C2 Hermite interpolation by Pythagorean hodograph space curves

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F07%3A00005642" target="_blank" >RIV/00216208:11320/07:00005642 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
C2 Hermite interpolation by Pythagorean hodograph space curves
Original language description
We solve the problem of C2 Hermite interpolation by Pythagorean Hodograph (PH) space curves. More precisely, for any set of C2 space boundary data (two points with associated Żrst and second derivatives) we construct a four{dimensional family of PH interpolants of degree 9 and introduce a symetrically invariant parameterization of this family. This parameterization is used to identify a particular solution, which has the following properties. Firstly, it preserves planarity, i.e., the interpolant to planar data is a planar PH curve. Secondly, it has the best possible approximation order 6. Thirdly, it is symmetric in the sense that the interpolant of the reversed' set of boundary data is simply the reversed' original interpolant. This particular PH interpolant is exploited for designing algorithms for converting (possibly piecewise) analytical curves into a piecewise PH curve of degree 9 which is globally C2.
Czech name
C2 Hermitovská interpolace Pythagorejskými křivkami
Czech description
V tomto článku plně řešíme problem C2 interpolace PH křivkami.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2007
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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