Three paths to rational curves with rational arc length
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Three paths to rational curves with rational arc length
Original language description
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.
Czech name
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Czech description
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Classification
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
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applied Mathematics and Computation
ISSN
0096-3003
e-ISSN
1873-5649
Volume of the periodical
478
Issue of the periodical within the volume
1 October 2024
Country of publishing house
US - UNITED STATES
Number of pages
13
Pages from-to
128842
UT code for WoS article
001246609500001
EID of the result in the Scopus database
2-s2.0-85193906087