Havrylenko Yevhen, Kholodniak Yuliia, Halko Serhii, Vershkov Oleksandr, Miroshnyk Oleksandr, Suprun Olena, Dereza Olena, Shchur Taras, Śrutek Mścisław
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.
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.
Entropy (Basel). 2021 Jul 20;23(7):923. doi: 10.3390/e23070923.
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.
本文解决了以指定精度对具有曲率规则变化的光滑轮廓进行建模的问题，该轮廓表示一条单调曲线。该轮廓是在凸曲线可能位置的区域内形成的，凸曲线可以对一系列点进行插值。如果一系列点可以由单调曲线进行插值，那么在其上分配这些点的参考曲线就是单调的这一假设，为实施所提出的方法来估计任意配置的点序列的插值误差提供了机会。所提出的通过椭圆弧和B样条形成凸规则轮廓的方法，确保了在可以由单调曲线插值的部分中对任何点序列进行插值。同时，可以控制轮廓相对于单调曲线可能位置区域边界的偏差。在解决属于单调曲线的点序列的插值问题时，对所开发方法的可能性进行了测试。这些问题是在SolidWorks CAD系统中通过使用基于研究工作中开发的方法创建的软件应用程序来解决的。
