include/colmap/lib/PoissonRecon/PPolynomial.inl

/*
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"

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

template< int Degree >
PPolynomial< Degree >::~PPolynomial( void )
{
	FreePointer( polys );
	polyCount = 0;
}
template< int Degree >
void PPolynomial< Degree >::set( Pointer( StartingPolynomial< Degree > ) sps , int count )
{
	int c=0;
	set( count );
	qsort( sps , count , sizeof( StartingPolynomial< Degree > ) , StartingPolynomial< Degree >::Compare );
	for( int 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 )
{
	FreePointer( polys );
	polyCount = size;
	if( size )
	{
		polys = AllocPointer< StartingPolynomial< Degree > >( size );
		memset( polys , 0 , sizeof( StartingPolynomial< Degree > )*size );
	}
}
template< int Degree >
void PPolynomial<Degree>::reset( size_t newSize )
{
	polyCount = newSize;
	polys = ReAllocPointer< StartingPolynomial< Degree > >( polys , newSize );
}
template< int Degree >
PPolynomial< Degree >& PPolynomial< Degree >::compress( double delta )
{
	int _polyCount = polyCount;
	Pointer( StartingPolynomial< Degree > ) _polys = polys;

	polyCount = 1 , polys = NullPointer( StartingPolynomial< Degree > );
	for( int i=1 ; i<_polyCount ; i++ ) if( _polys[i].start-_polys[i-1].start>delta ) polyCount++;
	if( polyCount==_polyCount ) polys = _polys;
	else
	{
		polys = AllocPointer< StartingPolynomial< Degree > >( polyCount );
		polys[0] = _polys[0] , polyCount = 0;
		for( int i=1 ; i<_polyCount ; i++ )
		{
			if( _polys[i].start-_polys[i-1].start>delta ) polys[ ++polyCount ] = _polys[i];
			else polys[ polyCount ].p += _polys[i].p;
		}
		polyCount++;
		FreePointer( _polys );
	}
	return *this;
}

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);
	if( s<0 ) qsort( q.polys , polyCount , sizeof( StartingPolynomial< Degree > ) , StartingPolynomial< Degree >::Compare );
	return q;
}
template< int Degree >
PPolynomial< Degree > PPolynomial< Degree >::reflect( double r ) const
{
	PPolynomial q;
	q.set( polyCount );
	for( size_t i=0 ; i<polyCount ; i++ )
	{
		q.polys[i].scale(-1.);
		if( r ) q.polys[i].shift( 2.*r );
	}
	qsort( q.polys , polyCount , sizeof( StartingPolynomial< Degree > ) , StartingPolynomial< Degree >::Compare );
	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 ) const
{
	PPolynomial<Degree+1> A;
	Polynomial<Degree+1> p;
	Pointer( StartingPolynomial< Degree+1 > ) sps;
	sps = AllocPointer< 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) );
	FreePointer( 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);
	}
}