Phong Lighting Equation

This article explains how all of the features of the Phong MAT affect each other. It can often be confusing how one feature affects another (you may assume the results multiply each other, when they may not). The the aim of this article is to help clear up some of that confusion.

This lighting equation assumes all features of the Phong MAT are used. It ignores all the math involved with calculating lighting, normal mapping, fog etc. It deals with only with how the colors are summed/multiplied. Features not being used can by simply removed from the equation. The function mix() linearly interpolated between the 1st and 2nd parameter, based on the 3rd parameter.

 lightingSum = 0;
 For each light:
 {
    trueLightColor = LightColor * ProjectionMapColor
    if (in a shadow)
       lightColorSum = mix(trueLightColor, ShadowColor, ShadowStrength)
    else
       lightColorSum = trueLightColor
    lightColorSum *= AttenationFactor

    diffuseComponent = DiffuseLightContribution * MaterialDiffuseColor * PointColor * DiffuseMap
    specularComponent = SpecularLightContribution * MaterialSpecularColor * SpecularMap

    totalLightContribution = (diffuseComponent + specularComponent) * lightColorSum
    lightingSum += totalLightContribution
 }

After we’re done calculating all of the lights, we have a single value for lightingSum which is the final value for all the lights.

Now apply the other features.

 finalColor = lightingSum
 finalColor += (MaterialAmbientColor * AmbientLightColor * PointColor)
 finalColor += EmitColor * EmitMapColor
 finalColor += ConstantColor * PointColor
 finalColor +=  RimLight(s)

At this point we save out a value called lightness. This is an overall value of how much light is affecting the surface.

 lightness = luminance(finalColor); // Luminance is defined as (r*0.3 + g*0.6 + b*0.1)

Now apply maps and other features

 finalColor *= ColorMap
 finalColor += EnvironementMap * EnvironmentMapColor
 finalColor = mix(FogColor * FogMapColor, finalColor, FogFactor)
 finalColor = mix(darknessEmitMapColor * darknessEmitColor, finalColor, lightness)

finalAlpha is calculated as follow:

 finalAlpha = PointAlpha * VaryingAlphaResult * AlphaMap * ColorMapAlpha
 if (light multiplies alpha)
    finalAlpha = finalAlpha * lightness

And so the color of the pixel is

 if (post multiply color by alpha)
    finalColor *= finalAlpha
 PixelColor = (finalColor.r, finalColor.g, finalColor.b, finalAlpha)