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Title: 3D class A Bézier curves with monotone curvature
Authors: Wang, Aizeng
He, Chuan
Zheng, Jianmin
Zhao, Gang
Keywords: Engineering::Computer science and engineering
Issue Date: 2023
Source: Wang, A., He, C., Zheng, J. & Zhao, G. (2023). 3D class A Bézier curves with monotone curvature. Computer-Aided Design, 159, 103501-.
Project: RG12/22 
Journal: Computer-Aided Design 
Abstract: 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.
ISSN: 0010-4485
DOI: 10.1016/j.cad.2023.103501
Schools: School of Computer Science and Engineering 
Rights: © 2023 Elsevier Ltd. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SCSE Journal Articles

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