20.500.12556/DiRROS-28916 On double Pythagorean-hodograph curves of degree seven 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. double Pythagorean-hodograph curves helical/non-helical curves quaternions Hopf map Frenet frame interpolation krivulje s pitagorejskim hodografom kvaternioni interpolacija true false true Angleški jezik Slovenski jezik Neznano 2026-04-14 09:16:07 2026-04-14 09:16:07 2026-04-15 03:57:34 0000-00-00 00:00:00 2026 0 0 20 str. article no. 102532 Vol. 126 Apr. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-04-01 519.6 0167-8396 10.1016/j.cagd.2026.102532 275061507 1-s2.0-S0167839626000257-main.pdf 1-s2.0-S0167839626000257-main.pdf 1 969A6834C66D421F6FD2DD7837B52B6A f779ea80bda197028de34efe38ca536dcbac20a9c304b9b412c75f45fdf99547 1ad1b442-37d2-11f1-9cc3-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=43127 https://www.sciencedirect.com/science/article/pii/S0167839626000257 1 d0320f38-37d1-11f1-9cc3-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=43126 Inštitut za matematiko, fiziko in mehaniko 0 0 0