Abstract
In their recent paper about how the duality between subdivision surface schemes lead to higher-degree continuity, Zorin and Schr?der consider only quadrilateral subdivision schemes. The dual of a quadrilateral scheme is again a quadrilateral scheme, while the dual of a triangular scheme is a hexagonal scheme. In this paper we propose such a hexagonal scheme, which can be considered a dual to Kobbelt ' Sqrt (3) scheme for triangular meshes. We introduce recursive subdivision rule for meshes with arbitrary topology, optimizing the surface continuity given a minimal support area. These rule have a simplicity comparable to the Doo-Sabin scheme: only new vertices of one type are introduced and every subdivision step removes the vertices of the previous steps. As hexagonal meshes are not encountered frequently in practice, we describe two different techniques to convert triangular meshes into hexagonal ones.