On $L^2$ approximation by planar Pythagorean-hodograph curves

Farouki, Rida T. (avtor), Knez, Marjetka (avtor), Vitrih, Vito (avtor), Žagar, Emil (avtor)

The $L^2$ approximation of planar curves by Pythagorean-hodograph (PH) polynomial curves is addressed, based on the distance defined by a metric for planar curves represented as complex valued functions of a real parameter. Because of the nonlinear nature of polynomial PH curves, constructing $L^2$ approximants involves solving a nonlinear optimization problem. However, a simplified method that requires only the solution of a linear system may be developed by formulating the $L^2$ approximation in the preimage space. The extension of the methodology to approximation by PH B-spline curves is also addressed, and several examples are provided to illustrate its implementation and potential.

• Jezik: Angleški jezik
• Ključne besede: $L^2$ approximation, complex polynomial, Pythagorean-hodograph curve, Pythagorean-hodograph spline, preimage
• 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: 2025
• Št. strani: Str. 296-310
• Številčenje: Vol. 233
• PID: 20.500.12556/RUL-167348
• UDK: 519.6
• ISSN pri članku: 1872-7166
• DOI: 10.1016/j.matcom.2025.02.001
• COBISS.SI-ID: 226119171
• Datum objave v RUL: 17.02.2025

Gradivo je del revije

• Naslov: Mathematics and computers in simulation
• Skrajšan naslov: Math. comput. simul.
• Založnik: Elsevier, International Association for Mathematics and Computers in Simulation
• ISSN: 1872-7166
• COBISS.SI-ID: 23159813

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: $L^2$ aproksimacija, PH krivulja, PH zlepek, praslika