Boundary representation, intersection, and evaluation of nurb based non-manifold objects

Boundary representation (B-rep), intersection, and evaluation schemes for NURB based non-manifold CSG objects are presented. The B-rep scheme follows a top-down, face-based approach. A definition of non-manifold objects and their set operations are given. The boundary evaluation process follows the intersect-merge-select strategy of Weiler (Weiler 1986). The generation of intersection geometry is performed in a bottom-up strategy. Intersection algorithms between entities of same and different dimensions are studied. The computation of face/face intersection is based on the concept of the marching method (Barnhill et al 1987; Barnhill & Kersey 1990). Several techniques have been developed to enhance the marching process, including the computation of initial points and tracing step sizes, control of intersection precision, and handling of branch points and tangential intersection curves (points). Inconsistency of the intersection results is corrected using criteria based on topological adjacency information. The proposed method finds all internal loops without performing loop detection (Hohmeyer 1991). New topological entities corresponding to the intersection results are created in the parameter space for each entity. These include vertices, edges and faces, but not 3D shells. The creation of topological faces is carried out by generating the boundary of each new face while traverse a net structure created during the intersection geometry generation process. Subsequent classification and selection are performed based on 2D topological entities, instead of 3D shells. The proposed methods has been implemented as the core of a NURB-based non-manifold modeling system.