Modeling Ellipsoids Using Nanocad as Part of the Educational Process

A. Ivaschenko; A. V. Stepura

doi:10.12737/2308-4898-2024-12-4-51-58

UDC

378

MODELING ELLIPSOIDS USING NANOCAD AS PART OF THE EDUCATIONAL PROCESS Modeling Ellipsoids Using Nanocad as Part of the Educational Process

АА Аа

Published in Geometry & Graphics · Pages 51–58 · Rubric: Methodical questions of teaching

DOI: https://doi.org/10.12737/2308-4898-2024-12-4-51-58

Received: 12.05.2025 Accepted: 12.05.2025 Published: 12.05.2025

Authors

A. Ivaschenko

A. V. Stepura

A. Ivaschenko

Academic degree: candidate of technical sciences

Moscow State University of Civil Engineering Associate Professor · Chair of Descriptive Geometry and Graphics

A. V. Stepura

Moscow State University of Civil Engineering Senior lecturer

ABSTRACT

The article considers the methods of geometric modeling by means of NanoCAD of the following surfaces of the second order: a sphere, an ellipsoid of revolution and a triaxial ellipsoid, parts of which were widely used in classical architecture and continue to be used as prototypes of domed and large-span roofs in modern architecture, which determines the relevance of this work. On the other hand, ellipsoids, as well as spheres, are the simplest surfaces of the second order for modeling and are relatively easy to implement in various CAD systems, including domestic ones SOMPAS-3D and NanoCAD. Depending on the degree of symmetry of the surface, various options for its construction can be used. In particular, a triaxial ellipsoid can be constructed in at least three ways: using programming in the built-in nanoLisp or VBA languages; using blocks with subsequent stretching/compression along the selected directions; using the operation of "pulling by sections", having previously constructed these sections. In case of constructing an ellipsoid of revolution, it is possible to additionally add the operation of rotating a half arc of the ellipse relative to its diameter (there are two options for rotation - relative to the major axis or relative to the minor axis of the generating ellipse). The sphere can be created by any of the above methods, and, in addition, it is possible to use built-in primitives. The article analyzes the advantages and disadvantages of the algorithms of each of the three main methods for constructing a triaxial ellipsoid, as the least symmetrical of the three surfaces under consideration. The labor intensity, the quality of the obtained result and the required degree of user training for choosing one or another option for surface modeling are analyzed. Algorithms for constructing surfaces are also given, accompanied by illustrations of the resulting intermediate and final results. In conclusion, conclusions are made on the degree of appropriateness of using one or another method of construction in the educational process.

KEYWORDS

sphere, ellipsoid of revolution, triaxial ellipsoid, geometric modeling, surface modeling technology, modeling algorithm

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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

Ivaschenko A. V., Stepura A. V. Modeling Ellipsoids Using Nanocad as Part of the Educational Process // Geometry & Graphics. 2024. no. 4. pp. 51-58. DOI: https://doi.org/10.12737/2308-4898-2024-12-4-51-58. (Date of access 09.09.2026).

MLA

A. Ivaschenko, Stepura A. V.. "Modeling Ellipsoids Using Nanocad as Part of the Educational Process." Geometry & Graphics 12.4 (2024): 51-58. DOI: https://doi.org/10.12737/2308-4898-2024-12-4-51-58.

APA

Ivaschenko A. V., Stepura A. V. (2024). Modeling Ellipsoids Using Nanocad as Part of the Educational Process. Geometry & Graphics, 12(4), 51-58. https://doi.org/10.12737/2308-4898-2024-12-4-51-58

Chicago

A. Ivaschenko, Stepura A. V.. "Modeling Ellipsoids Using Nanocad as Part of the Educational Process." Geometry & Graphics 12, no. 4 (2024): 51-58. https://doi.org/10.12737/2308-4898-2024-12-4-51-58.

WIKI

{{cite journal | author = Ivaschenko A. V., Stepura A. V. | title = Modeling Ellipsoids Using Nanocad as Part of the Educational Process | journal = Geometry & Graphics | year = 2024 | volume = 12 | issue = 4 | pages = 51-58 | doi = 10.12737/2308-4898-2024-12-4-51-58 }}

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MODELING ELLIPSOIDS USING NANOCAD AS PART OF THE EDUCATIONAL PROCESS Modeling Ellipsoids Using Nanocad as Part of the Educational Process

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