First-hit speed up in ray tracing surfaces of functions of two variables

Visualizing surfaces of functions of two variables by ray tracing generally follows the techniques which have been developed for ray tracing any other surfaces. But with regard to the special features of this type of surface and the fact that, in this case, the ‘scene’ to be ray-traced normally consists of only one single object, a special ray-tracing algorithm has been developed by several authors. This paper shows how to accelerate this algorithm by applying a new technique for a fast computation of the intersections of the so-called eye rays, which means rays cast from the observer’s eye into the scene, and the surface. These intersections are called first hits. Pseudocode of the new algorithm is given and examples of images are presented which show speed-up factors up to 4.8. CJ 1997 Elsevier Science Ltd. All rights reserved