20.500.12556/DiRROS-21507 On $L^2$ approximation by planar Pythagorean-hodograph curves The $L^2$ approximation of planar curves by Pythagorean-hodograph (PH) polynomial curves is addressed, based on the distance defined by a metric for planar curves represented as complex valued functions of a real parameter. Because of the nonlinear nature of polynomial PH curves, constructing $L^2$ approximants involves solving a nonlinear optimization problem. However, a simplified method that requires only the solution of a linear system may be developed by formulating the $L^2$ approximation in the preimage space. The extension of the methodology to approximation by PH B-spline curves is also addressed, and several examples are provided to illustrate its implementation and potential. $L^2$ approximation complex polynomial Pythagorean-hodograph curve Pythagorean-hodograph spline preimage $L^2$ aproksimacija PH krivulja PH zlepek praslika true false true Angleški jezik Slovenski jezik Neznano 2025-02-18 08:37:05 2025-02-18 08:37:05 2025-02-19 03:36:22 0000-00-00 00:00:00 2025 0 0 str. 296-310 Vol. 233 Jul. 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-07-01 519.6 1872-7166 10.1016/j.matcom.2025.02.001 226119171 1-s2.0-S0378475425000394-main.pdf 1-s2.0-S0378475425000394-main.pdf 1 C7BAA0D396A2AEE895B2974625D1BB8A 53f36132ae6f730062e738717390045133fcdd2a1158ae0fc520a6b7ed7f197c 57ab3801-edcb-11ef-9f1e-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=30729 https://www.sciencedirect.com/science/article/pii/S0378475425000394 1 27f4cae4-edcb-11ef-9f1e-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=30728 Inštitut za matematiko, fiziko in mehaniko 0 0 0