Dyadic and /spl radic/3-subdivision for uniform Powell-Sabin splines

Abstract

We give two different possibilities for subdivision of Powell-Sabin spline surfaces on uniform triangulations. In the first case, dyadic subdivision, a new vertex is introduced on each edge between two old vertices. In the second case, /spl radic/3-subdivision, a new vertex is introduced in the center of each triangle of the triangulation. We give subdivision rules to find the new control points of the refined surface for both cases.