Research Of Intersections And Trimming For Subdivision Surfaces Based On Triangular Mesh

Owing to its arbitrary topology, numerical stability and easier implementation, subdivision modeling technology has become the focus on computer-aided geometric design (CAGD) research in recent years. Subdivision which was in fact a limit of a mesh array, uses the recursive method, and following certain rules(always weighted average), the array comes to being by repeatedly inserting the new vertex into initial mesh. Subdivision surfaces applied to the surface modeling, subdivision surfaces intersection and the trimming is an important function of surface modeling.Based on intersection and trimming for subdivision surfaces of triangle mesh, we have done the following works:Firstly, the paper has introduced the relevant concepts and principles for subdivision surfaces and summed up several classic subdivision surface algorithms.Secondly, the paper has discussed and analyzed the impact of using bounding boxes and the bipartite graph structure in the insertsection of subdivision surfaces. Based on the bipartite graph structure and axis-aligned bounding boxes(AABB) surface intersections tests are implemented.Using this method can successfully computed intersection at high resolution.Thirdly ,the paper has discussed and analyzed a method for determining the intersection between two triangles in three-dimensional with a minimal additional cost. This algorithm are algebraic method.Intersection is successfully computed by using this mothodForthly, the paper has discussed and analyzed computing the location of subdivision surface for any point of control meshes,intersection and trimming is successfully realized.Fifthly, the paper chose the Half-Edge data structure which has faster inquiries as the basic structure,and has successfully achieved the purpose. Finally, the paper introduced the structure and the function about OpenGL, and used OpenGL in the intersection and trimming for subdivision surface.