CAN A CUBIC SPLINE CURVE BE G3

doi:10.4208/jcm.1910-m2019-0119

Journal of Computational Mathematics ›› 2021, Vol. 39 ›› Issue (2): 178-191.DOI: 10.4208/jcm.1910-m2019-0119

CAN A CUBIC SPLINE CURVE BE G³

Wujie Liu, Xin Li

School of Mathematical Science, University of Science and Technology of China, Hefei 230026, China

Received:2019-05-08 Revised:2019-10-15 Published:2021-03-15
Contact: Xin Li,Email:lixustc@ustc.edu.cn
Supported by:
The authors were supported by the NSF of China (No.61872328), NKBRPC (2011CB302400), SRF for ROCS SE, and the Youth Innovation Promotion Association CAS.

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Wujie Liu, Xin Li. CAN A CUBIC SPLINE CURVE BE G³[J]. Journal of Computational Mathematics, 2021, 39(2): 178-191.

This paper proposes a method to construct an G³ cubic spline curve from any given open control polygon. For any two inner Bézier points on each edge of a control polygon, we can define each Bézier junction point such that the spline curve is G²-continuous. Then by suitably choosing the inner Bézier points, we can construct a global G³ spline curve. The curvature combs and curvature plots show the advantage of the G³ cubic spline curve in contrast with the traditional C² cubic spline curve.

Key words: Cubic Spline, Geometric Continuity, G³ Continuity

CLC Number:

65D07

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CAN A CUBIC SPLINE CURVE BE G3

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CAN A CUBIC SPLINE CURVE BE G³