Reverse Loop Subdivision

Abstract

Reverse subdivision aims at constructing a coarse representation of an object given by a fine polygon mesh. In this paper, we derive a mask for reverse Loop subdivision. In contrast to the mask proposed before by Samavati and Bartels, the new mask applies to both regular and extraordinary vertices. The mask is parameterized, and thus can also be used to reverse 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, the proposed technique yields a multiresolution representation of textured subdivision surfaces. We illustrate its use with a set of examples.