4 Parallel polygon rendering with precomputed surface patches

Abstract

An algorithm for the rapid filling of trapezia on a processor array has been presented in this Chapter. The algorithm can serve as the basis for filling arbitrary polygons, the case of convex polygons being particularly simple. It uses precomputed surface patches which represent the intersection of a window with a particular halfplane or equivalently the sign plane of the planar integer that contains the evaluation of a linear function within a window. Thus the linear function evaluations required in order to determine the GOVERMASK (i.e. the pixels of a window covered by a polygon) can be avoided and the performance of the filling operation on bit-serial processor arrays is significantly improved (on such machines planar arithmetic is costly). Bit-parallel processor arrays can not take full advantage of the method because the surface patches are single bitplanes. Precomputation gains extra speed by using additional storage space for the patches. This is an increasingly advantageous trade-off with decreasing memory prices. Program transformations proved an effective tool for constructing an efficient version of the particular N-step Bresenham we needed.