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.