Edgebreaker is a simple scheme for compressing the triangle/vertex incidence graphs (

The abundance and importance of complex 3-D data bases in major industry segments, the affordability of interactive 3-D rendering for office and consumer use, and the exploitation of the Internet to distribute and share 3-D data have intensified the need for an effective 3-D geometric compression technique that would significantly reduce the time required to transmit 3-D models over digital communication channels, and the amount of memory or disk space required to store the models. Because the prevalent representation of 3-D models for graphics purposes is polyhedral and because polyhedral models are in general triangulated for rendering, this article introduces a new compressed representation for complex triangulated models and simple, yet efficient, compression and decompression algorithms. In this scheme, vertex positions are quantized within the desired accuracy, a vertex spanning tree is used to predict the position of each vertex from 2,3, or 4 of its ancestors in the tree, and the correction vectors are entropy encoded. Properties, such as normals, colors, and texture coordinates, are compressed in a similar manner. The connectivity is encoded with no loss of information to an average of less than two bits per triangle. The vertex spanning tree and a small set of jump edges are used to split the model into a simple polygon. A triangle spanning tree and a sequence of marching bits are used to encode the triangulation of the polygon. Our approach improves on Michael Deering's pioneering results by exploiting the geometric coherence of several ancestors in the vertex spanning tree, preserving the connectivity with no loss of information, avoiding vertex repetitions, and using about three fewer bits for the connectivity. However, since decompression requires random access to all vertices, this method must be modified for hardware rendering with limited onboard memory. Finally, we demonstrate implementation results for a variety of VRML models with up to two orders of magnitude compression.

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ÐMost systems that support visual interaction with 3D models use shape representations based on triangle meshes. The size of these representations imposes limits on applications for which complex 3D models must be accessed remotely. Techniques for simplifying and compressing 3D models reduce the transmission time. Multiresolution formats provide quick access to a crude model and then refine it progressively. Unfortunately, compared to the best nonprogressive compression methods, previously proposed progressive refinement techniques impose a significant overhead when the full resolution model must be downloaded. The CPM (Compressed Progressive Meshes) approach proposed here eliminates this overhead. It uses a new technique, which refines the topology of the mesh in batches, which each increase the number of vertices by up to 50 percent. Less than an amortized total of 4 bits per triangle encode where and how the topological refinements should be applied. We estimate the position of new vertices from the positions of their topological neighbors in the less refined mesh using a new estimator that leads to representations of vertex coordinates that are 50 percent more compact than previously reported progressive geometry compression techniques.

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