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

被引：1
|
作者：
Bay, Thierry [1 ]
Cattiaux-Huillard, Isabelle [1 ]
Romani, Lucia [2 ]
Saini, Laura [1 ,3 ]
机构：
[1] Univ Polytech Hauts de France, CERAMATHS, FR CNRS 2037, F-59313 Valenciennes, France
[2] Univ Bologna, Alma Mater Studiorum, Dip Matemat, Piazza Porta San Donato 5, I-40126 Bologna, Italy
[3] Junia, Comp Sci & Math, F-59000 Lille, France
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2023年 / 458卷
关键词：
Algebraic-Trigonometric curves; Pythagorean Hodograph; Polynomial parametric speed; G(1) andG(2 )Hermite interpolation; CONSTRUCTION;
D O I：
10.1016/j.amc.2023.128240
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页数：16
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