Consistent Geometric Modeling Approaches

Boolean set operations are important in solid modeling; however making them robust is problematic. This thesis summarizes the problems with robustness of geometric algorithms caused by approximated data and numerical computation and provides two different approaches to build a robust geometric modeler. An adaptive-single-tolerance approach has been developed in this thesis. This approach is more efficient, more general, and simpler compared with previously presented tolerance-based approaches. In addition, a novel approach to robustness by removing redundancy is presented in this thesis. An algorithm for Boolean set operation on solids with two manifolds surfaces bounded by planar and natural quadric surface has been developed based on the combination of these two approaches.