Dyadic and sqrt(3) subdivision for uniform Powell Sabin splines

We give the two different possibilities for subdivision of Powell-Sabin splines 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, sqrt(3)-subdivision, a new vertex is introduced in the center of each triangle of the triangulation. We give subdivision rules for both cases.© 2002 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.status: publishe