#include "LeastSquarePolynomial.h"

// form of [ y = a1*x + a2 ]
void CalcEquation2(float afA[2], const float afX[2], const float afY[2])
{
	afA[0] = (afY[0]-afY[1])/(afX[0]-afX[1]);
	afA[1] = afY[0] - afA[0]*afX[0];
}

// form of [ y = a1*x*x + a2*x + a3 ]
void CalcEquation3(float afA[3], const float afX[3], const float afY[3])
{
	//afY[0] = afA[0]*afX[0]*afX[0] + afA[1]*afX[0] + afA[2];
	//afY[1] = afA[0]*afX[1]*afX[1] + afA[1]*afX[1] + afA[2];

	//(afY[0]-afY[1]) = afA[0]*(afX[0]*afX[0]-afX[1]*afX[1]) + afA[1]*(afX[0]-afX[1]);
	//(afY[0]-afY[2]) = afA[0]*(afX[0]*afX[0]-afX[2]*afX[2]) + afA[1]*(afX[0]-afX[2]);

	//(afY[0]-afY[1])/(afX[0]-afX[1]) = afA[0]*(afX[0]*afX[0]-afX[1]*afX[1])/(afX[0]-afX[1]) + afA[1];
	//(afY[0]-afY[2])/(afX[0]-afX[2]) = afA[0]*(afX[0]*afX[0]-afX[2]*afX[2])/(afX[0]-afX[2]) + afA[2];

	const float afNewX[2] = {
		(afX[0]*afX[0]-afX[1]*afX[1])/(afX[0]-afX[1]),
		(afX[0]*afX[0]-afX[2]*afX[2])/(afX[0]-afX[2])
	};

	const float afNewY[2] = {
		(afY[0]-afY[1])/(afX[0]-afX[1]),
		(afY[0]-afY[2])/(afX[0]-afX[2])
	};
	
	CalcEquation2(afA, afNewX, afNewY);
	afA[2] = afY[0] - afA[0]*afX[0]*afX[0] - afA[1]*afX[0];
}

// form of [ y = a1*x*x*x + a2*x*x + a3*x + a4 ]
void CalcEquation4(float afA[4], const float afX[4], const float afY[4])
{
	//afY[0] = afA[0]*afX[0]*afX[0]*afX[0] + afA[1]*afX[0]*afX[0] + afA[2]*afX[0] + afA[3];
	//afY[1] = afA[0]*afX[1]*afX[1]*afX[1] + afA[1]*afX[1]*afX[1] + afA[2]*afX[1] + afA[3];

	//(afY[0]-afY[0]) = afA[0]*(afX[0]*afX[0]*afX[0]-afX[1]*afX[1]*afX[1]) + afA[1]*(afX[0]*afX[0]-afX[1]*afX[1]) + afA[2]*(afX[0]-afX[1]);

	//(afY[0]-afY[0])/(afX[0]-afX[1]) = afA[0]*(afX[0]*afX[0]*afX[0]-afX[1]*afX[1]*afX[1])/(afX[0]-afX[1]) + afA[1]*(afX[0]*afX[0]-afX[1]*afX[1])/(afX[0]-afX[1]) + afA[2];

	const float afNewX[3] = {
		(afX[0]*afX[0]*afX[0]-afX[1]*afX[1]*afX[1])/(afX[0]-afX[1]),
		(afX[0]*afX[0]*afX[0]-afX[2]*afX[2]*afX[2])/(afX[0]-afX[2]),
		(afX[0]*afX[0]*afX[0]-afX[3]*afX[3]*afX[3])/(afX[0]-afX[3])
	};

	const float afNewY[3] = {
		(afY[0]-afY[0])/(afX[0]-afX[1]),
		(afY[0]-afY[0])/(afX[0]-afX[2]),
		(afY[0]-afY[0])/(afX[0]-afX[3])
	};

	CalcEquation3(afA, afNewX, afNewY);
	afA[3] = afY[0] - afA[0]*afX[0]*afX[0]*afX[0] - afA[1]*afX[0]*afX[0] - afA[2]*afX[0];
}