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// This function written in TypeScript is not affiliated with the CIE (International Commission on Illumination),
// and is released into the public domain. It is provided "as is" without any warranty, express or implied.
// The classic CIE ΔE2000 implementation, which operates on two L*a*b* colors, and returns their difference.
// "l" ranges from 0 to 100, while "a" and "b" are unbounded and commonly clamped to the range of -128 to 127.
function ciede_2000(l_1: number, a_1: number, b_1: number, l_2: number, a_2: number, b_2: number): number {
// Working in TypeScript with the CIEDE2000 color-difference formula.
// k_l, k_c, k_h are parametric factors to be adjusted according to
// different viewing parameters such as textures, backgrounds...
const k_l = 1.0, k_c = 1.0, k_h = 1.0;
let n = (Math.sqrt(a_1 * a_1 + b_1 * b_1) + Math.sqrt(a_2 * a_2 + b_2 * b_2)) * 0.5;
n = n * n * n * n * n * n * n;
// A factor involving chroma raised to the power of 7 designed to make
// the influence of chroma on the total color difference more accurate.
n = 1.0 + 0.5 * (1.0 - Math.sqrt(n / (n + 6103515625.0)));
// Application of the chroma correction factor.
const c_1 = Math.sqrt(a_1 * a_1 * n * n + b_1 * b_1);
const c_2 = Math.sqrt(a_2 * a_2 * n * n + b_2 * b_2);
// atan2 is preferred over atan because it accurately computes the angle of
// a point (x, y) in all quadrants, handling the signs of both coordinates.
let h_1 = Math.atan2(b_1, a_1 * n), h_2 = Math.atan2(b_2, a_2 * n);
if (h_1 < 0.0)
h_1 += 2.0 * Math.PI;
if (h_2 < 0.0)
h_2 += 2.0 * Math.PI;
n = Math.abs(h_2 - h_1);
// Cross-implementation consistent rounding.
if (Math.PI - 1E-14 < n && n < Math.PI + 1E-14)
n = Math.PI;
// When the hue angles lie in different quadrants, the straightforward
// average can produce a mean that incorrectly suggests a hue angle in
// the wrong quadrant, the next lines handle this issue.
let h_m = (h_1 + h_2) * 0.5, h_d = (h_2 - h_1) * 0.5;
if (Math.PI < n) {
h_d += Math.PI;
// 📜 Sharma’s formulation doesn’t use the next line, but the one after it,
// and these two variants differ by ±0.0003 on the final color differences.
h_m += Math.PI;
// h_m += h_m < Math.PI ? Math.PI : -Math.PI;
}
const p = 36.0 * h_m - 55.0 * Math.PI;
n = (c_1 + c_2) * 0.5;
n = n * n * n * n * n * n * n;
// The hue rotation correction term is designed to account for the
// non-linear behavior of hue differences in the blue region.
const r_t = -2.0 * Math.sqrt(n / (n + 6103515625.0))
* Math.sin(Math.PI / 3.0 * Math.exp(p * p / (-25.0 * Math.PI * Math.PI)));
n = (l_1 + l_2) * 0.5;
n = (n - 50.0) * (n - 50.0);
// Lightness.
const l = (l_2 - l_1) / (k_l * (1.0 + 0.015 * n / Math.sqrt(20.0 + n)));
// These coefficients adjust the impact of different harmonic
// components on the hue difference calculation.
const t = 1.0 + 0.24 * Math.sin(2.0 * h_m + Math.PI * 0.5)
+ 0.32 * Math.sin(3.0 * h_m + 8.0 * Math.PI / 15.0)
- 0.17 * Math.sin(h_m + Math.PI / 3.0)
- 0.20 * Math.sin(4.0 * h_m + 3.0 * Math.PI / 20.0);
n = c_1 + c_2;
// Hue.
const h = 2.0 * Math.sqrt(c_1 * c_2) * Math.sin(h_d) / (k_h * (1.0 + 0.0075 * n * t));
// Chroma.
const c = (c_2 - c_1) / (k_c * (1.0 + 0.0225 * n));
// Returning the square root ensures that dE00 accurately reflects the
// geometric distance in color space, which can range from 0 to around 185.
return Math.sqrt(l * l + h * h + c * c + c * h * r_t);
}
// GitHub Project : https://github.com/michel-leonard/ciede2000-color-matching
// Online Tests : https://michel-leonard.github.io/ciede2000-color-matching
// L1 = 43.4 a1 = 41.0 b1 = 4.8
// L2 = 43.0 a2 = 36.0 b2 = -3.1
// CIE ΔE00 = 4.8162868508 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 4.8163001785 (Gaurav Sharma, OpenJDK, ...)
// Deviation between implementations ≈ 1.3e-5
// See the source code comments for easy switching between these two widely used ΔE*00 implementation variants.
///////////////////////////////////////////////
///////////////////////////////////////////////
/////// ///////
/////// CIEDE 2000 ///////
/////// Testing Random Colors ///////
/////// ///////
///////////////////////////////////////////////
///////////////////////////////////////////////
// This TypeScript program outputs a CSV file to standard output, with its length determined by the first CLI argument.
// Each line contains seven columns :
// - Three columns for the random standard L*a*b* color
// - Three columns for the random sample L*a*b* color
// - And the seventh column for the precise Delta E 2000 color difference between the standard and sample
// The output will be correct, this can be verified :
// - With the C driver, which provides a dedicated verification feature
// - By using the JavaScript validator at https://michel-leonard.github.io/ciede2000-color-matching
function randInRange(min: number, max: number): number {
const n = min + (max - min) * Math.random();
switch (Math.floor(Math.random() * 3)) {
case 0: return Math.round(n);
case 1: return Math.round(n * 10) / 10;
default: return Math.round(n * 100) / 100;
}
}
const arg = process.argv.length > 2 ? parseInt(process.argv[2], 10) : 10000;
const nIterations = isFinite(arg) && arg > 0 ? arg : 10000;
for (let i = 0; i < nIterations; ++i) {
const l1 = randInRange(0.0, 100.0);
const a1 = randInRange(-128.0, 128.0);
const b1 = randInRange(-128.0, 128.0);
const l2 = randInRange(0.0, 100.0);
const a2 = randInRange(-128.0, 128.0);
const b2 = randInRange(-128.0, 128.0);
const deltaE = ciede_2000(l1, a1, b1, l2, a2, b2);
process.stdout.write(`${l1},${a1},${b1},${l2},${a2},${b2},${deltaE}\n`);
}