Geometric models for industrial purposes are created in CAD systems making use of geometric constructions commands. At the same time, the so-called constructive or synthetic (as opposed to analytical) method to create a geometric model is implemented. The set of tools of any CAD system is limited, so accomplishing a specific task will require repeating a series of geometric constructions of the same type to form the desired shape. In this paper, a specific GC language (Geometry Constructions Language) is proposed to introduce an automated process of geometric modeling. To do this, theoretical issues of constructive geometry are analyzed, the main objects and syntax of the GC language are identified. The paper provides an example of building a model of a temple dome using GC language translator. It is noted that the GC language allows geometric modeling of regular curves (including trajectory of objects) and surfaces and applying new geometric correspondences and transformations. At the same time, geometric models in CAD systems are created faster since you don’t have to repeat manually the same type of construction or develop new equations and formulas for calculations.
During all-Russian academic competition on descriptive geometry, engineering and computer graphics in 2011 a task was proposed. This task’s condition was as follows: two planets rotate around a star in circular orbits of different diameter, which lie in the different planes passing through the star center and located at a 30 degree angle to each other; it is known that these orbits belong to the 4th order surface. It was necessary to find the orbits diameters ratio. This geometrical task decision’s analysis is cited in the paper.
The paper focuses on the complex use of distance learning techniques to support the training course of descriptive geometry and engineering graphics during on-site training in connection with transfer of all University’s faculties at the baccalaureate system. The approbation of suggested training system for engineering graphics supporting by computer means on several batches of different University’s faculties is assumed.
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.
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