colmap/lib/PoissonRecon/Polynomial.inl

/*
Copyright (c) 2006, Michael Kazhdan and Matthew Bolitho
All rights reserved.

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are permitted provided that the following conditions are met:

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may be used to endorse or promote products derived from this software without specific
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*/

#include <float.h>
#include <math.h>
#include <algorithm>
#include "Factor.h"

////////////////
// Polynomial //
////////////////
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<> double Polynomial< 0 >::operator() ( double t ) const { return coefficients[0]; }
template<> double Polynomial< 1 >::operator() ( double t ) const { return coefficients[0]+coefficients[1]*t; }
template<> 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< int Degree >
int Polynomial<Degree>::getSolutions( double c , double* roots , double EPS ) const
{
	double _roots[4][2];
	int _rCount=0;
	switch( Degree )
	{
		case 1: _rCount = Factor(                                                       coefficients[1] , coefficients[0]-c , _roots , EPS ) ; break;
		case 2:	_rCount = Factor(                                     coefficients[2] , coefficients[1] , coefficients[0]-c , _roots , EPS ) ; break;
		case 3: _rCount = Factor(                   coefficients[3] , coefficients[2] , coefficients[1] , coefficients[0]-c , _roots , EPS ) ; break;
//		case 4: _rCount = Factor( coefficients[4] , coefficients[3] , coefficients[2] , coefficients[1] , coefficients[0]-c , _roots , EPS ) ; break;
		default: printf( "Can't solve polynomial of degree: %d\n" , Degree );
	}
	int rCount = 0;
	for( int i=0 ; i<_rCount ; i++ ) if( fabs(_roots[i][1])<=EPS ) roots[rCount++] = _roots[i][0];
	return rCount;
}
// The 0-th order B-spline
template< >
Polynomial< 0 > Polynomial< 0 >::BSplineComponent( int i )
{
	Polynomial p;
	p.coefficients[0] = 1.;
	return p;
}

// The Degree-th order B-spline
template< int Degree >
Polynomial< Degree > Polynomial< Degree >::BSplineComponent( int i )
{
	// B_d^i(x) = \int_x^1 B_{d-1}^{i}(y) dy + \int_0^x B_{d-1}^{i-1} y dy
	//          = \int_0^1 B_{d-1}^{i}(y) dy - \int_0^x B_{d-1}^{i}(y) dy + \int_0^x B_{d-1}^{i-1} y dy
	Polynomial p;
	if( i<Degree )
	{
		Polynomial< Degree > _p = Polynomial< Degree-1 >::BSplineComponent( i ).integral();
		p -= _p;
		p.coefficients[0] += _p(1);
	}
	if( i>0 )
	{
		Polynomial< Degree > _p = Polynomial< Degree-1 >::BSplineComponent( i-1 ).integral();
		p += _p;
	}
	return p;
}


// The 0-th order B-spline values
template< > void Polynomial< 0 >::BSplineComponentValues( double x , double* values ){ values[0] = 1.; }
// The Degree-th order B-spline
template< int Degree > void Polynomial< Degree >::BSplineComponentValues( double x , double* values )
{
	const double Scale = 1./Degree;
	Polynomial< Degree-1 >::BSplineComponentValues( x , values+1 );
	values[0] = values[1] * (1.-x) * Scale;
	for( int i=1 ; i<Degree ; i++ )
	{
		double x1 = (x-i+Degree) , x2 = (-x+i+1);
		values[i] = ( values[i]*x1 + values[i+1]*x2 ) * Scale;
	}
	values[Degree] *= x * Scale;
}

// Using the recurrence formulation for Pascal's triangle
template< > void Polynomial< 0 >::BinomialCoefficients( int bCoefficients[1] ){ bCoefficients[0] = 1; }
template< int Degree > void Polynomial< Degree >::BinomialCoefficients( int bCoefficients[Degree+1] )
{
	Polynomial< Degree-1 >::BinomialCoefficients( bCoefficients );
	int leftValue = 0;
	for( int i=0 ; i<Degree ; i++ )
	{
		int temp = bCoefficients[i];
		bCoefficients[i] += leftValue;
		leftValue = temp;
	}
	bCoefficients[Degree] = 1;
}