| Due to the ability to construct complicated surface with any complex topology, Subdivision surface draws broad attention from domestic and foreign scholars. In most existing CAD/CAM software, the parametric surface is a main method of surface modeling. But the topology structure of surface model constructed by parametric surface is only equivalent to a planar surface, cylinder or torus, so can only apply tedious cutting and splicing to construct complicated surface. The subdivision surface is a limit surface obtained by continuous iterating over original control mesh, which can be adapted to any complex topology. Some problems related to subdivision surface aren’t resolved, which limit subdivision surface to be applied in the industry field. The boolean operation for subdivision surface is one of the basic and important issue, which is widely used in solid modeling, CNC tool path planning and parting surface design for complicated mold. To apply the subdivision surface to industry applications, this dissertation studies the boolean operation and related problems for Catmull-Clark subdivision surface. The main contents and conclusions are as follows:1. The Catmull-Clark subdivision surface model is piecewise constructed by Cell data structure. The cell data structure consists of inner layer and outer layer, the inner layer stores the subdivision surface patch data and the outer layer stores the topological relationships between the subdivision surface patches. Based on subdivision surface piecewise represention, the divide-and-conquer strategy is proposed. This strategy can simplify the complex surface problem and lay the foundation for the subsequent subdivision surface problems.2. Based on subdivision surface piecewise represention, the subdivision surface intersection is simplified to several subdivision surface patch intersection by utilizing divide-and-conquer strategy. Through subdivision surface patch multi-segmentation technology and bounding box collision detection technology, the intersection grid set can be obtained. By utilizing the characteristic of topological structure of subdivision surface patch, the first point of intersection curve can be obtained. According to the mesh topology, the subsequent intersection points can be sequentially calculated and an intersection curve can be obtained by connecting intersection points. The subdivision surface intersection curves can be obtained by combining intersection curves segments utilizing topological structure of subdivision surface patch. Finally, through some examples, it is testified that the algorithm can realize efficient and stable intersection operation. 3. The subdivision surface trimming is simplified to subdivision surface patch trimming by utilizing divide-and-conquer strategy. Firstly, the intersection curves are simplified and the mesh topology is modified. Then, the subdivision surface intersection curves Loop of trimming area is obtained. Finally, choose the mesh belongs to the trimming area through the intersection curves loop and get the subdivision surface patch trimming result. The subdivision surface trimming result can be obtained utilizing topological structure of subdivision surface patch and related region selection rule. Through some examples, it is testified that the algorithm is feasible and applicable.4. On the basis of subdivision surface trimming, the subdivision surface Boolean operation result can be obtained by selecting some specific subdivision Surface trimming results in accordance with correspondings Boolean operation command. The positional relationship between the two subdivision surfaces is determined by projecting subdivision surface to three planes along the X axis Y axis and Z axis in three-dimensional coordinates. The specific regions can be selected according to positional relationship to realize the subdivision surface boolean operation. Finally, through some examples, it is testified that the algorithm can realize boolean operation for all kinds subdivision surface and is feasible. |
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