On ▫$L^2$▫ approximation by planar Pythagorean-hodograph curvesFarouki, Rida T. (Avtor) Knez, Marjetka (Avtor) Vitrih, Vito (Avtor) Žagar, Emil (Avtor) ▫$L^2$▫ approximationcomplex polynomialPythagorean-hodograph curvePythagorean-hodograph splinepreimageThe ▫$L^2$▫ 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.20252025-05-30 12:50:55Članek v reviji21294sl