Optimal interpolation with spatial rational Pythagorean hodograph curves

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10474944" target="_blank" >RIV/00216208:11320/23:10474944 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=s4-wSVoOaJ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=s4-wSVoOaJ</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.amc.2023.128214" target="_blank" >10.1016/j.amc.2023.128214</a>

Result language
angličtina
Original language name
Optimal interpolation with spatial rational Pythagorean hodograph curves
Original language description
Using a residuum approach, we provide a complete description of the space of the rational spatial curves of given tangent directions. The rational Pythagorean hodograph curves are obtained as a special case when the norm of the direction field is a perfect square. The basis for the curve space is given explicitly. Consequently a number of interpolation problems (G1, C1, C2, C1/G2) in this space become linear, cusp avoidance can be encoded by linear inequalities, and optimization problems like minimal energy or optimal length are quadratic and can be solved efficiently via quadratic programming. We outline the interpolation/optimization strategy and demonstrate it on several examples.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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