polynomial.hpp
/*
Copyright (c) 2006, Michael Kazhdan and Matthew Bolitho
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are permitted provided that the following conditions are met:
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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;
}
}
}
pcl::poisson::Polynomial
Definition: polynomial.h:40
pcl::poisson::Polynomial::operator+=
Polynomial & operator+=(const Polynomial &p)
Definition: polynomial.hpp:127
pcl::poisson::Polynomial::Negate
static void Negate(const Polynomial &in, Polynomial &out)
Definition: polynomial.hpp:170
pcl::poisson::Polynomial::scale
Polynomial scale(double s) const
Definition: polynomial.hpp:242
pcl::poisson::Polynomial::integral
Polynomial< Degree+1 > integral(void) const
Definition: polynomial.hpp:74
pcl::poisson::Polynomial::shift
Polynomial shift(double t) const
Definition: polynomial.hpp:253
pcl::poisson::Polynomial::getSolutions
void getSolutions(double c, std::vector< double > &roots, double EPS) const
Definition: polynomial.hpp:275
pcl::poisson::Polynomial::operator()
double operator()(double t) const
Definition: polynomial.hpp:84
pcl::poisson::Polynomial::operator!=
int operator!=(const Polynomial &p) const
Definition: polynomial.hpp:109
pcl::poisson::Polynomial::setZero
void setZero(void)
Definition: polynomial.hpp:119
pcl::poisson::Polynomial::AddScaled
static void AddScaled(const Polynomial &p1, double w1, const Polynomial &p2, double w2, Polynomial &q)
Definition: polynomial.hpp:153
pcl::poisson::Polynomial::isZero
int isZero(void) const
Definition: polynomial.hpp:114
pcl::poisson::Polynomial::Scale
static void Scale(const Polynomial &p, double w, Polynomial &q)
Definition: polynomial.hpp:149
pcl::poisson::Polynomial::operator-
Polynomial operator-(void) const
Definition: polynomial.hpp:176
pcl::poisson::Polynomial::derivative
Polynomial< Degree-1 > derivative(void) const
Definition: polynomial.hpp:67
pcl::poisson::Polynomial::operator/=
Polynomial & operator/=(double s)
Definition: polynomial.hpp:208
pcl::poisson::Polynomial::operator=
Polynomial & operator=(const Polynomial< Degree2 > &p)
pcl::poisson::Polynomial::printnl
void printnl(void) const
Definition: polynomial.hpp:267
pcl::poisson::Polynomial::operator*=
Polynomial & operator*=(double s)
Definition: polynomial.hpp:202
pcl::poisson::Polynomial::Polynomial
Polynomial(void)
Definition: polynomial.hpp:48
pcl::poisson::Polynomial::operator-=
Polynomial & operator-=(const Polynomial &p)
Definition: polynomial.hpp:132
pcl::poisson::Polynomial::operator/
Polynomial operator/(double s) const
Definition: polynomial.hpp:235
pcl::poisson::Polynomial::coefficients
double coefficients[Degree+1]
Definition: polynomial.h:42
pcl::poisson::Polynomial::operator==
int operator==(const Polynomial &p) const
Definition: polynomial.hpp:104
pcl::poisson::Polynomial::Subtract
static void Subtract(const Polynomial &p1, const Polynomial &p2, Polynomial &q)
Definition: polynomial.hpp:166
pcl::poisson::Polynomial::BSplineComponent
static Polynomial BSplineComponent(int i)
Definition: polynomial.hpp:310
pcl::poisson::Polynomial::addScaled
Polynomial & addScaled(const Polynomial &p, double scale)
Definition: polynomial.hpp:122
pcl::poisson::Polynomial::integral
double integral(double tMin, double tMax) const
Definition: polynomial.hpp:90
pcl::poisson::Polynomial::operator+
Polynomial operator+(const Polynomial &p) const
Definition: polynomial.hpp:137
pcl::poisson::Polynomial::operator*
Polynomial< Degree+Degree2 > operator*(const Polynomial< Degree2 > &p) const
Definition: polynomial.hpp:183
pcl::poisson::Factor
PCL_EXPORTS int Factor(double a1, double a0, double roots[1][2], double EPS)
pcl
Definition: convolution.h:46