Approximate Reconstructions of Perturbed Rational Planar Cubics

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F19%3A43955845" target="_blank" >RIV/49777513:23520/19:43955845 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/chapter/10.1007/978-3-030-27331-6_2" target="_blank" >https://link.springer.com/chapter/10.1007/978-3-030-27331-6_2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-27331-6_2" target="_blank" >10.1007/978-3-030-27331-6_2</a>

Result language
angličtina
Original language name
Approximate Reconstructions of Perturbed Rational Planar Cubics
Original language description
This paper is devoted to a problem from geometric modelling and related applications when exact symbolic computations are sometimes used also on objects given inexactly, i.e., when it is not adequately respected that numerical or input errors may significantly influence fundamental properties of considered algebraic varieties, including e.g. their rationality. We formulate a simple algorithm for an approximation of a non-rational planar cubic which is assumed to be a perturbation of some unknown rational planar cubic. The input curve is given by a perturbed polynomial or by perturbed points sampled from the original curve. The algorithm consists of two main parts. First, we suggest geometric methods for the estimation of a singular point of the original curve. Then we select from the six-dimensional subspace of all rational cubics with a given singular point a suitable one that may also satisfy some further criteria. The designed method is presented on several commented examples.
Czech name
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Czech description
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Project
<a href="/en/project/LO1506" target="_blank" >LO1506: Sustainability support of the centre NTIS - New Technologies for the Information Society</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Advanced Methods for Geometric Modeling and Numerical Simulation
ISBN
978-3-030-27330-9
ISSN
2281-518X
e-ISSN
2281-5198
Number of pages
19
Pages from-to
23-41
Publisher name
Springer,
Place of publication
Cham
Event location
Řím
Event date
Jan 22, 2018
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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