The lineIntersection function from the thorny/math/poly2.js class file

lineIntersection.js

/**
 * Used to find an intersection between two points.
 * @param vector2 
 * @return obj|false if intersection happened returns array of x/y 
 * otherwise fales.
 */
lineIntersection: function (v1, v2, v3, v4) {
	var 
		bx,
		by, 
		dx, 
		dy,
		b_dot_d_perp,
		cx,
		cy,
		t,
		u;

	bx = v2.getX() - v1.getX();
	by = v2.getY() - v1.getY();
	dx = v4.getX() - v3.getX();
	dy = v4.getY() - v3.getY();

	b_dot_d_perp = bx * dy - by * dx;
	if (b_dot_d_perp === 0) {
		return false;
	}

	cx = v3.getX() - v1.getX();
	cy = v3.getY() - v1.getY();
	t = (cx * dy - cy * dx) / b_dot_d_perp;

	if (t < 0 || t > 1) {
		return false;
	}

	u = (cx * by - cy * bx) / b_dot_d_perp;

	if (u < 0 || u > 1) {
		return false;
	}	

	return vector2(v1.getX() + t * bx, v1.getY() + t * by);
}