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Improving Angular Speed Uniformity by C 1 Piecewise Reparameterization

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Automated Deduction in Geometry (ADG 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7993))

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Abstract

We show how to compute a C 1 piecewise-rational reparameterization that closely approximates to the arc-angle parameterization of any plane curve by C 1 piecewise Möbius transformation. By making use of the information provided by the first derivative of the angular speed function, the unit interval is partitioned such that the obtained reparameterization has high uniformity and continuous angular speed. An iteration process is used to refine the interval partition. Experimental results are presented to show the performance of the proposed method and the geometric behavior of the computed reparameterizations.

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Author information

Authors and Affiliations

  1. LMIB – School of Mathematics and Systems Science, Beihang University, Beijing, 100191, China

    Jing Yang

  2. Laboratoire d’Informatique de Paris 6, CNRS – Université Pierre et Marie Curie, 4 Place Jussieu, BP 169, 75252, Paris cedex 05, France

    Dongming Wang

  3. Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC, 27695, USA

    Hoon Hong

Authors
  1. Jing Yang
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  2. Dongming Wang
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  3. Hoon Hong
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Editor information

Editors and Affiliations

  1. Department of Computer Science, 1006, Laboratory of Advanced Research, University of Tsukuba, 305-8573, Tsukuba, Japan

    Tetsuo Ida

  2. School of Informatics, Informatics Forum, University of Edinburgh, 10 Crichton Street, EH8 9AB, Edinburgh, UK

    Jacques Fleuriot

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Yang, J., Wang, D., Hong, H. (2013). Improving Angular Speed Uniformity by C 1 Piecewise Reparameterization. In: Ida, T., Fleuriot, J. (eds) Automated Deduction in Geometry. ADG 2012. Lecture Notes in Computer Science(), vol 7993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40672-0_3

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  • DOI: https://doi.org/10.1007/978-3-642-40672-0_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40671-3

  • Online ISBN: 978-3-642-40672-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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