期刊
COMPUTER AIDED GEOMETRIC DESIGN
卷 93, 期 -, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.cagd.2022.102072
关键词
Bezier curve; Curve of Tschirnhaus type; Pythagorean-hodograph curve; Sinusoidal spiral; Tschirnhausen cubic; Typical curve
资金
- Consejena de Educacion Cultura y Deportes (Junta de Comunidades de Castilla-La Mancha) [PID2019-104586RB-I00, MCIN/AEI/10.13039/501100011033, SB-PLY/19/180501/000247]
- Universidad de Castilla-La Mancha - ERDF (European Regional Development Fund) [PID2019-104586RB-I00]
- MCIN/AEI [PID2019-104586RB-I00]
- Consejena de Educacion Cultura y Deportes (Junta de Comunidades de Castilla-La Mancha) [MCIN/AEI/10.13039/501100011033]
- Universidad de Castilla-La Mancha [SB-PLY/19/180501/000247]
- ERDF (European Regional Development Fund)
This article discusses the Pythagorean-hodograph curves of Tschirnhaus type, and their connection to typical curves and sinusoidal spirals. Several relevant results are rederived in the process.
Recently, Bizzarri et al. (2021) discussed the so-called Pythagorean-hodograph curves of Tschirnhaus type, a generalization to higher degrees of Tschirnhausen cubic. We recall that these curves in Bezier form coincide with the typical curves introduced by Mineur et al. (1998), as well as with a classical family of sinusoidal spirals. Therefore, they all enjoy the same properties, such as the rational character of their offsets or the existence of only one curve (up to similarities) for each degree. By elucidating this connection among curves of Tschirnhaus type, typical curves, and sinusoidal spirals, we rederive several relevant results found by Bizzarri et al. (2021). (C) 2022 The Author(s). Published by Elsevier B.V.
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