Towards a Geometric-Object-Oriented Language
Résumé
This paper proposes a geometric-object-oriented language for symbolic geometric computation, reasoning, and visualization. In this language, geometric objects are constructed with indefinite parametric data. Modifications and basic operations on these objects are enabled. Degeneracy and uncertainty are handled effectively by means of imposing conditions and assumptions and geometric statements are formulated by declaring relations among different objects. A system implemented on the basis of this language will allow the user to perform geometric computation and reasoning rigorously and to prove geometric theorems and generate geometric diagrams and interactive documents automatically. We present the overall design of the language, explain the capabilities, features, main components of the proposed system, provide specifications for some of its functors, report our experiments with a preliminary implementation of the system, and discuss some encountered difficulties and research problems.