A fast scan-line algorithm for rendering parametric surfaces

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Abstract
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.

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