RAY-TRACING TRIANGULAR TRIMMED FREE-FORM SURFACES

This paper presents a new approach to rendering triangular algebraic f ree-form surfaces. A hierarchical subdivision of the surface with asso ciated tight bounding volumes provides for quick identification of the surface regions likely to be hit by a ray. For each leaf of the hiera rchy, an approximation to the corresponding surface region is stored. The approximation is used to compute a good starting point for the ite ration, which ensures rapid convergence. Trimming curves are described by a tree of trimming primitives, such as squares, circles, polygons, and free-form curves, combined with Boolean operations. For trimmed s urfaces, an irregular adaptive subdivision is constructed to quickly e liminate all parts outside the trimming curve from consideration durin g rendering. Cost heuristics are introduced to optimize the rendering time further.