2006/06/13 by Jean Gallier, Gallier, Jean
Computer Science · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Graphics (cs.GR) #cs.CG #cs.GR
paper · pdf · doi:10.48550/arxiv.cs/0606061
20 pages
arxiv created 2006/06/13 · arxiv updated 2009/12/01
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.