Control Systems and Computers, N3, 2024, Article 1
https://doi.org/10.15407/csc.2024.03.003
Control Systems and Computers, 2024, Issue 3 (307), pp. 3-9
UCD 514.18
N.M. AUSHEVA, Doctor (Eng.), Professor, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Beresteyskyi Avenue, 37, Kyiv, Ukraine, 03056, ORCID: https://orcid.org/0000-0003-0816-2971, nataauscheva@gmail.com
O.S. KALENIUK, PhD (Eng.), National Technical University of Ukraine“ Igor Sikorsky Kyiv Polytechnic Institute”, Beresteyskyi Avenue, 37, Kyiv, Ukraine, 03056, ORCID: https://orcid.org/0009-0009-3141-4840, akalenuk@gmail.com
Iu.V. SYDORENKO, PhD (Eng.), Assistant Professor, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Beresteyskyi Avenue, 37, Kyiv, Ukraine, 03056, ORCID: https://orcid.org/0000-0002-1953-0410, suliko3@ukr.net
USING EXPONENTIAL COMPLEX POLYNOMIALS FOR CONSTRUCTING CLOSED CURVES WITH GIVEN PROPERTIES
In this paper, we present a method to compute the coefficients of a complex exponential polynomial of real argument that, while being decomposed into real and imaginary parts by Euler’s formula, obtains required interpolating and differential properties at any given points of its real graph. Moreover, imaginary components in their nodes of interpolation and differentiation serve as additional control tools that shape the polynomial appearance. Although the impact of these components is not yet studied extensively, we can still use them to achieve useful properties, e. g. we can minimize the total height of the polynomial graph.
From the geometry standpoint, having these properties implies that the parametric curves constructed with such polynomials can go through given points, have predetermined tangent vectors in those or other points, and retain enough variability to have additional useful properties, for instance, the total length of these curves, or their maximal curvature can also be minimized within limits.
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Keywords: exponential complex polynomial, periodic interpolation, closed curve, mathematical optimization, total length minimization.
- Salzer, H.E. (1948). “Coefficients for facilitating trigonometric interpolation”. Journal of Mathematics and Physics, 27(1-4), pp. 274-278.
https://doi.org/10.1002/sapm1948271274 - Sanchez-Reyes, J. (2009). “Periodic Bezier curves”. Computer Aided Geometric Design, 26(9), pp. 989-1005.
https://doi.org/10.1016/j.cagd.2009.08.002 - Ramanantoanina, A., Hormann, K. (2023). “Shape control tools for periodic Bézier curves”. Computer Aided Geometric Design, 103, Article 102193, 12 p.
https://doi.org/10.1016/j.cagd.2023.102193 - Ramanantoanina, A., Hormann, K. (2021).” New shape control tools for rational Bézier curve design”. Computer Aided Geometric Design, 88, Article 102003.
https://doi.org/10.1016/j.cagd.2021.102003 - Fletcher, R. (1988). Practical methods of optimization. NY : Wiley, 456 p.
Received 12.06.2024
