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// 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 = 79.1 a1 = 25.2 b1 = 4.6
// L2 = 76.8 a2 = 20.3 b2 = -3.5
// CIE ΔE00 = 6.0646407101 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 6.0646581356 (Gaurav Sharma, OpenJDK, ...)
// Deviation between implementations ≈ 1.7e-5
// See the source code comments for easy switching between these two widely used ΔE*00 implementation variants.
///////////////////////////////////////////////
///////////////////////////////////////////////
/////// ///////
/////// CIEDE 2000 ///////
/////// Testing Random Colors ///////
/////// ///////
///////////////////////////////////////////////
///////////////////////////////////////////////
// This Swift 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
let default_count = 10000.0
let argument = CommandLine.arguments.dropFirst().first
let count = Int(argument ?? "") ?? default_count
let real_count = count >= 0 ? count : default_count
for _ in 0..<real_count {
let l1Decimal = pow(10.0, Double(Int.random(in: 0...1)))
let l1 = round(Double.random(in: 0...100) * l1Decimal) / l1Decimal
let a1Decimal = pow(10.0, Double(Int.random(in: 0...1)))
let a1 = round(Double.random(in: -128...128) * a1Decimal) / a1Decimal
let b1Decimal = pow(10.0, Double(Int.random(in: 0...1)))
let b1 = round(Double.random(in: -128...128) * b1Decimal) / b1Decimal
let l2Decimal = pow(10.0, Double(Int.random(in: 0...1)))
let l2 = round(Double.random(in: 0...100) * l2Decimal) / l2Decimal
let a2Decimal = pow(10.0, Double(Int.random(in: 0...1)))
let a2 = round(Double.random(in: -128...128) * a2Decimal) / a2Decimal
let b2Decimal = pow(10.0, Double(Int.random(in: 0...1)))
let b2 = round(Double.random(in: -128...128) * b2Decimal) / b2Decimal
let deltaE = ciede_2000(l_1: l1, a_1: a1, b_1: b1, l_2: l2, a_2: a2, b_2: b2)
print("\(l1),\(a1),\(b1),\(l2),\(a2),\(b2),\(deltaE)")
}