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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.*
///////////////////////////////////////////////////////////////////////////////////////////
////// //////
////// Using 32-bit numbers results in an almost always negligible //////
////// difference of ±0.0002 in the calculated Delta E 2000. //////
////// //////
///////////////////////////////////////////////////////////////////////////////////////////
// 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: Float, a_1: Float, b_1: Float, l_2: Float, a_2: Float, b_2: Float): Float {
// 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 = 1.0f
val k_c = 1.0f
val k_h = 1.0f
var n = (sqrt(a_1 * a_1 + b_1 * b_1) + sqrt(a_2 * a_2 + b_2 * b_2)) * 0.5f;
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 = 1.0f + 0.5f * (1.0f - sqrt(n / (n + 6103515625.0f)));
// 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 < 0.0f)
h_1 += 2.0f * PI.toFloat()
if (h_2 < 0.0f)
h_2 += 2.0f * PI.toFloat()
n = abs(h_2 - h_1)
// Cross-implementation consistent rounding.
if (PI.toFloat() - 1E-6f < n && n < PI.toFloat() + 1E-6f)
n = PI.toFloat()
// 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) * 0.5f
var h_d = (h_2 - h_1) * 0.5f
if (PI.toFloat() < n) {
h_d += PI.toFloat();
// 📜 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.toFloat();
// if (h_m < PI.toFloat()) h_m += PI.toFloat(); else h_m -= PI.toFloat();
}
val p = 36.0f * h_m - 55.0f * PI.toFloat()
n = (c_1 + c_2) * 0.5f
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 = -2.0f * sqrt(n / (n + 6103515625.0f)) * sin(PI.toFloat() /
3.0f * exp((p * p) / (-25.0f * PI.toFloat() * PI.toFloat())))
n = (l_1 + l_2) * 0.5f
n = (n - 50.0f) * (n - 50.0f)
// Lightness.
val l = (l_2 - l_1) / (k_l * (1.0f + 0.015f * n / sqrt(20.0f + n)))
// These coefficients adjust the impact of different harmonic
// components on the hue difference calculation.
val t = 1.0f + 0.24f * sin(2.0f * h_m + PI.toFloat() * 0.5f) +
0.32f * sin(3.0f * h_m + 8.0f * PI.toFloat() / 15.0f) -
0.17f * sin(h_m + PI.toFloat() / 3.0f) -
0.20f * sin(4.0f * h_m + 3.0f * PI.toFloat() / 20.0f)
n = c_1 + c_2
// Hue.
val h = 2.0f * sqrt(c_1 * c_2) * sin(h_d) / (k_h * (1.0f + 0.0075f * n * t))
// Chroma.
val c = (c_2 - c_1) / (k_c * (1.0f + 0.0225f * 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 = 63.9 a1 = 45.9 b1 = 2.6
// L2 = 64.0 a2 = 40.5 b2 = -1.8
// CIE ΔE00 = 2.9873591571 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 2.9873722096 (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.