/**
 * @author Peter Kelley
 * @author pgkelley4@gmail.com
 */

/**
 * See if two line segments intersect. This uses the 
 * vector cross product approach described below:
 * http://stackoverflow.com/a/565282/786339
 * 
 * @param {Object} p point object with x and y coordinates
 *  representing the start of the 1st line.
 * @param {Object} p2 point object with x and y coordinates
 *  representing the end of the 1st line.
 * @param {Object} q point object with x and y coordinates
 *  representing the start of the 2nd line.
 * @param {Object} q2 point object with x and y coordinates
 *  representing the end of the 2nd line.
 */
function doLineSegmentsIntersect(p, p2, q, q2) {
	var r = subtractPoints(p2, p);
	var s = subtractPoints(q2, q);

	var uNumerator = crossProduct(subtractPoints(q, p), r);
	var denominator = crossProduct(r, s);

	if (uNumerator == 0 && denominator == 0) {
		// They are coLlinear
		
		// Do they touch? (Are any of the points equal?)
		if (equalPoints(p, q) || equalPoints(p, q2) || equalPoints(p2, q) || equalPoints(p2, q2)) {
			return true
		}
		// Do they overlap? (Are all the point differences in either direction the same sign)
		return !allEqual(
				(q.x - p.x < 0),
				(q.x - p2.x < 0),
				(q2.x - p.x < 0),
				(q2.x - p2.x < 0)) ||
			!allEqual(
				(q.y - p.y < 0),
				(q.y - p2.y < 0),
				(q2.y - p.y < 0),
				(q2.y - p2.y < 0));
	}

	if (denominator == 0) {
		// lines are paralell
		return false;
	}

	var u = uNumerator / denominator;
	var t = crossProduct(subtractPoints(q, p), s) / denominator;

	return (t >= 0) && (t <= 1) && (u >= 0) && (u <= 1);
}

/**
 * Calculate the cross product of the two points.
 * 
 * @param {Object} point1 point object with x and y coordinates
 * @param {Object} point2 point object with x and y coordinates
 * 
 * @return the cross product result as a float
 */
function crossProduct(point1, point2) {
	return point1.x * point2.y - point1.y * point2.x;
}

/**
 * Subtract the second point from the first.
 * 
 * @param {Object} point1 point object with x and y coordinates
 * @param {Object} point2 point object with x and y coordinates
 * 
 * @return the subtraction result as a point object
 */ 
function subtractPoints(point1, point2) {
	var result = {};
	result.x = point1.x - point2.x;
	result.y = point1.y - point2.y;

	return result;
}

/**
 * See if the points are equal.
 *
 * @param {Object} point1 point object with x and y coordinates
 * @param {Object} point2 point object with x and y coordinates
 *
 * @return if the points are equal
 */
function equalPoints(point1, point2) {
	return (point1.x == point2.x) && (point1.y == point2.y)
}

/**
 * See if all arguments are equal.
 *
 * @param {...} args arguments that will be compared by '=='.
 *
 * @return if all arguments are equal
 */
function allEqual(args) {
	var firstValue = arguments[0],
		i;
	for (i = 1; i < arguments.length; i += 1) {
		if (arguments[i] != firstValue) {
			return false;
		}
	}
	return true;
}