Please explain this color blending mode formula so I can replicate it in PHP/ImageMagick

Question

I've been trying to use ImageMagick to replicate Photoshops Colour Blend Mode. I found the following formulas in an online guide but I don't know what they mean. Do I just need to swap certain channels?

Answer 1

A while ago I reversed engineered Photoshop blending modes.

Have a look here:

http://www.kineticsystem.org/?q=node/13

And here below the code I use to convert between HSY (Hue, Saturation, Luminosity) to and from RGB (Red, Green, Blue). Photoshop use something called Hexacones to calculate the saturation.

Giovanni

/**
 * This is the formula used by Photoshop to convert a color from
 * RGB (Red, Green, Blue) to HSY (Hue, Saturation, Luminosity).
 * The hue is calculated using the exacone approximation of the saturation
 * cone.
 * @param rgb The input color RGB normalized components.
 * @param hsy The output color HSY normalized components.
 */
public static void rgbToHsy(double rgb[], double hsy[]) {

    double r = Math.min(Math.max(rgb[0], 0d), 1d);
    double g = Math.min(Math.max(rgb[1], 0d), 1d);
    double b = Math.min(Math.max(rgb[2], 0d), 1d);

    double h;
    double s;
    double y;

    // For saturation equals to 0 any value of hue are valid.
    // In this case we choose 0 as a default value.

    if (r == g && g == b) {            // Limit case.
        s = 0d; 
        h = 0d; 
    } else if ((r >= g) && (g >= b)) { // Sector 0: 0° - 60°
        s = r - b;
        h = 60d * (g - b) / s;
    } else if ((g > r) && (r >= b)) {  // Sector 1: 60° - 120°
        s = g - b;
        h = 60d * (g - r) / s  + 60d;
    } else if ((g >= b) && (b > r)) {  // Sector 2: 120° - 180°
        s = g - r;
        h = 60d * (b - r) / s + 120d;
    } else if ((b > g) && (g > r)) {   // Sector 3: 180° - 240°
        s = b - r;
        h = 60d * (b - g) / s + 180d;
    } else if ((b > r) && (r >= g)) {  // Sector 4: 240° - 300°
        s = b - g;
        h = 60d * (r - g) / s + 240d;
    } else {                           // Sector 5: 300° - 360°
        s = r - g;
        h = 60d * (r - b) / s + 300d;
    }

    y = R * r + G * g + B * b;

    // Approximations erros can cause values to exceed bounds.

    hsy[0] = h % 360;
    hsy[1] = Math.min(Math.max(s, 0d), 1d);
    hsy[2] = Math.min(Math.max(y, 0d), 1d);
}

/**
 * This is the formula used by Photoshop to convert a color from
 * HSY (Hue, Saturation, Luminosity) to RGB (Red, Green, Blue).
 * The hue is calculated using the exacone approximation of the saturation
 * cone.
 * @param hsy The input color HSY normalized components.
 * @param rgb The output color RGB normalized components.
 */
public static void hsyToRgb(double hsy[], double rgb[]) {

    double h = hsy[0] % 360;
    double s = Math.min(Math.max(hsy[1], 0d), 1d);
    double y = Math.min(Math.max(hsy[2], 0d), 1d);

    double r;
    double g;
    double b;

    double k; // Intermediate variable.

    if (h >= 0d && h < 60d) {           // Sector 0: 0° - 60°
        k = s * h / 60d;
        b = y - R * s - G * k;
        r = b + s;
        g = b + k;
    } else if (h >= 60d && h < 120d) {  // Sector 1: 60° - 120°
        k = s * (h - 60d) / 60d;
        g = y + B * s + R * k;
        b = g - s;
        r = g - k;
    } else if (h >= 120d && h < 180d) { // Sector 2: 120° - 180°
        k = s * (h - 120d) / 60d;
        r = y - G * s - B * k;
        g = r + s;
        b = r + k;
    } else if (h >= 180d && h < 240d) { // Sector 3: 180° - 240°
        k = s * (h - 180d) / 60d;
        b = y + R * s + G * k;
        r = b - s;
        g = b - k;
    } else if (h >= 240d && h < 300d) { // Sector 4: 240° - 300°
        k = s * (h - 240d) / 60d;
        g = y - B * s - R * k;
        b = g + s;
        r = g + k;
    } else {                          // Sector 5: 300° - 360°
        k = s * (h - 300d) / 60d;
        r = y + G * s + B * k;
        g = r - s;
        b = r - k;
    }

    // Approximations erros can cause values to exceed bounds.

    rgb[0] = Math.min(Math.max(r, 0d), 1d);
    rgb[1] = Math.min(Math.max(g, 0d), 1d);
    rgb[2] = Math.min(Math.max(b, 0d), 1d);
}

Answer 2

Wikipedia has a good article on blend modes http://en.wikipedia.org/wiki/Blend_modes

They give formulas for Multiply, Screen and Overlay modes.

Multiply
Formula: Result Color = (Top Color) * (Bottom Color) /255

Screen
Formula: Result Color = 255 - [((255 - Top Color)*(255 - Bottom Color))/255]

Overlay
Formula: Result Color = if (Bottom Color < 128) 
    then (2 * Top Color * Bottom Color / 255) 
    else (255 - 2 * (255 - Top Color) * (255 - Bottom Color) / 255)