On the Efficiency of Strategies for Subdividing Polynomial Triangular Surface Patches

In this paper, we investigate the efficiency of various strategies for subdividing polynomial triangular surface patches. We give a simple algorithm performing a regular subdivision in four calls to the standard de Casteljau algorithm (in its subdivision version). A naive version uses twelve calls. We also show that any method for obtaining a regular subdivision using the standard de Casteljau algorithm requires at least 4 calls. Thus, our method is optimal. We give another subdivision algorithm using only three calls to the de Casteljau algorithm. Instead of being regular, the subdivision pattern is diamond-like. Finally, we present a ``spider-like subdivision scheme producing six subtriangles in four calls to the de Casteljau algorithm.