Research On Implementation And Intersection Technology Of Catmull-Clark Subdivision Surface

With the development of the industrial products design heading into diversification, specialization, topology complication, the parameter surface's limitation is becoming more and more obvious. Trimming and joining of patches are needed while constructing complicated topology surfaces with the method of parameter surface, which is not only time-consuming ,but also has data-error. Comparing with the parameter surfaces,subdivision surface can conquer the deficiency above, describes arbitrary topology surface and has become a hot-hit. Among current subdivision schemes, the regular form of Catmull-Clark scheme is bi-cubic B-spline surface, and can be transformed into NURBS. Therefore Catmull-Clark scheme will most possibly be used in the future CAD /CAM systems. But there are still many problems to solve before its use in CAD /CAM and intersection is one of the crucial problems.This thesis mainly researchs on the Catmull-Clark subdivision surface's intersection ,which is the foundation of 3D surface modeling and NC tool path generation. The main contents are as follows:1. Catmull-Clark scheme is implemented in the computer with C++ and OpenGL. The data structure is simple and convenient. First of all, each vertex is tagged with a number. Then the information of corresponding vertexes for each line and each face is stored, so that the information of vertexes can be easily achieved according to the corresponding line and face during the subdivision process. Finally, an example is demonstrated using this scheme.2. Detect the intersection of Catmull-Clark schemes with axis-aliged bouding boxes and bipartite graph. Construct axis-aliged bouding box for the patches and their 1-neighbourhood vertexes, then store the numbers of the patches that potentially intersect. With the patches being subdivided, construct new bipartite graph according to the above one.3. Propose a precision control method of dihedral angle for intersection line computation. While the biggest angle between the patch and its 1-neighborhood patches comes to the given precision, stop subdividing and compute the intersected points according to the quadrilateral patches' geometrical relation. Finally, connect the intersected points to get the intersected curve.