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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2010, Volume 50, Number 8, Pages 1347–1356 (Mi zvmmf4915)  
This article is cited in 8 scientific papers (total in 8 papers)

Approximation of plane curves by circular arcs

I. Kh. Sabitov, A. V. Slovesnov

Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992 Russia
Full-text PDF (232 kB) Citations (8)
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Abstract: A method is proposed for approximating plane curves by circular arcs with length preservation. It is proved that, under certain rather mild constraints, any $C^3$-smooth curve (open or closed, possibly, with self-intersections) can be approximated by a $C^1$-smooth curve consisting of smoothly joined circular arcs. The approximation passes through interpolation nodes where it is tangent to the original curve, with the arc lengths between the nodes being preserved. The error of the approximation is estimated, and numerical examples are presented.
Key words: approximation of plane curves, circular arcs, curve length preservation, interpolation, error estimate.
Received: 22.12.2009
English version:
Computational Mathematics and Mathematical Physics, 2010, Volume 50, Issue 8, Pages 1279–1288
DOI: https://doi.org/10.1134/S0965542510080014
Bibliographic databases:
Document Type: Article
UDC: 519.674
Language: Russian
Citation: I. Kh. Sabitov, A. V. Slovesnov, “Approximation of plane curves by circular arcs”, Zh. Vychisl. Mat. Mat. Fiz., 50:8 (2010), 1347–1356; Comput. Math. Math. Phys., 50:8 (2010), 1279–1288
Citation in format AMSBIB
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    2. Lucas Silva, Alfredo Gay Neto, “Geometry reconstruction based on arc splines with application to wheel-rail contact simulation”, EC, 40:7/8 (2023), 1889  crossref
    3. Mengyu Fu, Kiril Solovey, Oren Salzman, Ron Alterovitz, “Toward certifiable optimal motion planning for medical steerable needles”, The International Journal of Robotics Research, 42:10 (2023), 798  crossref
    4. Rusanovskiy S.A., Khudyakov M.P., Cherenkov I N., “Modelling Technique of the Opening'S Bevel in Underwater Shipbuilding Hulls Objects For Welding Flanges”, Mar. Intellect. Technol., 2020, no. 1, 1, 28–37  crossref  isi
    5. A. V. Slovesnov, “O priblizhenii ploskikh krivykh liniyami vtorogo poryadka”, Sib. elektron. matem. izv., 15 (2018), 1576–1594  mathnet  crossref
    6. A. I. Kurnosenko, “On the length preserving approximation of plane curves by circular arcs”, Comput. Math. Math. Phys., 57:4 (2017), 590–606  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Kurnosenko A.I., “Biarcs and Bilens”, Comput. Aided Geom. Des., 30:3 (2013), 310–330  crossref  mathscinet  zmath  isi  elib  scopus
    8. Zhao J., Xu M., Fu W., “Space Arc Trajectory Planning Based on Pci Motion Control System”, Automatic Manufacturing Systems II, Pts 1 and 2, Advanced Materials Research, 542-543, eds. Tan R., Sun J., Liu Q., Trans Tech Publications Ltd, 2012, 573–577  crossref  isi  scopus
    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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