Arc length preserving G$^2$ Hermite interpolation of circular arcs

Žagar, Emil (author)

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.

• Language: English
• Keywords: geometric interpolation, circular arc, arc length, Pythagorean-hodograph curve, solution selection
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: 12 str.
• Numbering: Vol. 424, art. 115008
• PID: 20.500.12556/RUL-143842
• UDC: 519.651
• ISSN on article: 0377-0427
• DOI: 10.1016/j.cam.2022.115008
• COBISS.SI-ID: 134609923
• Publication date in RUL: 13.01.2023

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

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