// Find vertices before taking rotation into account
function findRectVertices(position, size) {
	var left = position[0];
	var right = position[0] + size[0];
	var top = position[1];
	var bottom = position[1] + size[1];
	
	return {
		LT: [ left, top ],
		RT: [ right, top ],
		RB: [ right, bottom ],
		LB: [ left, bottom ]
	};
}

/**
* Find point after rotation around another point by X degrees
*
* @param {Array} point The point to be rotated [X,Y]
* @param {Array} rotationCenterPoint The point that should be rotated around [X,Y]
* @param {Number} degrees The degrees to rotate the point
* @return {Array} Returns point after rotation [X,Y]
*/
function rotatePoint(point, rotationCenterPoint, degrees) {
	// Using radians for this formula
	var radians = degrees * Math.PI / 180;

	// Translate the plane on which rotation is occurring.
	// We want to rotate around 0,0. We'll add these back later.
	point[0] -= rotationCenterPoint[0];
	point[1] -= rotationCenterPoint[1];

	// Perform the rotation
	var newPoint = [];
	newPoint[0] = point[0] * Math.cos(radians) - point[1] * Math.sin(radians);
	newPoint[1] = point[0] * Math.sin(radians) + point[1] * Math.cos(radians);

	// Translate the plane back to where it was.
	newPoint[0] += rotationCenterPoint[0];
	newPoint[1] += rotationCenterPoint[1];

	return newPoint;
}

/**
* Find the vertices of a rotating rectangle
*
* @param {Array} position From left, top [X,Y]
* @param {Array} size Lengths [X,Y]
* @param {Number} degrees Degrees rotated around center
* @return {Object} Arrays LT, RT, RB, LB [X,Y]
*/
function findRectVertices(position, size, degrees) {
	var left = position[0];
	var right = position[0] + size[0];
	var top = position[1];
	var bottom = position[1] + size[1];

	var center = [ right - left, bottom - top ];
	var LT = [ left, top ];
	var RT = [ right, top ];
	var RB = [ right, bottom ];
	var LB = [ left, bottom ];

	return {
		LT: rotatePoint(LT, center, degrees),
		RT: rotatePoint(RT, center, degrees),
		RB: rotatePoint(RB, center, degrees),
		LB: rotatePoint(LB, center, degrees)
	};
}

/**
* Distance formula
*
* @param {Array} p1 First point [X,Y]
* @param {Array} p2 Second point [X,Y]
* @return {Number} Returns distance between points
*/
function distance(p1, p2) {
	return Math.sqrt( Math.pow(p1[0] - p2[0], 2) + Math.pow(p1[1] - p2[1], 2) );
}

/**
* Heron's formula (triangle area)
*
* @param {Number} d1 Distance, side 1
* @param {Number} d2 Distance, side 2
* @param {Number} d3 Distance, side 3
* @return {Number} Returns area of triangle
*/
function triangleArea(d1, d2, d3) {
	// See https://en.wikipedia.org/wiki/Heron's_formula
	var s = (d1 + d2 + d3) / 2;
	return Math.sqrt(s * (s - d1) * (s - d2) * (s - d3));
}

/**
* Determine if a click hit a rotated rectangle
*
* @param {Array} click Click position [X,Y]
* @param {Array} position Rect from left, top [X,Y]
* @param {Array} size Rect size as lengths [X,Y]
* @param {Number} degrees Degrees rotated around center
* @return {Boolean} Returns true if hit, false if miss
*/
function clickHit(click, position, size, degrees) {
	// Find the area of the rectangle
	// Round to avoid small JS math differences
	var rectArea = Math.round(size[0] * size[1]);

	// Find the vertices
	var vertices = findRectVertices(position, size, degrees);

	// Create an array of the areas of the four triangles
	var triArea = [
		// Click, LT, RT
		triangleArea(
			distance(click, vertices.LT),
			distance(vertices.LT, vertices.RT),
			distance(vertices.RT, click)
		),
		// Click, RT, RB
		triangleArea(
			distance(click, vertices.RT),
			distance(vertices.RT, vertices.RB),
			distance(vertices.RB, click)
		),
		// Click, RB, LB
		triangleArea(
			distance(click, vertices.RB),
			distance(vertices.RB, vertices.LB),
			distance(vertices.LB, click)
		),
		// Click, LB, LT
		triangleArea(
			distance(click, vertices.LB),
			distance(vertices.LB, vertices.LT),
			distance(vertices.LT, click)
		)
	];

	// Reduce this array with a sum function
	// Round to avoid small JS math differences
	triArea = Math.round(triArea.reduce(function(a,b) { return a + b; }, 0));

	// Finally do that simple thing we visualized earlier
	if (triArea > rectArea) {
		return true;
	}
	return false;
}