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CAGD
2008

On the deviation of a parametric cubic spline interpolant from its data polygon

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On the deviation of a parametric cubic spline interpolant from its data polygon
When fitting a parametric curve through a sequence of points, it is important in applications that the curve should not exhibit unwanted oscillations. In this paper we take the view that a good curve is one that does not deviate too far from the data polygon: the polygon formed by the data points. From this point of view, we study periodic cubic spline interpolation and derive bounds on the deviation with respect to three common choices of parameterization: uniform, chordal, and centripetal. If one wants small deviation, the centripetal spline is arguably the best choice among the three.
Michael S. Floater
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CAGD
Authors Michael S. Floater
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