libgofigure-dev 0.9.0-3+b1 / usr / include / gofigure2 / FunctionData.inl

/*=========================================================================
 Authors: Michael Kazhdan and Matthew Bolitho
 at Johns Hopkins University, 2006-10

 Copyright (c) 2006-10, Michael Kazhdan and Matthew Bolitho,
 Johns Hopkins University.
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//////////////////
// FunctionData //
//////////////////
template<int Degree,class Real>
const int FunctionData<Degree,Real>::DOT_FLAG=1;
template<int Degree,class Real>
const int FunctionData<Degree,Real>::D_DOT_FLAG=2;
template<int Degree,class Real>
const int FunctionData<Degree,Real>::D2_DOT_FLAG=4;
template<int Degree,class Real>
const int FunctionData<Degree,Real>::VALUE_FLAG=1;
template<int Degree,class Real>
const int FunctionData<Degree,Real>::D_VALUE_FLAG=2;

template<int Degree,class Real>
inline FunctionData<Degree,Real>::FunctionData(void)
{
  dotTable=dDotTable=d2DotTable=NULL;
  valueTables=dValueTables=NULL;
  res=0;
}

template<int Degree,class Real>
inline FunctionData<Degree,Real>::~FunctionData(void)
{
  if(res){
    if(  dotTable){delete[]   dotTable;}
    if( dDotTable){delete[]  dDotTable;}
    if(d2DotTable){delete[] d2DotTable;}
    if( valueTables){delete[]  valueTables;}
    if(dValueTables){delete[] dValueTables;}
    if(baseFunctions){delete[] baseFunctions;}
  }
  dotTable=dDotTable=d2DotTable=NULL;
  valueTables=dValueTables=NULL;
  baseFunctions=NULL;
  res=0;
}

template<int Degree,class Real>
inline void FunctionData<Degree,Real>::set(const int& maxDepth,const PPolynomial<Degree>& F,const int& iNormalize,const int& iUseDotRatios)
{
  this->normalize=iNormalize;
  this->useDotRatios=iUseDotRatios;

  depth=maxDepth;
  res=BinaryNode<double>::CumulativeCenterCount(depth);
  res2=(1<<(depth+1))+1;
  baseFunctions=new PPolynomial<Degree+1>[res];
  // Scale the function so that it has:
  // 0] Value 1 at 0
  // 1] Integral equal to 1
  // 2] Square integral equal to 1
  switch(normalize){
    case 2:
      baseFunction=F/sqrt((F*F).integral(F.polys[0].start,F.polys[F.polyCount-1].start));
      break;
    case 1:
      baseFunction=F/F.integral(F.polys[0].start,F.polys[F.polyCount-1].start);
      break;
    default:
      baseFunction=F/F(0);
  }
  dBaseFunction=baseFunction.derivative();
  double c1,w1;
  for(int i=0;i<res;i++){
    BinaryNode<double>::CenterAndWidth(i,c1,w1);
    baseFunctions[i]=baseFunction.scale(w1).shift(c1);
    // Scale the function so that it has L2-norm equal to one
    switch(normalize){
      case 2:
        baseFunctions[i]/=sqrt(w1);
        break;
      case 1:
        baseFunctions[i]/=w1;
        break;
    }
  }
}

template<int Degree,class Real>
inline void FunctionData<Degree,Real>::setDotTables(const int& flags)
{
  clearDotTables(flags);
  int size;
  size=(res*res+res)>>1;
  if(flags & DOT_FLAG){
    dotTable=new Real[size];
    memset(dotTable,0,sizeof(Real)*size);
  }
  if(flags & D_DOT_FLAG){
    dDotTable=new Real[size];
    memset(dDotTable,0,sizeof(Real)*size);
  }
  if(flags & D2_DOT_FLAG){
    d2DotTable=new Real[size];
    memset(d2DotTable,0,sizeof(Real)*size);
  }
  double t1,t2;
  t1=baseFunction.polys[0].start;
  t2=baseFunction.polys[baseFunction.polyCount-1].start;
  for(int i=0;i<res;i++){
    double c1,c2,w1,w2;
    BinaryNode<double>::CenterAndWidth(i,c1,w1);
    double start1	=t1*w1+c1;
    double end1		=t2*w1+c1;
    for(int j=0;j<=i;j++){
      BinaryNode<double>::CenterAndWidth(j,c2,w2);
      int idx=SymmetricIndex(i,j);

      double start	=t1*w2+c2;
      double end		=t2*w2+c2;

      if(start<start1){start=start1;}
      if(end>end1)	{end=end1;}
      if(start>=end){continue;}

      BinaryNode<double>::CenterAndWidth(j,c2,w2);
      Real dot=dotProduct(c1,w1,c2,w2);
      if(fabs(dot)<1e-15){continue;}
      if(flags & DOT_FLAG){dotTable[idx]=dot;}
      if(useDotRatios){
        if(flags & D_DOT_FLAG){
          dDotTable [idx]=-dDotProduct(c1,w1,c2,w2)/dot;
        }
        if(flags & D2_DOT_FLAG){d2DotTable[idx]=d2DotProduct(c1,w1,c2,w2)/dot;}
      }
      else{
        if(flags & D_DOT_FLAG){
          dDotTable[idx]= dDotProduct(c1,w1,c2,w2);
        }
        if(flags & D2_DOT_FLAG){d2DotTable[idx]=d2DotProduct(c1,w1,c2,w2);}
      }
    }
  }
}

template<int Degree,class Real>
inline void FunctionData<Degree,Real>::clearDotTables(const int& flags)
{
  if((flags & DOT_FLAG) && dotTable){
    delete[] dotTable;
    dotTable=NULL;
  }
  if((flags & D_DOT_FLAG) && dDotTable){
    delete[] dDotTable;
    dDotTable=NULL;
  }
  if((flags & D2_DOT_FLAG) && d2DotTable){
    delete[] d2DotTable;
    d2DotTable=NULL;
  }
}

template<int Degree,class Real>
inline void FunctionData<Degree,Real>::setValueTables(const int& flags,const double& smooth)
{
  clearValueTables();
  if(flags &   VALUE_FLAG){ valueTables=new Real[res*res2];}
  if(flags & D_VALUE_FLAG){dValueTables=new Real[res*res2];}
  PPolynomial<Degree+1> function;
  PPolynomial<Degree>  dFunction;
  for(int i=0;i<res;i++){
    if(smooth>0){
      function=baseFunctions[i].MovingAverage(smooth);
      dFunction=baseFunctions[i].derivative().MovingAverage(smooth);
    }
    else{
      function=baseFunctions[i];
      dFunction=baseFunctions[i].derivative();
    }
    for(int j=0;j<res2;j++){
      double x=double(j)/(res2-1);
      if(flags &   VALUE_FLAG){ valueTables[j*res+i]=Real( function(x));}
      if(flags & D_VALUE_FLAG){dValueTables[j*res+i]=Real(dFunction(x));}
    }
  }
}

template<int Degree,class Real>
inline void FunctionData<Degree,Real>::setValueTables(const int& flags,const double& valueSmooth,const double& normalSmooth)
{
  clearValueTables();
  if(flags &   VALUE_FLAG){ valueTables=new Real[res*res2];}
  if(flags & D_VALUE_FLAG){dValueTables=new Real[res*res2];}
  PPolynomial<Degree+1> function;
  PPolynomial<Degree>  dFunction;
  for(int i=0;i<res;i++){
    if(valueSmooth>0)	{ function=baseFunctions[i].MovingAverage(valueSmooth);}
    else				{ function=baseFunctions[i];}
    if(normalSmooth>0)	{dFunction=baseFunctions[i].derivative().MovingAverage(normalSmooth);}
    else				{dFunction=baseFunctions[i].derivative();}

    for(int j=0;j<res2;j++){
      double x=double(j)/(res2-1);
      if(flags &   VALUE_FLAG){ valueTables[j*res+i]=Real( function(x));}
      if(flags & D_VALUE_FLAG){dValueTables[j*res+i]=Real(dFunction(x));}
    }
  }
}


template<int Degree,class Real>
inline void FunctionData<Degree,Real>::clearValueTables(void)
{
  if( valueTables){delete[]  valueTables;}
  if(dValueTables){delete[] dValueTables;}
  valueTables=dValueTables=NULL;
}

template<int Degree,class Real>
inline Real FunctionData<Degree,Real>::dotProduct(const double& center1,const double& width1,const double& center2,const double& width2) const
{
  double r=fabs(baseFunction.polys[0].start);
  switch(normalize){
    case 2:
      return Real((baseFunction*baseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)*width1/sqrt(width1*width2));
    case 1:
      return Real((baseFunction*baseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)*width1/(width1*width2));
    default:
      return Real((baseFunction*baseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)*width1);
  }
}

template<int Degree,class Real>
inline Real FunctionData<Degree,Real>::dDotProduct(const double& center1,const double& width1,const double& center2,const double& width2) const
{
  double r=fabs(baseFunction.polys[0].start);
  switch(normalize){
    case 2:
      return Real((dBaseFunction*baseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)/sqrt(width1*width2));
    case 1:
      return Real((dBaseFunction*baseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)/(width1*width2));
    default:
      return Real((dBaseFunction*baseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r));
  }
}

template<int Degree,class Real>
inline Real FunctionData<Degree,Real>::d2DotProduct(const double& center1,const double& width1,const double& center2,const double& width2) const
{
  double r=fabs(baseFunction.polys[0].start);
  switch(normalize){
    case 2:
      return Real((dBaseFunction*dBaseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)/width2/sqrt(width1*width2));
    case 1:
      return Real((dBaseFunction*dBaseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)/width2/(width1*width2));
    default:
      return Real((dBaseFunction*dBaseFunction.scale(width2/width1).shift((center2-center1)/width1)).integral(-2*r,2*r)/width2);
  }
}

template<int Degree,class Real>
inline int FunctionData<Degree,Real>::SymmetricIndex(const int& i1,const int& i2){

  if(i1>i2)	{return ((i1*i1+i1)>>1)+i2;}
  else		{return ((i2*i2+i2)>>1)+i1;}
}

template<int Degree,class Real>
inline int FunctionData<Degree,Real>::SymmetricIndex(const int& i1,const int& i2,int& index)
{
  if(i1<i2){
    index=((i2*i2+i2)>>1)+i1;
    return 1;
  }
  else{
    index=((i1*i1+i1)>>1)+i2;
    return 0;
  }
}