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# This function written in Nim 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 math
const M_PI = 3.14159265358979323846264338328
# 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.
proc ciede_2000(l_1: float64, a_1: float64, b_1: float64, l_2: float64, a_2: float64, b_2: float64): float64 =
# Working in Nim 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...
let k_l = 1.0;
let k_c = 1.0;
let 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.
let c_1 = sqrt(a_1 * a_1 * n * n + b_1 * b_1);
let 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 = arctan2(b_1, a_1 * n);
var h_2 = arctan2(b_2, a_2 * n);
h_1 += 2.0 * M_PI * (h_1 < 0.0).float;
h_2 += 2.0 * M_PI * (h_2 < 0.0).float;
n = abs(h_2 - h_1);
# Cross-implementation consistent rounding.
if M_PI - 1E-14 < n and n < M_PI + 1E-14 :
n = 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.
var h_m = (h_1 + h_2) * 0.5;
var h_d = (h_2 - h_1) * 0.5;
if M_PI < n :
h_d += 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 += M_PI;
# h_m += (if h_m < M_PI : M_PI else : -M_PI);
let p = 36.0 * h_m - 55.0 * M_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.
let r_t = -2.0 * sqrt(n / (n + 6103515625.0)) *
sin(M_PI / 3.0 * exp(p * p / (-25.0 * M_PI * M_PI)));
n = (l_1 + l_2) * 0.5;
n = (n - 50.0) * (n - 50.0);
# Lightness.
let 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.
let t = 1.0 + 0.24 * sin(2.0 * h_m + M_PI * 0.5) +
0.32 * sin(3.0 * h_m + 8.0 * M_PI / 15.0) -
0.17 * sin(h_m + M_PI / 3.0) -
0.20 * sin(4.0 * h_m + 3.0 * M_PI / 20.0);
n = c_1 + c_2;
# Hue.
let h = 2.0 * sqrt(c_1 * c_2) * sin(h_d) / (k_h * (1.0 + 0.0075 * n * t));
# Chroma.
let 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 = 18.3 a1 = 39.7 b1 = 1.8
# L2 = 18.0 a2 = 33.6 b2 = -1.4
# CIE ΔE00 = 2.9608608115 (Bruce Lindbloom, Netflix’s VMAF, ...)
# CIE ΔE00 = 2.9608743231 (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 Nim 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
import random, strformat, std/os
from std/strutils import parseInt
let default_iterations = 10000.0
let arguments = commandLineParams()
let n_iterations = if arguments.len > 0:
try:
let input = parseInt(arguments[0])
if input > 0: input else: default_iterations
except ValueError:
default_iterations
else:
default_iterations
proc roundRandom(value: float64): float64 =
let decimals = rand(1)
if decimals == 0:
return round(value)
else:
return round(value, 1)
randomize()
for _ in 0 ..< n_iterations:
let l1 = roundRandom(rand(100.0))
let a1 = roundRandom(rand(-128.0..128.0))
let b1 = roundRandom(rand(-128.0..128.0))
let l2 = roundRandom(rand(100.0))
let a2 = roundRandom(rand(-128.0..128.0))
let b2 = roundRandom(rand(-128.0..128.0))
let delta_e = ciede_2000(l1, a1, b1, l2, a2, b2)
echo fmt"{l1},{a1},{b1},{l2},{a2},{b2},{delta_e}"