We consider methods of constructing intelligent systems of geometric modeling and propose a technique and software for implementing these methods. The results obtained can be used in computer-aided design.The construction of high-efficiency systems for computer-aided design (CAD) is a problem of current interest. The efficiency of such systems can be greatly elevated by using the modern achievements of computational and constructive geometry [9], methods of intelligent automated interactive programming [3], intelligent knowledge base systems, expert systems, decision-making systems, and methods of multi-criterial optimization.The general situation in the area under investigation can be characterized by the level attained in these areas of theoretical and applied science. The most important particular problems of computational and constructive geometry are: the algorithmic aspects of geometry, data structures for representing geometric objects, optimization of geometric data structures, synthesis of solid geometric objects, visualization of geometric objects, the finite element method, optimal triangulation algorithms, representation of geometric knowledge, elimination of contradictions, and automation of geometric proofs and constructions.Among the Russian publications in the area of constructive geometry one may note [1, 2], which are devoted to the axiomatization of the problem of synthesizing 3-dimensional objects. On the basis of these investigations, in particular, an interactive graphical system has been constructed for synthesizing an intramachine model of a 3-dimensional object via instructions for the positioning of the base elements (primitives) in space and prescribing geometric operations. However, the correctness of the construction process can be evaluated only on the basis of visual criteria of the user, i.e., from the mapping of geometric images on the screen with no way of using the knowledge base and system of logical inference, and no way of avoiding contradictions or automating the system of geometric proofs and constructions. What has just been said holds also in regard to the most widely used foreign software for computer-aided design, such as AutoCAD, CADPlan, EUCLID [7], etc.One of the central problems of constructive geometry is the optimization of the inramachine representations of complicated geometric objects (binary trees representing expressions over primitives in an algebra with signature f~ = {N*, t.J*, \* }, and also optimization of ring list structures representing the surfaces of complicated geometric objects) and algorithms over these representations. In particular the paper [9] already mentioned is devoted to these problems; in this paper quite efficient algorithms are proposed for minimizing binary trees. Also devoted to this topic is [8], in which a rapid algorithm is proposed for carrying out refined set-theoretic operations over constructively defined geometric objects. However questions as to the correctness of data structures (inconsistency and completeness of descriptio...

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