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

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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.
Rocznik
Strony
44--50
Opis fizyczny
Bibliogr. 32 poz., tab., wykr.
Twórcy
  • Dmytro Motornyi Tavria State Agrotechnological University, Department of Computer Sciences, Zaporizhzhia, Ukraine
  • Dmytro Motornyi Tavria State Agrotechnological University, Department of Engineering Mechanics and Computer Design, Zaporizhzhia, Ukraine
autor
  • Dmytro Motornyi Tavria State Agrotechnological University,Departmentof Electrical Engineering and Electromechanics named after Prof. V.V. Ovharov, Zaporizhzhia, Ukraine
  • Dnipro University of Technology, Department of Information Technologies and Computer Engineering, Dnipro, Ukraine
autor
  • Dmytro Motornyi Tavria State Agrotechnological University, Department of Foreign Languages, Zaporizhzhia, Ukraine
  • National University of Life and Environmental Sciences of Ukraine, Department of Descriptive Geometry, Computer Graphics and Design, Kiev, Ukraine
  • State Biotechnological University, Department of Electricity Supply and Energy Management, Kharkiv, Ukraine
autor
  • Cyclone Manufacturing Inc, Mississauga, Ontario, Canada
Bibliografia
  • [1] Argyros I. K., George S.: On the convergence of Newton-like methods restricted domains. Numer. Algorithms 75(3), 2017, 553-567 [http://doi.org/10.1007/s11075-016-0211-y].
  • [2] Bucsa S., Serban A., Balan M. C., Ionita C., Nastase G., Dobre C., Dobrovicescu A.: Exergetic Analysis of a Cryogenic Air Separation Unit. Entropy 24, 2022, 272 [http://doi.org/10.3390/e24020272].
  • [3] Chekalin A. A., Reshetnikov M. K., Shpilev V. V., Borodulina S. V.: Design of Engineering Surfaces Using Quartic Parabolas. IOP Conf. Ser.: Mater. Sci. Eng. 2007, 012015 [http://doi.org/10.1088/1755-1315/221/1/012015].
  • [4] Farin G., Rein G., Sapidis N., Worsey A. J.: Fairing cubic B-spline curves. Computer Aided Geom. Des. 4(1–2), 1987, 91-103 [http://doi.org/10.1016/0167-8396(87)90027-6].
  • [5] Fooladi M., Foroud A. A.: Recognition and assessment of different factors which affect flicker in wind turbine. IET Renew. Power Gener. 1, 2015, 250–259 [http://doi.org/10.1049/iet-rpg.2014.0419].
  • [6] Halko S., Halko K., Suprun O., Qawaqzeh M., Miroshnyk O.: Mathematical Modelling of Cogeneration Photoelectric Module Parameters for Hybrid Solar Charging Power Stations of Electric Vehicles. IEEE 3rd KhPI Week on Advanced Technology, Kharkiv, 2022, 1-6 [http://doi.org/10.1109/KhPIWeek57572.2022.9916397].
  • [7] Halko S., Suprun O., Miroshnyk O.: Influence of temperature on energy performance indicators of hybrid solar panels using cylindrical cogeneration photovoltaic modules. IEEE 2nd KhPI Week on Advanced Technology, 2021, 21259624, 132–136 [http://doi.org/10.1109/KhPIWeek53812.2021.9569975].
  • [8] Hashemian A., Hosseini S. F.: An integrated fitting and fairing approach for object reconstruction using smooth NURBS curves and surfaces. Comput. Math. with Appl. 76(7), 2018, 1555-1575 [http://doi.org/10.1016/j.camwa.2018.07.007].
  • [9] Hashemian A., Imani B. M.: Surface fairness: a quality metric for aesthetic assessment of compliant automotive bodies. J. Eng. Des. 29(1-2), 2018, 41-64 [http://doi.org/10.1080/09544828.2018.1435853].
  • [10] Havrylenko Y., Cortez J. I., Kholodniak Y., Alieksieieva H., Garcia G. T.: Modelling of surfaces of engineering products on the basis of array of points. Teh. Vjesn. 27(6), 2020, 2034–2043 [http://doi.org/10.17559/TV-20190720081227].
  • [11] Havrylenko Y., Kholodniak Y., Halko S., Vershkov O., Bondarenko L., Suprun O., Miroshnyk O., Shchur T., Śrutek M., Gackowska M.: Interpolation with Specified Error of a Point Series Belonging to a Monotone Curve. Entropy 23(5), 2021, 493 [http://doi.org/10.3390/e23050493].
  • [12] Havrylenko Y., Kholodniak Y., Halko S., Vershkov O., Miroshnyk O., Suprun O., Dereza O., Shchur T., Śrutek M.: Representation of a Monotone Curve by a Contour with Regular Change in Curvature. Entropy 23(7), 2021, 923 [http://doi.org/10.3390/e23070923].
  • [13] Havrylenko Y., Kholodniak Y., Vershkov O., Naidysh A.: Development of the method for the formation of one-dimensional contours by the assigned interpolation accuracy. East.-Eur. J. Enterp. Technol. 1(4(91)), 2018, 76-82 [http://doi.org/10.15587/1729-4061.2018.123921].
  • [14] Hosseini S. F., Moetakef-Imani B.: Innovative approach to computer-aided design of horizontal axis wind turbine blades. J. Comput. Des. Eng. 4(2), 2017, 98-105 [http://doi.org/10.1016/j.jcde.2016.11.001].
  • [15] Karaiev O., Bondarenko L., Halko S., Miroshnyk O., Vershkov O., Karaieva T., Shshur T., Findura P., Pristavka M.: Mathematical modelling of the fruit-stone culture seeds calibration process using flat sieves. Acta Technologica Agriculturae 24(3), 2021, 119–123 [http://doi.org/10.2478/ata-2021-0020].
  • [16] Ke Y., Fan S., Zhu W., Li A., Liu F., Shi X.: Feature-based reverse modeling strategies. Comput. Aided Des. 38(5), 2006, 485-506.
  • [17] Lan P., Yu Z., Du L., Lu N.: Integration of non-uniform Rational B-splines geometry and rational absolute nodal coordinates formulation finite element analysis. Acta Mech. Solida Sin. 27(5), 2014, 486-495 [http://doi.org/10.1016/S0894-9166(14)60057-4].
  • [18] Lee T.-W., Park J. E.: Entropy and Turbulence Structure. Entropy 24, 2022, 11 [http://doi.org/10.3390/e24010011].
  • [19] Li H.: Geometric error control in the parabola-blending linear interpolator. J. Syst. Sci. Complex. 26(5), 2013, 777-798 [http://doi.org/10.1007/s11424-013-3178-y].
  • [20] Li W., Xu S., Zheng J., Zhao G.: Target curvature driven fairing algorithm for planar cubic B-spline curves. Computer Aided Geom. Des. 21(5), 2004, 499-513 [http://doi.org/10.1016/j.cagd.2004.03.004].
  • [21] Okaniwa Sh., Nasri A., Lin H., Abbas A., Kineri Yu., Maekawa T.: Uniform B-Spline Curve Interpolation with Prescribed Tangent and Curvature Vectors. IEEE Trans. Vis. Comput. Graph. 18(9), 2016, 1474-1487 [http://doi.org/10.1109/TVCG.2011.262].
  • [22] Park H., Kim K., Lee S-C.: A method for approximate NURBS curve compatibility based on multiple curve refitting. Comput. Aided Des. 32(4), 2000, 237-252 [http://doi.org/10.1016/S0010-4485(99)00088-3].
  • [23] Pazyi V., Miroshnyk O., Moroz O., Trunova I., Savchenko O., Halko S.: Analysis of technical condition diagnostics problems and monitoring of distribution electrical network modes from smart grid platform position. IEEE KhPI Week on Advanced Technology, Kharkiv, 2020, 57-60 [http://doi.org/10.1109/KhPIWeek51551.2020.9250080].
  • [24] Peng Y. H., Yin Z. W.: The algorithms for trimmed surfaces construction and tool path generation in reverse engineering. Comput. Ind. Eng. 54(3), 2008, 624-633 [http://doi.org/10.1016/j.cie.2007.09.012].
  • [25] Pérez-Arribas F., Pérez-Fernández, R.: A B-spline design model for propeller blades. Adv. Eng. Softw. 118, 2018, 35–44 [http://doi.org/10.1016/j.advengsoft.2018.01.005].
  • [26] Pérez-Arribas F., Trejo-Vargas I.: Computer-aided design of horizontal axis turbine blades. Renew. Energ. 44, 2012, 252-260 [http://doi.org/10.1016/j.renene.2012.01.100].
  • [27] Piegl L. A., Tiller W.: Reducing control points in surface interpolation. IEEE Comput. Graph. Appl. 20(5), 2000, 6698012, 70-75 [http://doi.org/10.1109/38.865883].
  • [28] Qawaqzeh M., Szafraniec A., Halko S., Miroshnyk O., Zharkov A.: Modelling of a household electricity supply system based on a wind power plant. Przegląd Elektrotechniczny 96, 2020 [http://doi.org/10.15199/48.2020.11.08].
  • [29] Robbin J. W., Salomon D. A.: Introduction to Differential Geometry. Springer Spektrum, Zürich 2022.
  • [30] Shen W., Wang G., Huang F.: Direction monotonicity of a rational Bézier curve. Appl. Math. J. Chin. Univ. 31(1), 2016, 1–20 [http://doi.org/10.1007/s11766-016-3399-7].
  • [31] Szafraniec A., Halko S., Miroshnyk O., Figura R., Zharkov A., Vershkov O.: Magnetic field parameters mathematical modelling of windelectric heater. Przeglad elektrotechniczny 97(8), 2021, 36-41 [http://doi.org/10.15199/48.2021.08.07].
  • [32] Tabor S., Lezhenkin O., Halko S., Miroshnyk O., Kovalyshyn S., Vershkov O., Hryhorenko O.: Mathematical simulation of separating work tool technological process. 22nd International Scientific Conference on Progress of Mechanical Engineering Supported by Information Technology – POLSITA 2019, Czajowice, 2019, 132 [http://doi.org/10.1051/e3sconf/201913201025].
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).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ea7640cb-f4de-4c01-a737-b1aff11f8573
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