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Current geometric kernels suffer from poor abstraction and design of their data structures. In part, this is due to the lack of a general mathematical framework for geometric modelling and processing. As a result, there is a proliferation of ad hoc solutions, say external data structures, whenever new problems arise in industry, causing serious difficulties in software maintenance. This paper proposes such a framework based on subanalytic geometry and theory of stratifications, as well as a concise data structure for it, called DiX (Data in Xtratus). Basically, this is a non-manifold b-rep (boundary representation) data structure without oriented cells (e.g. half-edges, coedges or so). Thus, it is more concise than the traditional b-rep data structures provided that no oriented cells (e.g. half-edges, half-faces, etc.) are used at all. Nevertheless, all the adjacency and incidence data we need is retrieved by a single operator, called mask operator. Besides, the DiX data structure includes shape descriptors, as generalizations of loops and shells, to support shape reasoning as needed in the design and implementation of shape operators such as, for example, Euler operators.

A Concise B-Rep Data Structure For Stratified Subanalytic Objects