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// This function written in Wren 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.
// 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.
var ciede_2000 = Fn.new { |l_1, a_1, b_1, l_2, a_2, b_2|
// Working in Wren 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...
var k_l = 1.0
var k_c = 1.0
var k_h = 1.0
var n = ((a_1 * a_1 + b_1 * b_1).sqrt + (a_2 * a_2 + b_2 * b_2).sqrt) * 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 - (n / (n + 6103515625.0)).sqrt)
// Application of the chroma correction factor.
var c_1 = (a_1 * a_1 * n * n + b_1 * b_1).sqrt
var c_2 = (a_2 * a_2 * n * n + b_2 * b_2).sqrt
// 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 = b_1.atan(a_1 * n)
var h_2 = b_2.atan(a_2 * n)
if (h_1 < 0.0) h_1 = h_1 + 2.0 * Num.pi
if (h_2 < 0.0) h_2 = h_2 + 2.0 * Num.pi
n = (h_2 - h_1).abs
// Cross-implementation consistent rounding.
if (Num.pi - 1E-14 < n && n < Num.pi + 1E-14) n = Num.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 (Num.pi < n) {
h_d = h_d + Num.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 = h_m + Num.pi
// h_m = h_m + (h_m < Math.PI ? Math.PI : -Math.PI)
}
var p = 36.0 * h_m - 55.0 * Num.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.
var r_t = -2.0 * (n / (n + 6103515625.0)).sqrt * (Num.pi / 3.0 *
2.71828182845904523536.pow(p * p / (-25.0 * Num.pi * Num.pi))).sin
n = (l_1 + l_2) * 0.5
n = (n - 50.0) * (n - 50.0)
// Lightness.
var l = (l_2 - l_1) / (k_l * (1.0 + 0.015 * n / (20.0 + n).sqrt))
// These coefficients adjust the impact of different harmonic
// components on the hue difference calculation.
var t = 1.0 + 0.24 * (2.0 * h_m + Num.pi * 0.5).sin +
0.32 * (3.0 * h_m + 8.0 * Num.pi / 15.0).sin -
0.17 * (h_m + Num.pi / 3.0).sin -
0.20 * (4.0 * h_m + 3.0 * Num.pi / 20.0).sin
n = c_1 + c_2
// Hue.
var h = 2.0 * (c_1 * c_2).sqrt * h_d.sin / (k_h * (1.0 + 0.0075 * n * t))
// Chroma.
var 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 (l * l + h * h + c * c + c * h * r_t).sqrt
}
// GitHub Project : https://github.com/michel-leonard/ciede2000-color-matching
// Online Tests : https://michel-leonard.github.io/ciede2000-color-matching
// L1 = 48.7 a1 = 14.4 b1 = -2.3
// L2 = 49.5 a2 = 20.5 b2 = 4.5
// CIE ΔE00 = 6.0932725537 (Bruce Lindbloom, Netflix’s VMAF, ...)
// CIE ΔE00 = 6.0932863277 (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.
///////////////////////////////////////////////
///////////////////////////////////////////////
/////// ///////
/////// CIEDE 2000 ///////
/////// Testing Random Colors ///////
/////// ///////
///////////////////////////////////////////////
///////////////////////////////////////////////
// This Wren 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
class XorShift64 {
construct new(seed) {
_state = seed
}
nextInt() {
_state = _state ^ (_state << 13)
_state = _state ^ (_state >> 17)
_state = _state ^ (_state << 5)
return _state
}
nextFloat(min, max) {
var rand = nextInt() / 4294967296.0
return min + (max - min) * rand
}
}
import "os" for Process
var count = 10000.0
if (Process.arguments.count == 1) {
var input = Num.fromString(Process.arguments[0])
if (0 < input) {
count = input
}
}
var rng = XorShift64.new(0x2236b69a7d223bd)
for (i in 1..count) {
var l_1 = rng.nextInt() & 1 == 0 ? (10.0 * rng.nextFloat(0, 100)).round / 10.0 : rng.nextFloat(0, 100).round
var a_1 = rng.nextInt() & 1 == 0 ? (10.0 * rng.nextFloat(-128, 128)).round / 10.0 : rng.nextFloat(-128, 128).round
var b_1 = rng.nextInt() & 1 == 0 ? (10.0 * rng.nextFloat(-128, 128)).round / 10.0 : rng.nextFloat(-128, 128).round
var l_2 = rng.nextInt() & 1 == 0 ? (10.0 * rng.nextFloat(0, 100)).round / 10.0 : rng.nextFloat(0, 100).round
var a_2 = rng.nextInt() & 1 == 0 ? (10.0 * rng.nextFloat(-128, 128)).round / 10.0 : rng.nextFloat(-128, 128).round
var b_2 = rng.nextInt() & 1 == 0 ? (10.0 * rng.nextFloat(-128, 128)).round / 10.0 : rng.nextFloat(-128, 128).round
var res = ciede_2000.call(l_1, a_1, b_1, l_2, a_2, b_2)
System.print(l_1.toString + "," + a_1.toString + "," + b_1.toString + "," + l_2.toString + "," + a_2.toString + "," + b_2.toString + "," + res.toString)
}