In 1974 Catmull developed a new algorithm for rendering images of bivariate surface patches. This paper describes extensions of this algorithm in the areas of texture simulation and lighting models. The parameterization of a patch defines a coordinate system which is used as a key for mapping patterns onto the surface. The intensity of the pattern at each picture element is computed as a weighted average of regions of the pattern definition function. The shape and size of this weighting function are chosen using digital signal processing theory. The patch rendering algorithm allows accurate computation of the surface normal to the patch at each picture element, permitting the simulation of mirror reflections. The amount of light coming from a given direction is modeled in a similar manner to the texture mapping and then added to the intensity obtained from the texture mapping. Several examples of images synthesized using these new techniques are included.