20.500.12556/RUP-21294 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[sup]2 aproksimacija PH krivulja PH zlepek praslika true false true Angleški jezik Slovenski jezik Članek v reviji 2025-05-30 12:50:55 2025-05-30 12:50:56 2025-05-31 03:05:10 0000-00-00 00:00:00 2025 0 0 str. 296-310 Vol. 233 Jul. 2025 0000-00-00 Zaloznikova Objavljeno apc 0000-00-00 0000-00-00 2025-02-10 519.6 1872-7166 10.1016/j.matcom.2025.02.001 226119171 RAZ_Farouki_Rida_T._2025.pdf RAZ_Farouki_Rida_T._2025.pdf 1 296762E04B2C1DB0C220D6543772F267 e8e5f85bd6c695529304ad0e51f77bf543ba8c613a28a1be0415105af6afa452 9b835e8d-3d44-11f0-bc14-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=30965 https://www.sciencedirect.com/science/article/pii/S0378475425000394 1 eb06919b-3d43-11f0-bc14-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=30964 Fakulteta za matematiko, naravoslovje in informacijske tehnologije 0 0 0