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Title:Arc length preserving G2 Hermite interpolation of circular arcs
Authors:ID Žagar, Emil (Author)
Files:.pdf PDF - Presentation file, download (558,15 KB)
MD5: B29F95158AD246BA9A800A71234DE1BF
 
URL URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0377042722006069
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
Abstract:In this paper, the problem of interpolation of two points, two corresponding tangent directions and curvatures, and the arc length sampled from a circular arc (circular arc data) is considered. Planar Pythagorean–hodograph (PH) curves of degree seven are used since they possess enough free parameters and are capable of interpolating the arc length in an easy way. A general approach using the complex representation of PH curves is presented first and the strong dependence of the solution on the general data is demonstrated. For circular arc data, a complicated system of nonlinear equations is reduced to a numerical solution of only one algebraic equation of degree 6 and a detailed analysis of the existence of admissible solutions is provided. In the case of several solutions, some criteria for selecting the most appropriate one are described and an asymptotic analysis is given. Numerical examples are included which confirm theoretical results.
Keywords:geometric interpolation, circular arc, arc length, Pythagorean-hodograph curve, solution selection
Publication status:Published
Publication version:Version of Record
Publication date:01.05.2023
Year of publishing:2023
Number of pages:art. 115008 (12 str.)
Numbering:Vol. 424
PID:20.500.12556/DiRROS-18487 New window
UDC:519.651
ISSN on article:0377-0427
DOI:10.1016/j.cam.2022.115008 New window
COBISS.SI-ID:134609923 New window
Note:
Publication date in DiRROS:20.03.2024
Views:611
Downloads:283
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ŽAGAR, Emil, 2023, Arc length preserving G2 Hermite interpolation of circular arcs. Journal of computational and applied mathematics [online]. 2023. Vol. 424. [Accessed 7 April 2025]. DOI 10.1016/j.cam.2022.115008. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=18487
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Record is a part of a journal

Title:Journal of computational and applied mathematics
Shortened title:J. comput. appl. math.
Publisher:Elsevier
ISSN:0377-0427
COBISS.SI-ID:27496960 New window

Document is financed by a project

Funder:ARRS - Slovenian Research Agency
Project number:P1-0288
Name:Algebra in njena uporaba
Funder:ARRS - Slovenian Research Agency
Project number:J1-9104
Name:Analiza, geometrija in parcialne diferencialne enačbe
Funder:ARRS - Slovenian Research Agency
Project number:N1-0137
Name:Nelinearni Valovi in Spektralna Teorija
Funder:ARRS - Slovenian Research Agency
Project number:J1-3005
Name:Kompleksna in geometrijska analiza

Licences

License:CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Link:http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

Language:Slovenian
Keywords:geometrijska interpolacija, krožni lok, ločna dolžina, krivulja s pitagorejskim hodografom, izbira rešitve


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