Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics
We present an algorithm for C1 Hermite interpolation using Möbius transformations of planar polynomial Pythagoreanhodograph (PH) cubics. In general, with PH cubics, we cannot solve C1 Hermite interpolation problems, since their lack of parameters makes the problems overdetermined. In this paper, we...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/560246 |
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| Summary: | We present an algorithm for C1 Hermite interpolation
using Möbius transformations of planar polynomial Pythagoreanhodograph
(PH) cubics. In general, with PH cubics, we cannot
solve C1 Hermite interpolation problems, since their lack of parameters
makes the problems overdetermined. In this paper, we
show that, for each Möbius transformation, we can introduce an
extra parameter determined by the transformation, with which we
can reduce them to the problems determining PH cubics in the
complex plane ℂ. Möbius transformations preserve the PH property
of PH curves and are biholomorphic. Thus the interpolants
obtained by this algorithm are also PH and preserve the topology
of PH cubics. We present a condition to be met by a Hermite
dataset, in order for the corresponding interpolant to be simple or
to be a loop. We demonstrate the improved stability of these new
interpolants compared with PH quintics. |
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| ISSN: | 1085-3375 1687-0409 |