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Mean Distance from a Curve to Its Control Polygon

  • Conference paper
Mathematical Methods for Curves and Surfaces (MMCS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5862))

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Abstract

The mean distance between a curve and its control polygon is bounded in terms of the norm of second order differences of the control points. We also analyze the distance of a rational curve to its control polygon and suggest a choice of the weight for obtaining rational curves much closer to its control polygon than Bézier curves.

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References

  1. Carnicer, J.M., Floater, M.S., Peña, J.M.: The distance of a curve to its control polygon. Numerical methods of approximation theory and computer aided geometric design. RACSAM Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 96, 175–183 (2002)

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Author information

Authors and Affiliations

  1. Dept. Applied Mathematics/IUMA, University of Zaragoza, 50009, Zaragoza, Spain

    Jesús Carnicer

  2. Dept. Applied Mathematics, Escuela Politécnica Universitaria de Teruel, University of Zaragoza, 44003, Teruel, Spain

    Jorge Delgado

Authors
  1. Jesús Carnicer
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  2. Jorge Delgado
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Oslo, Norway

    Morten Dæhlen  & Tom Lyche  & 

  2. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Norway

    Michael Floater

  3. INSA de Rennes, Rennes, France

    Jean-Louis Merrien

  4. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Oslo, Norway

    Knut Mørken

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

    Larry L. Schumaker

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© 2010 Springer-Verlag Berlin Heidelberg

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Carnicer, J., Delgado, J. (2010). Mean Distance from a Curve to Its Control Polygon. In: Dæhlen, M., Floater, M., Lyche, T., Merrien, JL., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2008. Lecture Notes in Computer Science, vol 5862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11620-9_7

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  • DOI: https://doi.org/10.1007/978-3-642-11620-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11619-3

  • Online ISBN: 978-3-642-11620-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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