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Information × Registration Number 0223U002905, 0123U100809 , R & D reports Title Algorithms of asymptotically optimal polyline interpolation of flat curves popup.stage_title Head Frolov Oleg V., к.т.н. Registration Date 15-03-2023 Organization Simon Kuznets Kharkiv National University of Economics popup.description2  Approximation of curves by polylines attracts attention for the purpose of its application to the reproduction of objects of complex shape on a computer, CNC machines and 3D printers. At the same time, it is desirable to have the smallest number of segments that reconstruct the curve, while maintaining the necessary accuracy of reproduction. The object of research is the process of reproducing flat curves given by parametric equations by polylines. The purpose of the research is the development and improvement of adaptive piecewise linear approximation methods and their algorithmic support in computer modeling and computer aided design systems. The subject of the study is asymptotically optimal models for reconstruction curves with a given approximation error, which provide close to the minimum number of nodes. Research methods: data visualization, numerical and statistical analysis, optimization methods, geometric modeling methods based on analytical, differential geometry. Computer modeling and visualization of results using Matplotlib, NumPy, SciPy libraries and Python programming language were also used in the work. Obtained results: - it was found that the essence of the influence of the increase in the number of nodes of the initial discretization of the integral function - the node regulator on the quality of the reconstruction by the asymptotically optimal algorithm is to improve the indicators of the distribution of approximation errors by the segments of the approximating polyline, namely the reduction of the variation of the values of the error series, which reflects stabilization values of errors around the mean value; - research on the modeling of the reconstruction of flat curves with inflection points showed the suitability of using the integral function expression with the optimization of the α parameter to regulate the distribution of nodes of linear interpolation of such curves according to the asymptotically optimal algorithm. Product Description popup.authors Hryzun Liudmyla Zadachyn Viktor Frolov Oleg V. popup.nrat_date 2023-03-15 Close