Research And Application Of Subdivision Surfaces Based On Hexagonal 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. There have been lots of relatively mature theories on subdivision for triangular or rectangular mesh, so the special hexagonal mesh has gradually become the hotspot. Based on hexagonal mesh subdivision, 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 relationship between the Euler rules and subdivision surfaces, and then proposed the semi-regular hexagonal mesh concept. According to the dual and primal two different types of algorithms, the paper improved the corner-cutting algorithm for the hexagonal mesh and proposed a new edge-cutting subdivision algorithm, and also gave the two methods some comparison.Thirdly, the paper chose the Half-Edge data structure which has faster inquiries as the basic structure, and designed an Euler operation set including 12 basic Euler operations for the subdivision, and has successfully achieved the purpose.Finally, the paper introduced the structure and the function about OpenGL, and used OpenGL in the hexagonal subdivision.