The Generic Geometric Complex (GGC): a Modeling Scheme for Families of Decomposed Pointsets

Ari Rappoport

Modeling families of geometric objects is of major interest in modern geometric and solid modeling. Object families participate in virtually all important modeling schemes, including parametric, history-based, feature-based, constraint-based and assembly modeling.

In this paper we introduce the Generic Geometric Complex (GGC), a modeling scheme for families of objects modeled using the boundary representation, or more precisely, families of decomposed pointsets. Each member of the modeled family is modeled using an improved version of the selective geometric complex. 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 which 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.

Proceedings, Fourth ACM/Siggraph Symposium on Solid Modeling and Applications (Solid Modeling '97), May 1997, Atlanta, ACM Press, pp. 19-30.