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

  • M. Aigner
  • Z. Šír
  • B. Jüttler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4077)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • M. Aigner
    • 1
  • Z. Šír
    • 1
  • B. Jüttler
    • 1
  1. 1.Johannes Kepler University LinzAustria

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