Direct computation of a control vertex position on any subdivision level

Abstract

In this paper, we present general closed form equations for directly computing the position of a vertex at different subdivision levels for both triangular and quadrilateral meshes. These results are obtained using simple computations and they lead to very useful applications, especially for adaptive subdivision. We illustrate our method on Loop's and Catmull-Clark's subdivision schemes. © Springer-Verlag Berlin Heidelberg 2003.