A Parametric-Space-Based Scan-Line Algorithm for Rendering Bicubic Surfaces

This article presents a new scan-line algorithm for displaying bicubic surfaces. Patches are decomposed on regions of constant sign of the z component of the normal before the scan process. Most of the computations are done in parametric space. The algorithm computes the intersection of the surfaces with only a restricted subset of scan planes and obtains the intersection with other scan planes by linear interpolation between exact instersections. A bound of the algorithm's error is given. Finally, the new method is compared with Whitted's algorithm.