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On interpolation by Planar cubic $ G^2$ pythagorean-hodograph spline curves


Authors: Gasper Jaklic, Jernej Kozak, Marjeta Krajnc, Vito Vitrih and Emil Zagar
Journal: Math. Comp. 79 (2010), 305-326
MSC (2000): Primary 41A05, 41A15, 41A25, 41A30, 65D05, 65D07, 65D17; Secondary 65D10
DOI: https://doi.org/10.1090/S0025-5718-09-02298-4
Published electronically: July 29, 2009
MathSciNet review: 2552228
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, the geometric interpolation of planar data points and boundary tangent directions by a cubic $ G^2$ Pythagorean-hodograph (PH) spline curve is studied. It is shown that such an interpolant exists under some natural assumptions on the data. The construction of the spline is based upon the solution of a tridiagonal system of nonlinear equations. The asymptotic approximation order 4 is confirmed.


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Additional Information

Gasper Jaklic
Affiliation: FMF, University of Ljubljana, Slovenia and PINT, University of Primorska, Koper, Slovenia
Address at time of publication: Jadranska 19, 1000 Ljubljana, Slovenia
Email: gasper.jaklic@fmf.uni-lj.si

Jernej Kozak
Affiliation: FMF and IMFM, University of Ljubljana, Slovenia
Address at time of publication: Jadranska 19, 1000 Ljubljana, Slovenia
Email: jernej.kozak@fmf.uni-lj.si

Marjeta Krajnc
Affiliation: IMFM, University of Ljubljana, Slovenia
Address at time of publication: Jadranska 19, 1000 Ljubljana, Slovenia
Email: marjetka.krajnc@fmf.uni-lj.si

Vito Vitrih
Affiliation: PINT, University of Primorska, Koper, Slovenia
Address at time of publication: Muzejski trg 2, 6000 Koper, Slovenia
Email: vito.vitrih@upr.si

Emil Zagar
Affiliation: FMF and IMFM, University of Ljubljana, Slovenia
Address at time of publication: Jadranska 19, 1000 Ljubljana, Slovenia
Email: emil.zagar@fmf.uni-lj.si

DOI: https://doi.org/10.1090/S0025-5718-09-02298-4
Received by editor(s): June 6, 2008
Received by editor(s) in revised form: March 25, 2009
Published electronically: July 29, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.