Vertex-based boundary representation of nonmanifold geometric models

A geometric modeling system that extends modeling to include non-2-manifold objects is useful for several reasons. Various levels of representation, i.e., wireframe models, surface models, and solid models, are handled uniformly in a non-2-manifold modeling environment. This uniformity enhances current CAD systems by allowing a proper choice in level of representation, and provides a smooth transition between various levels of representation. Solutions to some geometry-related problems can be obtained more easily by mixing non-2-manifold entities with 2-manifold entities in the problem's model. This thesis presents the Tri-cyclic data structure that is a vertex-based non-2-manifold boundary representation scheme. A set of new topological elements is introduced for the neighborhood classification around a vertex. The data structure explicitly represents the adjacency information around non-2-manifold vertices and edges. A set of point set operators for the manipulation of models is also presented in this thesis. The point set operators operate on vertex, edge, face and region which are defined as point set elements. Point set elements of a model collectively and exhaustively cover entire R3. As the basis for point set operations, a bottom-up intersection algorithm for linear and planar facet non-2-manifold models has been developed. The algorithm operates by intersecting entities in an ordered manner from vertex to edge then face elements in contrast to intersecting pairs of faces in 2-manifold boundaries. Singular intersections are systematically handled by determining if an entity is within a tolerance region. 2-manifold models and non-2-manifold models are handled by the algorithm in a uniform manner. A system based on the representation scheme, including the point set operators and the intersection algorithm, has been implemented. This implementation is restricted to linear elements and planar facets. The limitations are discussed in the implementation sections.