Interpolation Scheme for Planar Cubic G super(2) Spline Curves

In this paper a method for interpolating planar data points by cubic G super(2) splines is presented. A spline is composed of polynomial segments that interpolate two data points, tangent directions and curvatures at these points. Necessary and sufficient, purely geometric conditions for the existen...

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Bibliographic Details
Published in:Acta applicandae mathematicae 2011-02, Vol.113 (2), p.129-143
Main Author: Krajnc, Marjeta
Format: Article
Language:English
Subjects:
Approximation
Curvature
Data points
Derivatives
Interpolation
Mathematical analysis
Segments
Splines
Online Access:Get full text
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Summary:In this paper a method for interpolating planar data points by cubic G super(2) splines is presented. A spline is composed of polynomial segments that interpolate two data points, tangent directions and curvatures at these points. Necessary and sufficient, purely geometric conditions for the existence of such a polynomial interpolant are derived. The obtained results are extended to the case when the derivative directions and curvatures are not prescribed as data, but are obtained by some local approximation or implied by shape requirements. As a result, the G super(2) spline is constructed entirely locally.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-010-9589-z