A Fast Algorithm for Rendering Parametric Surfaces

An algorithm for rendering shaded pictures of parametric surfaces is presented. The algorithm recursively subdivides each surface element on the basis of its screen-space curvature until it is sufficiently close to bilinear to be scan-converted by conventional polygon rendering techniques. The mathematical basis used to carry out the subdivsion yields the curvature criterion as a coefficient so that the tests for termination of the subdivision process are extremely simple. In addition, a surface is subdivided only in the parametric direction in which its curvature deviates from the tolerance. The algorithm incorporates a very simple solution to the problem of separations between subpatches.