\(G^2\) composite cubic Bézier curves (Q1300780)

The purpose of the present paper is to describe a method to create cubic Bézier curve segments that satisfy contact conditions at both endpoints. There are a number of partial solutions to this problem [cf. \textit{C. de Boor, K. Hölling} and \textit{M. Sabin}, Comput. Aided Geom. Design 4, 269-278 (1987; Zbl 0646.65004), \textit{T. N. T. Goodman} and \textit{K. Unsworth}, Comput. Aided Geom. Design 5, No. 4, 323-340 (1988; Zbl 0656.65005)]. However none of these methods allows the curvature at either end to be zero. With the proposed method the spline interpolates a sequence of points, tangents and curvatures and zero curvature can be assigned at a junction point, hence inflection points can be placed where desired but cannot occur otherwise.