New Problems of Descriptive Geometry

Girsh, A.

doi:10.12737/2308-4898-2020-18-33

Cited by 8 publications

(1 citation statement)

References 8 publications

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“…In our time, there is an understanding that the situation must be urgently corrected. Work on the subject of constructive geometric modeling continues [1,2,5,6,[36][37][38][39][40][41][42][43][44][45][46][47]. Relentless attempts are being made to revive geometric knowledge in higher education.…”

Section: Introductionmentioning

confidence: 99%

Problems of Graphic Design of the Results of a Geometric Experiment

Boyashova,

Musaeva,

Voloshinov

2023

Proceedings of the 33rd International Conference on Computer Graphics and Vision

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The article is devoted to the problems of graphical representation of drawings for purposes of interactive automated constructive geometry modeling. The authors demonstrate the necessity for studying principles of models creation to develop special informational technologies for visualizing, interpretation and processing of geometrical data. The article presents a retrospective review of methods for displaying geometric information, adopted among specialists in constructive geometric modeling. It is shown the importance to support scientific research in a field of geometry modelling, especially for multidimensional space for science, education and applied tasks implementation. The article formulates the goals and objectives of the further development of the system of constructive geometric modeling Simplex.

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Section: Introductionmentioning

confidence: 99%

Problems of Graphic Design of the Results of a Geometric Experiment

Boyashova,

Musaeva,

Voloshinov

2023

Proceedings of the 33rd International Conference on Computer Graphics and Vision

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Algorithmic Complex for Solving of Problems with Quadrics Using Imaginary Geometric Images

Voloshinov

2020

Geometry &Amp; Graphics

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The paper is devoted to the consideration of a number of issues related to the creation of an algorithmic complex designed to solve positional and metric problems with quadrics on a projection model . A feature of the complex is the active use of geometric schemes and algorithms involving imaginary geometric images. In the paper has been presented a detailed description of constructive geometric algorithms for constructing of conics, quadrics and associated geometric images in a system of constructive geometric modeling – Simplex. All the discussed algorithms are available for independent repetition by the reader. In the paper have been presented and implemented algorithms for constructing conic from a point, a polar, and three points; constructing conic from two pairs of complex conjugate points and one real point; determination of a point on a quadric’s surface; setting a quadric by nine points in three-dimensional space. A new alternative frame of the quadric has been considered, based on which have been solved problems of constructing a tangent and a normal to the quadric, finding an intersection line of an arbitrary plane with the quadric, and performing polar and inverse transformations with respect to the quadric. Have been proposed algorithms for constructing an autopolar tetrahedron with respect to the quadric, and for constructing a conic from an autopolar triangle and two points. Have been considered problems of determining a collinear transformation in three-dimensional space and control the quadric through it. The implementation of the algorithms considered in the paper allowed conclude that there is an urgent need to develop tools for modeling imaginary conics, without which the complex of solving problems with quadrics cannot be taken for the complete one.

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Computer Verification of Descriptive Geometry Task Solutions for Engineering and Graphic Education

Boykov

2020

Geometry &Amp; Graphics

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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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New Problems of Descriptive Geometry

Cited by 8 publications

References 8 publications

Problems of Graphic Design of the Results of a Geometric Experiment

Problems of Graphic Design of the Results of a Geometric Experiment

Algorithmic Complex for Solving of Problems with Quadrics Using Imaginary Geometric Images

Computer Verification of Descriptive Geometry Task Solutions for Engineering and Graphic Education

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