Approximate Reconstructions of Perturbed Rational Planar Cubics

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Approximate Reconstructions of Perturbed Rational Planar Cubics

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Approximate Reconstructions of Perturbed Rational Planar Cubics

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/LO1506" target="_blank" >LO1506: Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnost</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Advanced Methods for Geometric Modeling and Numerical Simulation

ISBN

978-3-030-27330-9

ISSN

2281-518X

e-ISSN

2281-5198

Počet stran výsledku

19

Strana od-do

23-41

Název nakladatele

Springer,

Místo vydání

Cham

Místo konání akce

Řím

Datum konání akce

22. 1. 2018

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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