Planar C^1 Hermite interpolation with uniform and non-uniform TC-biarcs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F13%3A43916872" target="_blank" >RIV/49777513:23520/13:43916872 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.cagd.2012.07.003" target="_blank" >http://dx.doi.org/10.1016/j.cagd.2012.07.003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cagd.2012.07.003" target="_blank" >10.1016/j.cagd.2012.07.003</a>
Alternative languages
Result language
angličtina
Original language name
Planar C^1 Hermite interpolation with uniform and non-uniform TC-biarcs
Original language description
Pythagorean hodograph curves (shortly PH curves), introduced in Farouki and Sakkalis (1990), form an important subclass of polynomial parametric curves and currently represent standard objects in geometric modelling. In this paper, we focus on Tschirnhausen cubic as the only one Pythagorean hodograph cubic and we study planar C^1 Hermite interpolation with two arcs of Tschirnhausen cubic joined with C^1 continuity (the so-called TC-biarc). We extend results presented in Farouki and Peters (1996) in several ways. We study an asymptotical behaviour of the conversion of an arbitrary planar curve with well defined tangent vectors everywhere to a C^1 PH cubic spline curve and we prove that the approximation order is 3. Further, we analyze the shape of TC-biarcs and provide a sufficient condition for input data guaranteeing TC-biarc without local and pairwise self-intersections. Finally, we generalize the basic uniform method to the non-uniform case, which introduces a free shape parameter,
Czech name
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Czech description
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Classification
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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Result continuities
Project
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Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
COMPUTER AIDED GEOMETRIC DESIGN
ISSN
0167-8396
e-ISSN
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Volume of the periodical
30
Issue of the periodical within the volume
1
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
20
Pages from-to
58-77
UT code for WoS article
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EID of the result in the Scopus database
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