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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.
#include <cmath>
// Expressly defining pi ensures that the code works on different platforms.
#ifndef M_PI
#define M_PI 3.14159265358979323846264338327950288419716939937511
#endif
// 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.
template<typename T>
static T ciede_2000(const T l_1, const T a_1, const T b_1, const T l_2, const T a_2, const T b_2) {
// Working in C++ 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 T k_l = T(1.0);
const T k_c = T(1.0);
const T k_h = T(1.0);
T n = (std::sqrt(a_1 * a_1 + b_1 * b_1) + std::sqrt(a_2 * a_2 + b_2 * b_2)) * T(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 = T(1.0) + T(0.5) * (T(1.0) - std::sqrt(n / (n + T(6103515625.0))));
// Application of the chroma correction factor.
const T c_1 = std::sqrt(a_1 * a_1 * n * n + b_1 * b_1);
const T c_2 = std::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.
T h_1 = std::atan2(b_1, a_1 * n);
T h_2 = std::atan2(b_2, a_2 * n);
h_1 += (h_1 < T(0.0)) * T(2.0) * T(M_PI);
h_2 += (h_2 < T(0.0)) * T(2.0) * T(M_PI);
n = std::fabs(h_2 - h_1);
// Cross-implementation consistent rounding.
if (T(M_PI) - T(1E-14) < n && n < T(M_PI) + T(1E-14))
n = T(M_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.
T h_m = (h_1 + h_2) * T(0.5);
T h_d = (h_2 - h_1) * T(0.5);
h_d += (T(M_PI) < n) * T(M_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 += (T(M_PI) < n) * T(M_PI);
// h_m += (T(M_PI) < n) * ((h_m < T(M_PI)) - (T(M_PI) <= h_m)) * T(M_PI);
const T p = T(36.0) * h_m - T(55.0) * T(M_PI);
n = (c_1 + c_2) * T(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.
const T r_t = T(-2.0) * std::sqrt(n / (n + T(6103515625.0)))
* std::sin(T(M_PI) / T(3.0) * std::exp(p * p / (T(-25.0) * T(M_PI) * T(M_PI))));
n = (l_1 + l_2) * T(0.5);
n = (n - T(50.0)) * (n - T(50.0));
// Lightness.
const T l = (l_2 - l_1) / (k_l * (T(1.0) + T(3.0) / T(200.0) * n / std::sqrt(T(20.0) + n)));
// These coefficients adjust the impact of different harmonic
// components on the hue difference calculation.
const T t = T(1.0) + T(6.0) / T(25.0) * std::sin(T(2.0) * h_m + T(M_PI) / T(2.0))
+ T(8.0) / T(25.0) * std::sin(T(3.0) * h_m + T(8.0) * T(M_PI) / T(15.0))
- T(17.0) / T(100.0) * std::sin(h_m + T(M_PI) / T(3.0))
- T(1.0) / T(5.0) * std::sin(T(4.0) * h_m + T(3.0) * T(M_PI) / T(20.0));
n = c_1 + c_2;
// Hue.
const T h = T(2.0) * std::sqrt(c_1 * c_2) * std::sin(h_d) / (k_h * (T(1.0) + T(3.0) / T(400.0) * n * t));
// Chroma.
const T c = (c_2 - c_1) / (k_c * (T(1.0) + T(9.0) / T(400.0) * 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 std::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 = 96.5 a1 = 47.8 b1 = 4.6
// L2 = 96.8 a2 = 53.2 b2 = -4.1
// CIE ΔE00 = 4.6680978034 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 4.6680847226 (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.