Abstract: Many rendering phenomena can be modeled with partial coverage. These include flames, smoke, hair, clouds, properly-filtered silhouettes, non-refractive glass, and special effects such as forcefields and magic. A challenge in rendering these is that the value of pixel partly covered by multiple surfaces depends on the depth order of the surfaces. One approach to avoid the cost of storing and sorting primitives or fragments is to alter the compositing operator so that it is order independent, thus allowing a pure streaming approach.

We describe two previous methods for implementing blended order-independent transparency, and then introduce two new methods derived from them. Both new methods guarantee correct coverage of background and strictly improve color representation over the previous methods. Because these require only classic OpenGL-style blending and bounded memory, they may be preferred to A-buffer like methods for mobile devices, consoles, and other constrained rendering environments. They are attractive for all platforms for models such as particle systems and hair, where discrete changes in surface ordering that will be perceived as popping are undesirable and a soft transition between surfaces is preferred.