var π = Math.PI
var _120 = radians(120)

module.exports = normalize

/**
 * describe `path` in terms of cubic bézier 
 * curves and move commands
 *
 * @param {Array} path
 * @return {Array}
 */

function normalize(path){
	// init state
	var prev
	var result = []
	var bezierX = 0
	var bezierY = 0
	var startX = 0
	var startY = 0
	var quadX = null
	var quadY = null
	var x = 0
	var y = 0

	for (var i = 0, len = path.length; i < len; i++) {
		var seg = path[i]
		var command = seg[0]
		switch (command) {
			case 'M':
				startX = seg[1]
				startY = seg[2]
				break
			case 'A':
				seg = arc(x, y,seg[1],seg[2],radians(seg[3]),seg[4],seg[5],seg[6],seg[7])
				// split multi part
				seg.unshift('C')
				if (seg.length > 7) {
					result.push(seg.splice(0, 7))
					seg.unshift('C')
				}
				break
			case 'S':
				// default control point
				var cx = x
				var cy = y
				if (prev == 'C' || prev == 'S') {
					cx += cx - bezierX // reflect the previous command's control
					cy += cy - bezierY // point relative to the current point
				}
				seg = ['C', cx, cy, seg[1], seg[2], seg[3], seg[4]]
				break
			case 'T':
				if (prev == 'Q' || prev == 'T') {
					quadX = x * 2 - quadX // as with 'S' reflect previous control point
					quadY = y * 2 - quadY
				} else {
					quadX = x
					quadY = y
				}
				seg = quadratic(x, y, quadX, quadY, seg[1], seg[2])
				break
			case 'Q':
				quadX = seg[1]
				quadY = seg[2]
				seg = quadratic(x, y, seg[1], seg[2], seg[3], seg[4])
				break
			case 'L':
				seg = line(x, y, seg[1], seg[2])
				break
			case 'H':
				seg = line(x, y, seg[1], y)
				break
			case 'V':
				seg = line(x, y, x, seg[1])
				break
			case 'Z':
				seg = line(x, y, startX, startY)
				break
		}

		// update state
		prev = command
		x = seg[seg.length - 2]
		y = seg[seg.length - 1]
		if (seg.length > 4) {
			bezierX = seg[seg.length - 4]
			bezierY = seg[seg.length - 3]
		} else {
			bezierX = x
			bezierY = y
		}
		result.push(seg)
	}

	return result
}

function line(x1, y1, x2, y2){
	return ['C', x1, y1, x2, y2, x2, y2]
}

function quadratic(x1, y1, cx, cy, x2, y2){
	return [
		'C',
		x1/3 + (2/3) * cx,
		y1/3 + (2/3) * cy,
		x2/3 + (2/3) * cx,
		y2/3 + (2/3) * cy,
		x2,
		y2
	]
}

// This function is ripped from 
// github.com/DmitryBaranovskiy/raphael/blob/4d97d4/raphael.js#L2216-L2304 
// which references w3.org/TR/SVG11/implnote.html#ArcImplementationNotes
// TODO: make it human readable

function arc(x1, y1, rx, ry, angle, large_arc_flag, sweep_flag, x2, y2, recursive) {
	if (!recursive) {
		var xy = rotate(x1, y1, -angle)
		x1 = xy.x
		y1 = xy.y
		xy = rotate(x2, y2, -angle)
		x2 = xy.x
		y2 = xy.y
		var x = (x1 - x2) / 2
		var y = (y1 - y2) / 2
		var h = (x * x) / (rx * rx) + (y * y) / (ry * ry)
		if (h > 1) {
			h = Math.sqrt(h)
			rx = h * rx
			ry = h * ry
		}
		var rx2 = rx * rx
		var ry2 = ry * ry
		var k = (large_arc_flag == sweep_flag ? -1 : 1)
			* Math.sqrt(Math.abs((rx2 * ry2 - rx2 * y * y - ry2 * x * x) / (rx2 * y * y + ry2 * x * x)))
		if (k == Infinity) k = 1 // neutralize
		var cx = k * rx * y / ry + (x1 + x2) / 2
		var cy = k * -ry * x / rx + (y1 + y2) / 2
		var f1 = Math.asin(((y1 - cy) / ry).toFixed(9))
		var f2 = Math.asin(((y2 - cy) / ry).toFixed(9))

		f1 = x1 < cx ? π - f1 : f1
		f2 = x2 < cx ? π - f2 : f2
		if (f1 < 0) f1 = π * 2 + f1
		if (f2 < 0) f2 = π * 2 + f2
		if (sweep_flag && f1 > f2) f1 = f1 - π * 2
		if (!sweep_flag && f2 > f1) f2 = f2 - π * 2
	} else {
		f1 = recursive[0]
		f2 = recursive[1]
		cx = recursive[2]
		cy = recursive[3]
	}
	// greater than 120 degrees requires multiple segments
	if (Math.abs(f2 - f1) > _120) {
		var f2old = f2
		var x2old = x2
		var y2old = y2
		f2 = f1 + _120 * (sweep_flag && f2 > f1 ? 1 : -1)
		x2 = cx + rx * Math.cos(f2)
		y2 = cy + ry * Math.sin(f2)
		var res = arc(x2, y2, rx, ry, angle, 0, sweep_flag, x2old, y2old, [f2, f2old, cx, cy])
	}
	var t = Math.tan((f2 - f1) / 4)
	var hx = 4 / 3 * rx * t
	var hy = 4 / 3 * ry * t
	var curve = [
		2 * x1 - (x1 + hx * Math.sin(f1)),
		2 * y1 - (y1 - hy * Math.cos(f1)),
		x2 + hx * Math.sin(f2),
		y2 - hy * Math.cos(f2),
		x2,
		y2
	]
	if (recursive) return curve
	if (res) curve = curve.concat(res)
	for (var i = 0; i < curve.length;) {
		var rot = rotate(curve[i], curve[i+1], angle)
		curve[i++] = rot.x
		curve[i++] = rot.y
	}
	return curve
}

function rotate(x, y, rad){
	return {
		x: x * Math.cos(rad) - y * Math.sin(rad),
		y: x * Math.sin(rad) + y * Math.cos(rad)
	}
}

function radians(degress){
	return degress * (π / 180)
}