Alpha Blending with No Division Operations

TL;DR

This paper introduces an integer-based alpha blending method that eliminates division operations, enabling highly accurate blending with fewer multiplications, suitable for efficient graphics processing.

Contribution

It presents an approximate alpha blending formula that replaces division with integer shift and add, matching high-precision results without division operations.

Findings

Exact match with double-precision floating-point results

Reduces number of multiplications needed

Enables integer-only alpha blending for efficiency

Abstract

Highly accurate alpha blending can be performed entirely with integer operations, and no divisions. To reduce the number of integer multiplications, multiple color components can be blended in parallel in the same 32-bit or 64-bit register. This tutorial explains how to avoid division operations when alpha blending with 32-bit RGBA pixels. An RGBA pixel contains four 8-bit components (red, green, blue, and alpha) whose values range from 0 to 255. Alpha blending requires multiplication of the color components by an alpha value, after which (for greatest accuracy) each of these products is divided by 255 and then rounded to the nearest integer. This tutorial presents an approximate alpha-blending formula that replaces the division operation with an integer shift and add -- and also enables the number of multiplications to be reduced. When the same blending calculation is carried out to high precision using double-precision floating-point division operations, the results are found to exactly match those produced by this approximation. C++ code examples are included.