Planar Typical Bézier Curves with a Single Curvature Extremum
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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-09-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/17/2148 |
| Summary: | 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. |
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| ISSN: | 2227-7390 |