Fun with premultiplied alpha

The computer graphics universe consists of pixels. Pixels, in turn, consist of components: red, green, blue, and the coverage or opacity value alpha. For various reasons it is convenient to store and process a given rgbα quadruple with the rgb values already multiplied by α. This was first pointed out in the original Porter-Duff compositing paper (1984) and I presented some further justifications in an earlier column (“Image Compositing-Theory”, ibid., p.83-7, Sept. 1994). This premultiplication has some other interesting implications, and that´s what I discuss this time