Swift / ciede-2000.swift 💾

// This function written in Swift 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.

import Foundation

// 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.
func ciede_2000(l_1: Double, a_1: Double, b_1: Double, l_2: Double, a_2: Double, b_2: Double) -> Double {
	// Working in Swift 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...
	let k_l = 1.0, k_c = 1.0, k_h = 1.0;
	var n = (sqrt(a_1 * a_1 + b_1 * b_1) + 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 - sqrt(n / (n + 6103515625.0)));
	// Application of the chroma correction factor.
	let c_1 = sqrt(a_1 * a_1 * n * n + b_1 * b_1);
	let c_2 = 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.
	var h_1 = atan2(b_1, a_1 * n), h_2 = atan2(b_2, a_2 * n);
	if h_1 < 0.0 { h_1 += 2.0 * .pi; }
	if h_2 < 0.0 { h_2 += 2.0 * .pi; }
	n = abs(h_2 - h_1);
	// Cross-implementation consistent rounding.
	if .pi - 1E-14 < n && n < .pi + 1E-14 { n = .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.
	var h_m = (h_1 + h_2) * 0.5, h_d = (h_2 - h_1) * 0.5;
	if .pi < n {
		h_d += .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 += .pi;
		// if h_m < .pi { h_m += .pi; } else { h_m -= .pi; }
	}
	let p = 36.0 * h_m - 55.0 * .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.
	let r_t = -2.0 * sqrt(n / (n + 6103515625.0))
			* sin(.pi / 3.0 * exp(p * p / (-25.0 * .pi * .pi)));
	n = (l_1 + l_2) * 0.5;
	n = (n - 50.0) * (n - 50.0);
	// Lightness.
	let l = (l_2 - l_1) / (k_l * (1.0 + 0.015 * n / sqrt(20.0 + n)));
	// These coefficients adjust the impact of different harmonic
	// components on the hue difference calculation.
	let t = 1.0 	+ 0.24 * sin(2.0 * h_m + .pi * 0.5)
			+ 0.32 * sin(3.0 * h_m + 8.0 * .pi / 15.0)
			- 0.17 * sin(h_m + .pi / 3.0)
			- 0.20 * sin(4.0 * h_m + 3.0 * .pi / 20.0);
	n = c_1 + c_2;
	// Hue.
	let h = 2.0 * sqrt(c_1 * c_2) * sin(h_d) / (k_h * (1.0 + 0.0075 * n * t));
	// Chroma.
	let 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 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 = 44.4   a1 = 30.3   b1 = 3.3
// L2 = 43.8   a2 = 24.5   b2 = -2.4
// CIE ΔE00 = 4.4951265489 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 4.4951440582 (Gaurav Sharma, OpenJDK, ...)
// Deviation between implementations ≈ 1.8e-5

// See the source code comments for easy switching between these two widely used ΔE*00 implementation variants.