The CIEDE2000 color difference calculation function is a C++ function that determines the color difference between two colors by converting their coordinates to a new chromaticity space and then calculating the deltaLPrime, deltaCPrime, and deltahPrime values. The function returns the CIEDE2000 color difference value based on these calculated values.

Run example

npm run import -- "ciede2000"

ciede2000

#include <math.h>

double deg2Rad(const double deg)
{
	return (deg * (M_PI / 180.0));
}


// source: https://github.com/gfiumara/CIEDE2000/blob/master/CIEDE2000.cpp
double CIEDE2000(double l1, double a1, double b1, double l2, double a2, double b2)
{
	/* 
	 * "For these and all other numerical/graphical 􏰀delta E00 values
	 * reported in this article, we set the parametric weighting factors
	 * to unity(i.e., k_L = k_C = k_H = 1.0)." (Page 27).
	 */
	const double k_L = 1.0, k_C = 1.0, k_H = 1.0;
	const double deg360InRad = deg2Rad(360.0);
	const double deg180InRad = deg2Rad(180.0);
	const double pow25To7 = 6103515625.0; /* pow(25, 7) */
	
	/*
	 * Step 1 
	 */
	/* Equation 2 */
	double C1 = sqrt((a1 * a1) + (b1 * b1));
	double C2 = sqrt((a2 * a2) + (b2 * b2));
	/* Equation 3 */
	double barC = (C1 + C2) / 2.0;
	/* Equation 4 */
	double G = 0.5 * (1 - sqrt(pow(barC, 7) / (pow(barC, 7) + pow25To7)));
	/* Equation 5 */
	double a1Prime = (1.0 + G) * a1;
	double a2Prime = (1.0 + G) * a2;
	/* Equation 6 */
	double CPrime1 = sqrt((a1Prime * a1Prime) + (b1 * b1));
	double CPrime2 = sqrt((a2Prime * a2Prime) + (b2 * b2));
	/* Equation 7 */
	double hPrime1;
	if (b1 == 0 && a1Prime == 0)
		hPrime1 = 0.0;
	else {
		hPrime1 = atan2(b1, a1Prime);
		/* 
		 * This must be converted to a hue angle in degrees between 0 
		 * and 360 by addition of 2􏰏 to negative hue angles.
		 */
		if (hPrime1 < 0)
			hPrime1 += deg360InRad;
	}
	double hPrime2;
	if (b2 == 0 && a2Prime == 0)
		hPrime2 = 0.0;
	else {
		hPrime2 = atan2(b2, a2Prime);
		/* 
		 * This must be converted to a hue angle in degrees between 0 
		 * and 360 by addition of 2􏰏 to negative hue angles.
		 */
		if (hPrime2 < 0)
			hPrime2 += deg360InRad;
	}
	
	/*
	 * Step 2
	 */
	/* Equation 8 */
	double deltaLPrime = l2 - l1;
	/* Equation 9 */
	double deltaCPrime = CPrime2 - CPrime1;
	/* Equation 10 */
	double deltahPrime;
	double CPrimeProduct = CPrime1 * CPrime2;
	if (CPrimeProduct == 0)
		deltahPrime = 0;
	else {
		/* Avoid the fabs() call */
		deltahPrime = hPrime2 - hPrime1;
		if (deltahPrime < -deg180InRad)
			deltahPrime += deg360InRad;
		else if (deltahPrime > deg180InRad)
			deltahPrime -= deg360InRad;
	}
	/* Equation 11 */
	double deltaHPrime = 2.0 * sqrt(CPrimeProduct) *
    sin(deltahPrime / 2.0);
	
	/*
	 * Step 3
	 */
	/* Equation 12 */
	double barLPrime = (l1 + l2) / 2.0;
	/* Equation 13 */
	double barCPrime = (CPrime1 + CPrime2) / 2.0;
	/* Equation 14 */
	double barhPrime, hPrimeSum = hPrime1 + hPrime2;
	if (CPrime1 * CPrime2 == 0) {
		barhPrime = hPrimeSum;
	} else {
		if (fabs(hPrime1 - hPrime2) <= deg180InRad)
			barhPrime = hPrimeSum / 2.0;
		else {
			if (hPrimeSum < deg360InRad)
				barhPrime = (hPrimeSum + deg360InRad) / 2.0;
			else
				barhPrime = (hPrimeSum - deg360InRad) / 2.0;
		}
	}
	/* Equation 15 */
	double T = 1.0 - (0.17 * cos(barhPrime - deg2Rad(30.0))) +
    (0.24 * cos(2.0 * barhPrime)) +
    (0.32 * cos((3.0 * barhPrime) + deg2Rad(6.0))) - 
    (0.20 * cos((4.0 * barhPrime) - deg2Rad(63.0)));
	/* Equation 16 */
	double deltaTheta = deg2Rad(30.0) *
    exp(-pow((barhPrime - deg2Rad(275.0)) / deg2Rad(25.0), 2.0));
	/* Equation 17 */
	double R_C = 2.0 * sqrt(pow(barCPrime, 7.0) /
    (pow(barCPrime, 7.0) + pow25To7));
	/* Equation 18 */
	double S_L = 1 + ((0.015 * pow(barLPrime - 50.0, 2.0)) /
    sqrt(20 + pow(barLPrime - 50.0, 2.0)));
	/* Equation 19 */
	double S_C = 1 + (0.045 * barCPrime);
	/* Equation 20 */
	double S_H = 1 + (0.015 * barCPrime * T);
	/* Equation 21 */
	double R_T = (-sin(2.0 * deltaTheta)) * R_C;
	
	/* Equation 22 */
  double deltaE = sqrt(
    pow(deltaLPrime / (k_L * S_L), 2.0) +
    pow(deltaCPrime / (k_C * S_C), 2.0) +
    pow(deltaHPrime / (k_H * S_H), 2.0) + 
    (R_T * (deltaCPrime / (k_C * S_C)) * (deltaHPrime / (k_H * S_H))));

	return (deltaE);
}

#include 

// Function to convert degrees to radians
static double deg2Rad(double deg) {
    // Avoid the calculation when deg is 0
    if (deg == 0.0) return 0.0;
    return (deg * M_PI / 180.0);
}

// Function to calculate CIEDE2000 color difference
static double ciede2000(double l1, double a1, double b1, double l2, double a2, double b2) {
    // Parametric weighting factors (default values)
    const double k_L = 1.0;
    const double k_C = 1.0;
    const double k_H = 1.0;

    // Precompute constants
    const double deg360InRad = deg2Rad(360.0);
    const double deg180InRad = deg2Rad(180.0);
    const double pow25To7 = pow(25, 7);

    // Step 1: Preprocess inputs
    double C1 = sqrt(a1 * a1 + b1 * b1);
    double C2 = sqrt(a2 * a2 + b2 * b2);
    double barC = (C1 + C2) / 2.0;

    // Step 1: Calculate G
    double G = 0.5 * (1 - pow(barC, 7) / (pow(barC, 7) + pow25To7));

    // Step 1: Transform inputs
    double a1Prime = (1.0 + G) * a1;
    double a2Prime = (1.0 + G) * a2;
    double CPrime1 = sqrt(a1Prime * a1Prime + b1 * b1);
    double CPrime2 = sqrt(a2Prime * a2Prime + b2 * b2);

    // Step 1: Calculate hue angles (in radians)
    double hPrime1;
    if (b1 == 0 && a1Prime == 0) hPrime1 = 0.0;
    else hPrime1 = atan2(b1, a1Prime);
    if (hPrime1 < 0) hPrime1 += deg360InRad;

    double hPrime2;
    if (b2 == 0 && a2Prime == 0) hPrime2 = 0.0;
    else hPrime2 = atan2(b2, a2Prime);
    if (hPrime2 < 0) hPrime2 += deg360InRad;

    // Step 2: Calculate delta values
    double deltaLPrime = l2 - l1;
    double deltaCPrime = CPrime2 - CPrime1;
    double CPrimeProduct = CPrime1 * CPrime2;
    double deltahPrime;
    if (CPrimeProduct == 0) deltahPrime = 0;
    else {
        deltahPrime = hPrime2 - hPrime1;
        if (deltahPrime < -deg180InRad) deltahPrime += deg360InRad;
        else if (deltahPrime > deg180InRad) deltahPrime -= deg360InRad;
    }
    double deltaHPrime = 2.0 * sqrt(CPrimeProduct) * sin(deltahPrime / 2.0);

    // Step 3: Calculate mean values
    double barLPrime = (l1 + l2) / 2.0;
    double barCPrime = (CPrime1 + CPrime2) / 2.0;

    // Step 3: Calculate hue angle for mean value
    double hPrimeSum = hPrime1 + hPrime2;
    double barhPrime;
    if (CPrime1 * CPrime2 == 0) barhPrime = hPrimeSum;
    else {
        if (fabs(hPrime1 - hPrime2) <= deg180InRad) barhPrime = hPrimeSum / 2.0;
        else {
            if (hPrimeSum < deg360InRad) barhPrime = (hPrimeSum + deg360InRad) / 2.0;
            else barhPrime = (hPrimeSum - deg360InRad) / 2.0;
        }
    }

    // Step 3: Calculate T and deltaTheta
    double T = 1.0 - (0.17 * cos(barhPrime - deg2Rad(30.0))) +
    (0.24 * cos(2.0 * barhPrime)) +
    (0.32 * cos((3.0 * barhPrime) + deg2Rad(6.0))) -
    (0.20 * cos((4.0 * barhPrime) - deg2Rad(63.0)));
    double deltaTheta = deg2Rad(30.0) * exp(-pow((barhPrime - deg2Rad(275.0)) / deg2Rad(25.0), 2.0));

    // Step 3: Calculate R_C, S_L, S_C, and S_H
    double R_C = 2.0 * sqrt(pow(barCPrime, 7.0) / (pow(barCPrime, 7.0) + pow25To7));
    double S_L = 1 + ((0.015 * pow(barLPrime - 50.0, 2.0)) / sqrt(20 + pow(barLPrime - 50.0, 2.0)));
    double S_C = 1 + (0.045 * barCPrime);
    double S_H = 1 + (0.015 * barCPrime * T);

    // Step 3: Calculate R_T
    double R_T = (-sin(2.0 * deltaTheta)) * R_C;

    // Step 4: Calculate deltaE
    double deltaE = sqrt(
    pow(deltaLPrime / (k_L * S_L), 2.0) +
    pow(deltaCPrime / (k_C * S_C), 2.0) +
    pow(deltaHPrime / (k_H * S_H), 2.0) +
    (R_T * (deltaCPrime / (k_C * S_C)) * (deltaHPrime / (k_H * S_H)))
    );

    return deltaE;
}

CIEDE2000 Color Difference Calculation Function

This is a C++ function that calculates the CIEDE2000 color difference between two colors. The function takes six input parameters:

• l1 and l2: The lightness values of the two colors
• a1 and a2: The a* values of the two colors (red-green axis)
• b1 and b2: The b* values of the two colors (yellow-blue axis)

Function Breakdown

The function can be divided into three main steps:

Step 1: Conversion of Color Coordinates

This step involves converting the input color coordinates to a new chromaticity space.

• Equations 2-5: Calculate the C1, C2, and G values
• Equations 6-7: Calculate the a1Prime, a2Prime, CPrime1, and CPrime2 values
• Equations 8-9: Calculate the hPrime1 and hPrime2 values ( hue angles in degrees between 0 and 360)

Step 2: Calculation of Color Difference

This step involves calculating the color difference between the two colors.

• Equations 8-10: Calculate the deltaLPrime, deltaCPrime, and deltahPrime values

Return Value

The function returns the CIEDE2000 color difference value, which is calculated using the deltaLPrime, deltaCPrime, and deltahPrime values.

Mathematical Functions Used

• sqrt(): Square root function
• pow(): Power function
• atan2(): Arctangent function
• M_PI: Constant representing pi

Constants Used

• M_PI: Constant representing pi
• pow25To7: Constant representing the result of pow(25, 7)