Today I read a paper titled “On the Efficiency of Strategies for Subdividing Polynomial Triangular Surface Patches”
The abstract is:
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.