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International Conference on Curves and Surfaces

Curves and Surfaces 2010: Curves and Surfaces pp 270–279Cite as

Shape Curvatures of Planar Rational Spirals

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6920))

Abstract

We discuss geometric conditions for a planar rational curve to be a spiral. The main used tool for characterizing a spiral is the so-called shape curvature which is a differential-geometric invariant of planar curves with respect to the group of orientation-preserving similarities. Different formulas for computation of shape curvature are given. Rational curves representing spirals and circular arcs possess a natural description in terms of the shape curvature. This description is applied to a complete classification of quadratic Bézier spirals.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Konstantin Preslavsky University, 115 Universitetska Str., 9712, Shumen, Bulgaria

    Georgi H. Georgiev

Authors
  1. Georgi H. Georgiev
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Editor information

Editors and Affiliations

  1. INRIA Sophia-Antipolis, 2004 Route des Lucioles, BP 93, 06902, Sophia Antipolis, France

    Jean-Daniel Boissonnat

  2. Laboratoire LJK, University Joseph Fourier, BP 53, 38420, Grenoble Cedex 9, France

    Patrick Chenin

  3. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4, Place Jussieu, 75005, Paris, France

    Albert Cohen

  4. Laboratoire de Mathématiques, INSA Rouen, Avenue de l’Université, 76800, St. Etienne du Rouvray, France

    Christian Gout

  5. University of Oslo, DMA, Blindern, P.O.Box 1053, 0316, Oslo, Norway

    Tom Lyche

  6. Laboratoire LJK, Université Joseph Fourier, BP 53, 38041, Grenoble Cedex 9, France

    Marie-Laurence Mazure

  7. Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA

    Larry Schumaker

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© 2012 Springer-Verlag Berlin Heidelberg

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Georgiev, G.H. (2012). Shape Curvatures of Planar Rational Spirals. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_17

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  • DOI: https://doi.org/10.1007/978-3-642-27413-8_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27412-1

  • Online ISBN: 978-3-642-27413-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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