| Naslov: | On double Pythagorean-hodograph curves of degree seven |
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| Avtorji: | ID Knez, Marjetka (Avtor)
ID Praprotnik, Selena (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (3,59 MB)
MD5: 969A6834C66D421F6FD2DD7837B52B6A
 URL - Izvorni URL, za dostop obiščite https://www.sciencedirect.com/science/article/pii/S0167839626000257
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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: | This paper presents a comprehensive and constructive analysis of degree 7 double Pythagorean-hodograph (DPH) curves for the three distinct structural classes. A unified framework is introduced for their construction, particularly useful for interpolation tasks involving prescribed boundary data. The approach explicitly identifies the degrees of freedom available in each class and distinguishes between helical and non-helical curve types. Furthermore, the structure of a specific rational curve in the complex plane that via the normalized Hopf map generates the tangent indicatrix is revealed for all degree 7 DPH curves. This confirms known results for helical curves and extends the interpretation to non-helical cases. The practical applicability of the derived curves is demonstrated through a numerical interpolation example, which also validates the stated number of degrees of freedom. |
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| Ključne besede: | double Pythagorean-hodograph curves, helical/non-helical curves, quaternions, Hopf map, Frenet frame, interpolation |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.04.2026 |
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| Leto izida: | 2026 |
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| Št. strani: | 20 str. |
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| Številčenje: | Vol. 126, article no. 102532 |
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| PID: | 20.500.12556/DiRROS-28916  |
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| UDK: | 519.6 |
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| ISSN pri članku: | 0167-8396 |
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| DOI: | 10.1016/j.cagd.2026.102532 |
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| COBISS.SI-ID: | 275061507 |
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| Datum objave v DiRROS: | 14.04.2026 |
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| Število ogledov: | 141 |
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| Število prenosov: | 130 |
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| Metapodatki: |    |
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