Reverse Loop subdivision for geometry and textures

Abstract

Reverse subdivision aims at constructing a coarser representation of an object given by a fine polygon mesh. In this paper, we first derive a mask for reverse Loop subdivision that can be applied to both regular and extraordinary vertices. The mask is parameterized, and thus can also be used in reversing variants of Loop subdivision, such as those proposed by Warren and Litke.We apply this mask not only to mesh geometry, but also to texture coordinates. This reverses the texture-mapping process described by DeRose, Kass and Truong, in which a texture originally defined for a coarse mesh was carried to the finer meshes obtained by subdivision. Combined with the forward subdivision, the proposed technique constitutes a multiresolution representation of textured subdivision surfaces. We illustrate its use with a set of examples.