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Fundam. Prikl. Mat., 2001, Volume 7, Issue 2, Pages 441–463 (Mi fpm569)  

This article is cited in 5 scientific papers (total in 5 papers)

Interpolation properties of planar spiral curves

A. I. Kurnosenko

Institute for High Energy Physics

Abstract: Some inequalities on the planar curves termed spirals (due to monotonous curvature function) are considered. For a spiral represented as a set of interpolation nodes, a region covering the parent curve is constructed. The width of the region provides an estimate of curve definiteness by the given discrete representation, this estimate being independent of any interpolation method. A similar problem is set up for any smooth curve, assuming that vertices are distanced “sufficiently far away” from one another. The problem originates from and can be applied to the practice of tolerance control in industry.

Full text: PDF file (1062 kB)

Bibliographic databases:
UDC: 514.1
Received: 01.02.1998

Citation: A. I. Kurnosenko, “Interpolation properties of planar spiral curves”, Fundam. Prikl. Mat., 7:2 (2001), 441–463

Citation in format AMSBIB
\Bibitem{Kur01}
\by A.~I.~Kurnosenko
\paper Interpolation properties of planar spiral curves
\jour Fundam. Prikl. Mat.
\yr 2001
\vol 7
\issue 2
\pages 441--463
\mathnet{http://mi.mathnet.ru/fpm569}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1866467}
\zmath{https://zbmath.org/?q=an:1054.53004}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Kurnosenko, “General properties of planar spiral curves”, J. Math. Sci. (N. Y.), 161:3 (2009), 405–418  mathnet  crossref  zmath
    2. A. I. Kurnosenko, “Short spirals”, J. Math. Sci. (N. Y.), 175:5 (2011), 517–522  mathnet  crossref
    3. I. Kh. Sabitov, A. V. Slovesnov, “Approximation of plane curves by circular arcs”, Comput. Math. Math. Phys., 50:8 (2010), 1279–1288  mathnet  crossref  mathscinet  adsnasa  isi
    4. Voronov S.V., “Image registration parameters prediction between local fragments centers of images in case of unknown model of spatial distortions”, Radiotekhnika, 2012, no. 9, 50–55  elib
    5. Kurnosenko A.I., “Biarcs and Bilens”, Comput. Aided Geom. Des., 30:3 (2013), 310–330  crossref  mathscinet  zmath  isi  elib
  • Фундаментальная и прикладная математика
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