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.

• Type: Conference
• Year: 2006
• Where: GMP
• Authors: Martin Aigner, Zbynek Sír, Bert Jüttler
• Keywords: Evolution Process, GMP 2006, PH Spline Curves, Time–like Parameter T