polynomial.hpp

/*
Copyright (c) 2006, Michael Kazhdan and Matthew Bolitho
All rights reserved.
 
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
 
Redistributions of source code must retain the above copyright notice, this list of
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the above copyright notice, this list of conditions and the following disclaimer
in the documentation and/or other materials provided with the distribution.
 
Neither the name of the Johns Hopkins University nor the names of its contributors
may be used to endorse or promote products derived from this software without specific
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EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO THE IMPLIED WARRANTIES
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*/
 
#include "factor.h"
 
#include <float.h>
#include <math.h>
 
#include <cstdio>
#include <cstring>
 
////////////////
// Polynomial //
////////////////
 
namespace pcl
{
  namespace poisson
  {
 
 
    template<int Degree>
    Polynomial<Degree>::Polynomial(void){memset(coefficients,0,sizeof(double)*(Degree+1));}
    template<int Degree>
    template<int Degree2>
    Polynomial<Degree>::Polynomial(const Polynomial<Degree2>& P){
      memset(coefficients,0,sizeof(double)*(Degree+1));
      for(int i=0;i<=Degree && i<=Degree2;i++){coefficients[i]=P.coefficients[i];}
    }
 
 
    template<int Degree>
    template<int Degree2>
    Polynomial<Degree>& Polynomial<Degree>::operator  = (const Polynomial<Degree2> &p){
      int d=Degree<Degree2?Degree:Degree2;
      memset(coefficients,0,sizeof(double)*(Degree+1));
      memcpy(coefficients,p.coefficients,sizeof(double)*(d+1));
      return *this;
    }
 
    template<int Degree>
    Polynomial<Degree-1> Polynomial<Degree>::derivative(void) const{
      Polynomial<Degree-1> p;
      for(int i=0;i<Degree;i++){p.coefficients[i]=coefficients[i+1]*(i+1);}
      return p;
    }
 
    template<int Degree>
    Polynomial<Degree+1> Polynomial<Degree>::integral(void) const{
      Polynomial<Degree+1> p;
      p.coefficients[0]=0;
      for(int i=0;i<=Degree;i++){p.coefficients[i+1]=coefficients[i]/(i+1);}
      return p;
    }
    template<> inline double Polynomial< 0 >::operator() ( double t ) const { return coefficients[0]; }
    template<> inline double Polynomial< 1 >::operator() ( double t ) const { return coefficients[0]+coefficients[1]*t; }
    template<> inline double Polynomial< 2 >::operator() ( double t ) const { return coefficients[0]+(coefficients[1]+coefficients[2]*t)*t; }
    template<int Degree>
    double Polynomial<Degree>::operator() ( double t ) const{
      double v=coefficients[Degree];
      for( int d=Degree-1 ; d>=0 ; d-- ) v = v*t + coefficients[d];
      return v;
    }
    template<int Degree>
    double Polynomial<Degree>::integral( double tMin , double tMax ) const
    {
      double v=0;
      double t1,t2;
      t1=tMin;
      t2=tMax;
      for(int i=0;i<=Degree;i++){
        v+=coefficients[i]*(t2-t1)/(i+1);
        if(t1!=-DBL_MAX && t1!=DBL_MAX){t1*=tMin;}
        if(t2!=-DBL_MAX && t2!=DBL_MAX){t2*=tMax;}
      }
      return v;
    }
    template<int Degree>
    int Polynomial<Degree>::operator == (const Polynomial& p) const{
      for(int i=0;i<=Degree;i++){if(coefficients[i]!=p.coefficients[i]){return 0;}}
      return 1;
    }
    template<int Degree>
    int Polynomial<Degree>::operator != (const Polynomial& p) const{
      for(int i=0;i<=Degree;i++){if(coefficients[i]==p.coefficients[i]){return 0;}}
      return 1;
    }
    template<int Degree>
    int Polynomial<Degree>::isZero(void) const{
      for(int i=0;i<=Degree;i++){if(coefficients[i]!=0){return 0;}}
      return 1;
    }
    template<int Degree>
    void Polynomial<Degree>::setZero(void){memset(coefficients,0,sizeof(double)*(Degree+1));}
 
    template<int Degree>
    Polynomial<Degree>& Polynomial<Degree>::addScaled(const Polynomial& p,double s){
      for(int i=0;i<=Degree;i++){coefficients[i]+=p.coefficients[i]*s;}
      return *this;
    }
    template<int Degree>
    Polynomial<Degree>& Polynomial<Degree>::operator += (const Polynomial<Degree>& p){
      for(int i=0;i<=Degree;i++){coefficients[i]+=p.coefficients[i];}
      return *this;
    }
    template<int Degree>
    Polynomial<Degree>& Polynomial<Degree>::operator -= (const Polynomial<Degree>& p){
      for(int i=0;i<=Degree;i++){coefficients[i]-=p.coefficients[i];}
      return *this;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::operator + (const Polynomial<Degree>& p) const{
      Polynomial q;
      for(int i=0;i<=Degree;i++){q.coefficients[i]=(coefficients[i]+p.coefficients[i]);}
      return q;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::operator - (const Polynomial<Degree>& p) const{
      Polynomial q;
      for(int i=0;i<=Degree;i++)  {q.coefficients[i]=coefficients[i]-p.coefficients[i];}
      return q;
    }
    template<int Degree>
    void Polynomial<Degree>::Scale(const Polynomial& p,double w,Polynomial& q){
      for(int i=0;i<=Degree;i++){q.coefficients[i]=p.coefficients[i]*w;}
    }
    template<int Degree>
    void Polynomial<Degree>::AddScaled(const Polynomial& p1,double w1,const Polynomial& p2,double w2,Polynomial& q){
      for(int i=0;i<=Degree;i++){q.coefficients[i]=p1.coefficients[i]*w1+p2.coefficients[i]*w2;}
    }
    template<int Degree>
    void Polynomial<Degree>::AddScaled(const Polynomial& p1,double w1,const Polynomial& p2,Polynomial& q){
      for(int i=0;i<=Degree;i++){q.coefficients[i]=p1.coefficients[i]*w1+p2.coefficients[i];}
    }
    template<int Degree>
    void Polynomial<Degree>::AddScaled(const Polynomial& p1,const Polynomial& p2,double w2,Polynomial& q){
      for(int i=0;i<=Degree;i++){q.coefficients[i]=p1.coefficients[i]+p2.coefficients[i]*w2;}
    }
 
    template<int Degree>
    void Polynomial<Degree>::Subtract(const Polynomial &p1,const Polynomial& p2,Polynomial& q){
      for(int i=0;i<=Degree;i++){q.coefficients[i]=p1.coefficients[i]-p2.coefficients[i];}
    }
    template<int Degree>
    void Polynomial<Degree>::Negate(const Polynomial& in,Polynomial& out){
      out=in;
      for(int i=0;i<=Degree;i++){out.coefficients[i]=-out.coefficients[i];}
    }
 
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::operator - (void) const{
      Polynomial q=*this;
      for(int i=0;i<=Degree;i++){q.coefficients[i]=-q.coefficients[i];}
      return q;
    }
    template<int Degree>
    template<int Degree2>
    Polynomial<Degree+Degree2> Polynomial<Degree>::operator * (const Polynomial<Degree2>& p) const{
      Polynomial<Degree+Degree2> q;
      for(int i=0;i<=Degree;i++){for(int j=0;j<=Degree2;j++){q.coefficients[i+j]+=coefficients[i]*p.coefficients[j];}}
      return q;
    }
 
    template<int Degree>
    Polynomial<Degree>& Polynomial<Degree>::operator += ( double s )
    {
      coefficients[0]+=s;
      return *this;
    }
    template<int Degree>
    Polynomial<Degree>& Polynomial<Degree>::operator -= ( double s )
    {
      coefficients[0]-=s;
      return *this;
    }
    template<int Degree>
    Polynomial<Degree>& Polynomial<Degree>::operator *= ( double s )
    {
      for(int i=0;i<=Degree;i++){coefficients[i]*=s;}
      return *this;
    }
    template<int Degree>
    Polynomial<Degree>& Polynomial<Degree>::operator /= ( double s )
    {
      for(int i=0;i<=Degree;i++){coefficients[i]/=s;}
      return *this;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::operator + ( double s ) const
    {
      Polynomial<Degree> q=*this;
      q.coefficients[0]+=s;
      return q;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::operator - ( double s ) const
    {
      Polynomial q=*this;
      q.coefficients[0]-=s;
      return q;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::operator * ( double s ) const
    {
      Polynomial q;
      for(int i=0;i<=Degree;i++){q.coefficients[i]=coefficients[i]*s;}
      return q;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::operator / ( double s ) const
    {
      Polynomial q;
      for( int i=0 ; i<=Degree ; i++ ) q.coefficients[i] = coefficients[i]/s;
      return q;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::scale( double s ) const
    {
      Polynomial q=*this;
      double s2=1.0;
      for(int i=0;i<=Degree;i++){
        q.coefficients[i]*=s2;
        s2/=s;
      }
      return q;
    }
    template<int Degree>
    Polynomial<Degree> Polynomial<Degree>::shift( double t ) const
    {
      Polynomial<Degree> q;
      for(int i=0;i<=Degree;i++){
        double temp=1;
        for(int j=i;j>=0;j--){
          q.coefficients[j]+=coefficients[i]*temp;
          temp*=-t*j;
          temp/=(i-j+1);
        }
      }
      return q;
    }
    template<int Degree>
    void Polynomial<Degree>::printnl(void) const{
      for(int j=0;j<=Degree;j++){
        printf("%6.4f x^%d ",coefficients[j],j);
        if(j<Degree && coefficients[j+1]>=0){printf("+");}
      }
      printf("\n");
    }
    template<int Degree>
    void Polynomial<Degree>::getSolutions(double c,std::vector<double>& roots,double EPS) const
    {
      double r[4][2];
      int rCount=0;
      roots.clear();
      switch(Degree){
      case 1:
        rCount=Factor(coefficients[1],coefficients[0]-c,r,EPS);
        break;
      case 2:
        rCount=Factor(coefficients[2],coefficients[1],coefficients[0]-c,r,EPS);
        break;
      case 3:
        rCount=Factor(coefficients[3],coefficients[2],coefficients[1],coefficients[0]-c,r,EPS);
        break;
        //  case 4:
        //    rCount=Factor(coefficients[4],coefficients[3],coefficients[2],coefficients[1],coefficients[0]-c,r,EPS);
        //    break;
      default:
        printf("Can't solve polynomial of degree: %d\n",Degree);
      }
      for(int i=0;i<rCount;i++){
        if(fabs(r[i][1])<=EPS){
          roots.push_back(r[i][0]);
        }
      }
    }
    template< > inline
    Polynomial< 0 > Polynomial< 0 >::BSplineComponent( int i )
    {
      Polynomial p;
      p.coefficients[0] = 1.;
      return p;
    }
    template< int Degree > inline
    Polynomial< Degree > Polynomial< Degree >::BSplineComponent( int i )
    {
      Polynomial p;
      if( i>0 )
      {
        Polynomial< Degree > _p = Polynomial< Degree-1 >::BSplineComponent( i-1 ).integral();
        p -= _p;
        p.coefficients[0] += _p(1);
      }
      if( i<Degree )
      {
        Polynomial< Degree > _p = Polynomial< Degree-1 >::BSplineComponent( i ).integral();
        p += _p;
      }
      return p;
    }
 
  }
}