Application of beam theory for the construction of twice differentiable closed contours based on discrete noisy points

Authors

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2022.4.10

Keywords:

spline, elastic beam, spring support, closed contour, imaginary point, noisy data

Abstract

The smoothing of measured noisy positions of discrete points has considerable significance in various industries and computer graphic applications. The idea of work consists of the employment of the technique of beam with spring supports. The local coordinates systems are established for beam straight line segments, where the initial angles between them are accounted for in the conjugation equations, which provide the angular continuity. The notions of imaginary points are introduced, the purpose of which is to approach the real length of the smoothed contour to the length of the straight chord. Several examples of closed denoised curve reconstruction from an unstructured and highly noisy 2D point cloud are presented.

Author Biographies

Igor Orynyak, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Doctor of Technical Sciences, a professor at the Applied Mathematics Department of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

Dmytro Koltsov, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Master's degree graduate of the Applied Mathematics Department of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

Oleg Chertov, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Professor, Doctor of Technical Sciences, Head of the Applied Mathematics Department of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

Roman Mazuryk, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Ph.D. student at the Applied Mathematics Department of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

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Published

2022-12-27

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Section

Mathematical methods, models, problems and technologies for complex systems research