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2012 Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics
Sunhong Lee, Hyun Chol Lee, Mi Ran Lee, Seungpil Jeong, Gwang-Il Kim
Abstr. Appl. Anal. 2012(SI13): 1-15 (2012). DOI: 10.1155/2012/560246


We present an algorithm for C1 Hermite interpolationusing Möbius transformations of planar polynomial Pythagoreanhodograph(PH) cubics. In general, with PH cubics, we cannotsolve C1 Hermite interpolation problems, since their lack of parametersmakes the problems overdetermined. In this paper, weshow that, for each Möbius transformation, we can introduce anextra parameter determined by the transformation, with which wecan reduce them to the problems determining PH cubics in thecomplex plane . Möbius transformations preserve the PH propertyof PH curves and are biholomorphic. Thus the interpolantsobtained by this algorithm are also PH and preserve the topologyof PH cubics. We present a condition to be met by a Hermitedataset, in order for the corresponding interpolant to be simple orto be a loop. We demonstrate the improved stability of these newinterpolants compared with PH quintics.


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Sunhong Lee. Hyun Chol Lee. Mi Ran Lee. Seungpil Jeong. Gwang-Il Kim. "Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics." Abstr. Appl. Anal. 2012 (SI13) 1 - 15, 2012.


Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1242.65034
MathSciNet: MR2914885
Digital Object Identifier: 10.1155/2012/560246

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI13 • 2012
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