20.500.12556/DiRROS-31390 On $L^2$ approximation by spatial Pythagorean-hodograph curves 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. $L^2$ approximation quaternions Pythagorean-hodograph curves B-splines preimage $L^2$ aproksimacija kvaternioni krivulje s pitagorejskim hodografom B-zlepki praslika true false true Angleški jezik Slovenski jezik Neznano 2026-07-31 08:35:15 2026-07-31 08:35:15 2026-08-01 03:50:38 0000-00-00 00:00:00 2027 0 0 16 str. article no. 117987 Vol. 491 Feb. 2027 0000-00-00 Zaloznikova NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2027-02-01 519.6 0377-0427 10.1016/j.cam.2026.117987 286529283 1-s2.0-S0377042726006291-main.pdf 1-s2.0-S0377042726006291-main.pdf 1 85C798ACBB919FC508EBFF78668BC879 2026362adbb1cdc1fb667126148c7ebc8ae2cab158a09aee1fd5fae1f402b2f2 862b73a3-8caa-11f1-a81a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=48582 https://www.sciencedirect.com/science/article/pii/S0377042726006291 1 feccec56-8ca9-11f1-a81a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=48581 Inštitut za matematiko, fiziko in mehaniko 0 0 0