On double Pythagorean-hodograph curves of degree seven

Knez, Marjetka (avtor), Praprotnik, Selena (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: double Pythagorean-hodograph curves, helical/non-helical curves, quaternions, Hopf map, Frenet frame, interpolation
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko ; FGG - Fakulteta za gradbeništvo in geodezijo
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.04.2026
• Leto izida: 2026
• Št. strani: 20 str.
• Številčenje: Vol. 126, article no. 102532
• PID: 20.500.12556/RUL-181708
• UDK: 519.6
• ISSN pri članku: 0167-8396
• DOI: 10.1016/j.cagd.2026.102532
• COBISS.SI-ID: 275061507
• Datum objave v RUL: 14.04.2026

Gradivo je del revije

• Naslov: Computer Aided Geometric Design
• Skrajšan naslov: Comput. aided geom. des.
• Založnik: Elsevier
• ISSN: 0167-8396
• COBISS.SI-ID: 25266176

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: krivulje s pitagorejskim hodografom, kvaternioni, interpolacija