Using prolog for constructing geometric objects defined by constraints

Abstract

Efficient algorithmic solutions are known for many problems in geometric modeling. Most algorithms are best implemented in a procedural programming language. For other problems, especially in interactive programs, no procedures may be found easily, but we may formulate the knowledge of our problem in a descriptive way with facts and ruies. Prolog is an appropriate language for finding solutions in the latter case. On the other hand, Prolog does not support efficiently the writing of procedures and arithmetic, which are still essential for solving geometrical problems.

We describe how a geometrical construction problem may be solved with Prolog. For computations such as line intersections, or for graphic display, we use the procedural programming language Modula-2. In order to combine the two languages we designed an interface language ‘logula’. An easy-to-use notation allows an application programmer to add new ‘built-in’ predicates, which are implemented as Modula-2 procedures.