Application of a metric for complex polynomials to bounded modification of planar Pythagorean-hodograph curves
Numerical Analysis
2024-02-16 v1 Numerical Analysis
Abstract
By interpreting planar polynomial curves as complex-valued functions of a real parameter, an inner product, norm, metric function, and the notion of orthogonality may be defined for such curves. This approach is applied to the complex pre-image polynomials that generate planar Pythagorean-hodograph (PH) curves, to facilitate the implementation of bounded modifications of them that preserve their PH nature. The problems of bounded modifications under the constraint of fixed curve end points and end tangent directions, and of increasing the arc length of a PH curve by a prescribed amount, are also addressed.
Keywords
Cite
@article{arxiv.2402.09850,
title = {Application of a metric for complex polynomials to bounded modification of planar Pythagorean-hodograph curves},
author = {Rida T. Farouki and Marjeta Knez and Vito Vitrih and Emil Žagar},
journal= {arXiv preprint arXiv:2402.09850},
year = {2024}
}