Constructing piecewise rational curves with Frenet frame continuity

Abstract We give a simple geometric construction for the Bezier points of two rational curves which join together with appropriate Frenet frame continuity. This is then used to give a geometric construction, from an arbitrary sequence of control points, for the Bezier points of a sequence of rational curves of degree n which join together with Frenet frame continuity of order m , for any m ⩽ n −1.