3D class A Bézier curves with monotone curvature
This paper introduces a special class of 3D Bézier curves that are defined by their degree, a starting point, the first leg of their control polygons, and a 3D affine transformation composing of a uniform scaling and a rotation. We present new formulas for the curvature of such Bézier curves and bas...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/169021 |
| _version_ | 1824457089135673344 |
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| author | Wang, Aizeng He, Chuan Zheng, Jianmin Zhao, Gang |
| author2 | School of Computer Science and Engineering |
| author_facet | School of Computer Science and Engineering Wang, Aizeng He, Chuan Zheng, Jianmin Zhao, Gang |
| author_sort | Wang, Aizeng |
| collection | NTU |
| description | This paper introduces a special class of 3D Bézier curves that are defined by their degree, a starting point, the first leg of their control polygons, and a 3D affine transformation composing of a uniform scaling and a rotation. We present new formulas for the curvature of such Bézier curves and based on the new formulas we derive sufficient conditions for the curves to have monotonic curvature. The conditions are expressed by a simple constraint on the rotation angle and the scaling factor. This facilitates constructing 3D Class A Bézier curves that are a generalization of planar typical curves proposed by Mineur et al. (1998), which are often used in automotive and other design applications. Some examples are provided to demonstrate the effectiveness of our construction. |
| first_indexed | 2025-02-19T04:04:27Z |
| format | Journal Article |
| id | ntu-10356/169021 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T04:04:27Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-10356/1690212023-06-27T04:22:14Z 3D class A Bézier curves with monotone curvature Wang, Aizeng He, Chuan Zheng, Jianmin Zhao, Gang School of Computer Science and Engineering Engineering::Computer science and engineering Class A Curves Bézier Curves This paper introduces a special class of 3D Bézier curves that are defined by their degree, a starting point, the first leg of their control polygons, and a 3D affine transformation composing of a uniform scaling and a rotation. We present new formulas for the curvature of such Bézier curves and based on the new formulas we derive sufficient conditions for the curves to have monotonic curvature. The conditions are expressed by a simple constraint on the rotation angle and the scaling factor. This facilitates constructing 3D Class A Bézier curves that are a generalization of planar typical curves proposed by Mineur et al. (1998), which are often used in automotive and other design applications. Some examples are provided to demonstrate the effectiveness of our construction. Ministry of Education (MOE) This work was supported by the Opening Fund of State Key Laboratory of Lunar and Planetary Sciences (Macau FDCT grant No. 119/2017/A3, Macau University of Science and Technology), the Natural Science Foundation of China (Project No. 61572056), and MOE AcRF Tier 1 Grant of Singapore (RG12/22). 2023-06-27T04:22:14Z 2023-06-27T04:22:14Z 2023 Journal Article Wang, A., He, C., Zheng, J. & Zhao, G. (2023). 3D class A Bézier curves with monotone curvature. Computer-Aided Design, 159, 103501-. https://dx.doi.org/10.1016/j.cad.2023.103501 0010-4485 https://hdl.handle.net/10356/169021 10.1016/j.cad.2023.103501 2-s2.0-85149380294 159 103501 en RG12/22 Computer-Aided Design © 2023 Elsevier Ltd. All rights reserved. |
| spellingShingle | Engineering::Computer science and engineering Class A Curves Bézier Curves Wang, Aizeng He, Chuan Zheng, Jianmin Zhao, Gang 3D class A Bézier curves with monotone curvature |
| title | 3D class A Bézier curves with monotone curvature |
| title_full | 3D class A Bézier curves with monotone curvature |
| title_fullStr | 3D class A Bézier curves with monotone curvature |
| title_full_unstemmed | 3D class A Bézier curves with monotone curvature |
| title_short | 3D class A Bézier curves with monotone curvature |
| title_sort | 3d class a bezier curves with monotone curvature |
| topic | Engineering::Computer science and engineering Class A Curves Bézier Curves |
| url | https://hdl.handle.net/10356/169021 |
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