This paper presents a new approach to rendering triangular algebraic free form surfaces. A hierarchical subdivision of the surface with associated tight bounding volumes provides for quick identification of the surface regions likely to be hit by a ray. For each leaf of the hierarchy an approximation to the corresponding surface region is stored. The approximation is used to compute a good starting point for the iteration, 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 surfaces an irregular adaptive subdivision is constructed to quickly eliminate all parts outside the trimming curve from consideration during rendering. Cost heuristics are introduced to optimize the rendering time further.