Research On Critical Technology Of Subdivision Surfaces

Subdivision surface can express smooth surface through low resolution control mesh and subdivision rules. It has been widely used in recent years, for it not only solves some problems in computer graphics, such as arbitrary topology and compatibility, but also retains several advantages of traditional NURBS, including the properties of localness and affine-invariance. This paper deals with Loop subdivision and its extension, the main work is as follows:(1) Loop subdivision scheme and its extension are implemented via the wing-edged structure, then subdivision theory is introduced together with some important conclusions in exact computation.(2) Two algorithms to generate the offset of Loop subdivision surface are developed. Based on theory of spline surface offset, the first one directly finds the control polygon mesh of the offset surface from the original control mesh. The general idea behind the second one is approximation. The control mesh is subdivided until the error between the control vertices and corresponding subdivision surface is less than a given threshold. Then the vertices substitute those points on the surface approximately.The last step is to calculate offset point for every vertex and connect them to form an offset surface.Because the curvature of surface itself may vary in a large domain, it induces an upper limit of feasible offset distance. The author proposed a method to estimate the offset distance. Offset error , which is a basic problem in subdivision surface, is also presented in the paper.(3) For the purpose of verifying subdivision surface and its offset algorithms , this paper has advanced NC tool path generation of subdivision surface. There are commonness and individuality between subdivision surface and spline surface, based on the research of the algorithm of NC tool path generation for spline surface, used in conjunction with subdivision property, two methods: cross-section method and projecting method are put forward.(4)Subdivision surface is quite adaptive to arbitrary topology, so the subdivision surface reconstruction techniques has also received much attention. This paper has investigated this technique for organized data, the specific work includes: (a) Rules for planning the data digitizing process is proposed to accommodate the requirement ofsubdivision surface reconstruction; (b) An algorithm is developed for reconstructing subdivision curve from organized data; (c) Furthermore, an algorithm of subdivision surface reconstruction is also brought forward.(5) Though with many advantages, subdivision surface is not sustained in most commercial CAD packages. Combined with subdivision algorithm and spline surface expression, an algorithm for constructing piecewise B-spline surfaces is presented in the paper.