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.

中文翻译：

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用曲率有规律变化的轮廓来表示单调曲线

本文解决了对具有指定精度的单调曲线表示具有规则变化的曲率的平滑轮廓建模的问题。轮廓是在凸曲线的可能位置区域内形成的，可以插入点序列。假设如果一系列点可以通过单调曲线进行插值，那么分配这些点的参考曲线是单调的，提供了实施所提出的方法来估计任意配置的点系列的插值误差的机会. 所提出的由椭圆弧和B样条形成凸规则轮廓的方法确保了可以通过单调曲线插值的部分中的任何点序列的插值。同时，可以控制轮廓从单调曲线可能位置的区域边界的偏转。在解决属于单调曲线的点序列的插值问题时，测试了所开发方法的可能性。这些问题在 SolidWorks 的 CAD 系统中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。