Parametric and Declarative Modeling of Families of Geometric Objects

Ari Rappoport

Classical solid modeling deals with modeling spaces whose entities are pointsets, structured pointsets, or pointsets with history. An important class of entities of interest in modern geometric modeling are families of such pointsets. Modeling families of objects is important for several key applications of solid modeling, among which are parametric design, assemblies and tolerancing.

In this talk I attempt to clearly define the terms commonly related to modeling famlilies of geometric objects and the important research problems and technical issues which arise when modeling such entities. An analogue is made between parametric and implicit representations for pointsets (that is, families of points) and parametric and declarative representations for families of pointsets. The declarative scheme known as variational modeling has no such useful analogue.

I discuss the implications of the above analysis to modeling schemes using declarative constraints and constructive (or generative) parametric methods. We discover yet again how important persistent and invariant naming are, not only for these methods to be well defined, but also to the integration of declarative constraints and constructive methods in a single modeling scheme.

Presented at the IFIP Workshop on Geometric Modeling in CAD, Airlie, VA, May 1996.