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Special attention is given to the adaptation of the technique for efficiency to both polynomial and rational Bezier patches. The resulting algorithms are simple and robust. Their speed depends mainly on the surface area of the object being rendered, not on the number of surface patches. The technique is particularly suitable for rapid display of geometrically complex objects. Since the technique directly renders from the definitions of the surfaces without needing polygons, it can maintain a relatively compact database. Several examples with timing are included. The technique described creates smooth, shaded images for parametrically defined surfaces. It depends on a general surface scan to generate a dense set of points that represents the surface. Hidden surfaces are eliminated by sorting the sample points into a z-buffer and retaining the points nearest the viewer. Alternative schemes are given for computing the surface normal for each point in the z-buffer. Conventional illumination routines can then be applied to determine the intensities at each pixel, although the reflection-mapping technique is preferred for this article.