Algebraic and geometric characterizations of a class of planar quartic curves with rational offsets

Planar polynomial curves have rational offset curves, if they are either Pythagorean-hodograph (PH) or indirect Pythagorean-hodograph (iPH) curves. In this paper, we derive an algebraic and two geometric characterizations for planar quartic iPH curves. The characterizations are given in terms of qua...

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Bibliographic Details
Published in:Computer aided geometric design 2020-05, Vol.79, p.101873, Article 101873
Main Authors: Hormann, Kai, Zheng, Jianmin
Format: Article
Language:English
Subjects:
Offset curves
Pythagorean hodograph
Quartic Bézier curves
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Summary:Planar polynomial curves have rational offset curves, if they are either Pythagorean-hodograph (PH) or indirect Pythagorean-hodograph (iPH) curves. In this paper, we derive an algebraic and two geometric characterizations for planar quartic iPH curves. The characterizations are given in terms of quantities related to the Bézier control polygon of the curve, and naturally extend to quartic and cubic PH and quadratic iPH curves. •We analyse the structure of planar quartic indirect PH curves.•We derive a simple algebraic characterization of these curves.•We derive two geometric characterization of these curves.
ISSN:0167-8396
1879-2332
DOI:10.1016/j.cagd.2020.101873