20.500.12556/DiRROS-18487 Arc length preserving $G^2$ Hermite interpolation of circular arcs In this paper, the problem of interpolation of two points, two corresponding tangent directions and curvatures, and the arc length sampled from a circular arc (circular arc data) is considered. Planar Pythagorean–hodograph (PH) curves of degree seven are used since they possess enough free parameters and are capable of interpolating the arc length in an easy way. A general approach using the complex representation of PH curves is presented first and the strong dependence of the solution on the general data is demonstrated. For circular arc data, a complicated system of nonlinear equations is reduced to a numerical solution of only one algebraic equation of degree 6 and a detailed analysis of the existence of admissible solutions is provided. In the case of several solutions, some criteria for selecting the most appropriate one are described and an asymptotic analysis is given. Numerical examples are included which confirm theoretical results. geometric interpolation circular arc arc length Pythagorean-hodograph curve solution selection geometrijska interpolacija krožni lok ločna dolžina krivulja s pitagorejskim hodografom izbira rešitve true false true Angleški jezik Slovenski jezik Neznano 2024-03-20 11:39:49 2024-03-20 11:39:50 2024-03-21 03:35:37 0000-00-00 00:00:00 2023 0 0 art. 115008 (12 str.) Vol. 424 May 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2023-05-01 519.651 0377-0427 10.1016/j.cam.2022.115008 134609923 1-s2.0-S0377042722006069-main.pdf 1-s2.0-S0377042722006069-main.pdf 1 B29F95158AD246BA9A800A71234DE1BF 1925596098f0ffadd18287a8e46c2d1f671fc0f6ef260b43bec149ddd4bd8dc4 85686344-e6a6-11ee-9dd4-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25193 https://www.sciencedirect.com/science/article/pii/S0377042722006069 1 2eb3a57c-e6a6-11ee-9dd4-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25192 Inštitut za matematiko, fiziko in mehaniko 0 0 0