Declarative characterization of a general architecture for constructive geometric constraint solvers

Abstract

Geometric constraint solving is a growing field devoted to solve geometric problems defined by relationships, called constraints, established between the geometric elements. There are several techniques to solve geometric constraint problems. In this work we focus on the Constructive technique. Usually, it works in two steps. In a first step, the problem is analyzed symbolically. If the problem is solvable by the technique, the output is the construction plan, that is, a sequence of abstract geometric constructions which defines parametrically the solution to the problem. Then, the construction plan is applied to a set of specific values assigned to the parameters. If no numerical incompatibilities arise, instances of the solution are generated.

In this paper we present a general architecture for constructive geometric constraint solvers. The basic components of this architecture are three functional units: the analyzer, the index selector and the constructor. Each functional unit is specified in terms of the entities that manipulates such as geometric constraint problems and construction plans. These relevant entities are declaratively characterized and its precise semantic is stated.