| 3D graphic models composed by triangular meshes have become increasingly popular due to the fast development of the Internet and the standardization of VRML (Virtual Reality Modeling Language). Triangular meshes are widely used for representing surfaces because of their flexibility for geometric modeling operations and fast rendering. However, the complexity of graphic models has increased much faster than the throughput enabled by today's graphics hardware and computer networks. Hence, one of the most fundamental issues to analyze the massive data sets is the development of techniques for representing, storing, transmitting, and rendering large volumes of graphic data efficiently.; In this research, we first present a fast mesh simplification algorithm based on the Quadric Error Metric method for the purpose of reducing redundancy in large models. By defining one-sided quadric error metric, the algorithm is able to utilize the half-edge collapse topological operation as a desirable feature. The flatness criterion is used to reduce simplification errors further. In order to facilitate flexible storage, transmission, and display of 3D models, a layered mesh simplification algorithm is developed. This is achieved without sacrificing the compression ratio in the proposed progressive mesh compression algorithm. A multiresolution framework of triangular meshes is constructed based on the proposed algorithm.; To solve the problem of the degraded quality of simplified meshes, a set of post-processing techniques were developed based on the Modified Butterfly subdivision (MBS) algorithm. Our proposed algorithms are able to produce meshes with very good visual quality, while the processing time and the storage space are greatly reduced. The MBS algorithm can produce very smooth surfaces from given control meshes. However, real-world objects are seldom as smooth as mathematical surfaces. Some important sharp features of objects such as creases, darts, and corners are lost with the MBS scheme. To solve this problem, a shape-preserving subdivision scheme was proposed by introducing a set of new subdivision rules for sharp edges. With these rules, users are able to create desirable shapes with piece-wise smooth surfaces. |
