Representation of a Monotone Curve by a Contour with Regular Change in Curvature
Yevhen Havrylenko,
Yuliia Kholodniak,
Serhii Halko,
Oleksandr Vershkov,
Oleksandr Miroshnyk,
Olena Suprun,
Olena Dereza,
Taras Shchur,
Mścisław Śrutek
Affiliations
Yevhen Havrylenko
Department of Technical Mechanics and Computer Design Named after Prof. V.M. Naidysh, Dmytro Motornyi Tavria State Agrotechnological University, 18 B.Khmelnytsky Ave, 72312 Melitopol, Ukraine
Yuliia Kholodniak
Department of Technical Mechanics and Computer Design Named after Prof. V.M. Naidysh, Dmytro Motornyi Tavria State Agrotechnological University, 18 B.Khmelnytsky Ave, 72312 Melitopol, Ukraine
Serhii Halko
Department of Electrical Engineering and Electromechanics Named after Prof. V.V. Ovharov, Dmytro Mo-tornyi Tavria State Agrotechnological University, 18 B.Khmelnytsky Ave, 72312 Melitopol, Ukraine
Oleksandr Vershkov
Department of Technical Mechanics and Computer Design Named after Prof. V.M. Naidysh, Dmytro Motornyi Tavria State Agrotechnological University, 18 B.Khmelnytsky Ave, 72312 Melitopol, Ukraine
Oleksandr Miroshnyk
Department of Electricity and Energy Management, Kharkiv Petro Vasylenko National Technical University of Agriculture, 19 Rizdviana Street, 61052 Kharkiv, Ukraine
Olena Suprun
Department of Foreign Languages, Dmytro Motornyi Tavria State Agrotechnological University, 18 B.Khmelnytsky Ave, 72312 Melitopol, Ukraine
Olena Dereza
Department of Technical Mechanics and Computer Design Named after Prof. V.M. Naidysh, Dmytro Motornyi Tavria State Agrotechnological University, 18 B.Khmelnytsky Ave, 72312 Melitopol, Ukraine
Taras Shchur
Department of Cars and Tractors, Faculty of Mechanics and Energy, Lviv National Agrarian University, Volodymyr Great 1 Street, 80381 Dubliany, Ukraine
Mścisław Śrutek
Faculty of Telecommunications, Computer Science and Electrical Engineering, UTP University of Science and Technology in Bydgoszcz, 85-796 Bydgoszcz, Poland
The problem of modelling a smooth contour with a regular change in curvature representing a monotone curve with specified accuracy is solved in this article. The contour was formed within the area of the possible location of a convex curve, which can interpolate a point series. The assumption that if a sequence of points can be interpolated by a monotone curve, then the reference curve on which these points have been assigned is monotone, provides the opportunity to implement the proposed approach to estimate the interpolation error of a point series of arbitrary configuration. The proposed methods for forming a convex regular contour by arcs of ellipses and B-spline ensure the interpolation of any point series in parts that can be interpolated by a monotone curve. At the same time, the deflection of the contour from the boundaries of the area of the possible location of the monotone curve can be controlled. The possibilities of the developed methods are tested while solving problems of the interpolation of a point series belonging to monotone curves. The problems are solved in the CAD system of SolidWorks with the use of software application created based on the methods developed in the research work.
