[occt.git] / src / GeomEvaluator / GeomEvaluator_OffsetSurface.cxx

// Created on: 2015-09-21
// Copyright (c) 2015 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 <GeomEvaluator_OffsetSurface.hxx>

#include <CSLib.hxx>
#include <CSLib_NormalStatus.hxx>
#include <Geom_BezierSurface.hxx>
#include <Geom_BSplineSurface.hxx>
#include <Geom_UndefinedValue.hxx>
#include <GeomAdaptor_Surface.hxx>
#include <gp_Vec.hxx>
#include <Standard_RangeError.hxx>
#include <Standard_NumericError.hxx>

IMPLEMENT_STANDARD_RTTIEXT(GeomEvaluator_OffsetSurface,GeomEvaluator_Surface)

namespace {

// tolerance for considering derivative to be null
const Standard_Real the_D1MagTol = 1.e-9;

// If calculation of normal fails, try shifting the point towards the center 
// of the parametric space of the surface, in the hope that derivatives 
// are better defined there.
//
// This shift is iterative, starting with Precision::PConfusion()
// and increasing by multiple of 2 on each step.
//
// NB: temporarily this is made as static function and not class method, 
// hence code duplications
static Standard_Boolean shiftPoint (const Standard_Real theUStart, const Standard_Real theVStart,
                                    Standard_Real& theU, Standard_Real& theV, 
                                    const Handle(Geom_Surface)& theSurf,
                                    const Handle(GeomAdaptor_Surface)& theAdaptor,
                                    const gp_Vec& theD1U, const gp_Vec& theD1V)
{
  // Get parametric bounds and closure status
  Standard_Real aUMin, aUMax, aVMin, aVMax;
  Standard_Boolean isUPeriodic, isVPeriodic;
  if (! theSurf.IsNull())
  {
    theSurf->Bounds (aUMin, aUMax, aVMin, aVMax);
    isUPeriodic = theSurf->IsUPeriodic();
    isVPeriodic = theSurf->IsVPeriodic();
  }
  else
  {
    aUMin = theAdaptor->FirstUParameter();
    aUMax = theAdaptor->LastUParameter();
    aVMin = theAdaptor->FirstVParameter();
    aVMax = theAdaptor->LastVParameter();
    isUPeriodic = theAdaptor->IsUPeriodic();
    isVPeriodic = theAdaptor->IsVPeriodic();
  }

  // check if either U or V is singular (normally one of them is)
  Standard_Boolean isUSingular = (theD1U.SquareMagnitude() < the_D1MagTol * the_D1MagTol);
  Standard_Boolean isVSingular = (theD1V.SquareMagnitude() < the_D1MagTol * the_D1MagTol);

  // compute vector to shift from start point to center of the surface;
  // if surface is periodic or singular in some direction, take shift in that direction zero
  Standard_Real aDirU = (isUPeriodic || (isUSingular && ! isVSingular) ? 0. : 0.5 * (aUMin + aUMax) - theUStart);
  Standard_Real aDirV = (isVPeriodic || (isVSingular && ! isUSingular) ? 0. : 0.5 * (aVMin + aVMax) - theVStart);
  Standard_Real aDist = Sqrt (aDirU * aDirU + aDirV * aDirV);

  // shift current point from its current position towards center, by value of twice
  // current distance from it to start (but not less than Precision::PConfusion());
  // fail if center is overpassed.
  Standard_Real aDU = theU - theUStart;
  Standard_Real aDV = theV - theVStart;
  Standard_Real aStep = Max (2. * Sqrt (aDU * aDU + aDV * aDV), Precision::PConfusion());
  if (aStep >= aDist)
  {
    return Standard_False;
  }

  aStep /= aDist;
  theU += aDirU * aStep;
  theV += aDirV * aStep;

//  std::cout << "Normal calculation failed at (" << theUStart << ", " << theVStart << "), shifting to (" << theU << ", " << theV << ")" << std::endl;

  return Standard_True;
}

// auxiliary function
template<class SurfOrAdapt>
static void derivatives(Standard_Integer theMaxOrder,
                        Standard_Integer theMinOrder,
                        const Standard_Real theU,
                        const Standard_Real theV,
                        const SurfOrAdapt& theBasisSurf,
                        const Standard_Integer theNU,
                        const Standard_Integer theNV,
                        const Standard_Boolean theAlongU,
                        const Standard_Boolean theAlongV,
                        const Handle(Geom_BSplineSurface)& theL,
                        TColgp_Array2OfVec& theDerNUV,
                        TColgp_Array2OfVec& theDerSurf)
{
  Standard_Integer i, j;
  gp_Pnt P;
  gp_Vec DL1U, DL1V, DL2U, DL2V, DL2UV, DL3U, DL3UUV, DL3UVV, DL3V;

  if (theAlongU || theAlongV)
  {
    theMaxOrder = 0;
    TColgp_Array2OfVec DerSurfL(0, theMaxOrder + theNU + 1, 0, theMaxOrder + theNV + 1);
    switch (theMinOrder)
    {
    case 1:
      theL->D1(theU, theV, P, DL1U, DL1V);
      DerSurfL.SetValue(1, 0, DL1U);
      DerSurfL.SetValue(0, 1, DL1V);
      break;
    case 2:
      theL->D2(theU, theV, P, DL1U, DL1V, DL2U, DL2V, DL2UV);
      DerSurfL.SetValue(1, 0, DL1U);
      DerSurfL.SetValue(0, 1, DL1V);
      DerSurfL.SetValue(1, 1, DL2UV);
      DerSurfL.SetValue(2, 0, DL2U);
      DerSurfL.SetValue(0, 2, DL2V);
      break;
    case 3:
      theL->D3(theU, theV, P, DL1U, DL1V, DL2U, DL2V, DL2UV, DL3U, DL3V, DL3UUV, DL3UVV);
      DerSurfL.SetValue(1, 0, DL1U);
      DerSurfL.SetValue(0, 1, DL1V);
      DerSurfL.SetValue(1, 1, DL2UV);
      DerSurfL.SetValue(2, 0, DL2U);
      DerSurfL.SetValue(0, 2, DL2V);
      DerSurfL.SetValue(3, 0, DL3U);
      DerSurfL.SetValue(2, 1, DL3UUV);
      DerSurfL.SetValue(1, 2, DL3UVV);
      DerSurfL.SetValue(0, 3, DL3V);
      break;
    default:
      break;
    }

    if (theNU <= theNV)
    {
      for (i = 0; i <= theMaxOrder + 1 + theNU; i++)
        for (j = i; j <= theMaxOrder + theNV + 1; j++)
          if (i + j > theMinOrder)
          {
            DerSurfL.SetValue(i, j, theL->DN(theU, theV, i, j));
            theDerSurf.SetValue(i, j, theBasisSurf->DN(theU, theV, i, j));
            if (i != j && j <= theNU + 1)
            {
              theDerSurf.SetValue(j, i, theBasisSurf->DN(theU, theV, j, i));
              DerSurfL.SetValue(j, i, theL->DN(theU, theV, j, i));
            }
          }
    }
    else
    {
      for (j = 0; j <= theMaxOrder + 1 + theNV; j++)
        for (i = j; i <= theMaxOrder + theNU + 1; i++)
          if (i + j > theMinOrder)
          {
            DerSurfL.SetValue(i, j, theL->DN(theU, theV, i, j));
            theDerSurf.SetValue(i, j, theBasisSurf->DN(theU, theV, i, j));
            if (i != j && i <= theNV + 1)
            {
              theDerSurf.SetValue(j, i, theBasisSurf->DN(theU, theV, j, i));
              DerSurfL.SetValue(j, i, theL->DN(theU, theV, j, i));
            }
          }
    }
    for (i = 0; i <= theMaxOrder + theNU; i++)
      for (j = 0; j <= theMaxOrder + theNV; j++)
      {
        if (theAlongU)
          theDerNUV.SetValue(i, j, CSLib::DNNUV(i, j, DerSurfL, theDerSurf));
        if (theAlongV)
          theDerNUV.SetValue(i, j, CSLib::DNNUV(i, j, theDerSurf, DerSurfL));
      }
  }
  else
  {
    for (i = 0; i <= theMaxOrder + theNU+ 1; i++)
    {
      for (j = i; j <= theMaxOrder + theNV + 1; j++)
      {
        if (i + j > theMinOrder)
        {
          theDerSurf.SetValue(i, j, theBasisSurf->DN(theU, theV, i, j));
          if (i != j
           && j <= theDerSurf.UpperRow()
           && i <= theDerSurf.UpperCol())
          {
            theDerSurf.SetValue(j, i, theBasisSurf->DN(theU, theV, j, i));
          }
        }
      }
    }
    for (i = 0; i <= theMaxOrder + theNU; i++)
      for (j = 0; j <= theMaxOrder + theNV; j++)
        theDerNUV.SetValue(i, j, CSLib::DNNUV(i, j, theDerSurf));
  }
}

inline Standard_Boolean IsInfiniteCoord (const gp_Vec& theVec)
{
  return Precision::IsInfinite (theVec.X()) ||
         Precision::IsInfinite (theVec.Y()) ||
         Precision::IsInfinite (theVec.Z());
}

inline void CheckInfinite (const gp_Vec& theVecU, const gp_Vec& theVecV)
{
  if (IsInfiniteCoord (theVecU) || IsInfiniteCoord (theVecV))
  {
    throw Standard_NumericError ("GeomEvaluator_OffsetSurface: Evaluation of infinite parameters");
  }
}

} // end of anonymous namespace

GeomEvaluator_OffsetSurface::GeomEvaluator_OffsetSurface(
        const Handle(Geom_Surface)& theBase,
        const Standard_Real theOffset,
        const Handle(Geom_OsculatingSurface)& theOscSurf)
  : GeomEvaluator_Surface(),
    myBaseSurf(theBase),
    myOffset(theOffset),
    myOscSurf(theOscSurf)
{
  if (!myOscSurf.IsNull())
    return; // osculating surface already exists

  // Create osculating surface for B-spline and Besier surfaces only
  if (myBaseSurf->IsKind(STANDARD_TYPE(Geom_BSplineSurface)) ||
      myBaseSurf->IsKind(STANDARD_TYPE(Geom_BezierSurface)))
    myOscSurf = new Geom_OsculatingSurface(myBaseSurf, Precision::Confusion());
}

GeomEvaluator_OffsetSurface::GeomEvaluator_OffsetSurface(
        const Handle(GeomAdaptor_Surface)& theBase,
        const Standard_Real theOffset,
        const Handle(Geom_OsculatingSurface)& theOscSurf)
  : GeomEvaluator_Surface(),
    myBaseAdaptor(theBase),
    myOffset(theOffset),
    myOscSurf(theOscSurf)
{
}

void GeomEvaluator_OffsetSurface::D0(
    const Standard_Real theU, const Standard_Real theV, gp_Pnt& theValue) const
{
  Standard_Real aU = theU, aV = theV;
  for (;;)
  {
    gp_Vec aD1U, aD1V;
    BaseD1 (aU, aV, theValue, aD1U, aD1V);

    CheckInfinite (aD1U, aD1V);

    try 
    {
      CalculateD0(aU, aV, theValue, aD1U, aD1V);
      break;
    } 
    catch (Geom_UndefinedValue&)
    {
      // if failed at parametric boundary, try taking derivative at shifted point
      if (! shiftPoint (theU, theV, aU, aV, myBaseSurf, myBaseAdaptor, aD1U, aD1V))
      {
        throw;
      }
    }
  }
}

void GeomEvaluator_OffsetSurface::D1(
    const Standard_Real theU, const Standard_Real theV,
    gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V) const
{
  Standard_Real aU = theU, aV = theV;
  for (;;)
  {
    gp_Vec aD2U, aD2V, aD2UV;
    BaseD2 (aU, aV, theValue, theD1U, theD1V, aD2U, aD2V, aD2UV);

    CheckInfinite (theD1U, theD1V);

    try 
    {
      CalculateD1(aU, aV, theValue, theD1U, theD1V, aD2U, aD2V, aD2UV);
      break;
    } 
    catch (Geom_UndefinedValue&)
    {
      // if failed at parametric boundary, try taking derivative at shifted point
      if (! shiftPoint (theU, theV, aU, aV, myBaseSurf, myBaseAdaptor, theD1U, theD1V))
      {
        throw;
      }
    }
  }
}

void GeomEvaluator_OffsetSurface::D2(
    const Standard_Real theU, const Standard_Real theV,
    gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V,
    gp_Vec& theD2U, gp_Vec& theD2V, gp_Vec& theD2UV) const
{
  Standard_Real aU = theU, aV = theV;
  for (;;)
  {
    gp_Vec aD3U, aD3V, aD3UUV, aD3UVV;
    BaseD3 (aU, aV, theValue, theD1U, theD1V,
            theD2U, theD2V, theD2UV, aD3U, aD3V, aD3UUV, aD3UVV);

    CheckInfinite (theD1U, theD1V);

    try
    {
      CalculateD2 (aU, aV, theValue, theD1U, theD1V,
                   theD2U, theD2V, theD2UV, aD3U, aD3V, aD3UUV, aD3UVV);
      break;
    } 
    catch (Geom_UndefinedValue&)
    {
      // if failed at parametric boundary, try taking derivative at shifted point
      if (! shiftPoint (theU, theV, aU, aV, myBaseSurf, myBaseAdaptor, theD1U, theD1V))
      {
        throw;
      }
    }
  }
}

void GeomEvaluator_OffsetSurface::D3(
    const Standard_Real theU, const Standard_Real theV,
    gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V,
    gp_Vec& theD2U, gp_Vec& theD2V, gp_Vec& theD2UV,
    gp_Vec& theD3U, gp_Vec& theD3V, gp_Vec& theD3UUV, gp_Vec& theD3UVV) const
{
  Standard_Real aU = theU, aV = theV;
  for (;;)
  {
    BaseD3 (aU, aV, theValue, theD1U, theD1V,
            theD2U, theD2V, theD2UV, theD3U, theD3V, theD3UUV, theD3UVV);

    CheckInfinite (theD1U, theD1V);

    try
    {
      CalculateD3 (aU, aV, theValue, theD1U, theD1V,
                   theD2U, theD2V, theD2UV, theD3U, theD3V, theD3UUV, theD3UVV);
      break;
    } 
    catch (Geom_UndefinedValue&)
    {
      // if failed at parametric boundary, try taking derivative at shifted point
      if (! shiftPoint (theU, theV, aU, aV, myBaseSurf, myBaseAdaptor, theD1U, theD1V))
      {
        throw;
      }
    }
  }
}

gp_Vec GeomEvaluator_OffsetSurface::DN(
    const Standard_Real theU, const Standard_Real theV,
    const Standard_Integer theDerU, const Standard_Integer theDerV) const
{
  Standard_RangeError_Raise_if(theDerU < 0, "GeomEvaluator_OffsetSurface::DN(): theDerU < 0");
  Standard_RangeError_Raise_if(theDerV < 0, "GeomEvaluator_OffsetSurface::DN(): theDerV < 0");
  Standard_RangeError_Raise_if(theDerU + theDerV < 1,
      "GeomEvaluator_OffsetSurface::DN(): theDerU + theDerV < 1");

  Standard_Real aU = theU, aV = theV;
  for (;;)
  {
    gp_Pnt aP;
    gp_Vec aD1U, aD1V;
    BaseD1 (aU, aV, aP, aD1U, aD1V);

    CheckInfinite (aD1U, aD1V);

    try
    {
      return CalculateDN (aU, aV, theDerU, theDerV, aD1U, aD1V);
    } 
    catch (Geom_UndefinedValue&)
    {
      // if failed at parametric boundary, try taking derivative at shifted point
      if (! shiftPoint (theU, theV, aU, aV, myBaseSurf, myBaseAdaptor, aD1U, aD1V))
      {
        throw;
      }
    }
  }
}


void GeomEvaluator_OffsetSurface::BaseD0(const Standard_Real theU, const Standard_Real theV,
                                         gp_Pnt& theValue) const
{
  if (!myBaseAdaptor.IsNull())
    myBaseAdaptor->D0(theU, theV, theValue);
  else
    myBaseSurf->D0(theU, theV, theValue);
}

void GeomEvaluator_OffsetSurface::BaseD1(const Standard_Real theU, const Standard_Real theV,
                                         gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V) const
{
  if (!myBaseAdaptor.IsNull())
    myBaseAdaptor->D1(theU, theV, theValue, theD1U, theD1V);
  else
    myBaseSurf->D1(theU, theV, theValue, theD1U, theD1V);
}

void GeomEvaluator_OffsetSurface::BaseD2(const Standard_Real theU, const Standard_Real theV,
                                         gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V,
                                         gp_Vec& theD2U, gp_Vec& theD2V, gp_Vec& theD2UV) const
{
  if (!myBaseAdaptor.IsNull())
    myBaseAdaptor->D2(theU, theV, theValue, theD1U, theD1V, theD2U, theD2V, theD2UV);
  else
    myBaseSurf->D2(theU, theV, theValue, theD1U, theD1V, theD2U, theD2V, theD2UV);
}

void GeomEvaluator_OffsetSurface::BaseD3(
    const Standard_Real theU, const Standard_Real theV,
    gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V,
    gp_Vec& theD2U, gp_Vec& theD2V, gp_Vec& theD2UV,
    gp_Vec& theD3U, gp_Vec& theD3V, gp_Vec& theD3UUV, gp_Vec& theD3UVV) const
{
  if (!myBaseAdaptor.IsNull())
    myBaseAdaptor->D3(theU, theV, theValue, theD1U, theD1V,
    theD2U, theD2V, theD2UV, theD3U, theD3V, theD3UUV, theD3UVV);
  else
    myBaseSurf->D3(theU, theV, theValue, theD1U, theD1V,
    theD2U, theD2V, theD2UV, theD3U, theD3V, theD3UUV, theD3UVV);
}


void GeomEvaluator_OffsetSurface::CalculateD0(
    const Standard_Real theU, const Standard_Real theV,
    gp_Pnt& theValue,
    const gp_Vec& theD1U, const gp_Vec& theD1V) const
{
  // Normalize derivatives before normal calculation because it gives more stable result.
  // There will be normalized only derivatives greater than 1.0 to avoid differences in last significant digit
  gp_Vec aD1U(theD1U);
  gp_Vec aD1V(theD1V);
  Standard_Real aD1UNorm2 = aD1U.SquareMagnitude();
  Standard_Real aD1VNorm2 = aD1V.SquareMagnitude();
  if (aD1UNorm2 > 1.0)
    aD1U /= Sqrt(aD1UNorm2);
  if (aD1VNorm2 > 1.0)
    aD1V /= Sqrt(aD1VNorm2);

  gp_Vec aNorm = aD1U.Crossed(aD1V);
  if (aNorm.SquareMagnitude() > the_D1MagTol * the_D1MagTol)
  {
    // Non singular case. Simple computations.
    aNorm.Normalize();
    theValue.SetXYZ(theValue.XYZ() + myOffset * aNorm.XYZ());
  }
  else
  {
    const Standard_Integer MaxOrder = 3;

    Handle(Geom_BSplineSurface) L;
    Standard_Boolean isOpposite = Standard_False;
    Standard_Boolean AlongU = Standard_False;
    Standard_Boolean AlongV = Standard_False;
    if (!myOscSurf.IsNull())
    {
      AlongU = myOscSurf->UOscSurf(theU, theV, isOpposite, L);
      AlongV = myOscSurf->VOscSurf(theU, theV, isOpposite, L);
    }
    const Standard_Real aSign = ((AlongV || AlongU) && isOpposite) ? -1. : 1.;

    TColgp_Array2OfVec DerNUV(0, MaxOrder, 0, MaxOrder);
    TColgp_Array2OfVec DerSurf(0, MaxOrder + 1, 0, MaxOrder + 1);
    Standard_Integer OrderU, OrderV;
    Standard_Real Umin = 0, Umax = 0, Vmin = 0, Vmax = 0;
    Bounds(Umin, Umax, Vmin, Vmax);

    DerSurf.SetValue(1, 0, theD1U);
    DerSurf.SetValue(0, 1, theD1V);
    if (!myBaseSurf.IsNull())
      derivatives(MaxOrder, 1, theU, theV, myBaseSurf, 0, 0, AlongU, AlongV, L, DerNUV, DerSurf);
    else
      derivatives(MaxOrder, 1, theU, theV, myBaseAdaptor, 0, 0, AlongU, AlongV, L, DerNUV, DerSurf);

    gp_Dir Normal;
    CSLib_NormalStatus NStatus = CSLib_Singular;
    CSLib::Normal(MaxOrder, DerNUV, the_D1MagTol, theU, theV, Umin, Umax, Vmin, Vmax,
                  NStatus, Normal, OrderU, OrderV);
    if (NStatus == CSLib_InfinityOfSolutions)
    {
      // Replace zero derivative and try to calculate normal
      gp_Vec aNewDU = theD1U;
      gp_Vec aNewDV = theD1V;
      if (ReplaceDerivative(theU, theV, aNewDU, aNewDV, the_D1MagTol * the_D1MagTol))
        CSLib::Normal(aNewDU, aNewDV, the_D1MagTol, NStatus, Normal);
    }

    if (NStatus != CSLib_Defined)
      throw Geom_UndefinedValue(
          "GeomEvaluator_OffsetSurface::CalculateD0(): Unable to calculate normal");

    theValue.SetXYZ(theValue.XYZ() + myOffset * aSign * Normal.XYZ());
  }
}

void GeomEvaluator_OffsetSurface::CalculateD1(
    const Standard_Real theU, const Standard_Real theV,
    gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V,
    const gp_Vec& theD2U, const gp_Vec& theD2V, const gp_Vec& theD2UV) const
{
  // Check offset side.
  Handle(Geom_BSplineSurface) L;
  Standard_Boolean isOpposite = Standard_False;
  Standard_Boolean AlongU = Standard_False;
  Standard_Boolean AlongV = Standard_False;

  // Normalize derivatives before normal calculation because it gives more stable result.
  // There will be normalized only derivatives greater than 1.0 to avoid differences in last significant digit
  gp_Vec aD1U(theD1U);
  gp_Vec aD1V(theD1V);
  Standard_Real aD1UNorm2 = aD1U.SquareMagnitude();
  Standard_Real aD1VNorm2 = aD1V.SquareMagnitude();
  if (aD1UNorm2 > 1.0)
    aD1U /= Sqrt(aD1UNorm2);
  if (aD1VNorm2 > 1.0)
    aD1V /= Sqrt(aD1VNorm2);

  Standard_Boolean isSingular = Standard_False;
  Standard_Integer MaxOrder = 0;
  gp_Vec aNorm = aD1U.Crossed(aD1V);
  if (aNorm.SquareMagnitude() <= the_D1MagTol * the_D1MagTol)
  {
    if (!myOscSurf.IsNull())
    {
      AlongU = myOscSurf->UOscSurf(theU, theV, isOpposite, L);
      AlongV = myOscSurf->VOscSurf(theU, theV, isOpposite, L);
    }

    MaxOrder = 3;
    isSingular = Standard_True;
  }

  const Standard_Real aSign = ((AlongV || AlongU) && isOpposite) ? -1. : 1.;
  
  if (!isSingular)
  {
    // AlongU or AlongV leads to more complex D1 computation
    // Try to compute D0 and D1 much simpler
    aNorm.Normalize();
    theValue.SetXYZ(theValue.XYZ() + myOffset * aSign * aNorm.XYZ());

    gp_Vec aN0(aNorm.XYZ()), aN1U, aN1V;
    Standard_Real aScale = (theD1U^theD1V).Dot(aN0);
    aN1U.SetX(theD2U.Y() * theD1V.Z() + theD1U.Y() * theD2UV.Z()
      - theD2U.Z() * theD1V.Y() - theD1U.Z() * theD2UV.Y());
    aN1U.SetY((theD2U.X() * theD1V.Z() + theD1U.X() * theD2UV.Z()
      - theD2U.Z() * theD1V.X() - theD1U.Z() * theD2UV.X()) * -1.0);
    aN1U.SetZ(theD2U.X() * theD1V.Y() + theD1U.X() * theD2UV.Y()
      - theD2U.Y() * theD1V.X() - theD1U.Y() * theD2UV.X());
    Standard_Real aScaleU = aN1U.Dot(aN0);
    aN1U.Subtract(aScaleU * aN0);
    aN1U /= aScale;

    aN1V.SetX(theD2UV.Y() * theD1V.Z() + theD2V.Z() * theD1U.Y()
      - theD2UV.Z() * theD1V.Y() - theD2V.Y() * theD1U.Z());
    aN1V.SetY((theD2UV.X() * theD1V.Z() + theD2V.Z() * theD1U.X()
      - theD2UV.Z() * theD1V.X() - theD2V.X() * theD1U.Z()) * -1.0);
    aN1V.SetZ(theD2UV.X() * theD1V.Y() + theD2V.Y() * theD1U.X()
      - theD2UV.Y() * theD1V.X() - theD2V.X() * theD1U.Y());
    Standard_Real aScaleV = aN1V.Dot(aN0);
    aN1V.Subtract(aScaleV * aN0);
    aN1V /= aScale;

    theD1U += myOffset * aSign * aN1U;
    theD1V += myOffset * aSign * aN1V;

    return;
  }
  
  Standard_Integer OrderU, OrderV;
  TColgp_Array2OfVec DerNUV(0, MaxOrder + 1, 0, MaxOrder + 1);
  TColgp_Array2OfVec DerSurf(0, MaxOrder + 2, 0, MaxOrder + 2);
  Standard_Real Umin = 0, Umax = 0, Vmin = 0, Vmax = 0;
  Bounds(Umin, Umax, Vmin, Vmax);

  DerSurf.SetValue(1, 0, theD1U);
  DerSurf.SetValue(0, 1, theD1V);
  DerSurf.SetValue(1, 1, theD2UV);
  DerSurf.SetValue(2, 0, theD2U);
  DerSurf.SetValue(0, 2, theD2V);
  if (!myBaseSurf.IsNull())
    derivatives(MaxOrder, 2, theU, theV, myBaseSurf, 1, 1, AlongU, AlongV, L, DerNUV, DerSurf);
  else
    derivatives(MaxOrder, 2, theU, theV, myBaseAdaptor, 1, 1, AlongU, AlongV, L, DerNUV, DerSurf);

  gp_Dir Normal;
  CSLib_NormalStatus NStatus;
  CSLib::Normal(MaxOrder, DerNUV, the_D1MagTol, theU, theV, Umin, Umax, Vmin, Vmax, NStatus, Normal, OrderU, OrderV);
  if (NStatus == CSLib_InfinityOfSolutions)
  {
    gp_Vec aNewDU = theD1U;
    gp_Vec aNewDV = theD1V;
    // Replace zero derivative and try to calculate normal
    if (ReplaceDerivative(theU, theV, aNewDU, aNewDV, the_D1MagTol * the_D1MagTol))
    {
      DerSurf.SetValue(1, 0, aNewDU);
      DerSurf.SetValue(0, 1, aNewDV);
      if (!myBaseSurf.IsNull())
        derivatives(MaxOrder, 2, theU, theV, myBaseSurf, 1, 1, AlongU, AlongV, L, DerNUV, DerSurf);
      else
        derivatives(MaxOrder, 2, theU, theV, myBaseAdaptor, 1, 1, AlongU, AlongV, L, DerNUV, DerSurf);
      CSLib::Normal(MaxOrder, DerNUV, the_D1MagTol, theU, theV, Umin, Umax, Vmin, Vmax,
                    NStatus, Normal, OrderU, OrderV);
    }
  }

  if (NStatus != CSLib_Defined)
    throw Geom_UndefinedValue(
        "GeomEvaluator_OffsetSurface::CalculateD1(): Unable to calculate normal");

  theValue.SetXYZ(theValue.XYZ() + myOffset * aSign * Normal.XYZ());

  theD1U = DerSurf(1, 0) + myOffset * aSign * CSLib::DNNormal(1, 0, DerNUV, OrderU, OrderV);
  theD1V = DerSurf(0, 1) + myOffset * aSign * CSLib::DNNormal(0, 1, DerNUV, OrderU, OrderV);
}

void GeomEvaluator_OffsetSurface::CalculateD2(
    const Standard_Real theU, const Standard_Real theV,
    gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V,
    gp_Vec& theD2U, gp_Vec& theD2V, gp_Vec& theD2UV,
    const gp_Vec& theD3U, const gp_Vec& theD3V, const gp_Vec& theD3UUV, const gp_Vec& theD3UVV) const
{
  gp_Dir Normal;
  CSLib_NormalStatus NStatus;
  CSLib::Normal(theD1U, theD1V, the_D1MagTol, NStatus, Normal);

  const Standard_Integer MaxOrder = (NStatus == CSLib_Defined) ? 0 : 3;
  Standard_Integer OrderU, OrderV;
  TColgp_Array2OfVec DerNUV(0, MaxOrder + 2, 0, MaxOrder + 2);
  TColgp_Array2OfVec DerSurf(0, MaxOrder + 3, 0, MaxOrder + 3);

  Standard_Real Umin = 0, Umax = 0, Vmin = 0, Vmax = 0;
  Bounds(Umin, Umax, Vmin, Vmax);

  DerSurf.SetValue(1, 0, theD1U);
  DerSurf.SetValue(0, 1, theD1V);
  DerSurf.SetValue(1, 1, theD2UV);
  DerSurf.SetValue(2, 0, theD2U);
  DerSurf.SetValue(0, 2, theD2V);
  DerSurf.SetValue(3, 0, theD3U);
  DerSurf.SetValue(2, 1, theD3UUV);
  DerSurf.SetValue(1, 2, theD3UVV);
  DerSurf.SetValue(0, 3, theD3V);
  //*********************

  Handle(Geom_BSplineSurface) L;
  Standard_Boolean isOpposite = Standard_False;
  Standard_Boolean AlongU = Standard_False;
  Standard_Boolean AlongV = Standard_False;
  if ((NStatus != CSLib_Defined) && !myOscSurf.IsNull())
  {
    AlongU = myOscSurf->UOscSurf(theU, theV, isOpposite, L);
    AlongV = myOscSurf->VOscSurf(theU, theV, isOpposite, L);
  }
  const Standard_Real aSign = ((AlongV || AlongU) && isOpposite) ? -1. : 1.;

  if (!myBaseSurf.IsNull())
    derivatives(MaxOrder, 3, theU, theV, myBaseSurf, 2, 2, AlongU, AlongV, L, DerNUV, DerSurf);
  else
    derivatives(MaxOrder, 3, theU, theV, myBaseAdaptor, 2, 2, AlongU, AlongV, L, DerNUV, DerSurf);

  CSLib::Normal(MaxOrder, DerNUV, the_D1MagTol, theU, theV, Umin, Umax, Vmin, Vmax,
                NStatus, Normal, OrderU, OrderV);
  if (NStatus != CSLib_Defined)
    throw Geom_UndefinedValue(
        "GeomEvaluator_OffsetSurface::CalculateD2(): Unable to calculate normal");

  theValue.SetXYZ(theValue.XYZ() + myOffset * aSign * Normal.XYZ());

  theD1U = DerSurf(1, 0) + myOffset * aSign * CSLib::DNNormal(1, 0, DerNUV, OrderU, OrderV);
  theD1V = DerSurf(0, 1) + myOffset * aSign * CSLib::DNNormal(0, 1, DerNUV, OrderU, OrderV);

  if (!myBaseSurf.IsNull())
  {
    theD2U = myBaseSurf->DN(theU, theV, 2, 0);
    theD2V = myBaseSurf->DN(theU, theV, 0, 2);
    theD2UV = myBaseSurf->DN(theU, theV, 1, 1);
  }
  else
  {
    theD2U = myBaseAdaptor->DN(theU, theV, 2, 0);
    theD2V = myBaseAdaptor->DN(theU, theV, 0, 2);
    theD2UV = myBaseAdaptor->DN(theU, theV, 1, 1);
  }

  theD2U += aSign * myOffset * CSLib::DNNormal(2, 0, DerNUV, OrderU, OrderV);
  theD2V += aSign * myOffset * CSLib::DNNormal(0, 2, DerNUV, OrderU, OrderV);
  theD2UV += aSign * myOffset * CSLib::DNNormal(1, 1, DerNUV, OrderU, OrderV);
}

void GeomEvaluator_OffsetSurface::CalculateD3(
    const Standard_Real theU, const Standard_Real theV,
    gp_Pnt& theValue, gp_Vec& theD1U, gp_Vec& theD1V,
    gp_Vec& theD2U, gp_Vec& theD2V, gp_Vec& theD2UV,
    gp_Vec& theD3U, gp_Vec& theD3V, gp_Vec& theD3UUV, gp_Vec& theD3UVV) const
{
  gp_Dir Normal;
  CSLib_NormalStatus NStatus;
  CSLib::Normal(theD1U, theD1V, the_D1MagTol, NStatus, Normal);
  const Standard_Integer MaxOrder = (NStatus == CSLib_Defined) ? 0 : 3;
  Standard_Integer OrderU, OrderV;
  TColgp_Array2OfVec DerNUV(0, MaxOrder + 3, 0, MaxOrder + 3);
  TColgp_Array2OfVec DerSurf(0, MaxOrder + 4, 0, MaxOrder + 4);
  Standard_Real Umin = 0, Umax = 0, Vmin = 0, Vmax = 0;
  Bounds(Umin, Umax, Vmin, Vmax);

  DerSurf.SetValue(1, 0, theD1U);
  DerSurf.SetValue(0, 1, theD1V);
  DerSurf.SetValue(1, 1, theD2UV);
  DerSurf.SetValue(2, 0, theD2U);
  DerSurf.SetValue(0, 2, theD2V);
  DerSurf.SetValue(3, 0, theD3U);
  DerSurf.SetValue(2, 1, theD3UUV);
  DerSurf.SetValue(1, 2, theD3UVV);
  DerSurf.SetValue(0, 3, theD3V);


  //*********************
  Handle(Geom_BSplineSurface) L;
  Standard_Boolean isOpposite = Standard_False;
  Standard_Boolean AlongU = Standard_False;
  Standard_Boolean AlongV = Standard_False;
  if ((NStatus != CSLib_Defined) && !myOscSurf.IsNull())
  {
    AlongU = myOscSurf->UOscSurf(theU, theV, isOpposite, L);
    AlongV = myOscSurf->VOscSurf(theU, theV, isOpposite, L);
  }
  const Standard_Real aSign = ((AlongV || AlongU) && isOpposite) ? -1. : 1.;

  if (!myBaseSurf.IsNull())
    derivatives(MaxOrder, 3, theU, theV, myBaseSurf, 3, 3, AlongU, AlongV, L, DerNUV, DerSurf);
  else
    derivatives(MaxOrder, 3, theU, theV, myBaseAdaptor, 3, 3, AlongU, AlongV, L, DerNUV, DerSurf);

  CSLib::Normal(MaxOrder, DerNUV, the_D1MagTol, theU, theV, Umin, Umax, Vmin, Vmax,
                NStatus, Normal, OrderU, OrderV);
  if (NStatus != CSLib_Defined)
    throw Geom_UndefinedValue(
        "GeomEvaluator_OffsetSurface::CalculateD3(): Unable to calculate normal");

  theValue.SetXYZ(theValue.XYZ() + myOffset * aSign * Normal.XYZ());

  theD1U = DerSurf(1, 0) + myOffset * aSign * CSLib::DNNormal(1, 0, DerNUV, OrderU, OrderV);
  theD1V = DerSurf(0, 1) + myOffset * aSign * CSLib::DNNormal(0, 1, DerNUV, OrderU, OrderV);

  if (!myBaseSurf.IsNull())
  {
    theD2U   = myBaseSurf->DN(theU, theV, 2, 0);
    theD2V   = myBaseSurf->DN(theU, theV, 0, 2);
    theD2UV  = myBaseSurf->DN(theU, theV, 1, 1);
    theD3U   = myBaseSurf->DN(theU, theV, 3, 0);
    theD3V   = myBaseSurf->DN(theU, theV, 0, 3);
    theD3UUV = myBaseSurf->DN(theU, theV, 2, 1);
    theD3UVV = myBaseSurf->DN(theU, theV, 1, 2);
  }
  else
  {
    theD2U   = myBaseAdaptor->DN(theU, theV, 2, 0);
    theD2V   = myBaseAdaptor->DN(theU, theV, 0, 2);
    theD2UV  = myBaseAdaptor->DN(theU, theV, 1, 1);
    theD3U   = myBaseAdaptor->DN(theU, theV, 3, 0);
    theD3V   = myBaseAdaptor->DN(theU, theV, 0, 3);
    theD3UUV = myBaseAdaptor->DN(theU, theV, 2, 1);
    theD3UVV = myBaseAdaptor->DN(theU, theV, 1, 2);
  }

  theD2U   += aSign * myOffset * CSLib::DNNormal(2, 0, DerNUV, OrderU, OrderV);
  theD2V   += aSign * myOffset * CSLib::DNNormal(0, 2, DerNUV, OrderU, OrderV);
  theD2UV  += aSign * myOffset * CSLib::DNNormal(1, 1, DerNUV, OrderU, OrderV);
  theD3U   += aSign * myOffset * CSLib::DNNormal(3, 0, DerNUV, OrderU, OrderV);
  theD3V   += aSign * myOffset * CSLib::DNNormal(0, 3, DerNUV, OrderU, OrderV);
  theD3UUV += aSign * myOffset * CSLib::DNNormal(2, 1, DerNUV, OrderU, OrderV);
  theD3UVV += aSign * myOffset * CSLib::DNNormal(1, 2, DerNUV, OrderU, OrderV);
}

gp_Vec GeomEvaluator_OffsetSurface::CalculateDN(
    const Standard_Real theU, const Standard_Real theV,
    const Standard_Integer theNu, const Standard_Integer theNv,
    const gp_Vec& theD1U, const gp_Vec& theD1V) const
{
  gp_Dir Normal;
  CSLib_NormalStatus NStatus;
  CSLib::Normal(theD1U, theD1V, the_D1MagTol, NStatus, Normal);
  const Standard_Integer MaxOrder = (NStatus == CSLib_Defined) ? 0 : 3;
  Standard_Integer OrderU, OrderV;
  TColgp_Array2OfVec DerNUV(0, MaxOrder + theNu, 0, MaxOrder + theNv);
  TColgp_Array2OfVec DerSurf(0, MaxOrder + theNu + 1, 0, MaxOrder + theNv + 1);

  Standard_Real Umin = 0, Umax = 0, Vmin = 0, Vmax = 0;
  Bounds(Umin, Umax, Vmin, Vmax);

  DerSurf.SetValue(1, 0, theD1U);
  DerSurf.SetValue(0, 1, theD1V);

  //*********************
  Handle(Geom_BSplineSurface) L;
  //   Is there any osculatingsurface along U or V;
  Standard_Boolean isOpposite = Standard_False;
  Standard_Boolean AlongU = Standard_False;
  Standard_Boolean AlongV = Standard_False;
  if ((NStatus != CSLib_Defined) && !myOscSurf.IsNull())
  {
    AlongU = myOscSurf->UOscSurf(theU, theV, isOpposite, L);
    AlongV = myOscSurf->VOscSurf(theU, theV, isOpposite, L);
  }
  const Standard_Real aSign = ((AlongV || AlongU) && isOpposite) ? -1. : 1.;

  if (!myBaseSurf.IsNull())
    derivatives(MaxOrder, 1, theU, theV, myBaseSurf, theNu, theNv, AlongU, AlongV, L, DerNUV, DerSurf);
  else
    derivatives(MaxOrder, 1, theU, theV, myBaseAdaptor, theNu, theNv, AlongU, AlongV, L, DerNUV, DerSurf);

  CSLib::Normal(MaxOrder, DerNUV, the_D1MagTol, theU, theV, Umin, Umax, Vmin, Vmax,
                NStatus, Normal, OrderU, OrderV);
  if (NStatus != CSLib_Defined)
    throw Geom_UndefinedValue(
        "GeomEvaluator_OffsetSurface::CalculateDN(): Unable to calculate normal");

  gp_Vec D;
  if (!myBaseSurf.IsNull())
    D = myBaseSurf->DN(theU, theV, theNu, theNv);
  else
    D = myBaseAdaptor->DN(theU, theV, theNu, theNv);

  D += aSign * myOffset * CSLib::DNNormal(theNu, theNv, DerNUV, OrderU, OrderV);
  return D;
}


void GeomEvaluator_OffsetSurface::Bounds(Standard_Real& theUMin, Standard_Real& theUMax,
                                         Standard_Real& theVMin, Standard_Real& theVMax) const
{
  if (!myBaseSurf.IsNull())
    myBaseSurf->Bounds(theUMin, theUMax, theVMin, theVMax);
  else
  {
    theUMin = myBaseAdaptor->FirstUParameter();
    theUMax = myBaseAdaptor->LastUParameter();
    theVMin = myBaseAdaptor->FirstVParameter();
    theVMax = myBaseAdaptor->LastVParameter();
  }
}


Standard_Boolean GeomEvaluator_OffsetSurface::ReplaceDerivative(
    const Standard_Real theU, const Standard_Real theV,
    gp_Vec& theDU, gp_Vec& theDV,
    const Standard_Real theSquareTol) const
{
  Standard_Boolean isReplaceDU = theDU.SquareMagnitude() < theSquareTol;
  Standard_Boolean isReplaceDV = theDV.SquareMagnitude() < theSquareTol;
  Standard_Boolean isReplaced = Standard_False;
  if (isReplaceDU ^ isReplaceDV)
  {
    Standard_Real aU = theU;
    Standard_Real aV = theV;
    Standard_Real aUMin = 0, aUMax = 0, aVMin = 0, aVMax = 0;
    Bounds(aUMin, aUMax, aVMin, aVMax);

    // Calculate step along non-zero derivative
    Standard_Real aStep;
    Handle(Adaptor3d_Surface) aSurfAdapt;
    if (!myBaseAdaptor.IsNull())
      aSurfAdapt = myBaseAdaptor;
    else
      aSurfAdapt = new GeomAdaptor_Surface(myBaseSurf);
    if (isReplaceDV)
    {
      aStep = Precision::Confusion() * theDU.Magnitude();
      if (aStep > aUMax - aUMin)
        aStep = (aUMax - aUMin) / 100.;
    }
    else
    {
      aStep = Precision::Confusion() * theDV.Magnitude();
      if (aStep > aVMax - aVMin)
        aStep = (aVMax - aVMin) / 100.;
    }

    gp_Pnt aP;
    gp_Vec aDU, aDV;
    // Step away from current parametric coordinates and calculate derivatives once again.
    // Replace zero derivative by the obtained.
    for (Standard_Real aStepSign = -1.0; aStepSign <= 1.0 && !isReplaced; aStepSign += 2.0)
    {
      if (isReplaceDV)
      {
        aU = theU + aStepSign * aStep;
        if (aU < aUMin || aU > aUMax)
          continue;
      }
      else
      {
        aV = theV + aStepSign * aStep;
        if (aV < aVMin || aV > aVMax)
          continue;
      }

      BaseD1(aU, aV, aP, aDU, aDV);

      if (isReplaceDU && aDU.SquareMagnitude() > theSquareTol)
      {
        theDU = aDU;
        isReplaced = Standard_True;
      }
      if (isReplaceDV && aDV.SquareMagnitude() > theSquareTol)
      {
        theDV = aDV;
        isReplaced = Standard_True;
      }
    }
  }
  return isReplaced;
}