A corner-cutting scheme for hexagonal subdivision surfaces

Abstract

In their recent paper about how the duality between subdivision surface schemes leads to higher-degree continuity, Zorin and Schroder 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's Sqrt(3) scheme for triangular meshes. We introduce recursive subdivision rules for meshes with arbitrary topology,, given a minimal support optimizing the surface continuity area. These rules 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.