coloroid.js

/**
 * Architects and visual constructors hungarian color space.
 *
 * http://hej.sze.hu/ARC/ARC-030520-A/arc030520a.pdf
 *
 * @module  color-space/coloroid
 */
import xyy from './xyy.js';
import xyz from './xyz.js';


/**
 * Main color space object
 */
var coloroid = {
	name: 'coloroid',
	alias: ['ATV'],

	//hue, saturation, luminosity
	//note that hue values are ids, not the numbers - not every value is possible
	//e.g. 38 will be rounded to 36
	channel: ['A','T','V'],
	min: [10, 0, 0],
	max: [76, 100, 100]
};


/**
 * Coloroid table
 * Regression of values is almost impossible, as hues don’t correlate
 * Even angle values are picked very inconsistently, based on aesthetical evaluation.
 *
 * - tgф, ctgф are removed, ф is searched instead
 * - eλ = xλ + yλ + zλ
 * - λ is removed as not used
 */
coloroid.table = [
	//A    angle  eλ        xλ       yλ
	[ 10,   59.0, 1.724349, 0.44987, 0.53641 ],
	[ 11,   55.3, 1.740844, 0.46248, 0.52444 ],
	[ 12,   51.7, 1.754985, 0.47451, 0.51298 ],
	[ 13,   48.2, 1.767087, 0.48601, 0.50325 ],
	[ 14,   44.8, 1.775953, 0.49578, 0.49052 ],
	[ 15,   41.5, 1.785073, 0.50790, 0.43035 ],
	[ 16,   38.2, 1.791104, 0.51874, 0.46934 ],
	[ 20,   34.9, 1.794831, 0.52980, 0.45783 ],
	[ 21,   31.5, 1.798664, 0.54137, 0.44559 ],
	[ 22,   28.0, 1.794819, 0.55367, 0.43253 ],
	[ 23,   24.4, 1.789610, 0.56680, 0.41811 ],
	[ 24,   20.6, 1.809483, 0.58128, 0.40176 ],
	[ 25,   16.6, 1.760983, 0.59766, 0.38300 ],
	[ 26,   12.3, 1.723443, 0.61653, 0.36061 ],
	[ 30,    7.7, 1.652891, 0.63896, 0.33358 ],
	[ 31,    2.8, 1.502607, 0.66619, 0.29930 ],
	[ 32,   -2.5, 1.072500, 0.70061, 0.26753 ],
	[ 33,   -8.4, 1.136637, 0.63925, 0.22631 ],
	[ 34,  -19.8, 1.232286, 0.53962, 0.19721 ],
	[ 35,  -31.6, 1.310120, 0.50340, 0.17495 ],
	[ 40,  -43.2, 1.376610, 0.46041, 0.15603 ],
	[ 41,  -54.6, 1.438692, 0.42386, 0.13846 ],
	[ 42,  -65.8, 1.501582, 0.38991, 0.12083 ],
	[ 43,  -76.8, 1.570447, 0.35586, 0.10328 ],
	[ 44,  -86.8, 1.645583, 0.32195, 0.08496 ],
	[ 45,  -95.8, 1.732083, 0.28657, 0.05155 ],
	[ 46, -108.4, 1.915753, 0.22202, 0.01771 ],
	[ 50, -117.2, 2.146310, 0.15664, 0.05227 ],
	[ 51, -124.7, 1.649939, 0.12736, 0.09020 ],
	[ 52, -131.8, 1.273415, 0.10813, 0.12506 ],
	[ 53, -138.5, 1.080809, 0.09414, 0.15741 ],
	[ 54, -145.1, 0.957076, 0.03249, 0.18958 ],
	[ 55, -152.0, 0.868976, 0.07206, 0.24109 ],
	[ 56, -163.4, 0.771731, 0.05787, 0.30378 ],
	[ 60, -177.2, 0.697108, 0.04353, 0.35696 ],
	[ 61,  171.6, 0.655803, 0.03291, 0.41971 ],
	[ 62,  152.4, 0.623958, 0.02240, 0.49954 ],
	[ 63,  148.4, 0.596037, 0.01196, 0.60321 ],
	[ 64,  136.8, 0.607413, 0.00425, 0.73542 ],
	[ 65,  125.4, 0.659923, 0.01099, 0.83391 ],
	[ 66,  114.2, 0.859517, 0.08050, 0.77474 ],
	[ 70,  103.2, 1.195683, 0.20259, 0.70460 ],
	[ 71,   93.2, 1.407534, 0.28807, 0.65230 ],
	[ 72,   84.2, 1.532829, 0.34422, 0.61930 ],
	[ 73,   77.3, 1.603792, 0.37838, 0.59533 ],
	[ 74,   71.6, 1.649448, 0.40290, 0.57716 ],
	[ 75,   66.9, 1.681080, 0.42141, 0.56222 ],
	[ 76,   62.8, 1.704979, 0.43647, 0.54895 ]
];


/**
Coloroid table source
Some negative angle typos are fixed.
Angle typo on the A=62 is fixed.
xλ typo on A=73 is fixed.


Beware, tg/ctg values don’t agree with angle.
Also don’t trust the calculated eλ = xλ + yλ + zλ.
Also, unfortunately, some values might be wrong, as coloroid range looks uneven.

A   λ       ф     tg ф    ctg ф   xλ       yλ       zλ       xλ      yλ      eλ

10  570.83   59.0          0.6009 0.775745 0.946572 0.002032 0.44987 0.54895 1.724349
11  572.64   55.3          0.6924 0.805130 0.933804 0.001910 0.46248 0.53641 1.740845
12  574.38   51.7          0.7898 0.832782 0.920395 0.001808 0.47451 0.52444 1.754986
13  576.06   48.2  1.1180  0.8941 0.858841 0.906482 0.001764 0.48601 0.51298 1.767088
14  577.50   44.8  0.9330  1.0070 0.880488 0.893741 0.001724 0.49578 0.50325 1.775953
15  579.31   41.5  0.8847         0.906652 0.876749 0.001672 0.50790 0.49052 1.785074
16  580.95   38.2  0.7869         0.929124 0.860368 0.001612 0.51874 0.43035 1.791104
20  582.65   34.9  0.6976         0.950909 0.842391 0.001531 0.52980 0.46934 1.794831
21  584.46   31.5  0.6128         0.972454 0.824779 0.001431 0.54137 0.45783 1.798665
22  586.43   28.0  0.5317         0.993753 0.799758 0.001308 0.55367 0.44559 1.794822
23  588.59   24.4  0.4536         1.014350 0.774090 0.001170 0.56680 0.43253 1.789610
24  591.06   20.6  0.3759         1.034402 0.774014 0.001067 0.58128 0.41811 1.779484
25  594.00   16.6  0.2974         1.052466 0.707496 0.001021 0.59766 0.40176 1.760984
26  597.74   12.3  0.2180         1.062544 0.660001 0.000898 0.61653 0.38300 1.723444
30  602.72    7.7  0.1352         1.056125 0.596070 0.000696 0.63896 0.36061 1.652892
31  610.14    2.8  0.0489         1.001027 0.501245 0.000335 0.66619 0.33358 1.502608
32  625.00   -2.5 -0.0435         0.751400 0.321000 0.000100 0.70061 0.29930 1.072500
33 -492.79   -8.4 -0.1477         0.726603 0.304093 0.105941 0.63925 0.26753 1.136638
34 -495.28  -19.8 -0.3600         0.689620 0.278886 0.263780 0.53962 0.22631 1.232286
35 -498.45  -31.6 -0.6152         0.659523 0.258373 0.392224 0.50340 0.19721 1.310122
40 -502.69  -43.2 -0.9391         0.633815 0.240851 0.501944 0.46041 0.17495 1.376610
41 -509.12  -54.6         -0.7107 0.609810 0.224490 0.604392 0.42386 0.15603 1.438692
42 -520.40  -65.8         -0.4494 0.585492 0.207915 0.708175 0.38991 0.13846 1.501583
43 -536.31  -76.8         -0.2345 0.558865 0.189767 0.821815 0.35586 0.12083 1.570447
44 -548.11  -86.8         -0.0559 0.529811 0.169965 0.945807 0.32195 0.10328 1.645584
45 -555.96  -95.8         -0.1016 0.496364 0.147168 1.088551 0.28657 0.08496 1.732085
46 -564.18 -108.4          0.3327 0.425346 0.098764 1.391643 0.22202 0.05155 1.915754
50  450.00 -117.2          0.5141 0.336200 0.038000 1.772110 0.15664 0.01771 2.146310
51  468.71 -124.7          0.6924 0.210174 0.086198 1.353567 0.12736 0.05227 1.649940
52  475.44 -131.8          0.8941 0.137734 0.114770 1.020911 0.10813 0.09020 1.273415
53  479.00 -138.5  0.8847         0.101787 0.135067 0.843955 0.09414 0.12506 1.080809
54  482.04 -145.1  0.6976         0.079004 0.150709 0.727363 0.03249 0.15741 0.957577
55  484.29 -152.0  0.5317         0.062658 0.164626 0.641692 0.07206 0.18958 0.868977
56  487.31 -163.4  0.2981         0.044691 0.185949 0.541091 0.05787 0.24109 0.771732
60  490.40 -177.2  0.0489         0.030372 0.211659 0.455077 0.04353 0.30378 0.697110
61  492.72  171.6 -0.1477         0.021655 0.234022 0.400126 0.03291 0.35696 0.655804
62  495.28  125.4 -0.3600         0.013989 0.261843 0.348126 0.02240 0.41971 0.623969
63  498.45  148.4 -0.6152         0.007215 0.301137 0.287685 0.01196 0.49954 0.596037
64  502.69  136.8 -0.9391 -1.0650 0.002586 0.366425 0.238402 0.00425 0.60321 0.607414
65  509.12  125.4 -1.4070 -0.7107 0.007260 0.485346 0.167317 0.01099 0.73542 0.659924
66  520.40  114.2         -0.4494 0.066010 0.717274 0.076233 0.08050 0.83391 0.859523
70  536.31  103.2         -0.2345 0.242272 0.926325 0.027086 0.20259 0.77474 1.195684
71  548.11   93.2         -0.0559 0.406663 0.990587 0.010284 0.28807 0.70460 1.410097
72  555.96   84.2          0.1016 0.527646 0.999862 0.005321 0.34422 0.65230 1.532830
73  560.74   77.3          0.2254 0.606873 0.993224 0.003695 0.37838 0.61930 1.603793
74  564.18   71.6          0.3327 0.664599 0.981981 0.002868 0.40290 0.59533 1.649449
75  566.78   66.9          0.4265 0.708358 0.970252 0.002470 0.42141 0.57716 1.681081
76  568.92   62.8          0.5140 0.744182 0.958592 0.002205 0.43647 0.56222 1.704981
*/




/** Create angle-sorted table */
var table = coloroid.table;
var angleTable = [].concat(table.slice(-13),table.slice(0, -13));


/**
 * Some precalculations
 * 2° D65 whitepoint is used
 */
var i = 'D65';
var o = 2;

var Xn = xyz.whitepoint[o][i][0];
var Yn = xyz.whitepoint[o][i][1];
var Zn = xyz.whitepoint[o][i][2];

var y0 = Xn / (Xn + Yn + Zn);
var x0 = Yn / (Xn + Yn + Zn);
var ew = (Xn + Yn + Zn) / 100;



/**
 * From xyY to coloroid
 *
 * @param {Array} arg xyY tuple
 *
 * @return {Array} ATV coloroid channels
 */
xyy.coloroid = function (arg) {
	var x = arg[0], y = arg[1], Y = arg[2];

	//coloroid luminocity is the same as hunter-lab lightness (the easier part)
	var V = 10 * Math.sqrt(Y);

	//get the hue angle, -π ... +π
	var angle = Math.atan2(y - y0, x - x0) * 180 / Math.PI;
	var row;

	//find the closest row in the table
	var prev = angleTable.length - 1;
	for (var i = 0; i < angleTable.length; i++) {
		if (angle > angleTable[i][1]) {
			break;
		}
		prev = i;
	}
	//round instead of ceil
	row = Math.abs(angleTable[i+1][1] - angle) > Math.abs(angleTable[prev][1] - angle) ? angleTable[i+1] : angleTable[prev];

	//get hue id
	var A = row[0];

	//calc saturation
	var yl = row[4], el = row[2], xl = row[3];

	//yl should be scaled to 0..100;
	var Yl = yl * el * 100;

	var T = 100 * Y*(x0*ew - x*ew) / (100*(x*el - xl*el) + Yl*(x0*ew - x*ew));
	// var T = 100 * Y*(1 - y*ew) / (100*(y*el - yl*el) + Yl*(1 - y*ew));

	return [A, T, V];
};





/**
 * Backwise - from coloroid to xyY
 *
 * @param {Array} arg Coloroid values
 *
 * @return {Array} xyY values
 */
coloroid.xyy = function (arg) {
	var A = arg[0], T = arg[1], V = arg[2];

	//find the closest row in the table
	var row;
	for (var i = 0; i < table.length; i++) {
		if (A <= table[i][0]) {
			row = table[i];
			break;
		}
	}

	var yl = row[4], el = row[2], xl = row[3];

	var Y = V*V / 100;

	var Yl = yl * el * 100;

	var x = (100*Y*x0*ew + 100*xl*el*T - Yl*T*x0*ew) / (100*T*el - Yl*T*ew + 100*Y*ew);
	var y = (100*Y + 100*T*yl*el - Yl*T) / (Y*ew*100 + T*100*el - T*Yl*ew);

	// var x = (100*Y*ew*x0 + 100*T*el*xl - T*Yl*ew*x0) / (100*T*el - T*Yl*ew + 100*Y*ew);
	// var y = 100*Y / (100*T*el + 100*T*ew*Yl + 100*ew*Y);

	// var x = (ew*x0*(V*V - 100*T*row[6]) + 100*T*el*xl) / (ew*(V*V - 100*T*row[6]) + 100*T*el);
	// var y = V*V/(ew*(V*V + 100*T*row[6]) + 100*T*el);

	return [x,y,Y];
};



/** Proper transformation to a XYZ (via xyY) */
xyz.coloroid = function (arg) {
	return xyy.coloroid(xyz.xyy(arg));
};
coloroid.xyz = function (arg) {
	return xyy.xyz(coloroid.xyy(arg));
};



export default coloroid;