Geometric typed feature structures: Carrying geometric information using typed feature structures

Abstract

This paper explores Geometric Typed Feature Structures as a concept for carrying geometric information based on the theory of Typed Feature Structures[Carpenter, 1992]. Geometric Typed Feature Structures cover an important aspect of design space explorers in which the symbol level representation must carry 3D geometric information. Order Types are the devices in Geometric Typed Feature Structures that carry the continuous infinite domain information, that is, geometry. In this paper, theories and algorithms are applied to two kinds of Order type examples for carrying numerical values and geometric information. We describe the requirements as well as the conditions in which an Order Type can be specified and synchronized with other domain knowledge. We show two examples of Order Types: lifted reals and IGOSet intervals based on the theory of Geometric Typed Feature Structures. In each example, we outline the mathematics linking it to the theory of Order Types.