ppolynomial.hpp

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/*
Copyright (c) 2006, Michael Kazhdan and Matthew Bolitho
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#include "factor.h"

// StartingPolynomial //

namespace pcl
{
  namespace poisson
  {


    template<int Degree>
    template<int Degree2>
    StartingPolynomial<Degree+Degree2> StartingPolynomial<Degree>::operator * (const StartingPolynomial<Degree2>& p) const{
      StartingPolynomial<Degree+Degree2> sp;
      if(start>p.start){sp.start=start;}
      else{sp.start=p.start;}
      sp.p=this->p*p.p;
      return sp;
    }
    template<int Degree>
    StartingPolynomial<Degree> StartingPolynomial<Degree>::scale(double s) const{
      StartingPolynomial q;
      q.start=start*s;
      q.p=p.scale(s);
      return q;
    }
    template<int Degree>
    StartingPolynomial<Degree> StartingPolynomial<Degree>::shift(double s) const{
      StartingPolynomial q;
      q.start=start+s;
      q.p=p.shift(s);
      return q;
    }


    template<int Degree>
    int StartingPolynomial<Degree>::operator < (const StartingPolynomial<Degree>& sp) const{
      if(start<sp.start){return 1;}
      else{return 0;}
    }
    template<int Degree>
    int StartingPolynomial<Degree>::Compare(const void* v1,const void* v2){
      double d=((StartingPolynomial*)(v1))->start-((StartingPolynomial*)(v2))->start;
      if                (d<0)   {return -1;}
      else if   (d>0)   {return  1;}
      else                      {return  0;}
    }

    // PPolynomial //
    template<int Degree>
    PPolynomial<Degree>::PPolynomial(void){
      polyCount=0;
      polys=NULL;
    }
    template<int Degree>
    PPolynomial<Degree>::PPolynomial(const PPolynomial<Degree>& p){
      polyCount=0;
      polys=NULL;
      set(p.polyCount);
      memcpy(polys,p.polys,sizeof(StartingPolynomial<Degree>)*p.polyCount);
    }

    template<int Degree>
    PPolynomial<Degree>::~PPolynomial(void){
      if(polyCount){free(polys);}
      polyCount=0;
      polys=NULL;
    }
    template<int Degree>
    void PPolynomial<Degree>::set(StartingPolynomial<Degree>* sps,int count){
      int i,c=0;
      set(count);
      qsort(sps,count,sizeof(StartingPolynomial<Degree>),StartingPolynomial<Degree>::Compare);
      for( i=0 ; i<count ; i++ )
      {
        if( !c || sps[i].start!=polys[c-1].start ) polys[c++] = sps[i];
        else{polys[c-1].p+=sps[i].p;}
      }
      reset( c );
    }
    template <int Degree>
    int PPolynomial<Degree>::size(void) const{return int(sizeof(StartingPolynomial<Degree>)*polyCount);}

    template<int Degree>
    void PPolynomial<Degree>::set( size_t size )
    {
      if(polyCount){free(polys);}
      polyCount=0;
      polys=NULL;
      polyCount=size;
      if(size){
        polys=(StartingPolynomial<Degree>*)malloc(sizeof(StartingPolynomial<Degree>)*size);
        memset(polys,0,sizeof(StartingPolynomial<Degree>)*size);
      }
    }
    template<int Degree>
    void PPolynomial<Degree>::reset( size_t newSize )
    {
      polyCount=newSize;
      polys=(StartingPolynomial<Degree>*)realloc(polys,sizeof(StartingPolynomial<Degree>)*newSize);
    }

    template<int Degree>
    PPolynomial<Degree>& PPolynomial<Degree>::operator = (const PPolynomial<Degree>& p){
      set(p.polyCount);
      memcpy(polys,p.polys,sizeof(StartingPolynomial<Degree>)*p.polyCount);
      return *this;
    }

    template<int Degree>
    template<int Degree2>
    PPolynomial<Degree>& PPolynomial<Degree>::operator  = (const PPolynomial<Degree2>& p){
      set(p.polyCount);
      for(int i=0;i<int(polyCount);i++){
        polys[i].start=p.polys[i].start;
        polys[i].p=p.polys[i].p;
      }
      return *this;
    }

    template<int Degree>
    double PPolynomial<Degree>::operator ()( double t ) const
    {
      double v=0;
      for( int i=0 ; i<int(polyCount) && t>polys[i].start ; i++ ) v+=polys[i].p(t);
      return v;
    }

    template<int Degree>
    double PPolynomial<Degree>::integral( double tMin , double tMax ) const
    {
      int m=1;
      double start,end,s,v=0;
      start=tMin;
      end=tMax;
      if(tMin>tMax){
        m=-1;
        start=tMax;
        end=tMin;
      }
      for(int i=0;i<int(polyCount) && polys[i].start<end;i++){
        if(start<polys[i].start){s=polys[i].start;}
        else{s=start;}
        v+=polys[i].p.integral(s,end);
      }
      return v*m;
    }
    template<int Degree>
    double PPolynomial<Degree>::Integral(void) const{return integral(polys[0].start,polys[polyCount-1].start);}
    template<int Degree>
    PPolynomial<Degree> PPolynomial<Degree>::operator + (const PPolynomial<Degree>& p) const{
      PPolynomial q;
      int i,j;
      size_t idx=0;
      q.set(polyCount+p.polyCount);
      i=j=-1;

      while(idx<q.polyCount){
        if              (j>=int(p.polyCount)-1)                         {q.polys[idx]=  polys[++i];}
        else if (i>=int(  polyCount)-1)                         {q.polys[idx]=p.polys[++j];}
        else if(polys[i+1].start<p.polys[j+1].start){q.polys[idx]=  polys[++i];}
        else                                                                            {q.polys[idx]=p.polys[++j];}
        idx++;
      }
      return q;
    }
    template<int Degree>
    PPolynomial<Degree> PPolynomial<Degree>::operator - (const PPolynomial<Degree>& p) const{
      PPolynomial q;
      int i,j;
      size_t idx=0;
      q.set(polyCount+p.polyCount);
      i=j=-1;

      while(idx<q.polyCount){
        if              (j>=int(p.polyCount)-1)                         {q.polys[idx]=  polys[++i];}
        else if (i>=int(  polyCount)-1)                         {q.polys[idx].start=p.polys[++j].start;q.polys[idx].p=p.polys[j].p*(-1.0);}
        else if(polys[i+1].start<p.polys[j+1].start){q.polys[idx]=  polys[++i];}
        else                                                                            {q.polys[idx].start=p.polys[++j].start;q.polys[idx].p=p.polys[j].p*(-1.0);}
        idx++;
      }
      return q;
    }
    template<int Degree>
    PPolynomial<Degree>& PPolynomial<Degree>::addScaled(const PPolynomial<Degree>& p,double scale){
      int i,j;
      StartingPolynomial<Degree>* oldPolys=polys;
      size_t idx=0,cnt=0,oldPolyCount=polyCount;
      polyCount=0;
      polys=NULL;
      set(oldPolyCount+p.polyCount);
      i=j=-1;
      while(cnt<polyCount){
        if              (j>=int( p.polyCount)-1)                                {polys[idx]=oldPolys[++i];}
        else if (i>=int(oldPolyCount)-1)                                {polys[idx].start= p.polys[++j].start;polys[idx].p=p.polys[j].p*scale;}
        else if (oldPolys[i+1].start<p.polys[j+1].start){polys[idx]=oldPolys[++i];}
        else                                                                                    {polys[idx].start= p.polys[++j].start;polys[idx].p=p.polys[j].p*scale;}
        if(idx && polys[idx].start==polys[idx-1].start) {polys[idx-1].p+=polys[idx].p;}
        else{idx++;}
        cnt++;
      }
      free(oldPolys);
      reset(idx);
      return *this;
    }
    template<int Degree>
    template<int Degree2>
    PPolynomial<Degree+Degree2> PPolynomial<Degree>::operator * (const PPolynomial<Degree2>& p) const{
      PPolynomial<Degree+Degree2> q;
      StartingPolynomial<Degree+Degree2> *sp;
      int i,j,spCount=int(polyCount*p.polyCount);

      sp=(StartingPolynomial<Degree+Degree2>*)malloc(sizeof(StartingPolynomial<Degree+Degree2>)*spCount);
      for(i=0;i<int(polyCount);i++){
        for(j=0;j<int(p.polyCount);j++){
          sp[i*p.polyCount+j]=polys[i]*p.polys[j];
        }
      }
      q.set(sp,spCount);
      free(sp);
      return q;
    }
    template<int Degree>
    template<int Degree2>
    PPolynomial<Degree+Degree2> PPolynomial<Degree>::operator * (const Polynomial<Degree2>& p) const{
      PPolynomial<Degree+Degree2> q;
      q.set(polyCount);
      for(int i=0;i<int(polyCount);i++){
        q.polys[i].start=polys[i].start;
        q.polys[i].p=polys[i].p*p;
      }
      return q;
    }
    template<int Degree>
    PPolynomial<Degree> PPolynomial<Degree>::scale( double s ) const
    {
      PPolynomial q;
      q.set(polyCount);
      for(size_t i=0;i<polyCount;i++){q.polys[i]=polys[i].scale(s);}
      return q;
    }
    template<int Degree>
    PPolynomial<Degree> PPolynomial<Degree>::shift( double s ) const
    {
      PPolynomial q;
      q.set(polyCount);
      for(size_t i=0;i<polyCount;i++){q.polys[i]=polys[i].shift(s);}
      return q;
    }
    template<int Degree>
    PPolynomial<Degree-1> PPolynomial<Degree>::derivative(void) const{
      PPolynomial<Degree-1> q;
      q.set(polyCount);
      for(size_t i=0;i<polyCount;i++){
        q.polys[i].start=polys[i].start;
        q.polys[i].p=polys[i].p.derivative();
      }
      return q;
    }
    template<int Degree>
    PPolynomial<Degree+1> PPolynomial<Degree>::integral(void) const{
      int i;
      PPolynomial<Degree+1> q;
      q.set(polyCount);
      for(i=0;i<int(polyCount);i++){
        q.polys[i].start=polys[i].start;
        q.polys[i].p=polys[i].p.integral();
        q.polys[i].p-=q.polys[i].p(q.polys[i].start);
      }
      return q;
    }
    template<int Degree>
    PPolynomial<Degree>& PPolynomial<Degree>::operator  += ( double s ) {polys[0].p+=s;}
    template<int Degree>
    PPolynomial<Degree>& PPolynomial<Degree>::operator  -= ( double s ) {polys[0].p-=s;}
    template<int Degree>
    PPolynomial<Degree>& PPolynomial<Degree>::operator  *= ( double s )
    {
      for(int i=0;i<int(polyCount);i++){polys[i].p*=s;}
      return *this;
    }
    template<int Degree>
    PPolynomial<Degree>& PPolynomial<Degree>::operator  /= ( double s )
    {
      for(size_t i=0;i<polyCount;i++){polys[i].p/=s;}
      return *this;
    }
    template<int Degree>
    PPolynomial<Degree> PPolynomial<Degree>::operator + ( double s ) const
    {
      PPolynomial q=*this;
      q+=s;
      return q;
    }
    template<int Degree>
    PPolynomial<Degree> PPolynomial<Degree>::operator - ( double s ) const
    {
      PPolynomial q=*this;
      q-=s;
      return q;
    }
    template<int Degree>
    PPolynomial<Degree> PPolynomial<Degree>::operator * ( double s ) const
    {
      PPolynomial q=*this;
      q*=s;
      return q;
    }
    template<int Degree>
    PPolynomial<Degree> PPolynomial<Degree>::operator / ( double s ) const
    {
      PPolynomial q=*this;
      q/=s;
      return q;
    }

    template<int Degree>
    void PPolynomial<Degree>::printnl(void) const{
      Polynomial<Degree> p;

      if(!polyCount){
        Polynomial<Degree> p;
        printf("[-Infinity,Infinity]\n");
      }
      else{
        for(size_t i=0;i<polyCount;i++){
          printf("[");
          if            (polys[i  ].start== DBL_MAX){printf("Infinity,");}
          else if       (polys[i  ].start==-DBL_MAX){printf("-Infinity,");}
          else                                                          {printf("%f,",polys[i].start);}
          if(i+1==polyCount)                                    {printf("Infinity]\t");}
          else if (polys[i+1].start== DBL_MAX){printf("Infinity]\t");}
          else if       (polys[i+1].start==-DBL_MAX){printf("-Infinity]\t");}
          else                                                          {printf("%f]\t",polys[i+1].start);}
          p=p+polys[i].p;
          p.printnl();
        }
      }
      printf("\n");
    }
    template< >
    PPolynomial< 0 > PPolynomial< 0 >::BSpline( double radius )
    {
      PPolynomial q;
      q.set(2);

      q.polys[0].start=-radius;
      q.polys[1].start= radius;

      q.polys[0].p.coefficients[0]= 1.0;
      q.polys[1].p.coefficients[0]=-1.0;
      return q;
    }
    template< int Degree >
    PPolynomial< Degree > PPolynomial<Degree>::BSpline( double radius )
    {
      return PPolynomial< Degree-1 >::BSpline().MovingAverage( radius );
    }
    template<int Degree>
    PPolynomial<Degree+1> PPolynomial<Degree>::MovingAverage( double radius )
    {
      PPolynomial<Degree+1> A;
      Polynomial<Degree+1> p;
      StartingPolynomial<Degree+1>* sps;

      sps=(StartingPolynomial<Degree+1>*)malloc(sizeof(StartingPolynomial<Degree+1>)*polyCount*2);

      for(int i=0;i<int(polyCount);i++){
        sps[2*i  ].start=polys[i].start-radius;
        sps[2*i+1].start=polys[i].start+radius;
        p=polys[i].p.integral()-polys[i].p.integral()(polys[i].start);
        sps[2*i  ].p=p.shift(-radius);
        sps[2*i+1].p=p.shift( radius)*-1;
      }
      A.set(sps,int(polyCount*2));
      free(sps);
      return A*1.0/(2*radius);
    }
    template<int Degree>
    void PPolynomial<Degree>::getSolutions(double c,std::vector<double>& roots,double EPS,double min,double max) const{
      Polynomial<Degree> p;
      std::vector<double> tempRoots;

      p.setZero();
      for(size_t i=0;i<polyCount;i++){
        p+=polys[i].p;
        if(polys[i].start>max){break;}
        if(i<polyCount-1 && polys[i+1].start<min){continue;}
        p.getSolutions(c,tempRoots,EPS);
        for(size_t j=0;j<tempRoots.size();j++){
          if(tempRoots[j]>polys[i].start && (i+1==polyCount || tempRoots[j]<=polys[i+1].start)){
            if(tempRoots[j]>min && tempRoots[j]<max){roots.push_back(tempRoots[j]);}
          }
        }
      }
    }

    template<int Degree>
    void PPolynomial<Degree>::write(FILE* fp,int samples,double min,double max) const{
      fwrite(&samples,sizeof(int),1,fp);
      for(int i=0;i<samples;i++){
        double x=min+i*(max-min)/(samples-1);
        float v=(*this)(x);
        fwrite(&v,sizeof(float),1,fp);
      }
    }

  }
}