A Boundary-Incomplete Representation for n-Dimensional Non-Manifold Geometric Objects

摘要

This paper introduces a new representation scheme for non-manifold geometric objects as a generalization of common B-Reps (Boundary Representations) to n-dimensional stratified objects possibly having incomplete boundaries. This scheme has been implemented as a geometric kernel called DiX (Data in Xtratus). Its mathematical model derives from the subanalytic geometry and theory of stratifications. It is more concise than the traditional B-Rep data structures because it does not use oriented strata (e.g. half-edges, co-edges, etc.) explicitly. Nevertheless, each stratum may have a geometric orientation (e.g. a vector normal to a face or 2-stratum). Retrieving incidence and order data is accomplished by means of two operators: the bowtie and necktie operators. The DiX data structure also includes shape descriptors for both strata and stratified objects to keep the representation unamabiguous, as well as to support shape reasoning as needed in many geometric applications (e.g. computer aided design and manufacture, computer axial tomography, virtual reality, computer animation, etc.).