3D Simulation of Second-Order Surfaces

Lyudmila Remontova; Leonid Nesterenko; V. Burlov; Nikita Orlov

doi:10.12737/22843

3D SIMULATION OF SECOND-ORDER SURFACES 3D Simulation of Second-Order Surfaces

АА Аа

Published in Geometry & Graphics · Volume 4, Issue 4 · Pages 48–59 · Rubric: Methodical questions of teaching

DOI: https://doi.org/10.12737/22843

Received: 24.11.2016 Accepted: 18.12.2016 Published: 18.12.2016 Language of publication: ru-RU

Authors

Lyudmila Remontova

Leonid Nesterenko

V. Burlov

Nikita Orlov

Lyudmila Remontova

Leonid Nesterenko

V. Burlov

Nikita Orlov

ABSTRACT

This paper’s material is destined for high educational institutions’ graduate students and teachers whose professional activity is connected with problems of descriptive geometry and engineering graphics teaching improving on the basis of modern computer technology. The paper will be useful to students of technical universities in their further understanding the course of descriptive geometry and inoculation them an interest in their personal geometric and graphic training, without which a quality engineering creativity is impossible. The paper focuses on use of KOMPAS-3D software possibilities which enables solution of nearly all educational, as well as professional engineering and graphics problems. At the same time, the promotion of domestic IT-product in educational area is an urgent task, arising from the problem of technical education at the present stage of public education’s system development. A number of examples related to solution of spatial problems connected with second-order surfaces simulation have been considered. On the basis of descriptive geometry’s laws applicable to surface problems, a feature of their solution and display on computer screen has been illustrated. For example, in the graphic editor KOMPAS-3D there is the Ellipse command, but there are no Hyperbola or Parabola commands. But without these curves it is impossible to create a 3D model of hyperboloid (one- or two-sheet), paraboloid, or hyperbolic paraboloid. To create these curves it has been proposed to use conics of circular cone, canonical or parametric equations of hyperbolas and parabolas. For each of these options the examples of second-order surfaces 3D models creation have been considered.

KEYWORDS

cone, cylinder, section, library, canonical and parametric equations, hyperbola, parabola, associative drawing, paraboloid, one- and two-sheet hyperboloid, hyperbolic paraboloid, plot of functional dependence

Text

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JATS XML

Zamestitel' glavnogo redaktora, chlen redsoveta

Vladimir Vyshnyepolskiy

Glavnyy redaktor

A. A. Ishchenko

Vypuskayuschiy redaktor

Dar'ya Sklyankina

501@infra-m.ru

Deputy editor-in-chief, member of the editorial Board

N. Sal'kov

nikolaysalkov@mail.ru

GOST

Remontova L., Nesterenko L., Burlov V., Orlov N. 3D Simulation of Second-Order Surfaces // Geometry & Graphics. 2016. no. 4. pp. 48-59. DOI: https://doi.org/10.12737/22843. (Date of access 11.11.2026).

MLA

Lyudmila Remontova, Nesterenko L., Burlov V., Orlov N.. "3D Simulation of Second-Order Surfaces." Geometry & Graphics 4.4 (2016): 48-59. DOI: https://doi.org/10.12737/22843.

APA

Remontova L., Nesterenko L., Burlov V., Orlov N. (2016). 3D Simulation of Second-Order Surfaces. Geometry & Graphics, 4(4), 48-59. https://doi.org/10.12737/22843

Chicago

Lyudmila Remontova, Nesterenko L., Burlov V., Orlov N.. "3D Simulation of Second-Order Surfaces." Geometry & Graphics 4, no. 4 (2016): 48-59. https://doi.org/10.12737/22843.

WIKI

{{cite journal | author = Remontova L., Nesterenko L., Burlov V., Orlov N. | title = 3D Simulation of Second-Order Surfaces | journal = Geometry & Graphics | year = 2016 | volume = 4 | issue = 4 | pages = 48-59 | doi = 10.12737/22843 }}

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3D SIMULATION OF SECOND-ORDER SURFACES 3D Simulation of Second-Order Surfaces

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