A mathematical model for boundary representations of n-dimensional geometric objects

Abstract

The major purpose of this paper is to introduce a general theory within which previous boundary representations (Breps) are a special case. Basically, this theory combines sub-analyt,ic geometry and theory of stratifications. The sub-analyt,ic geometry covers almost, all geometric engineering artefacts, and it is a generalisation of the semi-analytic geometry, which in turn is a generalisation of the semialgebraic geometry used by most geometric kernels. On the other hand, the theory of stratifications provides the most general manifold structures for geometric objects that it is possible to consider in geometric modelling. Whitney stratifications are particularly useful in geometric modelling because they provide a general abstraction for the #structure of boundary representations of objects in IV’. Remarkably, it is well-known in mathematics that sub-analytic objects are Whitney stratifiable, and this mathematically matches and validates the usual geometry-structure design of boundary representation data structures. Thus, the general B-rep introduced here represents Whitney-stratified sub-analytic objects, though the global design of the data structure is classical: the geometry (sub-analytic geometry) separated from the structure (Whitney stratification). 1 Theoretical evolution of boundary repre-