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[occt.git] / src / BSplSLib / BSplSLib_Cache.cxx

// Copyright (c) 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 <BSplSLib_Cache.hxx>
#include <BSplSLib.hxx>

#include <NCollection_LocalArray.hxx>

#include <TColgp_HArray2OfPnt.hxx>
#include <TColStd_HArray1OfInteger.hxx>
#include <TColStd_HArray1OfReal.hxx>
#include <TColStd_HArray2OfReal.hxx>


IMPLEMENT_STANDARD_RTTIEXT(BSplSLib_Cache,Standard_Transient)

//! Converts handle of array of Standard_Real into the pointer to Standard_Real
static Standard_Real* ConvertArray(const Handle(TColStd_HArray2OfReal)& theHArray)
{
  const TColStd_Array2OfReal& anArray = theHArray->Array2();
  return (Standard_Real*) &(anArray(anArray.LowerRow(), anArray.LowerCol()));
}

BSplSLib_Cache::BSplSLib_Cache(const Standard_Integer&        theDegreeU,
                               const Standard_Boolean&        thePeriodicU,
                               const TColStd_Array1OfReal&    theFlatKnotsU,
                               const Standard_Integer&        theDegreeV,
                               const Standard_Boolean&        thePeriodicV,
                               const TColStd_Array1OfReal&    theFlatKnotsV,
                               const TColStd_Array2OfReal*    theWeights)
: myIsRational(theWeights != NULL),
  myParamsU (theDegreeU, thePeriodicU, theFlatKnotsU),
  myParamsV (theDegreeV, thePeriodicV, theFlatKnotsV)
{
  Standard_Integer aMinDegree = Min (theDegreeU, theDegreeV);
  Standard_Integer aMaxDegree = Max (theDegreeU, theDegreeV);
  Standard_Integer aPWColNumber = (myIsRational ? 4 : 3);
  myPolesWeights = new TColStd_HArray2OfReal(1, aMaxDegree + 1, 1, aPWColNumber * (aMinDegree + 1));
}

Standard_Boolean BSplSLib_Cache::IsCacheValid(Standard_Real theParameterU,
                                              Standard_Real theParameterV) const
{
  return myParamsU.IsCacheValid (theParameterU) && 
         myParamsV.IsCacheValid (theParameterV);
}

void BSplSLib_Cache::BuildCache(const Standard_Real&           theParameterU,
                                const Standard_Real&           theParameterV,
                                const TColStd_Array1OfReal&    theFlatKnotsU,
                                const TColStd_Array1OfReal&    theFlatKnotsV,
                                const TColgp_Array2OfPnt&      thePoles,
                                const TColStd_Array2OfReal*    theWeights)
{
  // Normalize the parameters for periodical B-splines
  Standard_Real aNewParamU = myParamsU.PeriodicNormalization (theParameterU);
  Standard_Real aNewParamV = myParamsV.PeriodicNormalization (theParameterV);

  myParamsU.LocateParameter (aNewParamU, theFlatKnotsU);
  myParamsV.LocateParameter (aNewParamV, theFlatKnotsV);

  // BSplSLib uses different convention for span parameters than BSplCLib
  // (Start is in the middle of the span and length is half-span),
  // thus we need to amend them here
  Standard_Real aSpanLengthU = 0.5 * myParamsU.SpanLength;
  Standard_Real aSpanStartU = myParamsU.SpanStart + aSpanLengthU;
  Standard_Real aSpanLengthV = 0.5 * myParamsV.SpanLength;
  Standard_Real aSpanStartV = myParamsV.SpanStart + aSpanLengthV;

  // Calculate new cache data
  BSplSLib::BuildCache (aSpanStartU,  aSpanStartV,
                        aSpanLengthU, aSpanLengthV,
                        myParamsU.IsPeriodic, myParamsV.IsPeriodic,
                        myParamsU.Degree,     myParamsV.Degree,
                        myParamsU.SpanIndex,  myParamsV.SpanIndex,
                        theFlatKnotsU,        theFlatKnotsV,
                        thePoles, theWeights, myPolesWeights->ChangeArray2());
}


void BSplSLib_Cache::D0(const Standard_Real& theU, 
                        const Standard_Real& theV, 
                              gp_Pnt&        thePoint) const
{
  Standard_Real aNewU = myParamsU.PeriodicNormalization (theU);
  Standard_Real aNewV = myParamsV.PeriodicNormalization (theV);

  // BSplSLib uses different convention for span parameters than BSplCLib
  // (Start is in the middle of the span and length is half-span),
  // thus we need to amend them here
  Standard_Real aSpanLengthU = 0.5 * myParamsU.SpanLength;
  Standard_Real aSpanStartU = myParamsU.SpanStart + aSpanLengthU;
  Standard_Real aSpanLengthV = 0.5 * myParamsV.SpanLength;
  Standard_Real aSpanStartV = myParamsV.SpanStart + aSpanLengthV;

  aNewU = (aNewU - aSpanStartU) / aSpanLengthU;
  aNewV = (aNewV - aSpanStartV) / aSpanLengthV;

  Standard_Real* aPolesArray = ConvertArray(myPolesWeights);
  Standard_Real aPoint[4];

  Standard_Integer aDimension = myIsRational ? 4 : 3;
  Standard_Integer aCacheCols = myPolesWeights->RowLength();
  Standard_Integer aMinMaxDegree[2] = {Min(myParamsU.Degree, myParamsV.Degree),
                                       Max(myParamsU.Degree, myParamsV.Degree)};
  Standard_Real aParameters[2];
  if (myParamsU.Degree > myParamsV.Degree)
  {
    aParameters[0] = aNewV;
    aParameters[1] = aNewU;
  }
  else
  {
    aParameters[0] = aNewU;
    aParameters[1] = aNewV;
  }

  NCollection_LocalArray<Standard_Real> aTransientCoeffs(aCacheCols); // array for intermediate results

  // Calculate intermediate value of cached polynomial along columns
  PLib::NoDerivativeEvalPolynomial(aParameters[1], aMinMaxDegree[1],
                                   aCacheCols, aMinMaxDegree[1] * aCacheCols,
                                   aPolesArray[0], aTransientCoeffs[0]);

  // Calculate total value
  PLib::NoDerivativeEvalPolynomial(aParameters[0], aMinMaxDegree[0],
                                   aDimension, aDimension * aMinMaxDegree[0],
                                   aTransientCoeffs[0], aPoint[0]);

  thePoint.SetCoord(aPoint[0], aPoint[1], aPoint[2]);
  if (myIsRational)
    thePoint.ChangeCoord().Divide(aPoint[3]);
}


void BSplSLib_Cache::D1(const Standard_Real& theU, 
                        const Standard_Real& theV, 
                              gp_Pnt&        thePoint, 
                              gp_Vec&        theTangentU, 
                              gp_Vec&        theTangentV) const
{
  Standard_Real aNewU = myParamsU.PeriodicNormalization (theU);
  Standard_Real aNewV = myParamsV.PeriodicNormalization (theV);

  // BSplSLib uses different convention for span parameters than BSplCLib
  // (Start is in the middle of the span and length is half-span),
  // thus we need to amend them here
  Standard_Real aSpanLengthU = 0.5 * myParamsU.SpanLength;
  Standard_Real aSpanStartU = myParamsU.SpanStart + aSpanLengthU;
  Standard_Real aSpanLengthV = 0.5 * myParamsV.SpanLength;
  Standard_Real aSpanStartV = myParamsV.SpanStart + aSpanLengthV;

  Standard_Real anInvU = 1.0 / aSpanLengthU;
  Standard_Real anInvV = 1.0 / aSpanLengthV;
  aNewU = (aNewU - aSpanStartU) * anInvU;
  aNewV = (aNewV - aSpanStartV) * anInvV;

  Standard_Real* aPolesArray = ConvertArray(myPolesWeights);
  Standard_Real aPntDeriv[16]; // result storage (point and derivative coordinates)
  for (Standard_Integer i = 0; i< 16; i++) aPntDeriv[i] = 0.0;

  Standard_Integer aDimension = myIsRational ? 4 : 3;
  Standard_Integer aCacheCols = myPolesWeights->RowLength();
  Standard_Integer aMinMaxDegree[2] = {Min(myParamsU.Degree, myParamsV.Degree),
                                       Max(myParamsU.Degree, myParamsV.Degree)};

  Standard_Real aParameters[2];
  if (myParamsU.Degree > myParamsV.Degree)
  {
    aParameters[0] = aNewV;
    aParameters[1] = aNewU;
  }
  else
  {
    aParameters[0] = aNewU;
    aParameters[1] = aNewV;
  }

  NCollection_LocalArray<Standard_Real> aTransientCoeffs(aCacheCols<<1); // array for intermediate results

  // Calculate intermediate values and derivatives of bivariate polynomial along variable with maximal degree
  PLib::EvalPolynomial(aParameters[1], 1, aMinMaxDegree[1], aCacheCols, aPolesArray[0], aTransientCoeffs[0]);

  // Calculate a point on surface and a derivative along variable with minimal degree
  PLib::EvalPolynomial(aParameters[0], 1, aMinMaxDegree[0], aDimension, aTransientCoeffs[0], aPntDeriv[0]);

  // Calculate derivative along variable with maximal degree
  PLib::NoDerivativeEvalPolynomial(aParameters[0], aMinMaxDegree[0], aDimension, 
                                   aMinMaxDegree[0] * aDimension, aTransientCoeffs[aCacheCols], 
                                   aPntDeriv[aDimension<<1]);

  Standard_Real* aResult = aPntDeriv;
  Standard_Real aTempStorage[12];
  if (myIsRational) // calculate derivatives divided by weight's derivatives
  {
    BSplSLib::RationalDerivative(1, 1, 1, 1, aPntDeriv[0], aTempStorage[0]);
    aResult = aTempStorage;
    aDimension--;
  }

  thePoint.SetCoord(aResult[0], aResult[1], aResult[2]);
  if (myParamsU.Degree > myParamsV.Degree)
  {
    theTangentV.SetCoord(aResult[aDimension], aResult[aDimension + 1], aResult[aDimension + 2]);
    Standard_Integer aShift = aDimension<<1;
    theTangentU.SetCoord(aResult[aShift], aResult[aShift + 1], aResult[aShift + 2]);
  }
  else
  {
    theTangentU.SetCoord(aResult[aDimension], aResult[aDimension + 1], aResult[aDimension + 2]);
    Standard_Integer aShift = aDimension<<1;
    theTangentV.SetCoord(aResult[aShift], aResult[aShift + 1], aResult[aShift + 2]);
  }
  theTangentU.Multiply(anInvU);
  theTangentV.Multiply(anInvV);
}


void BSplSLib_Cache::D2(const Standard_Real& theU, 
                        const Standard_Real& theV, 
                              gp_Pnt&        thePoint, 
                              gp_Vec&        theTangentU, 
                              gp_Vec&        theTangentV, 
                              gp_Vec&        theCurvatureU, 
                              gp_Vec&        theCurvatureV, 
                              gp_Vec&        theCurvatureUV) const
{
  Standard_Real aNewU = myParamsU.PeriodicNormalization (theU);
  Standard_Real aNewV = myParamsV.PeriodicNormalization (theV);

  // BSplSLib uses different convention for span parameters than BSplCLib
  // (Start is in the middle of the span and length is half-span),
  // thus we need to amend them here
  Standard_Real aSpanLengthU = 0.5 * myParamsU.SpanLength;
  Standard_Real aSpanStartU = myParamsU.SpanStart + aSpanLengthU;
  Standard_Real aSpanLengthV = 0.5 * myParamsV.SpanLength;
  Standard_Real aSpanStartV = myParamsV.SpanStart + aSpanLengthV;

  Standard_Real anInvU = 1.0 / aSpanLengthU;
  Standard_Real anInvV = 1.0 / aSpanLengthV;
  aNewU = (aNewU - aSpanStartU) * anInvU;
  aNewV = (aNewV - aSpanStartV) * anInvV;

  Standard_Real* aPolesArray = ConvertArray(myPolesWeights);
  Standard_Real aPntDeriv[36]; // result storage (point and derivative coordinates)
  for (Standard_Integer i = 0; i < 36; i++) aPntDeriv[i] = 0.0;

  Standard_Integer aDimension = myIsRational ? 4 : 3;
  Standard_Integer aCacheCols = myPolesWeights->RowLength();
  Standard_Integer aMinMaxDegree[2] = {Min(myParamsU.Degree, myParamsV.Degree),
                                       Max(myParamsU.Degree, myParamsV.Degree)};

  Standard_Real aParameters[2];
  if (myParamsU.Degree > myParamsV.Degree)
  {
    aParameters[0] = aNewV;
    aParameters[1] = aNewU;
  }
  else
  {
    aParameters[0] = aNewU;
    aParameters[1] = aNewV;
  }

  NCollection_LocalArray<Standard_Real> aTransientCoeffs(3 * aCacheCols); // array for intermediate results
  // Calculating derivative to be evaluate and
  // nulling transient coefficients when max or min derivative is less than 2
  Standard_Integer aMinMaxDeriv[2] = {Min(2, aMinMaxDegree[0]), 
                                      Min(2, aMinMaxDegree[1])};
  for (Standard_Integer i = aMinMaxDeriv[1] + 1; i < 3; i++)
  {
    Standard_Integer index = i * aCacheCols;
    for (Standard_Integer j = 0; j < aCacheCols; j++) 
      aTransientCoeffs[index++] = 0.0;
  }

  // Calculate intermediate values and derivatives of bivariate polynomial along variable with maximal degree
  PLib::EvalPolynomial(aParameters[1], aMinMaxDeriv[1], aMinMaxDegree[1], 
                       aCacheCols, aPolesArray[0], aTransientCoeffs[0]);

  // Calculate a point on surface and a derivatives along variable with minimal degree
  PLib::EvalPolynomial(aParameters[0], aMinMaxDeriv[0], aMinMaxDegree[0], 
                       aDimension, aTransientCoeffs[0], aPntDeriv[0]);

  // Calculate derivative along variable with maximal degree and mixed derivative
  PLib::EvalPolynomial(aParameters[0], 1, aMinMaxDegree[0], aDimension, 
                       aTransientCoeffs[aCacheCols], aPntDeriv[3 * aDimension]);

  // Calculate second derivative along variable with maximal degree
  PLib::NoDerivativeEvalPolynomial(aParameters[0], aMinMaxDegree[0], aDimension, 
                                   aMinMaxDegree[0] * aDimension, aTransientCoeffs[aCacheCols<<1], 
                                   aPntDeriv[6 * aDimension]);

  Standard_Real* aResult = aPntDeriv;
  Standard_Real aTempStorage[36];
  if (myIsRational) // calculate derivatives divided by weight's derivatives
  {
    BSplSLib::RationalDerivative(2, 2, 2, 2, aPntDeriv[0], aTempStorage[0]);
    aResult = aTempStorage;
    aDimension--;
  }

  thePoint.SetCoord(aResult[0], aResult[1], aResult[2]);
  if (myParamsU.Degree > myParamsV.Degree)
  {
    theTangentV.SetCoord(aResult[aDimension], aResult[aDimension + 1], aResult[aDimension + 2]);
    Standard_Integer aShift = aDimension<<1;
    theCurvatureV.SetCoord(aResult[aShift], aResult[aShift + 1], aResult[aShift + 2]);
    aShift += aDimension;
    theTangentU.SetCoord(aResult[aShift], aResult[aShift + 1], aResult[aShift + 2]);
    aShift += aDimension;
    theCurvatureUV.SetCoord(aResult[aShift], aResult[aShift + 1], aResult[aShift + 2]);
    aShift += (aDimension << 1);
    theCurvatureU.SetCoord(aResult[aShift], aResult[aShift + 1], aResult[aShift + 2]);
  }
  else
  {
    theTangentU.SetCoord(aResult[aDimension], aResult[aDimension + 1], aResult[aDimension + 2]);
    Standard_Integer aShift = aDimension<<1;
    theCurvatureU.SetCoord(aResult[aShift], aResult[aShift + 1], aResult[aShift + 2]);
    aShift += aDimension;
    theTangentV.SetCoord(aResult[aShift], aResult[aShift + 1], aResult[aShift + 2]);
    aShift += aDimension;
    theCurvatureUV.SetCoord(aResult[aShift], aResult[aShift + 1], aResult[aShift + 2]);
    aShift += (aDimension << 1);
    theCurvatureV.SetCoord(aResult[aShift], aResult[aShift + 1], aResult[aShift + 2]);
  }
  theTangentU.Multiply(anInvU);
  theTangentV.Multiply(anInvV);
  theCurvatureU.Multiply(anInvU * anInvU);
  theCurvatureV.Multiply(anInvV * anInvV);
  theCurvatureUV.Multiply(anInvU * anInvV);
}