| Naslov: | On $L^2$ approximation by spatial Pythagorean-hodograph curves |
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| Avtorji: | ID Farouki, Rida T. (Avtor)
ID Knez, Marjetka (Avtor)
ID Vitrih, Vito (Avtor)
ID Žagar, Emil (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (5,65 MB)
MD5: 85C798ACBB919FC508EBFF78668BC879
 URL - Izvorni URL, za dostop obiščite https://www.sciencedirect.com/science/article/pii/S0377042726006291
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | Two methods for the $L^2$ approximation of smooth space curves by spatial Pythagorean-hodograph (PH) curves are considered. The first method employs direct approximation in ${\mathbb R}^3$, which results in a non-linear system of equations that may be solved by a numerical iteration or optimization scheme. The second method performs the optimization in the quaternion preimage space of PH curves, which results in a linear system of equations. The preimage of a curve in ${\mathbb R}^3$ is a surface in the quaternion space, and an appropriate locus on this surface must be identified for the given space curve. This is accomplished by observing that PH curves equipped with a rational rotation-minimizing frame (RMF) have preimages that are geodesic loci on the surface, and computing a discretized approximation to the RMF on the given curve. The methods are also extended to the approximation of spatial B-spline curves. Detailed algorithm descriptions are provided for both methods, and several computed examples illustrate their performance. |
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| Ključne besede: | $L^2$ approximation, quaternions, Pythagorean-hodograph curves, B-splines, preimage |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.02.2027 |
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| Leto izida: | 2027 |
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| Št. strani: | 16 str. |
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| Številčenje: | Vol. 491, article no. 117987 |
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| PID: | 20.500.12556/DiRROS-31390  |
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| UDK: | 519.6 |
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| ISSN pri članku: | 0377-0427 |
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| DOI: | 10.1016/j.cam.2026.117987 |
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| COBISS.SI-ID: | 286529283 |
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| Opomba: |
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| Datum objave v DiRROS: | 31.07.2026 |
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| Število ogledov: | 89 |
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| Število prenosov: | 82 |
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| Metapodatki: |    |
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