layeredTexture

Here we present two descriptions of the different blend modes. The first description is a non-technical definition of each blend mode for the benefit of someone who wants to know what each one does. The second is a technical definition of each blend mode for the benefit of someone who is attempting to imitate their function in hardware. In both cases we will refer to the texture whose blend mode is being specified as the "foreground" texture, and the result of all of the underlying textures blended together (according to their particular blend modes) as the "background" texture.

The non-technical definitions are as follows:

• None: The foreground texture covers up the background texture entirely.
• Over: The foreground texture is applied like a decal to the background. The shape of the decal is determined by the foreground alpha.
• In: The result is the background texture cut in the shape of the foreground alpha.
• Out: The result is the opposite of In. It is as if the shape of the foreground alpha has been cut out of the background.
• Add: The result color is the foreground color added to the background color as if being projected on the background through a slide projector. The result color is then applied over the background color using the foreground alpha to define the opacity of the result.
• Subtract: The result color is the foreground color subtracted from the background color. The result color is then applied over the background color using the foreground alpha to define the opacity of the result.
• Multiply: The result color is the foreground color multiplied by the background color. The result color is then applied over the background color using the foreground alpha to define the opacity of the result.
• Difference: The result color is the difference between the foreground color and the background color. The result color is then applied over the background color using the foreground alpha to define the opacity of the result. Difference is not supported by hardware texturing.
• Lighten: The result color of each pixel is the background color or foreground color, whichever is lighter. The result color is then applied over the background color using the foreground alpha to define the opacity of the result. Lighten is not supported by hardware texturing.
• Darken: The result color of each pixel is the background color or foreground color, whichever is darker. The result color is then applied over the background color using the foreground alpha to define the opacity of the result. Darken is not supported by hardware texturing.
• Saturate: The result color is the background color with saturation increased in proportion to the foreground color scaled by foreground alpha. If the foreground color is red, for example, the result color will be the background color with more saturated reds.
• Desaturate: The result color is the background color with saturation decreased in proportion to the foreground color scaled by foreground alpha. If the foreground color is red, for example, the result color will be the background color with desaturated reds.
• Illuminate: The result color is the background color mixed with the foreground color, brighter where the foreground is bright and darker where the foreground is dark. It is as if the foreground texture represents the light falling on the background. The result color is then applied over the background color using the foreground alpha to define the opacity of the result.

The following descriptions describe the blend modes in a technical fashion.

Let "fc" be the foreground color
Let "fa" be the foreground alpha
Let "bc" be the background color
Let "ba" be the background alpha
Let "color" be the result color

Let "alpha" be the result alpha

• None:
  color = fc
  alpha = fa
  
• Over:
  color = fc * fa + (bc * (1 - fa))
  alpha = 1 - ((1 - ba) * (1 - fa))
  
• In:
  color = bc * fa
  alpha = ba * fa
  
• Out:
  color = bc * (1 - fa)
  alpha = ba * (1 - fa)
  
• Add:
  color = bc + (fc * fa)
  alpha = ba
  
• Subtract:
  color = bc - (fc * fa)
  alpha = ba
  
• Multiply:
  color = bc * (fc * fa + 1 - fa)
  alpha = ba
  
• Difference:
  color = (abs((fc * fa) - bc)) * fa + bc * (1 - fa)
  alpha = ba
  
• Lighten:
  color = (max((fc * fa), bc)) * fa + bc * (1 - fa)
  alpha = ba
  
• Darken:
  color = (min((fc * fa), bc)) * fa + bc * (1 - fa)
  alpha = ba
  
• Saturate:
  color = bc * (1 + (fc * fa))
  alpha = ba
  
• Desaturate:
  color = bc * (1 - (fc * fa))
  alpha = ba
  
• Illuminate:
  color = bc * (2 * fc * fa + 1 - fa)
  alpha = ba