20.500.12556/RUL-167348 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 Članek v reviji 2025-02-17 12:58:42 2025-02-17 12:58:46 2025-02-18 03:55:43 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 0000-00-00 519.6 1872-7166 10.1016/j.matcom.2025.02.001 226119171 1-s2.0-S0378475425000394-main.pdf 1-s2.0-S0378475425000394-main.pdf 1 505FB73CDB8E60E7D1D8692777EA47C6 e8ce39a48cc69558c8aacf34a253d9e6f4eaf0da4d2e8c93407b5ebc7b873756 f2adc0f1-ed25-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=199712 https://www.sciencedirect.com/science/article/pii/S0378475425000394 0 a723f513-ed25-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=199711 Fakulteta za matematiko in fiziko 0 0 0