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// This function written in Kotlin 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 kotlin.math.*
// 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.
fun ciede_2000(l_1: Double, a_1: Double, b_1: Double, l_2: Double, a_2: Double, b_2: Double): Double {
// Working in Kotlin 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...
val k_l = 1.0;
val k_c = 1.0;
val 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.
val c_1 = sqrt(a_1 * a_1 * n * n + b_1 * b_1);
val 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);
var 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;
var 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;
}
val 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.
val 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.
val 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.
val 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.
val h = 2.0 * sqrt(c_1 * c_2) * sin(h_d) / (k_h * (1.0 + 0.0075 * n * t));
// Chroma.
val 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 = 66.9 a1 = 51.9 b1 = 2.7
// L2 = 67.4 a2 = 46.5 b2 = -2.3
// CIE ΔE00 = 3.0587957739 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 3.0588093140 (Gaurav Sharma, OpenJDK, ...)
// Deviation between implementations ≈ 1.4e-5
// See the source code comments for easy switching between these two widely used ΔE*00 implementation variants.