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New Proper Reparameterization of Plane Rational Bézier Curves

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Abstract

Coincidence detection of two curves or two surfaces has wide application in computer-aided design (CAD) and computer-aided geometric design (CAGD). Proper reparameterization is the most complicated part in the detection. This paper presents and proves the efficient and necessary coincidence condition for two rational Bézier curves in a new way. It also proposes an effective and efficient proper reparameterization method, Algorithm 1, for detecting a rational Bézier curve which can be degenerated into a new one of a lower degree. A numerical proper reparameterization method, Algorithm 2, and examples are also presented. Algorithm 1 is up to ten times faster than other prevailing methods, and Algorithm 2 is twice as fast and half as close as other prevailing methods. New CAD systems using Algorithm 1 and Algorithm 2 will hold accuracy and little computation time.

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Authors and Affiliations

  1. School of Computer, Hangzhou Dianzi University, Hangzhou, 310018, China

    Zhen-Fei Wang  (王振飞) & Xiao-Diao Chen  (陈小雕)

  2. Haihe Laboratory of Information Technology Application Innovation, Tianjin, 300480, China

    Xiao-Diao Chen  (陈小雕)

  3. School of Software, Tsinghua University, Beijing, 100084, China

    Jun-Hai Yong  (雍俊海)

Authors
  1. Zhen-Fei Wang  (王振飞)
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  2. Xiao-Diao Chen  (陈小雕)
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  3. Jun-Hai Yong  (雍俊海)
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Corresponding author

Correspondence to Xiao-Diao Chen  (陈小雕).

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Conflict of Interest The authors declare that they have no conflict of interest.

Additional information

This research work was partially supported by the National Natural Science Foundation of China under Grant Nos. 61972120 and 62021002 and the Haihe Lab of ITAI Project (22HHXCJC00006). The last author was supported by the National Key Research and Development Program of China under Grant Nos. 2020YFB1708900 and TC190A4DA/3.

Zhen-Fei Wang received his B.S. degree in computer science and technology from Zhengzhou University of Aeronautics, Zhengzhou, in 2020. He is currently a Master student in computer science and technology from Hangzhou Dianzi University, Hangzhou. His current research interests include curve/surface intersection, reparameterization, and related applications for computer graphics.

Xiao-Diao Chen is a faculty member at the School of Computer, Hangzhou Dianzi University, Hangzhou. He received his Bachelor’s degree from Zhejiang University, Hangzhou, in 2000, and his Ph.D. degree from Tsinghua University, Beijing, in 2006. His research interests include approximation and interpolation methods, and their applications in computer graphics and image processing.

Jun-Hai Yong is a professor at the School of Software, BNRist, Tsinghua University, Beijing. He received his B.S. and Ph.D. degrees in computer science from Tsinghua University, Beijing, in 1996 and 2000, respectively. His main research interests include computer-aided design and computer graphics. He obtained a lot of awards such as the National Excellent Doctoral Dissertation Award, the National Science Fund for Distinguished Young Scholars, and the Outstanding Service Award by Elsevier.

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Wang, ZF., Chen, XD. & Yong, JH. New Proper Reparameterization of Plane Rational Bézier Curves. J. Comput. Sci. Technol. 39, 1193–1206 (2024). https://doi.org/10.1007/s11390-022-2188-4

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  • DOI: https://doi.org/10.1007/s11390-022-2188-4

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