OCCT

// Created on: 1991-09-09
// Created by: Michel Chauvat
// Copyright (c) 1991-1999 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 <CSLib.hxx>
#include <CSLib_NormalPolyDef.hxx>
#include <gp.hxx>
#include <gp_Dir.hxx>
#include <gp_Vec.hxx>
#include <math_FunctionRoots.hxx>
#include <PLib.hxx>
#include <Precision.hxx>
#include <TColgp_Array2OfVec.hxx>
#include <TColStd_Array1OfReal.hxx>
#include <TColStd_Array2OfReal.hxx>

void CSLib::Normal (

const gp_Vec&        D1U, 
const gp_Vec&        D1V,
const Standard_Real        SinTol, 
CSLib_DerivativeStatus& theStatus,
gp_Dir&              Normal
) {

// Function: Calculation of the normal from tangents by u and by v.

  Standard_Real D1UMag = D1U.SquareMagnitude(); 
  Standard_Real D1VMag = D1V.SquareMagnitude();
  gp_Vec D1UvD1V = D1U.Crossed(D1V);

  if (D1UMag <= gp::Resolution() && D1VMag <= gp::Resolution()) {
     theStatus = CSLib_D1IsNull;
  }
  else if (D1UMag <= gp::Resolution())           theStatus = CSLib_D1uIsNull;
  else if (D1VMag <= gp::Resolution())           theStatus = CSLib_D1vIsNull;
//  else if ((D1VMag / D1UMag) <= RealEpsilon())   theStatus = CSLib_D1vD1uRatioIsNull;
//  else if ((D1UMag / D1VMag) <= RealEpsilon())   theStatus = CSLib_D1uD1vRatioIsNull;
  else  {
    Standard_Real Sin2 = 
    D1UvD1V.SquareMagnitude() / (D1UMag * D1VMag);
    
    if (Sin2 < (SinTol * SinTol))  { theStatus = CSLib_D1uIsParallelD1v; }
    else { Normal = gp_Dir (D1UvD1V);   theStatus = CSLib_Done; }
  }
}

void CSLib::Normal (

const gp_Vec&    D1U,
const gp_Vec&    D1V,
const gp_Vec&    D2U,
const gp_Vec&    D2V, 
const gp_Vec&    DUV,
const Standard_Real    SinTol,
Standard_Boolean&      Done,
CSLib_NormalStatus& theStatus,
gp_Dir&          Normal
) {

//  Calculation of an approximate normale in case of a null normal.
//  Use limited development of the normal of order 1:
//     N(u0+du,v0+dv) = N0 + dN/du(u0,v0) * du + dN/dv(u0,v0) * dv + epsilon
//  -> N ~ dN/du + dN/dv.



  gp_Vec D1Nu = D2U.Crossed (D1V);
  D1Nu.Add (D1U.Crossed (DUV));

  gp_Vec D1Nv = DUV.Crossed (D1V);
  D1Nv.Add (D1U.Crossed (D2V));

  Standard_Real LD1Nu = D1Nu.SquareMagnitude();
  Standard_Real LD1Nv = D1Nv.SquareMagnitude();


  if (LD1Nu <= RealEpsilon() && LD1Nv <= RealEpsilon())  { 
      theStatus = CSLib_D1NIsNull;
      Done = Standard_False;
  }
  else if (LD1Nu < RealEpsilon()) {
      theStatus = CSLib_D1NuIsNull;
      Done = Standard_True;
      Normal = gp_Dir (D1Nv);
  }
  else if (LD1Nv < RealEpsilon()) {
      theStatus = CSLib_D1NvIsNull;
      Done = Standard_True;
      Normal = gp_Dir (D1Nu);
  }
  else if ((LD1Nv / LD1Nu) <= RealEpsilon()) { 
      theStatus = CSLib_D1NvNuRatioIsNull;
      Done = Standard_False;
  }
  else if ((LD1Nu / LD1Nv) <= RealEpsilon()) { 
      theStatus = CSLib_D1NuNvRatioIsNull;
      Done = Standard_False;
  }
  else {
    gp_Vec D1NCross = D1Nu.Crossed (D1Nv);
    Standard_Real Sin2 = D1NCross.SquareMagnitude() / (LD1Nu * LD1Nv);

    if (Sin2 < (SinTol * SinTol))  { 
      theStatus = CSLib_D1NuIsParallelD1Nv;
      Done = Standard_True;
      Normal = gp_Dir (D1Nu);
    }    
    else { 
      theStatus = CSLib_InfinityOfSolutions;
      Done = Standard_False;
    }
  }

}
void CSLib::Normal (

const gp_Vec&        D1U, 
const gp_Vec&        D1V,
const Standard_Real        MagTol, 
CSLib_NormalStatus& theStatus,
gp_Dir&              Normal
) {
// Function: Calculate the normal from tangents by u and by v.

  Standard_Real D1UMag = D1U.Magnitude(); 
  Standard_Real D1VMag = D1V.Magnitude();
  gp_Vec D1UvD1V = D1U.Crossed(D1V);
  Standard_Real NMag =D1UvD1V .Magnitude();

  if (NMag <= MagTol || D1UMag <= MagTol || D1VMag <= MagTol ) {

     theStatus = CSLib_Singular;
//     if (D1UMag <= MagTol || D1VMag <= MagTol && NMag > MagTol) MagTol = 2* NMag;
}
  else
  {
    // Firstly normalize tangent vectors D1U and D1V (this method is more stable)
    gp_Dir aD1U(D1U);
    gp_Dir aD1V(D1V);
    Normal = gp_Dir(aD1U.Crossed(aD1V));
    theStatus = CSLib_Defined;
  }
  

}
// Calculate normal vector in singular cases
//
void CSLib::Normal(const Standard_Integer MaxOrder, 
                   const TColgp_Array2OfVec& DerNUV, 
                   const Standard_Real SinTol, 
                   const Standard_Real U,
                   const Standard_Real V,
                   const Standard_Real Umin,
                   const Standard_Real Umax,
                   const Standard_Real Vmin,
                   const Standard_Real Vmax,
                   CSLib_NormalStatus& theStatus,
                   gp_Dir& Normal, 
                   Standard_Integer& OrderU, 
                   Standard_Integer& OrderV)
{
//  Standard_Integer i,l,Order=-1;
  Standard_Integer i=0,Order=-1;
  Standard_Boolean Trouve=Standard_False;
//  theStatus = Singular;
  Standard_Real Norme;
  gp_Vec D;
  //Find k0 such that all derivatives N=dS/du ^ dS/dv are null
  //till order k0-1
  while(!Trouve && Order < MaxOrder)
  {
    Order++;
    i=Order;
    while((i>=0) && (!Trouve))
    {
      Standard_Integer j=Order-i;
      D=DerNUV(i,j);
      Norme=D.Magnitude();
      Trouve=(Trouve ||(Norme>=SinTol));
      i--;
    }
  }
  OrderU=i+1;
  OrderV=Order-OrderU;
  //Vko first non null derivative of N : reference
  if(Trouve)
  {
     if(Order == 0) 
     {
         theStatus = CSLib_Defined;
         Normal=D.Normalized();
     }
     else
     {
      gp_Vec Vk0;  
      Vk0=DerNUV(OrderU,OrderV);
      TColStd_Array1OfReal Ratio(0,Order);
      //Calculate lambda i
      i=0;
      Standard_Boolean definie=Standard_False;
      while(i<=Order && !definie)
      {
         if(DerNUV(i,Order-i).Magnitude()<=SinTol) Ratio(i)=0;
         else
         {
            if(DerNUV(i,Order-i).IsParallel(Vk0,1e-6)) 
            {
//            Ratio(i) = DerNUV(i,Order-i).Magnitude() / Vk0.Magnitude();
//            if(DerNUV(i,Order-i).IsOpposite(Vk0,1e-6)) Ratio(i)=-Ratio(i);
               Standard_Real r = DerNUV(i,Order-i).Magnitude() / Vk0.Magnitude();
               if(DerNUV(i,Order-i).IsOpposite(Vk0,1e-6)) r=-r;
               Ratio(i)=r;
          
            }
            else
            {
	      definie=Standard_True;
//
            }
         }
         i++;
      }//end while
      if(!definie)
      {  //All lambda i exist
         Standard_Integer SP;
         Standard_Real inf,sup;
         inf = 0.0 - M_PI;
         sup = 0.0 + M_PI;
         Standard_Boolean FU,LU,FV,LV;

         //Creation of the domain of definition depending on the position
         //of a single point (medium, border, corner).
         FU=(Abs(U-Umin) < Precision::PConfusion());
         LU=(Abs(U-Umax) < Precision::PConfusion() );
         FV=(Abs(V-Vmin) < Precision::PConfusion() );
         LV=(Abs(V-Vmax) < Precision::PConfusion() );
         if (LU)
         {
            inf = M_PI / 2;
            sup = 3 * inf;
            if (LV)
            {
              inf = M_PI;
            }
            if (FV)
            {
              sup = M_PI;
            }
         }
         else if (FU)
         {
            sup = M_PI / 2;
	    inf = -sup;
	    if (LV)
            { 
              sup = 0;
            }
	    if (FV)
            {
              inf = 0;
            }
	 }
	 else if (LV)
	 {
	    inf = 0.0 - M_PI;
	    sup = 0;
         }
	 else if (FV)
	 {
            inf = 0;
	    sup = M_PI;
	 }
	 Standard_Boolean CS=0;
	 Standard_Real Vprec = 0., Vsuiv = 0.;
	 //Creation of the polynom
	 CSLib_NormalPolyDef  Poly(Order,Ratio);
	 //Find zeros of SAPS
	 math_FunctionRoots FindRoots(Poly,inf,sup,200,1e-5,
			           Precision::Confusion(),
                                   Precision::Confusion());
	 //If there are zeros
	 if (FindRoots.IsDone() && FindRoots.NbSolutions() > 0)
	    {
               //ranking by increasing order of roots of SAPS in Sol0

               TColStd_Array1OfReal Sol0(0,FindRoots.NbSolutions()+1);
               Sol0(1)=FindRoots.Value(1);
               Standard_Integer n=1;
               while(n<=FindRoots.NbSolutions())
               {
	          Standard_Real ASOL=FindRoots.Value(n);
	          Standard_Integer j=n-1;
	          while((j>=1) && (Sol0(j)> ASOL))
                  {
	             Sol0(j+1)=Sol0(j);
	             j--;
	          }
	          Sol0(j+1)=ASOL;
	          n++;
               }//end while(n
               //Add limits of the domains 
               Sol0(0)=inf;
               Sol0(FindRoots.NbSolutions()+1)=sup;
               //Find change of sign of SAPS in comparison with its
               //values to the left and right of each root
               Standard_Integer ifirst=0;
               for (i=0;i<=FindRoots.NbSolutions();i++) 
               {
                   if(Abs(Sol0(i+1)-Sol0(i)) > Precision::PConfusion())
                   {
                      Poly.Value((Sol0(i)+Sol0(i+1))/2.0,Vsuiv);
                      if(ifirst == 0) 
                      {
                         ifirst=i;
                         CS=Standard_False;
                         Vprec=Vsuiv;
                      }
                      else 
                      {
                         CS=(Vprec*Vsuiv)<0;
                         Vprec=Vsuiv;
                      }
                   }
               }
            }
         else
            {
               //SAPS has no root, so forcedly do not change the sign
               CS=Standard_False;
               Poly.Value(inf,Vsuiv);
            }
         //fin if(MFR.IsDone() && MFR.NbSolutions()>0)

         if(CS)
         //Polynom changes the sign
            SP=0;
	 else if(Vsuiv>0)
	         //Polynom is always positive
                 SP=1;
              else
                 //Polynom is always negative
                 SP=-1;
         if(SP==0)
             theStatus = CSLib_InfinityOfSolutions;
         else
         {
            theStatus = CSLib_Defined;
            Normal=SP*Vk0.Normalized();
         }
       }
       else 
       {
         theStatus = CSLib_Defined;
         Normal=D.Normalized();
       }
    }
   }
}
//
// Calculate the derivative of the non-normed normal vector
//
gp_Vec CSLib::DNNUV(const Standard_Integer Nu, 
		    const Standard_Integer Nv,
		    const TColgp_Array2OfVec& DerSurf)
{
  Standard_Integer i,j;
  gp_Vec D(0,0,0),VG,VD,PV;
  for(i=0;i<=Nu;i++)
    for(j=0;j<=Nv;j++){
      VG=DerSurf.Value(i+1,j);
      VD=DerSurf.Value(Nu-i,Nv+1-j);
      PV=VG^VD;
      D=D+PLib::Bin(Nu,i)*PLib::Bin(Nv,j)*PV;
    }
  return D;
}

//=======================================================================
//function : DNNUV
//purpose  : 
//=======================================================================

gp_Vec CSLib::DNNUV(const Standard_Integer Nu,
		    const Standard_Integer Nv,
		    const TColgp_Array2OfVec& DerSurf1,
		    const TColgp_Array2OfVec& DerSurf2) 
{
  Standard_Integer i,j;
  gp_Vec D(0,0,0),VG,VD,PV;
  for(i=0;i<=Nu;i++)
    for(j=0;j<=Nv;j++){
      VG=DerSurf1.Value(i+1,j);
      VD=DerSurf2.Value(Nu-i,Nv+1-j);
      PV=VG^VD;
      D=D+PLib::Bin(Nu,i)*PLib::Bin(Nv,j)*PV;
    }
  return D;
}

//
// Calculate the derivatives of the normed normal vector depending on the  derivatives
// of the non-normed normal vector
//
gp_Vec CSLib::DNNormal(const Standard_Integer Nu,
		       const Standard_Integer Nv,
		       const TColgp_Array2OfVec& DerNUV,
		       const Standard_Integer Iduref,
		       const Standard_Integer Idvref)
{
  const Standard_Integer Kderiv = Nu + Nv;
  TColgp_Array2OfVec DerVecNor(0,Kderiv,0,Kderiv);
  TColStd_Array2OfReal TabScal(0,Kderiv,0,Kderiv);
  TColStd_Array2OfReal TabNorm(0,Kderiv,0,Kderiv);
  gp_Vec DerNor = (DerNUV.Value (Iduref, Idvref)).Normalized();
  DerVecNor.SetValue(0,0,DerNor);
  Standard_Real Dnorm = DerNUV.Value (Iduref, Idvref) * DerVecNor.Value (0, 0);
  TabNorm.SetValue(0,0,Dnorm);
  TabScal.SetValue(0,0,0.);

  for (Standard_Integer Mderiv = 1; Mderiv <= Kderiv; Mderiv++)
  {
    for (Standard_Integer Pderiv = 0; Pderiv <= Mderiv; Pderiv++)
    {
      const Standard_Integer Qderiv = Mderiv - Pderiv;
      if (Pderiv > Nu || Qderiv > Nv)
      {
        continue;
      }

      //  Compute n . derivee(p,q) of n
      Standard_Real Scal = 0.;
      if (Pderiv > Qderiv)
      {
        for (Standard_Integer Jderiv = 1; Jderiv <= Qderiv; Jderiv++)
        {
          Scal = Scal - PLib::Bin (Qderiv, Jderiv)
                      * (DerVecNor.Value (0, Jderiv) * DerVecNor.Value (Pderiv, Qderiv - Jderiv));
        }

        for (Standard_Integer Jderiv = 0; Jderiv < Qderiv; Jderiv++)
        {
          Scal = Scal - PLib::Bin (Qderiv, Jderiv)
                      * (DerVecNor.Value (Pderiv, Jderiv) * DerVecNor.Value (0, Qderiv - Jderiv));
        }

        for (Standard_Integer Ideriv = 1; Ideriv < Pderiv; Ideriv++)
        {
          for (Standard_Integer Jderiv = 0; Jderiv <= Qderiv; Jderiv++)
          {
            Scal = Scal - PLib::Bin (Pderiv, Ideriv)
                        * PLib::Bin (Qderiv, Jderiv)
                        * (DerVecNor.Value (Ideriv, Jderiv) * DerVecNor.Value (Pderiv - Ideriv, Qderiv - Jderiv));
          }
        }
      }
      else
      {
        for (Standard_Integer Ideriv = 1; Ideriv <= Pderiv; Ideriv++)
        {
          Scal = Scal - PLib::Bin (Pderiv, Ideriv)
                      * DerVecNor.Value (Ideriv, 0)
                      * DerVecNor.Value (Pderiv - Ideriv, Qderiv);
        }

        for (Standard_Integer Ideriv = 0; Ideriv < Pderiv; Ideriv++)
        {
          Scal = Scal - PLib::Bin (Pderiv, Ideriv)
                      * DerVecNor.Value (Ideriv, Qderiv)
                      * DerVecNor.Value (Pderiv - Ideriv, 0);
        }

        for (Standard_Integer Ideriv = 0; Ideriv <= Pderiv; Ideriv++)
        {
          for (Standard_Integer Jderiv = 1; Jderiv < Qderiv; Jderiv++)
          {
            Scal = Scal - PLib::Bin (Pderiv, Ideriv)
                        * PLib::Bin (Qderiv, Jderiv)
                        * (DerVecNor.Value (Ideriv, Jderiv) * DerVecNor.Value (Pderiv - Ideriv, Qderiv - Jderiv));
          }
        }
      }
      TabScal.SetValue (Pderiv, Qderiv, Scal/2.);

      // Compute the derivative (n,p) of NUV Length
      Dnorm = (DerNUV.Value (Pderiv + Iduref, Qderiv + Idvref)) * DerVecNor.Value (0, 0);
      for (Standard_Integer Jderiv = 0; Jderiv < Qderiv; Jderiv++)
      {
        Dnorm = Dnorm - PLib::Bin (Qderiv + Idvref, Jderiv + Idvref)
                      * TabNorm.Value (Pderiv, Jderiv)
                      * TabScal.Value (0, Qderiv - Jderiv);
      }

      for (Standard_Integer Ideriv = 0; Ideriv < Pderiv; Ideriv++)
      {
        for (Standard_Integer Jderiv = 0; Jderiv <= Qderiv; Jderiv++)
        {
          Dnorm = Dnorm - PLib::Bin (Pderiv + Iduref, Ideriv + Iduref)
                        * PLib::Bin (Qderiv + Idvref, Jderiv + Idvref)
                        * TabNorm.Value (Ideriv, Jderiv)
                        * TabScal.Value (Pderiv - Ideriv, Qderiv - Jderiv);
        }
      }
      TabNorm.SetValue (Pderiv, Qderiv, Dnorm);

      // Compute derivative (p,q) of n
      DerNor = DerNUV.Value (Pderiv + Iduref, Qderiv + Idvref);
      for (Standard_Integer Jderiv = 1; Jderiv <= Qderiv; Jderiv++)
      {
        DerNor = DerNor - PLib::Bin (Pderiv + Iduref, Iduref)
                        * PLib::Bin (Qderiv + Idvref, Jderiv + Idvref)
                        * TabNorm.Value (0, Jderiv)
                        * DerVecNor.Value (Pderiv, Qderiv - Jderiv);
      }

      for (Standard_Integer Ideriv = 1; Ideriv <= Pderiv; Ideriv++)
      {
        for (Standard_Integer Jderiv = 0; Jderiv <= Qderiv; Jderiv++)
        {
          DerNor = DerNor - PLib::Bin (Pderiv + Iduref, Ideriv + Iduref)
                          * PLib::Bin (Qderiv + Idvref, Jderiv + Idvref)
                          * TabNorm.Value (Ideriv, Jderiv)
                          * DerVecNor.Value (Pderiv - Ideriv, Qderiv - Jderiv);
        }
      }
      DerNor = DerNor / PLib::Bin (Pderiv + Iduref, Iduref)
                      / PLib::Bin (Qderiv + Idvref, Idvref)
                      / TabNorm.Value (0, 0);
      DerVecNor.SetValue (Pderiv, Qderiv, DerNor);
    }
  }
  return DerVecNor.Value(Nu,Nv);
}