (SupBound(3) - InfBound(3));
      InfBound(3) -= range;
      SupBound(3) += range;
    }
    if(!Precision::IsInfinite(InfBound(4)) &&
       !Precision::IsInfinite(SupBound(4))) {
      Standard_Real range = (SupBound(4) - InfBound(4));
      InfBound(4) -= range;
      SupBound(4) += range;
    }
  }    
}

Standard_Boolean BlendFunc_ConstRadInv::IsSolution(const math_Vector& Sol,
						   const Standard_Real Tol)
{
  math_Vector valsol(1,4);
  Value(Sol,valsol);
  if (Abs(valsol(1)) <= Tol &&  
      valsol(2)*valsol(2) + valsol(3)*valsol(3) +
      valsol(4)*valsol(4) <= Tol*Tol) {
    return Standard_True;
  }
  return Standard_False;

}


Standard_Boolean BlendFunc_ConstRadInv::Value(const math_Vector& X,
                                              math_Vector& F)
{
  gp_Pnt ptcur;
  gp_Vec d1cur;
  curv->D1(X(2),ptcur,d1cur);

  const gp_Vec nplan = d1cur.Normalized();
  const Standard_Real theD = -(nplan.XYZ().Dot(ptcur.XYZ()));

  const gp_Pnt2d pt2d(csurf->Value(X(1)));

  gp_Pnt pts1,pts2;
  gp_Vec d1u1,d1v1,d1u2,d1v2;
  if (first)
  {
    surf1->D1(pt2d.X(),pt2d.Y(),pts1,d1u1,d1v1);
    surf2->D1(X(3),X(4),pts2,d1u2,d1v2);
  }
  else
  {
    surf1->D1(X(3),X(4),pts1,d1u1,d1v1);
    surf2->D1(pt2d.X(),pt2d.Y(),pts2,d1u2,d1v2);
  }

  F(1) = (nplan.X() * (pts1.X() + pts2.X()) + 
	  nplan.Y() * (pts1.Y() + pts2.Y()) + 
	  nplan.Z() * (pts1.Z() + pts2.Z())) /2. + theD;

  gp_Vec ns1 = d1u1.Crossed(d1v1);
  if (ns1.Magnitude() < Eps) {
    if (first) BlendFunc::ComputeNormal(surf1, pt2d, ns1);
    else {
      gp_Pnt2d P(X(3), X(4));
      BlendFunc::ComputeNormal(surf1, P, ns1);
    }
  }

  gp_Vec ns2 = d1u2.Crossed(d1v2);
  if (ns2.Magnitude() < Eps) {
    if (!first) BlendFunc::ComputeNormal(surf2, pt2d, ns2);
    else {
      gp_Pnt2d P(X(3), X(4));
      BlendFunc::ComputeNormal(surf2, P, ns2);
    }
  }

  Standard_Real norm1 = nplan.Crossed(ns1).Magnitude();
  Standard_Real norm2 = nplan.Crossed(ns2).Magnitude();
  if (norm1 < Eps)  {
    norm1 = 1; 
  }
  if (norm2 < Eps)  {
    norm2 = 1; // Unsatisfactory, but it is not necessary to stop
  }  

  gp_Vec resul;
  ns1.SetLinearForm(nplan.Dot(ns1)/norm1,nplan, -1./norm1,ns1);
  ns2.SetLinearForm(nplan.Dot(ns2)/norm2,nplan, -1./norm2,ns2);
  resul.SetLinearForm(ray1,ns1,-1.,pts2.XYZ(),-ray2,ns2,pts1.XYZ());
  F(2) = resul.X();
  F(3) = resul.Y();
  F(4) = resul.Z();

  return Standard_True;
}


Standard_Boolean BlendFunc_ConstRadInv::Derivatives(const math_Vector& X,
                                                    math_Matrix& D)
{
  gp_Vec d1u1,d1v1,d1u2,d1v2;
  gp_Vec d2u1,d2v1,d2uv1,d2u2,d2v2,d2uv2;
  gp_Vec d1cur,d2cur;
  gp_Vec ns1,ns2,nplan,dnplan,ncrossns1,ncrossns2,resul1,resul2,temp;
  gp_Pnt pts1,pts2,ptcur;
  gp_Pnt2d p2d;
  gp_Vec2d v2d;
  Standard_Real norm1,norm2,ndotns1,ndotns2,normtgcur;
  Standard_Real grosterme,theD;

  curv->D2(X(2),ptcur,d1cur,d2cur);
  normtgcur = d1cur.Magnitude();
  nplan = d1cur.Normalized();
  theD = -(nplan.XYZ().Dot(ptcur.XYZ()));

  dnplan.SetLinearForm(theD, nplan, d2cur);
  dnplan /= normtgcur;

  csurf->D1(X(1),p2d,v2d);
  if (first)
  {
    surf1->D2(p2d.X(),p2d.Y(),pts1,d1u1,d1v1,d2u1,d2v1,d2uv1);
    surf2->D2(X(3),X(4),pts2,d1u2,d1v2,d2u2,d2v2,d2uv2);
    temp.SetLinearForm(v2d.X(),d1u1,v2d.Y(),d1v1);
    D(1,1) = nplan.Dot(temp)/2.;
    temp.SetXYZ(0.5*(pts1.XYZ()+pts2.XYZ()) - ptcur.XYZ());
    D(1,2) = dnplan.Dot(temp) - normtgcur;
    D(1,3) = nplan.Dot(d1u2)/2.;
    D(1,4) = nplan.Dot(d1v2)/2.;
  }
  else
  {
    surf1->D2(X(3),X(4),pts1,d1u1,d1v1,d2u1,d2v1,d2uv1);
    surf2->D2(p2d.X(),p2d.Y(),pts2,d1u2,d1v2,d2u2,d2v2,d2uv2);
    temp.SetLinearForm(v2d.X(),d1u2,v2d.Y(),d1v2);
    D(1,1) = nplan.Dot(temp)/2.;
    temp.SetXYZ(0.5*(pts1.XYZ()+pts2.XYZ()) - ptcur.XYZ());
    D(1,2) = dnplan.Dot(temp) - normtgcur;
    D(1,3) = nplan.Dot(d1u1)/2.;
    D(1,4) = nplan.Dot(d1v1)/2.;
  }

  ns1 = d1u1.Crossed(d1v1);
  if (ns1.Magnitude() < Eps) {
   if (first) BlendFunc::ComputeNormal(surf1, p2d, ns1);
    else {
      gp_Pnt2d P(X(3), X(4));
      BlendFunc::ComputeNormal(surf1, P, ns1);
    }
  }

  ns2 = d1u2.Crossed(d1v2);
  if (ns2.Magnitude() < Eps) {
   if (!first) BlendFunc::ComputeNormal(surf2, p2d, ns2);
    else {
      gp_Pnt2d P(X(3), X(4));
      BlendFunc::ComputeNormal(surf2, P, ns2);
    }
  }

  ncrossns1 = nplan.Crossed(ns1);
  ncrossns2 = nplan.Crossed(ns2);
  norm1 = ncrossns1.Magnitude();
  norm2 = ncrossns2.Magnitude();
  if (norm1 < Eps)  {
    norm1 = 1; // Unsatisfactory, but it is not necessary to stop
#ifdef OCCT_DEBUG
    std::cout << " ConstRadInv : Surface singuliere " << std::endl;
#endif
  }
  if (norm2 < Eps)  {
    norm2 = 1; // Unsatisfactory, but it is not necessary to stop
#ifdef OCCT_DEBUG
    std::cout << " ConstRadInv : Surface singuliere " << std::endl;
#endif
  } 

  ndotns1 = nplan.Dot(ns1);
  ndotns2 = nplan.Dot(ns2);

  // Derived compared to u1

  temp = d2u1.Crossed(d1v1).Added(d1u1.Crossed(d2uv1));
  grosterme = ncrossns1.Dot(nplan.Crossed(temp))/norm1/norm1;
  resul1.SetLinearForm(-ray1/norm1*(grosterme*ndotns1-nplan.Dot(temp)),nplan,
		       ray1*grosterme/norm1,ns1,
		       -ray1/norm1,temp,
		       d1u1);


  // Derived compared to v1

  temp = d2uv1.Crossed(d1v1).Added(d1u1.Crossed(d2v1));
  grosterme = ncrossns1.Dot(nplan.Crossed(temp))/norm1/norm1;
  resul2.SetLinearForm(-ray1/norm1*(grosterme*ndotns1-nplan.Dot(temp)),nplan,
		       ray1*grosterme/norm1,ns1,
		       -ray1/norm1,temp,
		       d1v1);

  if (first) {
    D(2,1) = v2d.X()*resul1.X() + v2d.Y()*resul2.X();
    D(3,1) = v2d.X()*resul1.Y() + v2d.Y()*resul2.Y();
    D(4,1) = v2d.X()*resul1.Z() + v2d.Y()*resul2.Z();
  }
  else {
    D(2,3) = resul1.X();
    D(3,3) = resul1.Y();
    D(4,3) = resul1.Z();

    D(2,4) = resul2.X();
    D(3,4) = resul2.Y();
    D(4,4) = resul2.Z();
  }


  // derived compared to w (parameter on guideline)
  // It is assumed that the radius is constant

  grosterme = ncrossns1.Dot(dnplan.Crossed(ns1))/norm1/norm1;
  resul1.SetLinearForm(-ray1/norm1*(grosterme*ndotns1-dnplan.Dot(ns1)),nplan,
		       ray1*ndotns1/norm1,dnplan,
		       ray1*grosterme/norm1,ns1);


  grosterme = ncrossns2.Dot(dnplan.Crossed(ns2))/norm2/norm2;
  resul2.SetLinearForm(ray2/norm2*(grosterme*ndotns2-dnplan.Dot(ns2)),nplan,
		       -ray2*ndotns2/norm2,dnplan,
		       -ray2*grosterme/norm2,ns2);


  D(2,2) = resul1.X() + resul2.X();
  D(3,2) = resul1.Y() + resul2.Y();
  D(4,2) = resul1.Z() + resul2.Z();



  // Derived compared to u2
  temp = d2u2.Crossed(d1v2).Added(d1u2.Crossed(d2uv2));
  grosterme = ncrossns2.Dot(nplan.Crossed(temp))/norm2/norm2;
  resul1.SetLinearForm(ray2/norm2*(grosterme*ndotns2-nplan.Dot(temp)),nplan,
		       -ray2*grosterme/norm2,ns2,
		       ray2/norm2,temp);
  resul1.Subtract(d1u2);

  // Derived compared to v2
  temp = d2uv2.Crossed(d1v2).Added(d1u2.Crossed(d2v2));
  grosterme = ncrossns2.Dot(nplan.Crossed(temp))/norm2/norm2;
  resul2.SetLinearForm(ray2/norm2*(grosterme*ndotns2-nplan.Dot(temp)),nplan,
		       -ray2*grosterme/norm2,ns2,
		       ray2/norm2,temp);
  resul2.Subtract(d1v2);

  if (!first) {
    D(2,1) = v2d.X()*resul1.X() + v2d.Y()*resul2.X();
    D(3,1) = v2d.X()*resul1.Y() + v2d.Y()*resul2.Y();
    D(4,1) = v2d.X()*resul1.Z() + v2d.Y()*resul2.Z();
  }
  else {
    D(2,3) = resul1.X();
    D(3,3) = resul1.Y();
    D(4,3) = resul1.Z();

    D(2,4) = resul2.X();
    D(3,4) = resul2.Y();
    D(4,4) = resul2.Z();
  }


  return Standard_True;
}

Standard_Boolean BlendFunc_ConstRadInv::Values(const math_Vector& X,
					       math_Vector& F,
					       math_Matrix& D)
{
  gp_Vec d1u1,d1v1,d1u2,d1v2,d1cur;
  gp_Vec d2u1,d2v1,d2uv1,d2u2,d2v2,d2uv2,d2cur;
  gp_Vec ns1,ns2,nplan,dnplan,ncrossns1,ncrossns2,resul1,resul2,temp;
  gp_Pnt ptcur,pts1,pts2;
  gp_Pnt2d p2d;
  gp_Vec2d v2d;
  Standard_Real norm1,norm2,ndotns1,ndotns2,normtgcur;
  Standard_Real grosterme,theD;

  curv->D2(X(2),ptcur,d1cur,d2cur);
  normtgcur = d1cur.Magnitude();
  nplan = d1cur.Normalized();
  theD = -(nplan.XYZ().Dot(ptcur.XYZ()));
  dnplan.SetLinearForm(-nplan.Dot(d2cur),nplan,d2cur);
  dnplan /= normtgcur;

  csurf->D1(X(1),p2d,v2d);

  if (first)
  {
    surf1->D2(p2d.X(),p2d.Y(),pts1,d1u1,d1v1,d2u1,d2v1,d2uv1);
    surf2->D2(X(3),X(4),pts2,d1u2,d1v2,d2u2,d2v2,d2uv2);

    temp.SetLinearForm(v2d.X(),d1u1,v2d.Y(),d1v1);
    D(1,1) = nplan.Dot(temp)/2.;
    temp.SetXYZ(0.5*(pts1.XYZ()+pts2.XYZ())-ptcur.XYZ());
    D(1,2) = dnplan.Dot(temp) - normtgcur;
    D(1,3) = nplan.Dot(d1u2)/2.;
    D(1,4) = nplan.Dot(d1v2)/2.;
  }
  else
  {
    surf1->D2(X(3),X(4),pts1,d1u1,d1v1,d2u1,d2v1,d2uv1);
    surf2->D2(p2d.X(),p2d.Y(),pts2,d1u2,d1v2,d2u2,d2v2,d2uv2);

    temp.SetLinearForm(v2d.X(),d1u2,v2d.Y(),d1v2);
    D(1,1) = nplan.Dot(temp)/2.;
    temp.SetXYZ(0.5*(pts1.XYZ()+pts2.XYZ())-ptcur.XYZ());
    D(1,2) = dnplan.Dot(temp) - normtgcur;
    D(1,3) = nplan.Dot(d1u1)/2.;
    D(1,4) = nplan.Dot(d1v1)/2.;
  }

  F(1) = (nplan.X()* (pts1.X() + pts2.X()) + 
	  nplan.Y()* (pts1.Y() + pts2.Y()) + 
	  nplan.Z()* (pts1.Z() + pts2.Z())) /2. + theD;


  ns1 = d1u1.Crossed(d1v1);
  if (ns1.Magnitude() < Eps) {
    if (first) BlendFunc::ComputeNormal(surf1, p2d, ns1);
    else {
      gp_Pnt2d P(X(3), X(4));
      BlendFunc::ComputeNormal(surf1, P, ns1);
    }
  }

  ns2 = d1u2.Crossed(d1v2);
  if (ns2.Magnitude() < Eps) {
    if (!first) BlendFunc::ComputeNormal(surf2, p2d, ns2);
    else {
      gp_Pnt2d P(X(3), X(4));
      BlendFunc::ComputeNormal(surf2, P, ns2);
    }
  }

  ncrossns1 = nplan.Crossed(ns1);
  ncrossns2 = nplan.Crossed(ns2);
  norm1 = ncrossns1.Magnitude();
  norm2 = ncrossns2.Magnitude();
  if (norm1 < Eps)  {
    norm1 = 1; // Unsatisfactory, but it is not necessary to stop
#ifdef OCCT_DEBUG
    std::cout << " ConstRadInv : Surface singuliere " << std::endl;
#endif
  }
  if (norm2 < Eps)  {
    norm2 = 1; // Unsatisfactory, but it is not necessary to stop
#ifdef OCCT_DEBUG
    std::cout << " ConstRadInv : Surface singuliere " << std::endl;
#endif
  } 

  ndotns1 = nplan.Dot(ns1);
  ndotns2 = nplan.Dot(ns2);

  temp.SetLinearForm(ndotns1/norm1,nplan, -1./norm1,ns1);
  resul1.SetLinearForm(ray1,temp,gp_Vec(pts2,pts1));
  temp.SetLinearForm(ndotns2/norm2,nplan,-1./norm2,ns2);
  resul1.Subtract(ray2*temp);

  F(2) = resul1.X();
  F(3) = resul1.Y();
  F(4) = resul1.Z();

  // Derived compared to u1

  temp = d2u1.Crossed(d1v1).Added(d1u1.Crossed(d2uv1));
  grosterme = ncrossns1.Dot(nplan.Crossed(temp))/norm1/norm1;
  resul1.SetLinearForm(-ray1/norm1*(grosterme*ndotns1-nplan.Dot(temp)),nplan,
		       ray1*grosterme/norm1,ns1,
		       -ray1/norm1,temp,
		       d1u1);


  // Derived compared to v1

  temp = d2uv1.Crossed(d1v1).Added(d1u1.Crossed(d2v1));
  grosterme = ncrossns1.Dot(nplan.Crossed(temp))/norm1/norm1;
  resul2.SetLinearForm(-ray1/norm1*(grosterme*ndotns1-nplan.Dot(temp)),nplan,
		       ray1*grosterme/norm1,ns1,
		       -ray1/norm1,temp,
		       d1v1);

  if (first) {
    D(2,1) = v2d.X()*resul1.X() + v2d.Y()*resul2.X();
    D(3,1) = v2d.X()*resul1.Y() + v2d.Y()*resul2.Y();
    D(4,1) = v2d.X()*resul1.Z() + v2d.Y()*resul2.Z();
  }
  else {
    D(2,3) = resul1.X();
    D(3,3) = resul1.Y();
    D(4,3) = resul1.Z();

    D(2,4) = resul2.X();
    D(3,4) = resul2.Y();
    D(4,4) = resul2.Z();
  }

  // derived compared to w (parameter on guideline)
  // It is assumed that the raduis is constant

  grosterme = ncrossns1.Dot(dnplan.Crossed(ns1))/norm1/norm1;
  resul1.SetLinearForm(-ray1/norm1*(grosterme*ndotns1-dnplan.Dot(ns1)),nplan,
		       ray1*ndotns1/norm1,dnplan,
		       ray1*grosterme/norm1,ns1);


  grosterme = ncrossns2.Dot(dnplan.Crossed(ns2))/norm2/norm2;
  resul2.SetLinearForm(ray2/norm2*(grosterme*ndotns2-dnplan.Dot(ns2)),nplan,
		       -ray2*ndotns2/norm2,dnplan,
		       -ray2*grosterme/norm2,ns2);


  D(2,2) = resul1.X() + resul2.X();
  D(3,2) = resul1.Y() + resul2.Y();
  D(4,2) = resul1.Z() + resul2.Z();



  // Derived compared to u2
  temp = d2u2.Crossed(d1v2).Added(d1u2.Crossed(d2uv2));
  grosterme = ncrossns2.Dot(nplan.Crossed(temp))/norm2/norm2;
  resul1.SetLinearForm(ray2/norm2*(grosterme*ndotns2-nplan.Dot(temp)),nplan,
		       -ray2*grosterme/norm2,ns2,
		       ray2/norm2,temp);
  resul1.Subtract(d1u2);

  // Derived compared to v2
  temp = d2uv2.Crossed(d1v2).Added(d1u2.Crossed(d2v2));
  grosterme = ncrossns2.Dot(nplan.Crossed(temp))/norm2/norm2;
  resul2.SetLinearForm(ray2/norm2*(grosterme*ndotns2-nplan.Dot(temp)),nplan,
		       -ray2*grosterme/norm2,ns2,
		       ray2/norm2,temp);
  resul2.Subtract(d1v2);

  if (!first) {
    D(2,1) = v2d.X()*resul1.X() + v2d.Y()*resul2.X();
    D(3,1) = v2d.X()*resul1.Y() + v2d.Y()*resul2.Y();
    D(4,1) = v2d.X()*resul1.Z() + v2d.Y()*resul2.Z();
  }
  else {
    D(2,3) = resul1.X();
    D(3,3) = resul1.Y();
    D(4,3) = resul1.Z();

    D(2,4) = resul2.X();
    D(3,4) = resul2.Y();
    D(4,4) = resul2.Z();
  }
  return Standard_True;
}