Single-set and class-of-sets semantics for 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. Our description of the distinction between these two approaches focuses on the nature of the topological regularity on which they are based (classical regularity vs. ǫ-regularity). It is shown in this note that both approaches may be useful, depending on what information is available. As an illustrative example, an elementary result is given, for a point-membership-classification algorithm, that is sufficiently general to be of practical interest but sufficiently special to be transparent.