Компьютерная проверка решений задач начертательной геометрии для инженерно-графического образования

Abstract

In this paper is formulated the relevance of computer tools creation for verification of descriptive geometry task solutions. Are analyzed the shortcomings of available methods and systems for such verification. A new verification method is proposed – the mode of superposition based on overlaying a student’s solution with a template and formal evaluation the overlaying results. To create templates for a wide range of descriptive geometry tasks, it is proposed to use a formal grammar of the correct solution, which is constructed using special nonterminal symbols – “and”, “or”, “transform” and “instance”. As the grammar’s terminal symbols are used geometric figures. Thus, the template consists of a graphic part (a set of figures) and a structural description (grammar). An implementation of this verification method is demonstrated as a software system for verifying of descriptive geometry task solutions in the form of DXF-files. A functional model of the verification system is given. The automatic formation of a template from a graphical model, which is created in a vector graphics editor and does not require a symbolic description, is considered, as well as processing procedure for a student’s solution, during which the verifiable model goes through phases of normalization, filtration, and extracting of higher-level elements. An example of checking for two solutions (the correct one and containing errors) of the task for constructing a perpendicular to a plane of general position is given. The work of a subsystem for verification result visualization is demonstrated too. The created system can be implemented in Internet-libraries of tasks, or in distance learning systems, and can be used for remote support of geometric-graphic courses. Conclusions about feasibility of introducing the proposed method as a tool in CAD-systems are made.