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Approximation of Generalized Ovals and Lemniscates towards Geometric Modeling

Author

Listed:
  • 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
    Saint-Petersburg State Institute of Technology, Technical University, 190013 St. Petersburg, Russia)

  • Wladimir Reschetilowski

    (Faculty of Mechanical Science and Engineering, Technische Universität Dresden, 01062 Dresden, Germany)

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.

Suggested Citation

  • Valery Ochkov & Inna Vasileva & Ekaterina Borovinskaya & Wladimir Reschetilowski, 2021. "Approximation of Generalized Ovals and Lemniscates towards Geometric Modeling," Mathematics, MDPI, vol. 9(24), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3325-:d:707040
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    References listed on IDEAS

    as
    1. Mei Seen Wo & R. U. Gobithaasan & Kenjiro T. Miura, 2014. "Log-Aesthetic Magnetic Curves and Their Application for CAD Systems," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-16, October.
    2. H. Haron & A. Rehman & D. I. S. Adi & S. P. Lim & T. Saba, 2012. "Parameterization Method on B-Spline Curve," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-22, January.
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