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The generic geometric complex (GGC): a modeling scheme for families of decomposed pointsets

Modeling of families of geometric objects is a major topic in modem geometric and solid modeling. Object families are central to many important solid modeling applications, including parametric modeling schemes based on features, constraints and design history. In this paper we introduce the Generic Geometric Complex (GGC), a modeling scheme for families of decomposed pointsets. Each member of the modeled family is modeled using an improved version of the selective geometric complex. Hence, the GGC can be viewed as a generalization of the boundary representation to a modeling scheme for families of objects. The GGC models a family in the classifying sense, supporting the object membership classification query. Association of corresponding boundary entities (e.g. vertices, edges and faces) in different members of the modeled family is supported by the entity-to-name (E2N) and name-to-entity (N2E) queries. We refer to generic naming mechanisms that possess knowledge only about the boundaries of the modeled objects as invariant naming schemes. We discuss several concrete ingredients of generic names, present a general algorithm for invariant naming of entities in selective geometric complexes in any dimension, and completely characterize invariant naming in the 2-D case.