Fast rendering of relativistic objects

Abstract

This paper presents a number of simple techniques that allow very fast rendering of multiple independently moving objects under the conditions of special relativity, as well as a brief tutorial in the theory of special relativity for non-experts. In addition to geometric rendering, a simplified lighting model is presented, which allows the apparent colour changes of objects to be observed, along with changes in the apparent direction of illumination. The geometric rendering can be summarized as a two-stage process. In the first, the Lorentz contraction is applied to each object in the observer's reference frame, and in the second the apparent visual position is found for every object. Once the visual geometry is found, the coloration of each object is handled, with a traditional graphics engine such as a z-buffer performing the final rendering. Rendering speeds in excess of 30,000 polygons a second were obtained on a 133 MHz Silicon Graphics Indigo2 workstation. © 1998 John Wiley & Sons, Ltd.