An axiomatic approach for solving geometric problems symbolically

This paper describes a new approach for solving geometric constraint problems and problems in geometry theorem proving. We developed a rewrite-rule mechanism operating on geometric predicates. Termination and completeness of the problem solving algorithm can be obtained through well foundedness and confluence of the set of rewrite rules. To guarantee these properties we adapted the Knuth-Bendix completion algorithm to the specific requirements of the geometric problem. A symbolic, geometric solution has the advantage over the usual algebraic approach that it speaks the language of geometry. Therefore, it has the potential to be used in many practical applications in interactive Computer Aided Design.