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Efficient Piecewise Linear Approximation of Bézier Curves with Improved Sharp Error Bound

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Geometric Modeling and Processing - GMP 2006 (GMP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4077))

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Abstract

This paper presents an efficient algorithm for piecewise linear approximation of Bézier curves with improved sharp error bound. Given a Bézier curve of arbitrary degree, an approximation polygon having the same number of vertices as that of the control polygon is obtained through efficient local refinement of the initial control vertices. The approximation produces improved error bound compared with several existing solutions. With the explicit sharp error bound, it is also possible for prior estimation of necessary subdivisions to meet a pre-defined tolerance. The approximation can also be locally and adaptively refined for reducing the number of vertices of the piecewise linear approximation while meeting the required tolerance.

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Author information

Authors and Affiliations

  1. Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong (SAR), China

    Weiyin Ma & Renjiang Zhang

  2. College of Science, On leave from China Jiliang University, Hangzhou, 310018, China

    Renjiang Zhang

Authors
  1. Weiyin Ma
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  2. Renjiang Zhang
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Editor information

Editors and Affiliations

  1. Seoul National University, Korea

    Myung-Soo Kim

  2. Carnegie Mellon University, Pittsburgh, PA, USA

    Kenji Shimada

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© 2006 Springer-Verlag Berlin Heidelberg

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Ma, W., Zhang, R. (2006). Efficient Piecewise Linear Approximation of Bézier Curves with Improved Sharp Error Bound. In: Kim, MS., Shimada, K. (eds) Geometric Modeling and Processing - GMP 2006. GMP 2006. Lecture Notes in Computer Science, vol 4077. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11802914_12

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  • DOI: https://doi.org/10.1007/11802914_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36711-6

  • Online ISBN: 978-3-540-36865-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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