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Title:On L2 approximation by planar Pythagorean-hodograph curves
Authors:ID Farouki, Rida T. (Author)
ID Knez, Marjetka (Author)
ID Vitrih, Vito (Author)
ID Žagar, Emil (Author)
Files:.pdf PDF - Presentation file, download (1,31 MB)
MD5: C7BAA0D396A2AEE895B2974625D1BB8A
 
URL URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0378475425000394
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
Abstract:The L2 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 L2 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 L2 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.
Keywords:L2 approximation, complex polynomial, Pythagorean-hodograph curve, Pythagorean-hodograph spline, preimage
Publication status:Published
Publication version:Version of Record
Publication date:01.07.2025
Year of publishing:2025
Number of pages:str. 296-310
Numbering:Vol. 233
PID:20.500.12556/DiRROS-21507 New window
UDC:519.6
ISSN on article:1872-7166
DOI:10.1016/j.matcom.2025.02.001 New window
COBISS.SI-ID:226119171 New window
Note:
Publication date in DiRROS:18.02.2025
Views:128
Downloads:71
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FAROUKI, Rida T., KNEZ, Marjetka, VITRIH, Vito and ŽAGAR, Emil, 2025, On L2 approximation by planar Pythagorean-hodograph curves. Mathematics and computers in simulation [online]. 2025. Vol. 233, p. 296–310. [Accessed 13 March 2025]. DOI 10.1016/j.matcom.2025.02.001. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=21507
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Record is a part of a journal

Title:Mathematics and computers in simulation
Shortened title:Math. comput. simul.
Publisher:Elsevier Science
ISSN:1872-7166
COBISS.SI-ID:23159813 New window

Document is financed by a project

Funder:ARIS - Slovenian Research and Innovation Agency
Project number:P1-0288-2015
Name:Algebre in kolobarji
Funder:ARIS - Slovenian Research and Innovation Agency
Project number:N1-0137-2020
Name:Nelinearni Valovi in Spektralna Teorija
Funder:ARIS - Slovenian Research and Innovation Agency
Project number:N1-0237-2022
Name:Holomorfne parcialne diferencialne relacije
Funder:ARIS - Slovenian Research and Innovation Agency
Project number:J1-3005-2021
Name:Kompleksna in geometrijska analiza
Funder:ARIS - Slovenian Research and Innovation Agency
Project number:P1-0404-2019
Name:Matematično modeliranje in enkripcija: od teoretičnih konceptov do vsakodnevnih aplikacij
Funder:ARIS - Slovenian Research and Innovation Agency
Project number:N1-0296-2023
Name:Gladki izogeometrični prostori zlepkov nad večdelnimi domenami
Funder:ARIS - Slovenian Research and Innovation Agency
Project number:J1-4414-2022
Name:ProBiS-Fold pristop za določanje vezavnih mest za celoten strukturni človeški proteom pri odkrivanju zdravil

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:L2 aproksimacija, PH krivulja, PH zlepek, praslika


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