A model for n-dimensional boundary topology
Henning Østergård Hansen, Niels Jørgen Christensen · 1993
The principle of representing a solid object by the structure of its boundary elements is a special case of describing an n-dimensional object by its (n-1)-dimensional bounding surface.By analogy to 2-and 3-dimensional objects, a model representation for the topology of n-dimensional boundary representation is defined, A characteristic property of the proposed representation is, that any boundary element separating two higher-dimensional objects is split in two topological parts, one belonging to each side in space.The result is a hierarchical 'split-element' representation that is well suited for modeling applications.An interesting feature is that the orientability of a topologic structure can easily be determined.An implementation of the data structure is defined, and its applicability to high-level modeling operations is demonstrated. BOUNDARY TOPOLOGYThe faces, edges and vertices of a 3-dimensional boundary representation are referred to as the topological elements of the model.In an n-dimensional boundary representation, the representation of topological elements must be generalized, and an n-dimensional type of topological element must be defined.We will describe some different approaches to this problem, looking first at 3-D models.