Research On Key Technology In Subdivision Surface Modeling

Subdivision surface has lots of good properties, witch not only contain polygon mesh topology arbitrary, but also parametric surface continuity, consistency and affine invariance, etc, so it has been researched and applied widely in surface modeling. Adaptive subdivision technologies solved the problem that the number of face was increaced by multiple in uniform subdivisions; technologies of intersection and trimming solved some difficulties in engineering applications; technologies of sharp features solved the problems of acute effects generation of solid model, etc. However, most of these technologies were considered from how to improve the surface quality, and rarely involved the data structure to support subdivision surfaces. For so great varieties of subdivision schemes and the problems having existed in adaptive subdivision methods, a unified subdivision scheme was proposed by researching the basic data structures, and the problem of topology cracks produced in adaptive subdivision process was solved in this paper. The main tasks are as follows:1. The basic theory on subdivision surface modeling was researched. The basic idea and method of subdivision were formulated systematicly. Some classic subdivision schemes were introduced, and the classification and traits of subdivision were summarized. At the same time, the key idea of adaptive subdivision technology was introduced in brief. They laid the theoretical foundation for proposing the data structure which supported the unified subdivision and adaptive subdivision.2. The data structures existed to support the subdivision surface were analysised and summaried. Given its management capabilities of any topological mesh, and combined with the features of primal/dual subdivision schemes, the half-edge data structure was choiced to expand. Its formal representation was given by combinatorial maps. A unified subdivision mode was constructed, which achieved the purposes that various subdivision schemes were supported in the same data structure, thereby reducing the development cost of modeling tools. 3. On the basis of the data model supporting adaptive unified subdivision, a multiresolution half-edge data structure was further extracted, and the traversal algorithm was given. The primal and dual subdivision schemes were expressed with this structure. Combining the idea of adaptive subdivision, a meshod of adaptive subdivision management and a access algorithm of topological links were advanced, and compared with adaptive subdivision methods based on quadtree. At last, the analysis and comparison with the quadtree structure was made in both time complexity and space complexity. Results indicated that the structure is universal, and supports a variety of subdivision schemes. Moreover, topology cracks in the mesh are avoided during the adaptive subdivision.