Partial fraction decomposition for rational Pythagorean hodograph curves

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10474945" target="_blank" >RIV/00216208:11320/23:10474945 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=z93.2a2B7k" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=z93.2a2B7k</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cam.2023.115196" target="_blank" >10.1016/j.cam.2023.115196</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Partial fraction decomposition for rational Pythagorean hodograph curves

Popis výsledku v původním jazyce

All rational parametric curves with prescribed polynomial tangent direction form a vector space. Via tangent directions with rational norm, this includes the important case of rational Pythagorean hodograph curves. We study vector subspaces defined by fixing the denominator polynomial and describe the construction of canonical bases for them. We also show (as an analogy to the fraction decomposition of rational functions) that any element of the vector space can be obtained as a finite sum of curves with single roots at the denominator. Our results give insight into the structure of these spaces, clarify the role of their polynomial and truly rational (non-polynomial) curves, and suggest applications to interpolation problems. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Název v anglickém jazyce

Partial fraction decomposition for rational Pythagorean hodograph curves

Popis výsledku anglicky

All rational parametric curves with prescribed polynomial tangent direction form a vector space. Via tangent directions with rational norm, this includes the important case of rational Pythagorean hodograph curves. We study vector subspaces defined by fixing the denominator polynomial and describe the construction of canonical bases for them. We also show (as an analogy to the fraction decomposition of rational functions) that any element of the vector space can be obtained as a finite sum of curves with single roots at the denominator. Our results give insight into the structure of these spaces, clarify the role of their polynomial and truly rational (non-polynomial) curves, and suggest applications to interpolation problems. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Journal of Computational and Applied Mathematics

ISSN

0377-0427

e-ISSN

1879-1778

Svazek periodika

428

Číslo periodika v rámci svazku

15 August 2023

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

13

Strana od-do

115196

Kód UT WoS článku

000955892600001

EID výsledku v databázi Scopus

2-s2.0-85150028013