On G1 and G2 Hermite interpolation by spatial Algebraic-Trigonometric Pythagorean Hodograph curves with polynomial parametric speed

Thierry Bay, Isabelle Cattiaux-Huillard, Lucia Romani and Laura Saini

Applied Mathematics and Computation, 2023, vol. 458, issue C

Abstract: In this paper we focus on the class of Algebraic-Trigonometric Pythagorean Hodograph curves (ATPH for short) that is characterized by a purely polynomial parametric speed. Within such a class of ATPH curves, we first construct interpolants to spatial G1 Hermite data equipped with curvature values. With respect to the solutions proposed in [24], the G1 Hermite ATPH interpolants we here propose are characterized by C0- and C1-continuous curvature plots. Secondly, we investigate the existence of ATPH interpolants to spatial G2 Hermite data and show that solutions exist under some restrictions on the Hermite input data.

Keywords: Algebraic-Trigonometric curves; Pythagorean Hodograph; Polynomial parametric speed; G1 and G2 Hermite interpolation (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323004095

DOI: 10.1016/j.amc.2023.128240

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