Generative geometric modeling in a functional environment

Abstract

Some aspects of geometric design programming using a functional language and a dimension-independent approach to geometric data structureare discussed in this paper. In particular it is shown that such an environment allows for a very easy implementation of geometric transformations, hierarchical assemblies and parametric curves, surfaces and solids. Since geometric shapes are associated to generating functions, and geometric expressions can be passed to functions as actual parameters, this approach allows for a very powerful programming approach to variational geometry. The paper also aims to show that this language can accommodate both the description of methods for generating geometric shapes (see e.g. the definition of either the Coons surfaces or the Bezier curves) as well as the use of such methods to generate specific shape instances. Finally, the language allows for both bottom-up and top-down development of the designed shape, as it is shown in the appendix, where the generation of the model of a parametric umbrella by successive refinements is discussed.