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} }