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

Žagar, Emil (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: geometric interpolation, circular arc, arc length, Pythagorean-hodograph curve, solution selection
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2023
• Št. strani: 12 str.
• Številčenje: Vol. 424, art. 115008
• PID: 20.500.12556/RUL-143842
• UDK: 519.651
• ISSN pri članku: 0377-0427
• DOI: 10.1016/j.cam.2022.115008
• COBISS.SI-ID: 134609923
• Datum objave v RUL: 13.01.2023

Gradivo je del revije

• Naslov: Journal of computational and applied mathematics
• Skrajšan naslov: J. comput. appl. math.
• Založnik: Elsevier
• ISSN: 0377-0427
• COBISS.SI-ID: 27496960

Licence

• Licenca: CC BY-NC-ND 4.0, Creative Commons Priznanje avtorstva-Nekomercialno-Brez predelav 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc-nd/4.0/deed.sl
• Opis: Najbolj omejujoča licenca Creative Commons. Uporabniki lahko prenesejo in delijo delo v nekomercialne namene in ga ne smejo uporabiti za nobene druge namene.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: geometrijska interpolacija, krožni lok, ločna dolžina, krivulja s pitagorejskim hodografom, izbira rešitve