Abstract:
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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. |