### CAN A CUBIC SPLINE CURVE BE G3

Wujie Liu, Xin Li

1. 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.

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.

CLC Number:

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