#include "curve.h"


int Hermite::inflection(Real *l, const Real &p0, const Real &p1, const Real &t0, const Real &t1) {
	Real root;
	if (solve_equation(
		&root,
		-3*p0 + 3*p1 - 2*t0 -   t1,
		 6*p0 - 6*p1 + 3*t0 + 3*t1 ))
	{
		if (less(0, root) && less(root, 1)) {
			if (l) *l = root;
			return 1;
		}
	}
	return 0;
}

int Hermite::bends(Real *l, const Real &p0, const Real &p1, const Real &t0, const Real &t1) {
	Real roots[2];
	int count = solve_equation(
		roots,
		                 t0       ,
		-6*p0 + 6*p1 - 4*t0 - 2*t1,
		 6*p0 - 6*p1 + 3*t0 + 3*t1 );
	int valid_count = 0;	
	for(Real *i = roots, *end = i + count; i != end; ++i)
		if (less(0, *i) && less(*i, 1)) {
			if (l) l[valid_count] = *i;
			++valid_count;
		}
	return valid_count;
}

Range Hermite::bounds_accurate(const Real &p0, const Real &p1, const Real &t0, const Real &t1) {
	Range range(p0);
	range.expand(p1);
	Real roots[2];
	int count = bends(roots, p0, p1, t0, t1);
	for(Real *i = roots, *end = i + count; i != end; ++i)
		range.expand( p(*i, p0, p1, t0, t1) );
	return range;
}

int Hermite::intersections(Real *l, const Real &p, const Real &p0, const Real &p1, const Real &t0, const Real &t1) {
	Real roots[3];
	int count = solve_equation(
		roots,
		   p0 - p               ,
		                 t0     ,
		-3*p0 + 3*p1 - 2*t0 - t1,
		 2*p0 - 2*p1 +   t0 + t1 );
	int valid_count = 0;
	for(Real *i = roots, *end = i + count; i != end; ++i)
		if (less(0, *i) && less(*i, 1)) {
			if (l) l[valid_count] = *i;
			++valid_count;
		}
	return valid_count;
}


int Bezier::inflection(Real *l, const Real &p0, const Real &p1, const Real &pp0, const Real &pp1) {
	Real root;
	if (solve_equation(
		&root,
		 p0 - 2*pp0 +   pp1     ,
		-p0 + 3*pp0 - 3*pp1 + p1 ))
	{
		if (less(0, root) && less(root, 1)) {
			if (l) *l = root;
			return 1;
		}
	}
	return 0;
}

int Bezier::bends(Real *l, const Real &p0, const Real &p1, const Real &pp0, const Real &pp1) {
	Real roots[2];
	int count = solve_equation(
		roots,
		 -p0 +   pp0             ,
		2*p0 - 4*pp0 + 2*pp1     ,
		 -p0 + 3*pp0 - 3*pp1 + p1 );
	int valid_count = 0;	
	for(Real *i = roots, *end = i + count; i != end; ++i)
		if (less(0, *i) && less(*i, 1)) {
			if (l) l[valid_count] = *i;
			++valid_count;
		}
	return valid_count;
}

Range Bezier::bounds_accurate(const Real &p0, const Real &p1, const Real &pp0, const Real &pp1) {
	Range range(p0);
	range.expand(p1);
	Real roots[2];
	int count = bends(roots, p0, p1, pp0, pp1);
	for(Real *i = roots, *end = i + count; i != end; ++i)
		range.expand( p(*i, p0, p1, pp0, pp1) );
	return range;
}

int Bezier::intersections(Real *l, const Real &p, const Real &p0, const Real &p1, const Real &pp0, const Real &pp1) {
	Real roots[3];
	int count = solve_equation(
		roots,
		   p0 - p                 ,
		-3*p0 + 3*pp0             ,
		 3*p0 - 6*pp0 + 3*pp1     ,
		  -p0 + 3*pp0 - 3*pp1 + p1 );
	int valid_count = 0;
	for(Real *i = roots, *end = i + count; i != end; ++i)
		if (less(0, *i) && less(*i, 1)) {
			if (l) l[valid_count] = *i;
			++valid_count;
		}
	return valid_count;
}