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Parametric and Declarative Modeling of Families of Geometric Objects

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.