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// This function written in C# 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.
///////////////////////////////////////////////////////////////////////////////////////////
////// //////
////// Measured at 5,797,179 calls per second. //////
////// 💡 This function is up to 30% faster than 64-bit. //////
////// //////
////// Using 32-bit numbers results in an almost always negligible //////
////// difference of ±0.0002 in the calculated Delta E 2000. //////
////// //////
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// 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.
static float ciede_2000(float l_1, float a_1, float b_1, float l_2, float a_2, float b_2) {
// Working in C# (.NET Core) 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 float k_l = 1.0f, k_c = 1.0f, k_h = 1.0f;
float n = (MathF.Sqrt(a_1 * a_1 + b_1 * b_1)
+ MathF.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 - MathF.Sqrt(n / (n + 6103515625.0f)));
// Application of the chroma correction factor.
float c_1 = MathF.Sqrt(a_1 * a_1 * n * n + b_1 * b_1);
float c_2 = MathF.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.
float h_1 = MathF.Atan2(b_1, a_1 * n), h_2 = MathF.Atan2(b_2, a_2 * n);
if (h_1 < 0.0f) h_1 += 2.0f * MathF.PI;
if (h_2 < 0.0f) h_2 += 2.0f * MathF.PI;
// 32-bit implementations do not have consistent rounding between implementations.
n = MathF.Abs(h_2 - h_1);
// 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.
float h_m = (h_1 + h_2) * 0.5f, h_d = (h_2 - h_1) * 0.5f;
if (MathF.PI < n) {
h_d += MathF.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 += MathF.PI;
// if (h_m < MathF.PI) h_m += MathF.PI; else h_m -= MathF.PI;
}
float p = 36.0f * h_m - 55.0f * MathF.PI;
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.
float r_t = -2.0f * MathF.Sqrt(n / (n + 6103515625.0f))
* MathF.Sin(MathF.PI / 3.0f
* MathF.Exp(p * p / (-25.0f * MathF.PI * MathF.PI)));
n = (l_1 + l_2) * 0.5f;
n = (n - 50.0f) * (n - 50.0f);
// Lightness.
float l = (l_2 - l_1) / (k_l * (1.0f + 0.015f * n / MathF.Sqrt(20.0f + n)));
// These coefficients adjust the impact of different harmonic
// components on the hue difference calculation.
float t = 1.0f + 0.24f * MathF.Sin(2.0f * h_m + MathF.PI * 0.5f)
+ 0.32f * MathF.Sin(3.0f * h_m + 8.0f * MathF.PI / 15.0f)
- 0.17f * MathF.Sin(h_m + MathF.PI / 3.0f)
- 0.20f * MathF.Sin(4.0f * h_m + 3.0f * MathF.PI / 20.0f);
n = c_1 + c_2;
// Hue.
float h = 2.0f * MathF.Sqrt(c_1 * c_2)
* MathF.Sin(h_d) / (k_h * (1.0f + 0.0075f * n * t));
// Chroma.
float 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 MathF.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 = 4.5 a1 = 13.1 b1 = -2.2
// L2 = 1.8 a2 = 19.2 b2 = 3.6
// CIE ΔE00 = 5.9840819132 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 5.9840962048 (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.