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2006
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Least-Squares Approximation by Pythagorean Hodograph Spline Curves Via an Evolution Process

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Least-Squares Approximation by Pythagorean Hodograph Spline Curves Via an Evolution Process
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.
Martin Aigner, Zbynek Sír, Bert Jüttle
Added 11 Jun 2010
Updated 11 Jun 2010
Type Conference
Year 2006
Where GMP
Authors Martin Aigner, Zbynek Sír, Bert Jüttler
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