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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 11, Pages 1962–1971 (Mi zvmmf378)  
This article is cited in 5 scientific papers (total in 5 papers)

Bernstein polynomials and composite Bézier curves

M. I. Grigor'eva, V. N. Malozemova, A. N. Sergeevb

a Faculty of Mathematics and Mechanics, St. Petersburg State University, Universitetskii pr. 28, Petrodvorets, 198504, Russia
b Engineering and Economical Academy, ul. Marata 27, St. Petersburg, 191002, Russia
Full-text PDF (866 kB) Citations (5)
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Abstract: Analytical principles of the theory of Bézier curves are presented. A new approach to the construction of composite Bézier curves of prescribed smoothness both on a plane and in a multidimensional Euclidean space is proposed.
Key words: Bernstein polynomials, constructing Bézier curves on the basis of Bernstein polynomials, geometric design.
Received: 27.04.2006
Revised: 19.06.2006
English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 11, Pages 1872–1881
DOI: https://doi.org/10.1134/S0965542506110042
Bibliographic databases:
Document Type: Article
UDC: 519.652.3
Language: Russian
Citation: M. I. Grigor'ev, V. N. Malozemov, A. N. Sergeev, “Bernstein polynomials and composite Bézier curves”, Zh. Vychisl. Mat. Mat. Fiz., 46:11 (2006), 1962–1971; Comput. Math. Math. Phys., 46:11 (2006), 1872–1881
Citation in format AMSBIB
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\by M.~I.~Grigor'ev, V.~N.~Malozemov, A.~N.~Sergeev
\paper Bernstein polynomials and composite B\'ezier curves
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 11
\pages 1962--1971
\mathnet{http://mi.mathnet.ru/zvmmf378}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2304069}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 11
\pages 1872--1881
\crossref{https://doi.org/10.1134/S0965542506110042}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33845305509}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf378
  • https://www.mathnet.ru/eng/zvmmf/v46/i11/p1962
    • This publication is cited in the following 5 articles:
    1. Vladimir Kostyukov, Igor Evdokimov, Vladislav Gissov, Lecture Notes in Computer Science, 14214, Interactive Collaborative Robotics, 2023, 322  crossref
    2. V. A. Kostjukov, M. Y. Medvedev, V. Kh. Pshikhopov, “Algorithms for Planning Smoothed Individual Trajectories of Ground Robots”, Mehatronika, avtomatizaciâ, upravlenie, 23:11 (2022), 585  crossref
    3. A. S. Ilinskii, I. S. Polyanskii, D. E. Stepanov, “O skhodimosti baritsentricheskogo metoda v reshenii vnutrennikh zadach Dirikhle i Neimana v R2 dlya uravneniya Gelmgoltsa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:1 (2021), 3–18  mathnet  crossref
    4. D. L. Vinokurskii, K. Yu. Ganshin, O. S. Mezentseva, F. V. Samoilov, “Planirovanie traektorii gruppy bespilotnykh letatelnykhapparatov s ispolzovaniem godografa Pifagora i sostavnykh krivykh Bernshteina-Beze na ploskosti”, Vestnik KRAUNTs. Fiz.-mat. nauki, 31:2 (2020), 70–78  mathnet  crossref
    5. Mohammad Asif Zaman, Shuvro Chowdhury, “Modified Bézier Curves with Shape-Preserving Characteristics Using Differential Evolution Optimization Algorithm”, Advances in Numerical Analysis, 2013 (2013), 1  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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