INTERPOLATION USING SPLINE FUNCTION

DOI: 10.31673/2786-8362.2024.025091

Abstract

This article discusses
typical areas of problems for the application of spline functions for the purpose of data interpolation and
approximation. An analysis of a large list of modern science literature on the selected topic is presented.
Various types of splines, their mathematical properties and areas of application are analyzed. Special
attention is paid to the advantages of splines compared to other interpolation methods, due to their high
accuracy of approximation, the smoothness of the formed curves, relative simplicity, the possibility of
convenient control of the shape and curvature by changing the parameters.
The paper also focuses on the advantages of using splines in the context of vector graphics, including
scalability and high resolution of images regardless of their size. Spline-based vector graphics allow
creation of visualizations that retain their accuracy and detail at any magnification, which is especially
important for technical drawings, computer graphics and deep machine learning.
Various examples of the feasibility of using splines in various fields of science, engineering, signal
processing and machine learning are illustrated. These instances demonstrate how splines can be effectively
used to solve practical problems while providing high approximation accuracy. The article emphasizes that
the use of splines allows not only to improve the quality of interpolation, but also to significantly simplify
the process of complex systems modeling.

Keywords: interpolation, segmentation, vectorization, spline, Bezier curve, topological space.

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