| Title: | On $L^2$ approximation by planar Pythagorean-hodograph curves |
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| Authors: | ID Farouki, Rida T. (Author)
ID Knez, Marjetka (Author)
ID Vitrih, Vito (Author)
ID Žagar, Emil (Author) |
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| Files: |  PDF - Presentation file, download (1,31 MB)
MD5: C7BAA0D396A2AEE895B2974625D1BB8A
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0378475425000394
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| 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. |
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| Keywords: | $L^2$ approximation, complex polynomial, Pythagorean-hodograph curve, Pythagorean-hodograph spline, preimage |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.07.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 296-310 |
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| Numbering: | Vol. 233 |
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| PID: | 20.500.12556/DiRROS-21507  |
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| UDC: | 519.6 |
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| ISSN on article: | 1872-7166 |
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| DOI: | 10.1016/j.matcom.2025.02.001 |
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| COBISS.SI-ID: | 226119171 |
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| Note: |
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| Publication date in DiRROS: | 18.02.2025 |
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| Views: | 720 |
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| Downloads: | 502 |
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| Metadata: |    |
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