/**
 * https://en.wikipedia.org/wiki/TSL_color_space
 * http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.86.6037&rep=rep1&type=pdf
 *
 * Tint, Saturation, Lightness
 *
 * @module  color-space/tsl
 */
'use strict'

var rgb = require('./rgb');

var tsl = module.exports = {
	name: 'tsl',
	min: [0,0,0],
	max: [1, 1, 1],
	channel: ['tint','saturation','lightness']
};


/**
 * TSL to RGB
 *
 * @param {Array} tsl RGB values
 *
 * @return {Array} TSL values
 */
tsl.rgb = function(tsl) {
	var T = tsl[0],
		S = tsl[1],
		L = tsl[2];

	//wikipedia solution
	/*
	// var x = - 1 / Math.tan(Math.PI * 2 * T);
	var x = -Math.sin(2*Math.PI*T);
	if ( x != 0 ) x = Math.cos(2*Math.PI*T)/x;

	var g = T > .5 ? -S * Math.sqrt( 5 / (9 * (x*x + 1)) ) :
			T < .5 ? S * Math.sqrt( 5 / (9 * (x*x + 1)) ) : 0;
	var r = T === 0 ? 0.7453559 * S : (x * g + 1/3);

	var R = k * r, G = k * g, B = k * (1 - r - g);
	*/

	var x = Math.tan(2 * Math.PI * (T - 1/4));
	x *= x;

	var r = Math.sqrt(5 * S*S / (9 * (1/x + 1))) + 1/3;
	var g = Math.sqrt(5 * S*S / (9 * (x + 1))) + 1/3;

	var k = L / (.185 * r + .473 * g + .114);

	var B = k * (1 - r - g);
	var G = k * g;
	var R = k * r;

	return [
		R * 255, G * 255, B * 255
	];
};


/**
 * RGB to TSL
 *
 * @param {Array} tsl TSL values
 *
 * @return {Array} RGB values
 */
rgb.tsl = function(rgb) {
	var r = rgb[0] / 255,
		g = rgb[1] / 255,
		b = rgb[2] / 255;

	var r_ = (r / (r + g + b) || 0) - 1/3,
		g_ = (g / (r + g + b) || 0) - 1/3;
	var T = g_ > 0 ? .5 * Math.atan(r_/ g_) / Math.PI + .25 :
			g_ < 0 ? .5 * Math.atan(r_/ g_) / Math.PI + .75 : 0;

	var S = Math.sqrt(9/5 * (r_*r_ + g_*g_));

	var L = (r * 0.299) + (g * 0.587) + (b * 0.114);

	return [T, S, L];
};