Representing Non-Manifold Geometric Objects in n Dimensions: Incidence, Order, and Shape

B-Reps (Boundary Representations) represent geometric objects defined as stratified point sets. This paper extends boundary representations of non-manifold geometric objects to n-dimensional stratified objects possibly having incomplete boundaries. The proposed representation has given rise to a new geometric kernel called DiX (Data in Xtratus), having been derived from a mathematical model based on the subanalytic geometry and theory of stratifications. It may meet applications in computer aided design and manufacture, computer axial tomography, virtual reality, computer animation, etc. Key–Words: I.3.5: Computational Geometry and Object Modeling: Curve, surface, solid, and object representations; Boundary representations.