| Title: | On ▫$L^2$▫ 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: |  RAZ_Farouki_Rida_T._2025.pdf (1,33 MB)
MD5: 296762E04B2C1DB0C220D6543772F267
 https://www.sciencedirect.com/science/article/pii/S0378475425000394
|
|---|
| Language: | English |
|---|
| Work type: | Article |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
|
|---|
| Abstract: | 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. |
|---|
| Keywords: | ▫$L^2$▫ approximation, complex polynomial, Pythagorean-hodograph curve, Pythagorean-hodograph spline, preimage |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 10.02.2025 |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | str. 296-310 |
|---|
| Numbering: | Vol. 233 |
|---|
| PID: | 20.500.12556/RUP-21294  |
|---|
| UDC: | 519.6 |
|---|
| ISSN on article: | 1872-7166 |
|---|
| DOI: | 10.1016/j.matcom.2025.02.001 |
|---|
| COBISS.SI-ID: | 226119171 |
|---|
| Publication date in RUP: | 30.05.2025 |
|---|
| Views: | 2221 |
|---|
| Downloads: | 9 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
