Approximation of Generalized Ovals and Lemniscates towards Geometric Modeling

Valery Ochkov, Inna Vasileva, Ekaterina Borovinskaya and Wladimir Reschetilowski
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Valery Ochkov: Department of Theoretical Bases of Heat Engineering, National Research University Moscow Power Engineering Institute, 111250 Moscow, Russia
Inna Vasileva: Department of Mathematics, Military Educational and Scientific Center of the Air Force “N.E. Zhukovsky and Y.A. Gagarin Air Force Academy”, 394064 Voronezh, Russia
Ekaterina Borovinskaya: Faculty of Mechanical Science and Engineering, Technische Universität Dresden, 01062 Dresden, Germany
Wladimir Reschetilowski: Faculty of Mechanical Science and Engineering, Technische Universität Dresden, 01062 Dresden, Germany

Mathematics, 2021, vol. 9, issue 24, 1-17

Abstract: This paper considers an approach towards the building of new classes of symmetric closed curves with two or more focal points, which can be obtained by generalizing classical definitions of the ellipse, Cassini, and Cayley ovals. A universal numerical method for creating such curves in mathematical packages is introduced. Specific aspects of the provided numerical data in computer-aided design systems with B-splines for three-dimensional modeling are considered. The applicability of the method is demonstrated, as well as the possibility to provide high smoothness of the curvature profile at the specified accuracy of modeling.

Keywords: geometric modeling and applications; B-splines; Cassini ovals; Cayley ovals; lemniscates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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