Approximation of Generalized Ovals and Lemniscates towards Geometric Modeling
Valery Ochkov,
Inna Vasileva,
Ekaterina Borovinskaya,
Wladimir Reschetilowski
Affiliations
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
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.
