Paper Info
Title
On the deviation of a parametric cubic spline interpolant from its data polygon
Abstract
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.
Year
DOI
Venue
2008
10.1016/j.cagd.2007.08.001
Computer Aided Geometric Design
Keywords
Field
DocType
cubic spline interpolation,best choice,common choice,data polygon,data point,parameterization,centripetal spline,periodic cubic spline interpolation,parametric cubic spline interpolant,parametric curve,derive bound,good curve,small deviation,cubic spline,oscillations
Polygon,Mathematical optimization,Curve orientation,Spline interpolation,Curve fitting,Smoothing spline,Flat spline,Affine-regular polygon,Simple polygon,Mathematics
Journal
Volume
Issue
ISSN
25
3
Computer Aided Geometric Design
Citations 
PageRank 
References 
13
1.68
2
Authors
1
Name
Order
Citations
PageRank
Michael S. Floater11333117.22