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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Least–Squares Approximation by Pythagorean Hodograph Spline Curves Via an Evolution Process
verfasst von : M. Aigner, Z. Šír, B. Jüttler
Erschienen in: Geometric Modeling and Processing - GMP 2006
Verlag: Springer Berlin Heidelberg
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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.