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Conception et mise en oeuvre d'un système déclaratif de géométrie dynamique

Abstract : The objective of this thesis is to demonstrate the feasibility of a declarative dynamic geometry system. GDRev, which stands for Reversible Declarative Geometry, is such a system and has been design and implemented with the teaching of geometry in mind. From the logical point of view, GDRev is based on the definition of a logic language ELDL, which stands for Extented Logical Description Language. LDL is used to express specifications of geometric figures which form the mathematical objects underlying drawings of figures. LDL provides clauses which allow specifications to be recursive and allow specifications to be expressed in modular format. GDRev possesses a construction and animation language whose semantics are defined using ELDL. The GDRev interface can be viewed as a declarative extension of that of Cabri-Géomètre. On the one hand, the interface must provide equivalent direct manipulation operations carried out on the figure and on the drawing, and, on the other hand, it must maintain at all times a coherence between the figure and drawing. From the algorithmic point of view, GDRev solves geometric constraints using cooperation of solvers based on the concurrent constraint programming paradigm. Three general solvers, one linear, one quadratic, one interval, cooperate with three specific solvers that are original to this work. One of the specific solvers is the object completion solver which creates automatically geometric objects necessary for constructing the figure. The second is the property completion solver which adds automatically redondant properties to obtain a construction of the figure. The ruler and compass solver calculates an optimized construction with which to drag the figure rapidly. GDRev is implemented using interaction between the interfaces which are written in Visual C++ and the geometric constraint solver which is written in Prolog IV. The tests carried out on the system have given encouraging results, especially those concerning the choice of heuristics used.
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Submitted on : Wednesday, February 18, 2004 - 11:44:50 AM
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  • HAL Id : tel-00004819, version 1



Stéphane Channac. Conception et mise en oeuvre d'un système déclaratif de géométrie dynamique. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 1999. Français. ⟨tel-00004819⟩



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