CAN A CUBIC SPLINE CURVE BE G3

This paper proposes a method to construct an G3 cubic spline curve from any given open control polygon.For any two inner Bezier points on each edge of a control polygon,we can define each Bezier junction point such that the spline curve is G2-continuous.Then by suitably choosing the inner Bezier 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.