Paper Info
Title
Algebraic and geometric characterizations of a class of Algebraic-Hyperbolic Pythagorean-Hodograph curves
Abstract
In this paper, we study algebraic and geometric characteristics of a class of Algebraic-Hyperbolic curves that possess Pythagorean-Hodograph (PH) properties, which are called AHPH curves. These curves are defined on the space Γn=span{1,t,…,tn−3,sinh⁡t,cosh⁡t}, n∈N﹨{1,2}. We prove that all non-degenerate AHPH curves belong to Γ4. For this particular case, we give an explicit expression in terms of canonical basis functions. To reveal the geometric properties of AHPH curves, we study the geometric constraints on their Bézier like control polygons. The main result shows that an AH curve is an AHPH curve if and only if the interior angles of its control polygon are equal, and the second leg-length of the control polygon is the geometric mean of the other two leg-lengths. Our main idea is to represent a planar parametric curve in complex form. As an application, we give some examples of G1 Hermite interpolation using AHPH curves. We point out that there are no more than two AHPH curves for any given G1 Hermite conditions.
Year
DOI
Venue
2022
10.1016/j.cagd.2022.102121
Computer Aided Geometric Design
Keywords
DocType
Volume
Geometric construction,Geometric continuity,Hermite interpolation,Algebraic-Hyperbolic curve,PH curve
Journal
97
ISSN
Citations 
PageRank 
0167-8396
0
0.34
References 
Authors
0
2
Name
Order
Citations
PageRank
Lincong Fang1132.75
Yujun Li200.68