#include <math.h>
#include "lighting.h"
/* Find the distance between two points */
int dist(int x1, int y1, int x2, int y2)
{
	return sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
}

/* Find the square of the distance between two points */
int sqr_dist(int x1, int y1, int x2, int y2)
{
	return (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
}

/* Returns 1 if (x1,y1) is between the other two, 2 if (x2,y2) is, and so on */
/* Returns 0 if two or more points are coincident */
/* Naturally, the points must be very close to collinear */
int middle_point(int x1, int y1, int x2, int y2, int x3, int y3)
{
	/* Check for coincident points */
	if ((x1 == x2 && y1 == y2) || (x1 == x3 && y1 == y3) ||
			(x2 == x3 && y2 == y3)) return 0;
	
	/* See if point 3 is in the middle */
	if ((x1 < x3 && x3 < x2) || (x2 < x3 && x3 < x1) ||
	    (y1 < y3 && y3 < y2) || (y2 < y3 && y3 < y1)) return 3;

	/* Okay, then, point 1 */
	if ((x2 < x1 && x1 < x3) || (x3 < x1 && x1 < x2) ||
	    (y2 < y1 && y1 < y3) || (y3 < y1 && y1 < y2)) return 1;

	/* It must be 2 */
	return 2;
}

/* Finds intersection and stores in (*_x, *_y); returns 0 if lines are skew */
/* If c == 0, (x1, y1) - (x2, y2) is treated as a ray */
int intersection(int x1, int y1, int x2, int y2, int x3, int y3, int x4,
int y4, int* _x, int* _y, int c)
{
	int den, num, x, y;
	
	den = (y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - y1);
	if (den == 0) return 0;

	num = (x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3);
	x = x1 + num * (x2 - x1) / den;
	if (c) {if (!((x1 <= x && x <= x2) || (x1 >= x && x >= x2))) return 0;}
	else if (!((x1 <= x && x1 <= x2) || (x1 >= x && x1 >= x2))) return 0;
	if (!((x3 <= x && x <= x4) || (x3 >= x && x >= x4))) return 0;

	y = y1 + num * (y2 - y1) / den;
	if (c) {if (!((y1 <= y && y <= y2) || (y1 >= y && y >= y2))) return 0;}
	else if (!((y1 <= y && y1 <= y2) || (y1 >= y && y1 >= y2))) return 0;
	if (!((y3 <= y && y <= y4) || (y3 >= y && y >= y4))) return 0;

	*_x = x;
	*_y = y;
	return 1;
}

/* True if (xa,ya) and (xb,yb) are on the same side of (x1,y1)-(x2,y2) */
int same_side(int x1, int y1, int x2, int y2, int xa, int ya, int xb,
		int yb)
{
	int pa, pb;
	x2 -= x1; y2 -= y1;
	xa -= x1; ya -= y1;
	xb -= x1; yb -= y1;
	pa = xa * y2 - ya * x2;
	pb = xb * y2 - yb * x2;

	return (pa < 0 && pb < 0) || (pa == 0 && pb == 0) || (pa > 0 && pb > 0);
}

/* True if (x1,y1), (x2,y2), and (x3,y3) are (nearly) collinear */
int collinear(int x1, int y1, int x2, int y2, int x3, int y3)
{
	unsigned int d = (x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1);
	return d * d <= sqr_dist(x1, y1, x3, y3);
}