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

KaiHormann aUniversità della Svizzera italiana Jianmin Zheng Nanyang Technological University, Singapore

Computational Geometry mathscidoc:2105.09001

Computer Aided Geometric Design, 79, 1-15, 2020.5
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.
Quartic Bézier curves, Offset curves, Pythagorean hodograph
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@inproceedings{kaihormann2020algebraic,
  title={Algebraic and geometric characterizations of a class of planar quartic curves with rational offsets},
  author={KaiHormann, and Jianmin Zheng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210524112425719684829},
  booktitle={Computer Aided Geometric Design},
  volume={79},
  pages={1-15},
  year={2020},
}
KaiHormann, and Jianmin Zheng. Algebraic and geometric characterizations of a class of planar quartic curves with rational offsets. 2020. Vol. 79. In Computer Aided Geometric Design. pp.1-15. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210524112425719684829.
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