Single Resolution Compression of Arbitrary Triangular Meshes with Properties

• Authors: Chandrajit L Bajaj;Valerio Pascucci;Guozhong Zhuang
• Venue: DCC '99 Proceedings of the Conference on Data Compression
• Year: 1999

Polygonal meshes have been used as the primary geometric model representation for net- worked gaming and for complex interactive design in manufacturing. Accurate polygonal mesh approximation of a surface with sharp features (holes, highly varying curvatures) re- quires extremely large number of triangles. Transmission of such large triangle meshes is critical to many applications that interactively manipulate geometry models in remote net- worked environments. The need for succinct representation is therefore not only to reduce static storage requirements, but also to consume less network bandwidth and thus reduce the transmission time. Although geometry compression and coding is an emerging disci- pline, these techniques have matured for 2D digital images into standards such as JPEG [16] and MPEG [6]. In designing e_cient geometry compression schemes, one attempts to take advantage of existing 2D image compression techniques.Prior Work Deering [5] represents triangular mesh connectivity by generalized triangle strips. Stack operators are used in order to reuse vertices. In this way, the total number of random accesses to all vertices of the mesh is reduced. This method does not directly compress non-manifold meshes and its compression ratio is not high. Chow [3] presents an algorithm which represents a mesh by several generalized meshes. This method is optimized for real-time rendering but is not compression efficient because of the large requirement of connectivity encoding ((log n + 9) per vertex). Again, this method only considers manifold meshes.In Topological Surgery [14], vertices are organized into a spanning tree and triangles into simple polygons which are further grouped into a series of triangle strips. The connectivity coding of this scheme is efficient, about 2-3 bits per triangle. One of its disadvantages is its inability to directly encode non-manifold meshes. As a preprocessing step, it splits a non-manifold object into several manifold components, thereby duplicating all non-manifold features: vertices, edges, and faces. Touma and Gotsman present an algorithm for connec- tivity coding of orientable manifold meshes [15]. The efficiency of this lossless connectivity coding is determined by the distribution of the degrees of all vertices. Progressive trans- mission and embedded coding are discussed in [11, 10, 12]. A compact representation of multiresolution surfaces that support progressive transmission is present in [2]. In this paper, we propose a new layering structure to partition an arbitrary triangular mesh (no-manifold and arbitrary-genus) into generalized triangle strips. An efficient and exible encoding of the connectivity , vertex coordinates and attribute data yields excellent single resolution compression. This scheme gracefully solves the "crack" problem and also prevent error propagation while providing efficient prediction coding for both geometry and Figure 1: Block diagram of the encoder and decoder photometry data such as positions, color, normal, and texture coordinates. Figure 1 shows the diagram for both the encoder and decoder. The rest of this paper is as follows. Section 2 introduces the layering scheme to partition input data. Section 3 and Section 4 address the coding of connectivity and geometry. The attribute coding is discussed in Section 5. Experimental results are presented in Section 6.