Basic Boolean Operation Research in Catmull-Clark Subdivision Surface

The Boolean operation is the most complex and important problem in CAD/CAM, and the quadrangle is applied in CAD/CAM engineering widely. Being without global analytic representation, the research on subdivision surface Boolean operation is more difficult than that of the parameter surface and implicit surfaces. A kind of basic Boolean operation for plane quadrangle mesh including surface intersection, trimming and gridding-level Boolean operation in the Catmull-Clark subdivision surface is presented in this paper. In the first place, the calculation of subdivision surface intersection is converted into that of control mesh intersection: the 1-neighborhood zone of intersecting quadrangle mesh on the control mesh is constructed, and then the 1-neighborhood zone is subdivided continuously to improve the precision of intersection. The intersection points between the intersection quadrangle are calculated, which are linked according to their topology relation, so the intersection line which satisfies the given precision is calculated. When the subdivision surface intersection is finished, the surface trimming will be realized by modifying the topology structure and vertices positions of control mesh at those intersection points. Finally, a kind of the subdivision surface gridding-level Boolean operation including intersection, union and difference operation is proposed, and the basic principles and application instances are given as well.