A fast scan-line algorithm for rendering parametric surfaces

An algorithm for rendering shaded pictures of parametric curved surfaces is presented. The algorithm recursively subdivides each surface element on the basis of its screen-space parametric curvature until it is sufficiently close to bilinear to be scan-converted by conventional polygon rendering techniques. The mathematical basis chosen to carry out the subdivision process 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 sibling subpatches.