Three paths to rational curves with rational arc length
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10492503" target="_blank" >RIV/00216208:11320/24:10492503 - isvavai.cz</a>
Výsledek na webu
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=XHo21ysqDp" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=XHo21ysqDp</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.amc.2024.128842" target="_blank" >10.1016/j.amc.2024.128842</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Three paths to rational curves with rational arc length
Popis výsledku v původním jazyce
We solve the so far open problem of constructing all spatial rational curves with rational arc length functions. More precisely, we present three different methods for this construction. The first method adapts a recent approach of (Kalkan et al. 2022) to rational PH curves and requires solving a modestly sized system of linear equations. The second constructs the curve by imposing zero -residue conditions, thus extending ideas of previous papers by (Farouki and Sakkalis 2019) and the authors themselves (Schr & ouml;cker and & Scaron;& iacute;r 2023). The third method generalizes the dual approach of (Pottmann 1995) from planar to spatial curves. The three methods share the same quaternion based representation in which not only the PH curve but also its arc length function are compactly expressed. We also present a new proof based on the quaternion polynomial factorization theory of the well known characterization of the Pythagorean quadruples.
Název v anglickém jazyce
Three paths to rational curves with rational arc length
Popis výsledku anglicky
We solve the so far open problem of constructing all spatial rational curves with rational arc length functions. More precisely, we present three different methods for this construction. The first method adapts a recent approach of (Kalkan et al. 2022) to rational PH curves and requires solving a modestly sized system of linear equations. The second constructs the curve by imposing zero -residue conditions, thus extending ideas of previous papers by (Farouki and Sakkalis 2019) and the authors themselves (Schr & ouml;cker and & Scaron;& iacute;r 2023). The third method generalizes the dual approach of (Pottmann 1995) from planar to spatial curves. The three methods share the same quaternion based representation in which not only the PH curve but also its arc length function are compactly expressed. We also present a new proof based on the quaternion polynomial factorization theory of the well known characterization of the Pythagorean quadruples.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10102 - Applied mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2024
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Applied Mathematics and Computation
ISSN
0096-3003
e-ISSN
1873-5649
Svazek periodika
478
Číslo periodika v rámci svazku
1 October 2024
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
13
Strana od-do
128842
Kód UT WoS článku
001246609500001
EID výsledku v databázi Scopus
2-s2.0-85193906087