Geometric Programming: A Programming Approach to Geometric Design

摘要

This article presents a functional programming approach to geometric design with embedded polyhedral complexes. Its main goals are to show the expressive power of the language as well as its usefulness for geometric design. The language, named PLASM (the Programming LAnguage for Solid Modeling), introduces a very high level approach to "constructive" or "generative" modeling. Geometrical objects are generated by evaluating some suitable language expressions. Because generating expressions can be easily combined, the language also extends the standard variational geometry approach by supporting classes of geometric objects with varying topology and shape. The design language PLASM can be roughly considered as a geometry-oriented extension of a subset of the functional language FL. The language takes a dimension-independent approach to geometry representation and algorithms. In particular it implements an algebraic calculus over embedded polyhedra of any dimension. The generated objects are always geometrically consistent because the validity of geometry is guaranteed at a syntactical level. Such an approach allows one to use a representation scheme which is weaker than those usually adopted in solid modelers, thus encompassing a broader geometric domain, which contains solids, surfaces, and wire-frames, as well as higher-dimensional objects.