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Least–Squares Approximation by Pythagorean Hodograph Spline Curves Via an Evolution Process

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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

The problem of approximating a given set of data points by splines composed of Pythagorean Hodograph (PH) curves is addressed. In order to solve this highly non-linear problem, we formulate an evolution process within the family of PH spline curves. This process generates a one–parameter family of curves which depends on a time–like parameter t. The best approximant is shown to be a stationary point of this evolution. The evolution process – which is shown to be related to the Gauss–Newton method – is described by a differential equation, which is solved by Euler’s method.

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Author information

Authors and Affiliations

  1. Johannes Kepler University Linz, Austria

    M. Aigner, Z. Šír & B. Jüttler

Authors
  1. M. Aigner
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  2. Z. Šír
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  3. B. Jüttler
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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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Aigner, M., Šír, Z., Jüttler, B. (2006). Least–Squares Approximation by Pythagorean Hodograph Spline Curves Via an Evolution Process. 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_4

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  • DOI: https://doi.org/10.1007/11802914_4

  • 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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