Calculating opacity value mathematically

Question

How is opacity calculated mathematically?

There is opacity value in Photoshop, CSS etc. Actually this opacity is the transparent behavior of a layer. That we all kno

Answer 1

The formula for combining C1 = (R1,G1,B1) and C2 = (R2,G2,B2) into a new color C3, where C2 is overlayed on top of C1 with opacity p is usually ( (1-p)R1 + p*R2, (1-p)*G1 + p*G2, (1-p)*B1 + p*B2 ).

See Wikipedia article on transparency for more information.

Answer 2

The following javascript gives a method that can be used to calculate the opacity color value manually:

    function calculateTransparentColor(foregroundColor, backgroundColor, opacity) {
        if (opacity < 0.0 || opacity > 1.0) {
            alert("assertion, opacity should be between 0 and 1");
        }
        opacity = opacity * 1.0; // to make it float
        let foregroundRGB = colorHexToRGB(foregroundColor);
        let backgroundRGB = colorHexToRGB(backgroundColor);
        let finalRed = Math.round(backgroundRGB.r * (1-opacity) + foregroundRGB.r * opacity);
        let finalGreen = Math.round(backgroundRGB.g * (1-opacity) + foregroundRGB.g * opacity);
        let finalBlue = Math.round(backgroundRGB.b * (1-opacity) + foregroundRGB.b * opacity);
        return colorRGBToHex(finalRed, finalGreen, finalBlue);
    }

    var COLOR_REGEX = /^#([0-9a-fA-F]{2})([0-9a-fA-F]{2})([0-9a-fA-F]{2})$/;
    function colorHexToRGB(htmlColor) {
         
        let arrRGB = htmlColor.match(COLOR_REGEX);
        if (arrRGB == null) {
            alert("Invalid color passed, the color should be in the html format. Example: #ff0033");
        }
        let red = parseInt(arrRGB[1], 16);
        let green = parseInt(arrRGB[2], 16);
        let blue = parseInt(arrRGB[3], 16);
        return {"r":red, "g":green, "b":blue};
    }

    function colorRGBToHex(red, green, blue) {
        if (red < 0 || red > 255 || green < 0 || green > 255 || blue < 0 || blue > 255) {
            alert("Invalid color value passed. Should be between 0 and 255.");
        }

        let hexRed = formatHex(red.toString(16));
        let hexGreen = formatHex(green.toString(16));
        let hexBlue = formatHex(blue.toString(16));

        return "#" + hexRed + hexGreen + hexBlue;
    }

    function formatHex(value) {
        value = value + "";
        if (value.length == 1) {
            return "0" + value;
        }
        return value;
    }

    // Now we test it!
    let theColor = calculateTransparentColor('#ff0000', '#00ff00', 0.5)
    console.log("The color #ff0000 on a background of #00ff00 with 50% opacity produces: " + theColor);


    

Answer 3

Formula for Result of mixing two transparent pixels:

C1=[R1,G1,B1] is the foreground pixel color.

C2=[R2,G2,B2] is the background pixel color.

p1 is the opacity percentage of the foreground pixel.

p2 is the opacity percentage of the background pixel.

New_Pixel_Color = (p1*c1+p2*c2-p1*p2*c2)/(p1+p2-p1*p2)

New_Pixel_opacity = p1+p2-p1*p2

You can test and enjoy it!