Wrap&Zip decompression of the connectivity of triangle meshes compressed with Edgebreaker

Abstract

The Edgebreaker compression (Rossignac, 1999; King and Rossignac, 1999) is guaranteed to encode any unlabeled triangulated planar graph of t triangles with at most 1.84t bits. It stores the graph as a CLERS string—a sequence of t symbols from the set { C,L,E,R,S} , each represented by a 1, 2 or 3 bit code. We show here that, in practice, the string can be further compressed to between 0.91t and 1.26t bits using an entropy code. These results improve over the 2.3t bits code proposed by Keeler and Westbrook (1995) and over the various 3D triangle mesh compression techniques published recently (Gumhold and Strasser, 1998; Itai and Rodeh, 1982; Naor, 1990; Touma and Gotsman, 1988; Turan, 1984), which exhibit either larger constants or cannot guarantee a linear worst case storage complexity. The decompression proposed by Rossignac (1999) is complicated and exhibits a non-linear time complexity. The main contribution reported here is a simpler and efficient decompression algorithm, called Wrap&Zip, which has a linear time and space complexity. Wrap&Zip reads the CLERS string and builds a triangle tree—a triangulated, simply connected, topological polygon without interior vertices. During that process, it uses a simple rule to orient the external edges of this polygon and to “zip” (i.e., identify) all pairs of adjacent external edges that are oriented away from their common vertex. Because triangulated planar graphs can only model the connectivity (triangle/vertex incidence) of 3D triangle meshes that are homeomorphic to a sphere, we introduce here simple extensions of the Edgebreaker and Wrap&Zip techniques for compressing more general, manifold, triangle meshes with holes and handles. Manifold representations of non-manifold meshes are discussed by Rossignac and Cardoze (1999) and Gueziec et al. (1998, 1999). The simple and efficient solution provided by the combination of Wrap&Zip with of the work reported in (Rossignac, 1999; King and Rossignac, 1999) yields a simple and effective solution for compressing the connectivity information of large and small triangle meshes that must be downloaded over the Internet. The CLERS stream may be interleaved with an encoding of the vertex coordinates and photometric attributes enabling inline decompression. The availability of local incidence information permits to use, during decompression, the location and attributes of neighboring vertices to predict new ones, and thus supports most of the recently proposed vertex compression techniques (Deering, 1995; Gumhold and Strasser, 1999; Taubin and Rossignac, 1998; Touma and Gotsman, 1998).