Volume 39, Issue 2
Can a Cubic Spline Curve Be G3

J. Comp. Math., 39 (2021), pp. 178-191.

Published online: 2020-11

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• Abstract

This paper proposes a method to construct an $G^3$ 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 $G^2$-continuous. Then by suitably choosing the inner Bézier points, we can construct a global $G^3$ spline curve. The curvature combs and curvature plots show the advantage of the $G^3$ cubic spline curve in contrast with the traditional $C^2$ cubic spline curve.

• Keywords

Cubic Spline, Geometric Continuity, $G^3$ Continuity.

65D07

lixustc@ustc.edu.cn (Xin Li)

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@Article{JCM-39-178, author = {Liu , Wujie and Li , Xin }, title = {Can a Cubic Spline Curve Be G3}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {39}, number = {2}, pages = {178--191}, abstract = {

This paper proposes a method to construct an $G^3$ 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 $G^2$-continuous. Then by suitably choosing the inner Bézier points, we can construct a global $G^3$ spline curve. The curvature combs and curvature plots show the advantage of the $G^3$ cubic spline curve in contrast with the traditional $C^2$ cubic spline curve.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1910-m2019-0119}, url = {http://global-sci.org/intro/article_detail/jcm/18370.html} }
TY - JOUR T1 - Can a Cubic Spline Curve Be G3 AU - Liu , Wujie AU - Li , Xin JO - Journal of Computational Mathematics VL - 2 SP - 178 EP - 191 PY - 2020 DA - 2020/11 SN - 39 DO - http://doi.org/10.4208/jcm.1910-m2019-0119 UR - https://global-sci.org/intro/article_detail/jcm/18370.html KW - Cubic Spline, Geometric Continuity, $G^3$ Continuity. AB -

This paper proposes a method to construct an $G^3$ 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 $G^2$-continuous. Then by suitably choosing the inner Bézier points, we can construct a global $G^3$ spline curve. The curvature combs and curvature plots show the advantage of the $G^3$ cubic spline curve in contrast with the traditional $C^2$ cubic spline curve.

Wujie Liu & Xin Li. (2020). Can a Cubic Spline Curve Be G3. Journal of Computational Mathematics. 39 (2). 178-191. doi:10.4208/jcm.1910-m2019-0119
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