Research On Related Algorithms Of Subdivision Surface Theory

Subdivision surface is a geometric modeling technology of discrete surface based onmesh. Much new geometry elements are generated from the original control mesh by usinga specified algorithm, and the old and new elements are connected using the topologicalrules. A new control mesh will be generated. The original control mesh will converge asmooth resulting surface when repeatedly applying the subdivision generating procedure. Inthis paper, subdivision surface is the research object. The main contents are as follows:(1) The development course of subdivision surfaces is briefly reviewed.The emphasisis that the research results on subdivision surface are summarized and analyzed.(2)The basic theory of subdivision surface is introduced.The emphasis is that theselection of parameter and the character of the limit of subdivision surface are researched indeep.(3) the typical subdivision surface algorithm are comprehensively explained,includingCatmull-Clark subdivision、 Doo-Sabin subdivision、 Loop subdivision、 Butterflysubdivision and sqrt(3) subdivision. The emphasis is that the mathematical principles andcharacteristics of them are comparative analysis.(4)The number of geometry elements within control mesh grows exponentially as theincrease of subdivision levels in general subdivision algorithm. In order to solve thisproblem,an adaptive subdivision surface algorithm is given. This algorithm bases on theincluded angle of the two normal vector of the two adjacent triangles to judge the moresmooth. This algorithm decrease the number of control mesh, and meanwhile the quality ofsubdivision surface is guaranteed. All these save lots of time and space for successivestorage, transmission and modification.