What is a parametric family of solids?

Abstract

Classical solid modeling systems are being rapidly replaced by new parametric solid modeling systems, where solid models are defined and manipulated through high-level, parameterized, and user-modifiable definitions. We show that such parametric solid modeling systems inherited the unsolved technical problems of earlier dual representation (boundary and CSG) systems which may limit their functionality and performance. In particular, the modern systems may not robustly support parametric and variational modeling, because the meaning of a `parametric family' is not always well-defined. We investigate existing practices in parametric modeling, discuss corresponding mathematical models and limitations of parametric families, and explore technical difficulties that must be resolved to take full advantage of parametric solid modeling.