Linguistic Approach to Geometric Modeling of Hierarchical Systems

Geometric modeling is the cornerstone of computer-aided design (CAD). Currently, geometric modeling is done either interactively, using the geometric constructs (i.e., line, circle, etc.) supported by the CAD system, or by writing a program that generates the geometry of interest automatically. While both interactive and automatic geometric modeling are more efficient than manual drafting, they have their limitations. This paper describes an approach to geometric modeling that is superior to the interactive and automated modeling approaches with respect to ease of use, flexibility, and cost-effectiveness. This approach involves defining a geometry linguistically and then generating the geometry from its linguistic definition automatically. The approach manifests itself in three activities: (1) linguistically representing the geometry using a suitable vocabulary; (2) translating the linguistic definition of the geometry into a logic program; and (3) generating the geometry via logical deduction in a logic-based CAD system. These activities are discussed and illustrated in the context of the geometry of a simple bridge structure.