Improvement of the algorithm for setting the characteristics of interpolation monotone curve

• Autorzy: Kholodniak Yuliia , Havrylenko Yevhen , Halko Serhii , Hnatushenko Volodymyr , Suprun Olena , Volina Tatiana , Miroshnyk Oleksandr , Shchur Taras

Identyfikatory

DOI

10.35784/iapgos.5392

Warianty tytułu

PL

Ulepszenie algorytmu wyznaczanie charakterystyki interpolacyjnej krzywej monotonicznej

• Języki publikacji: EN

Abstrakty

EN

Interpolation of a point series is a necessary step in solving such problems as building graphs de-scribing phenomena or processes, as wellas modelling based on a set of reference points of the line frames defining the surface. To obtain an adequate model, the following conditions are imposed upon the interpolating curve: a minimum number of singular points (kinking points, inflection points or points of extreme curvature) and a regular curvature change along the curve. The aim of the work is to develop the algorithm for assigning characteristics (position of normals and curvature value) to the interpolating curve at reference points, at which the curve complies with the specified conditions. The characteristics of the curve are assigned within the area of their possible location. The possibilities of the proposed algorithm are investigated by interpolating the point series assignedto the branches of the parabola. In solving the test example, deviations of the normals and curvature radii from the corresponding characteristicsof the original curve have been determined. The values obtained confirm the correctness of the solutions proposed in the paper.

PL

Interpolacja szeregu punktowego jest niezbędnym krokiem w rozwiązywaniu takich problemów, jak budowanie grafów opisujących zjawiska lub procesy, a także modelowanie w oparciu o zbiór punktów odniesienia układów liniowychdefiniujących powierzchnię. Aby uzyskać odpowiedni model, na interpolowaną krzywą stawia się następujące warunki: minimalną liczbę punktów osobliwych (punktów załamania, punktów przegięcia lub punktów skrajnej krzywizny) oraz regularną zmianę krzywizny wzdłuż krzywej. Celem pracy jest opracowanie algorytmu przypisania charakterystyk (położenia normalnych i wartości krzywizny) krzywej interpolacyjnej w punktach odniesienia, w których krzywa spełnia określone warunki. Charakterystyki krzywych nadawane są w obszarze ich możliwego położenia. Możliwości proponowanego algorytmu są badane poprzez interpolację szeregów punktów przypisanych do gałęzi paraboli. W rozwiązaniu przykładu testowego wyznaczono odchylenia normalnych i promieni krzywizny od odpowiednich charakterystyk pierwotnej krzywej. Otrzymane wartości potwierdzają poprawność zaproponowanych w pracy rozwiązań.

Słowa kluczowe

EN

interpolation; monotone curve; singular points; normal; centre of curvature; evolute; curvature radius

PL

interpolacja; krzywa monotoniczna; punkty osobliwe; normalna; środek krzywizny; ewolucja; promień krzywizny

• Wydawca: Wydawnictwo Politechniki Lubelskiej
• Czasopismo: Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
• Rocznik: 2023
• Tom: T. 13, nr 4
• Strony: 44--50
• Opis fizyczny: Bibliogr. 32 poz., tab., wykr.

Twórcy

autor

Kholodniak Yuliia

• Dmytro Motornyi Tavria State Agrotechnological University, Department of Computer Sciences, Zaporizhzhia, Ukraine

• https://orcid.org/0000-0001-8966-9269

autor

Havrylenko Yevhen

• Dmytro Motornyi Tavria State Agrotechnological University, Department of Engineering Mechanics and Computer Design, Zaporizhzhia, Ukraine

• https://orcid.org/0000-0003-4501-445X

autor

Halko Serhii

• Dmytro Motornyi Tavria State Agrotechnological University,Departmentof Electrical Engineering and Electromechanics named after Prof. V.V. Ovharov, Zaporizhzhia, Ukraine

• https://orcid.org/0000-0001-7991-0311

autor

Hnatushenko Volodymyr

• Dnipro University of Technology, Department of Information Technologies and Computer Engineering, Dnipro, Ukraine

• https://orcid.org/0000-0003-3140-3788

autor

Suprun Olena

• Dmytro Motornyi Tavria State Agrotechnological University, Department of Foreign Languages, Zaporizhzhia, Ukraine

• https://orcid.org/0000-0003-4369-712X

autor

Volina Tatiana

• National University of Life and Environmental Sciences of Ukraine, Department of Descriptive Geometry, Computer Graphics and Design, Kiev, Ukraine

• https://orcid.org/0000-0001-8610-2208

autor

Miroshnyk Oleksandr

• State Biotechnological University, Department of Electricity Supply and Energy Management, Kharkiv, Ukraine

• https://orcid.org/0000-0002-6144-7573

autor

Shchur Taras

• Cyclone Manufacturing Inc, Mississauga, Ontario, Canada

• https://orcid.org/0000-0003-0205-032X

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).