On L2 approximation by planar Pythagorean-hodograph curves

Rida T. Farouki, Marjeta Knez, Vito Vitrih and Emil Žagar

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 233, issue C, 296-310

Abstract: The L2 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 L2 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 L2 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.

Keywords: L2 approximation; Complex polynomial; Pythagorean-hodograph curve; Pythagorean-hodograph spline; Preimage (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:233:y:2025:i:c:p:296-310

DOI: 10.1016/j.matcom.2025.02.001

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