Layer Blending Algorithms

By solid-matrix

Prerequisite

• The formulas are only fitted for RGB color system.
• In the formulas
  • $ A $: the color vector in the bottom layer
  • $ B $: the color vector in the top layer
  • $ C $: the color vector in the blended layer

Algorithms

Darken $$ C=\min(A,B) $$

Lighten $$ C = \max(A,B) $$

Multiply $$ C=\frac{A\times B}{255} $$

Screen $$ C = 255-\frac{(255-A)\times(255-B)}{255} = A+B-\frac{A\times B}{255} $$

Color Burn $$ C=A-\frac{(255-A)\times(255-B)}{B} = 255\times \frac{A+B-255}{B} $$

Color Dodge $$ C=A+\frac{A\times B}{255-B} = \frac{255\times A}{255-B} $$

Linear Burn $$ C=A+B-255 $$

Linear Dodge $$ C=A+B $$

Overlay $$ C = \begin{cases} \frac{A\times B}{128} & \text{if }A\le128 \ 255-\frac{(255-A)\times(255-B)}{128} & \text{if }A\gt128 \end{cases} $$

Hard Light $$ C = \begin{cases} \frac{A\times B}{128} & \text{if }B\le128 \ 255-\frac{(255-A)\times(255-B)}{128} & \text{if }B\gt128 \end{cases} $$

Soft Light $$ C = \begin{cases} \frac{A\times B}{128}+\frac{A}{255}^2 \times(255-2B) & \text{if }B\le128 \ \frac{A\times(255-B)}{128} + \sqrt{\frac{A}{255}}\times(2B-255) & \text{if }B\gt128 \end{cases} $$

Vivid Light $$ C = \begin{cases} A-\frac{(255-A)\times(255-2B)}{2B} & \text{if }B\le128 \ A+\frac{A\times(2B-255)}{2\times(255-B)} & \text{if }B\gt128 \end{cases} $$

Linear Light $$ C=A+2B-255 $$

Pin Light $$ C = \begin{cases} C=\min(A,2B) & \text{if }B\le128 \ C=\min(A,2B-255) & \text{if }B\gt128 \end{cases} $$

Hard Mix $$ C= \begin{cases} 255 & \text{if }A+B\ge255 \ 0 & \text{if } A+B\lt 255 \end{cases} $$

Difference $$ C = |A-B| $$

Exclusion $$ C=A+B-\frac{A\times B}{128} $$