// Created on: 1997-02-21
// Created by: Laurent BOURESCHE
// 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 <Adaptor2d_HCurve2d.hxx>
#include <Adaptor3d_HCurve.hxx>
#include <Adaptor3d_HSurface.hxx>
#include <BRepBlend_SurfCurvConstRadInv.hxx>
#include <math_Matrix.hxx>

//=======================================================================
//function : BRepBlend_SurfCurvConstRadInv
//purpose  : 
//=======================================================================
BRepBlend_SurfCurvConstRadInv::BRepBlend_SurfCurvConstRadInv
(const Handle(Adaptor3d_HSurface)& S,
 const Handle(Adaptor3d_HCurve)& C,
 const Handle(Adaptor3d_HCurve)& Cg) : surf(S),curv(C),guide(Cg)
{
}

//=======================================================================
//function : Set
//purpose  : 
//=======================================================================

void BRepBlend_SurfCurvConstRadInv::Set(const Standard_Real R,
					const Standard_Integer Choix) 
{
  choix = Choix;
  switch (choix) {
  case 1:
  case 2:
    {
      ray = -Abs(R);
    }
    break;
  case 3:
  case 4:
    {
      ray = Abs(R);
    }
    break;
  default:
    {
      ray = -Abs(R);
    }
  }
}

//=======================================================================
//function : NbEquations
//purpose  : 
//=======================================================================

Standard_Integer BRepBlend_SurfCurvConstRadInv::NbEquations() const
{
  return 3;
}

//=======================================================================
//function : Value
//purpose  : 
//=======================================================================

Standard_Boolean BRepBlend_SurfCurvConstRadInv::Value(const math_Vector& X,
						      math_Vector& F) 
{
  gp_Pnt ptgui;
  gp_Vec d1gui;
  guide->D1(X(1),ptgui,d1gui);
  gp_Vec nplan = d1gui.Normalized();
  Standard_Real theD = -(nplan.XYZ().Dot(ptgui.XYZ()));
  gp_Pnt ptcur = curv->Value(X(2));
  F(1) = nplan.XYZ().Dot(ptcur.XYZ()) + theD;
  gp_Pnt2d p2drst = rst->Value(X(3));
  gp_Pnt pts;
  gp_Vec du,dv;
  surf->D1(p2drst.X(),p2drst.Y(),pts,du,dv);
  F(2) = nplan.XYZ().Dot(pts.XYZ()) + theD;
  gp_Vec ns = du.Crossed(dv);
  Standard_Real norm = nplan.Crossed(ns).Magnitude();
  Standard_Real unsurnorm = 1./norm;
  ns.SetLinearForm(nplan.Dot(ns),nplan, -1.,ns);
  ns.Multiply(unsurnorm);
  gp_Vec ref(ptcur,pts);
  ref.SetLinearForm(ray,ns,ref);
  F(3) = ref.SquareMagnitude() - ray*ray;
  return Standard_True;
}

//=======================================================================
//function : Derivatives
//purpose  : 
//=======================================================================

Standard_Boolean BRepBlend_SurfCurvConstRadInv::Derivatives(const math_Vector& X,
							    math_Matrix& D) 
{
  gp_Pnt ptgui;
  gp_Vec d1gui,d2gui;
  guide->D2(X(1),ptgui,d1gui,d2gui);
  Standard_Real normd1gui = d1gui.Magnitude();
  Standard_Real unsurnormd1gui = 1./normd1gui;
  gp_Vec nplan = d1gui.Multiplied(unsurnormd1gui);
  gp_Vec dnplan;
  dnplan.SetLinearForm(-nplan.Dot(d2gui),nplan,d2gui);
  dnplan.Multiply(unsurnormd1gui);
  Standard_Real dtheD = - nplan.XYZ().Dot(d1gui.XYZ()) - dnplan.XYZ().Dot(ptgui.XYZ());
  gp_Pnt ptcur;
  gp_Vec d1cur;
  curv->D1(X(2),ptcur,d1cur);
  D(1,1) = dnplan.XYZ().Dot(ptcur.XYZ()) + dtheD;
  D(1,2) = nplan.XYZ().Dot(d1cur.XYZ());
  D(1,3) = 0.;

  gp_Pnt2d p2drst;
  gp_Vec2d d1rst;
  rst->D1(X(3),p2drst,d1rst);
  gp_Pnt pts;
  gp_Vec d1u,d1v,d2u,d2v,duv;
  surf->D2(p2drst.X(),p2drst.Y(),pts,d1u,d1v,d2u,d2v,duv);
  D(2,1) = dnplan.XYZ().Dot(pts.XYZ()) + dtheD;
  D(2,2) = 0.;
  gp_Vec dwrstpts;
  dwrstpts.SetLinearForm(d1rst.X(),d1u,d1rst.Y(),d1v);
  D(2,3) = nplan.XYZ().Dot(dwrstpts.XYZ());

  gp_Vec nsurf = d1u.Crossed(d1v);
  gp_Vec dunsurf = d2u.Crossed(d1v).Added(d1u.Crossed(duv));
  gp_Vec dvnsurf = d1u.Crossed(d2v).Added(duv.Crossed(d1v));
  gp_Vec dwrstnsurf;
  dwrstnsurf.SetLinearForm(d1rst.X(),dunsurf,d1rst.Y(),dvnsurf);

  gp_Vec nplancrosnsurf = nplan.Crossed(nsurf);
  gp_Vec dwguinplancrosnsurf = dnplan.Crossed(nsurf);
  gp_Vec dwrstnplancrosnsurf = nplan.Crossed(dwrstnsurf);

  Standard_Real norm2      = nplancrosnsurf.SquareMagnitude();
  Standard_Real norm       = sqrt(norm2);
  Standard_Real unsurnorm  = 1./norm;
  Standard_Real raysurnorm = ray*unsurnorm;
  Standard_Real unsurnorm2 = unsurnorm * unsurnorm;
  Standard_Real raysurnorm2 = ray*unsurnorm2;
  Standard_Real dwguinorm = unsurnorm*nplancrosnsurf.Dot(dwguinplancrosnsurf);
  Standard_Real dwrstnorm = unsurnorm*nplancrosnsurf.Dot(dwrstnplancrosnsurf);

  Standard_Real nplandotnsurf   = nplan.Dot(nsurf);
  Standard_Real dwguinplandotnsurf = dnplan.Dot(nsurf);
  Standard_Real dwrstnplandotnsurf = nplan.Dot(dwrstnsurf);

  gp_Vec temp,dwguitemp,dwrsttemp;
  temp.SetLinearForm(nplandotnsurf,nplan,-1.,nsurf);
  dwguitemp.SetLinearForm(nplandotnsurf,dnplan,dwguinplandotnsurf,nplan);
  dwrsttemp.SetLinearForm(dwrstnplandotnsurf,nplan,-1.,dwrstnsurf);

  gp_Vec corde(ptcur,pts);
  gp_Vec ref,dwguiref,dwrstref;
  ref.SetLinearForm(raysurnorm,temp,corde);
  dwguiref.SetLinearForm(raysurnorm,dwguitemp,-raysurnorm2*dwguinorm,temp);
  dwrstref.SetLinearForm(raysurnorm,dwrsttemp,-raysurnorm2*dwrstnorm,temp,dwrstpts);

  ref.Add(ref);
  D(3,1) = ref.Dot(dwguiref);
  D(3,2) = -ref.Dot(d1cur);
  D(3,3) = ref.Dot(dwrstref);

  return Standard_True;
}

//=======================================================================
//function : Values
//purpose  : 
//=======================================================================

Standard_Boolean BRepBlend_SurfCurvConstRadInv::Values(const math_Vector& X,
						       math_Vector& F,
						       math_Matrix& D) 
{
  gp_Pnt ptgui;
  gp_Vec d1gui(0.,0.,0.),d2gui(0.,0.,0.);
  guide->D2(X(1),ptgui,d1gui,d2gui);
  Standard_Real normd1gui = d1gui.Magnitude();
  Standard_Real unsurnormd1gui = 1./normd1gui;
  gp_Vec nplan = d1gui.Multiplied(unsurnormd1gui);
  Standard_Real theD = -(nplan.XYZ().Dot(ptgui.XYZ()));
  gp_Vec dnplan;
  dnplan.SetLinearForm(-nplan.Dot(d2gui),nplan,d2gui);
  dnplan.Multiply(unsurnormd1gui);
  Standard_Real dtheD = - nplan.XYZ().Dot(d1gui.XYZ()) - dnplan.XYZ().Dot(ptgui.XYZ());
  gp_Pnt ptcur;
  gp_Vec d1cur;
  curv->D1(X(2),ptcur,d1cur);
  F(1) = nplan.XYZ().Dot(ptcur.XYZ()) + theD;
  D(1,1) = dnplan.XYZ().Dot(ptcur.XYZ()) + dtheD;
  D(1,2) = nplan.XYZ().Dot(d1cur.XYZ());
  D(1,3) = 0.;

  gp_Pnt2d p2drst;
  gp_Vec2d d1rst;
  rst->D1(X(3),p2drst,d1rst);
  gp_Pnt pts;
  gp_Vec d1u,d1v,d2u,d2v,duv;
  surf->D2(p2drst.X(),p2drst.Y(),pts,d1u,d1v,d2u,d2v,duv);
  F(2) = nplan.XYZ().Dot(pts.XYZ()) + theD;
  D(2,1) = dnplan.XYZ().Dot(pts.XYZ()) + dtheD;
  D(2,2) = 0.;
  gp_Vec dwrstpts;
  dwrstpts.SetLinearForm(d1rst.X(),d1u,d1rst.Y(),d1v);
  D(2,3) = nplan.XYZ().Dot(dwrstpts.XYZ());

  gp_Vec nsurf = d1u.Crossed(d1v);
  gp_Vec dunsurf = d2u.Crossed(d1v).Added(d1u.Crossed(duv));
  gp_Vec dvnsurf = d1u.Crossed(d2v).Added(duv.Crossed(d1v));
  gp_Vec dwrstnsurf;
  dwrstnsurf.SetLinearForm(d1rst.X(),dunsurf,d1rst.Y(),dvnsurf);

  gp_Vec nplancrosnsurf = nplan.Crossed(nsurf);
  gp_Vec dwguinplancrosnsurf = dnplan.Crossed(nsurf);
  gp_Vec dwrstnplancrosnsurf = nplan.Crossed(dwrstnsurf);

  Standard_Real norm2      = nplancrosnsurf.SquareMagnitude();
  Standard_Real norm       = sqrt(norm2);
  Standard_Real unsurnorm  = 1./norm;
  Standard_Real raysurnorm = ray*unsurnorm;
  Standard_Real unsurnorm2 = unsurnorm * unsurnorm;
  Standard_Real raysurnorm2 = ray*unsurnorm2;
  Standard_Real dwguinorm = unsurnorm*nplancrosnsurf.Dot(dwguinplancrosnsurf);
  Standard_Real dwrstnorm = unsurnorm*nplancrosnsurf.Dot(dwrstnplancrosnsurf);

  Standard_Real nplandotnsurf   = nplan.Dot(nsurf);
  Standard_Real dwguinplandotnsurf = dnplan.Dot(nsurf);
  Standard_Real dwrstnplandotnsurf = nplan.Dot(dwrstnsurf);

  gp_Vec temp,dwguitemp,dwrsttemp;
  temp.SetLinearForm(nplandotnsurf,nplan,-1.,nsurf);
  dwguitemp.SetLinearForm(nplandotnsurf,dnplan,dwguinplandotnsurf,nplan);
  dwrsttemp.SetLinearForm(dwrstnplandotnsurf,nplan,-1.,dwrstnsurf);

  gp_Vec corde(ptcur,pts);
  gp_Vec ref,dwguiref,dwrstref;
  ref.SetLinearForm(raysurnorm,temp,corde);
  F(3) = ref.SquareMagnitude() - ray*ray;
  dwguiref.SetLinearForm(raysurnorm,dwguitemp,-raysurnorm2*dwguinorm,temp);
  dwrstref.SetLinearForm(raysurnorm,dwrsttemp,-raysurnorm2*dwrstnorm,temp,dwrstpts);

  ref.Add(ref);
  D(3,1) = ref.Dot(dwguiref);
  D(3,2) = -ref.Dot(d1cur);
  D(3,3) = ref.Dot(dwrstref);
  return Standard_True;
}

//=======================================================================
//function : Set
//purpose  : 
//=======================================================================

void BRepBlend_SurfCurvConstRadInv::Set(const Handle(Adaptor2d_HCurve2d)& Rst) 
{
  rst = Rst;
}

//=======================================================================
//function : GetTolerance
//purpose  : 
//=======================================================================

void BRepBlend_SurfCurvConstRadInv::GetTolerance(math_Vector& Tolerance,
						 const Standard_Real Tol) const
{
  Tolerance(1) = guide->Resolution(Tol);
  Tolerance(2) = curv->Resolution(Tol);
  Standard_Real ru,rv;
  ru = surf->UResolution(Tol);
  rv = surf->VResolution(Tol);
  Tolerance(3) = rst->Resolution(Min(ru,rv)); 
}

//=======================================================================
//function : GetBounds
//purpose  : 
//=======================================================================

void BRepBlend_SurfCurvConstRadInv::GetBounds(math_Vector& InfBound,
					      math_Vector& SupBound) const
{
  InfBound(1) = guide->FirstParameter();
  SupBound(1) = guide->LastParameter();
  InfBound(2) = curv->FirstParameter();
  SupBound(2) = curv->LastParameter();
  InfBound(3) = rst->FirstParameter();
  SupBound(3) = rst->LastParameter();
}

//=======================================================================
//function : IsSolution
//purpose  : 
//=======================================================================

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