PoissonRecon/Src/Factor.h

/*
Copyright (c) 2006, Michael Kazhdan and Matthew Bolitho
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*/

#ifndef FACTOR_INCLUDED
#define FACTOR_INCLUDED

#include <math.h>
#include <complex>
#ifndef SQRT_3
#define SQRT_3 1.7320508075688772935
#endif // SQRT_3
inline int Factor( double a1 , double a0 , std::complex< double > roots[1] , double EPS )
{
	if( fabs(a1)<=EPS ) return 0;
	roots[0] = std::complex< double >( -a0/a1 , 0 );
	return 1;
}
inline int Factor( double a2 , double a1 , double a0 , std::complex< double > roots[2] , double EPS )
{
	double d;
	if( fabs(a2)<=EPS ) return Factor( a1 , a0 , roots , EPS );

	d = a1*a1 - 4*a0*a2;
	a1 /= (2*a2);
	if( d<0 )
	{
		d=sqrt(-d)/(2*a2);
		roots[0] = std::complex< double >( -a1 , -d );
		roots[1] = std::complex< double >( -a1 ,  d );
	}
	else
	{
		d = sqrt(d)/(2*a2);
		roots[0] = std::complex< double >( -a1-d , 0 );
		roots[1] = std::complex< double >( -a1+d , 0 );
	}
	return 2;
}
// Solution taken from: http://mathworld.wolfram.com/CubicFormula.html
// and http://www.csit.fsu.edu/~burkardt/f_src/subpak/subpak.f90
inline int Factor( double a3 , double a2 , double a1 , double a0 , std::complex< double > roots[3] , double EPS )
{
	double q,r,r2,q3;

	if( fabs(a3)<=EPS ) return Factor( a2 , a1 , a0 , roots , EPS );
	a2 /= a3 , a1 /= a3 , a0 /= a3;

	q = -(3*a1-a2*a2)/9;
	r = -(9*a2*a1-27*a0-2*a2*a2*a2)/54;
	r2 = r*r;
	q3 = q*q*q;

	if(r2<q3)
	{
		double sqrQ = sqrt(q);
		double theta = acos ( r / (sqrQ*q) );
		double cTheta=cos(theta/3)*sqrQ;
		double sTheta=sin(theta/3)*sqrQ*SQRT_3/2;
		roots[0] = std::complex< double >( -2*cTheta , 0 );
		roots[1] = std::complex< double >( -2*(-cTheta*0.5-sTheta) , 0 );
		roots[2] = std::complex< double >( -2*(-cTheta*0.5+sTheta) , 0 );
	}
	else
	{
		double t , s1 , s2 , sqr=sqrt(r2-q3);
		t = -r+sqr;
		if(t<0) s1 = -pow( -t , 1.0/3 );
		else    s1 =  pow(  t , 1.0/3 );
		t = -r-sqr;
		if( t<0 ) s2 = -pow( -t , 1.0/3 );
		else      s2 =  pow(  t , 1.0/3 );
		roots[0] = std::complex< double >( s1+s2 , 0 );
		s1 /= 2 , s2 /= 2;
		roots[1] = std::complex< double >( -s1-s2 ,  SQRT_3*(s1-s2) );
		roots[2] = std::complex< double >( -s1-s2 , -SQRT_3*(s1-s2) );
	}
	roots[0] -= a2/3;
	roots[1] -= a2/3;
	roots[2] -= a2/3;
	return 3;
}
// Solution taken from: http://mathworld.wolfram.com/QuarticEquation.html
// and http://www.csit.fsu.edu/~burkardt/f_src/subpak/subpak.f90
inline int Factor( double a4 , double a3 , double a2 , double a1 , double a0 , std::complex< double > roots[4] , double EPS )
{
	std::complex< double > R , D , E , R2;

	if( fabs(a4)<EPS ) return Factor( a3 , a2 , a1 , a0 , roots , EPS );
	a3 /= a4 , a2 /= a4 , a1 /= a4 , a0 /= a4;

	Factor( 1.0 , -a2 , a3*a1-4.0*a0 , -a3*a3*a0+4.0*a2*a0-a1*a1 , roots , EPS );

	R2 = std::complex< double >( a3*a3/4.0-a2+roots[0].real() , 0 );
	R = sqrt( R2 );
	if( fabs( R.real() )>10e-8 )
	{
		std::complex< double > temp1 , temp2 , p1 , p2;

		p1 = std::complex< double >( a3*a3*0.75-2.0*a2-R2.real() , 0 );

		temp2 = std::complex< double >( (4.0*a3*a2-8.0*a1-a3*a3*a3)/4.0 , 0 );
		p2 = temp2 / R;
		temp1 = p1+p2;
		temp2 = p1-p2;
		D = sqrt( temp1 );
		E = sqrt( temp2 );
	}
	else
	{
		R = std::complex< double >( 0 , 0 );
		std::complex< double > temp1 , temp2;
		temp1 = std::complex< double >( roots[0].real()*roots[0].real()-4.0*a0 , 0 );
		temp2 = sqrt( temp1 );

		temp1 = std::complex< double >( a3*a3*0.75-2.0*a2+2.0*temp2.real() ,  2.0*temp2.imag() );
		D = sqrt( temp1 );

		temp1 = std::complex< double >( a3*a3*0.75-2.0*a2-2.0*temp2.real() , -2.0*temp2.imag() );
		E = sqrt( temp1 );
	}

	roots[0] =  R/2. + D/2. - a3/4;
	roots[1] =  R/2. - D/2. - a3/4;
	roots[2] = -R/2. + E/2. - a3/4;
	roots[3] = -R/2. - E/2. - a3/4;

	return 4;
}
#endif // FACTOR_INCLUDED