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Topological Regularity in Semantics of Geometric Models

Two major approaches to defining the semantics of inaccurate boundary representations have been proposed in the literature. They are referred to here as single-set semantics, and class-of-sets semantics, respectively. The two approaches differ in the nature of the topological regularity on which they are based (classical regularity vs. 2-regularity). It is shown in this paper that the two models are complementary, and that each may be useful, depending on the context. As an illustrative example, an elementary proof is given for a point-membership-classification result that is sufficiently general to be of practical interest, but sufficiently special to be transparent.