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Least-squares approximation by Pythagorean hodograph spline curves via an evolution process. (English) Zbl 1160.68603

Kim, Myung-Soo (ed.) et al., Geometric modeling and processing – GMP 2006. 4th international conference, Pittsburgh, PA, USA, July 26–28, 2006. Proceedings. Berlin: Springer (ISBN 3-540-36711-X/pbk). Lecture Notes in Computer Science 4077, 45-58 (2006).
Summary: 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.
For the entire collection see [Zbl 1113.68008].

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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