@article{Li2024, 
author = {Yujun Li},
title = {Characteristics of planar sextic indirect-PH curves},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {2215-2231},
keywords = {geometric design, characteristics, Pythagorean hodograph, control polygon},
url = {https://www.sciopen.com/article/10.3934/math.2024110},
doi = {10.3934/math.2024110},
abstract = {By a fractional quadratic transformation, an indirect-PH curve can have rational offsets. In this paper, I study properties of planar sextic indirect-PH curves, in terms of their Bézier control polygon legs. With our results, sextic Bézier curves can be efficiently tested whether they are indirect-PH curves. The main strategy to achieve our results is using complex representation of planar parametric curve. Sextic indirect-PH curves can be classified into three classes according to different factorizations of their hodographs. Necessary and sufficient conditions for all classes of sextic indirect-PH curves can be described by non-linear complex systems. By analyzing these non-linear systems, algebraic conditions for a sextic Bézier curve to be an indirect-PH curve are first discussed, then geometric characteristics in terms of legs of its control polygon are revealed.}
}