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Planar Typical Bézier Curves with a Single Curvature Extremum
| Content Provider | MDPI |
|---|---|
| Author | He, Chuan Zhao, Gang Wang, Aizeng Li, Shaolin Cai, Zhan Chuan |
| Copyright Year | 2021 |
| Description | 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. |
| Starting Page | 2148 |
| e-ISSN | 22277390 |
| DOI | 10.3390/math9172148 |
| Journal | Mathematics |
| Issue Number | 17 |
| Volume Number | 9 |
| Language | English |
| Publisher | MDPI |
| Publisher Date | 2021-09-03 |
| Access Restriction | Open |
| Subject Keyword | Mathematics Industrial Engineering Typical Bézier Curves Monotonic Curvature Curvature Extremum G1 Interpolation |
| Content Type | Text |
| Resource Type | Article |
