Planar Typical Bézier Curves with a Single Curvature Extremum

Chuan He, Gang Zhao, Aizeng Wang, Shaolin Li and Zhanchuan Cai
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Chuan He: School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
Gang Zhao: School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
Aizeng Wang: School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
Shaolin Li: State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau 999078, China
Zhanchuan Cai: Faculty of Information Technology, Macau University of Science and Technology, Macau 999078, China

Mathematics, 2021, vol. 9, issue 17, 1-16

Abstract: This paper focuses on planar typical Bézier curves with a single curvature extremum, which is a supplement of typical curves with monotonic curvature by Y. Mineur et al. We have proven that the typical curve has at most one curvature extremum and given a fast calculation formula of the parameter at the curvature extremum. This will allow designers to execute a subdivision at the curvature extremum to obtain two pieces of typical curves with monotonic curvature. In addition, we put forward a sufficient condition for typical curve solutions under arbitrary degrees for the G1 interpolation problem. Some numerical experiments are provided to demonstrate the effectiveness and efficiency of our approach.

Keywords: typical Bézier curves; monotonic curvature; curvature extremum; G1 interpolation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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