G2 composite cubic Bézier curves

We present an algorithm for creating planar G2 spline curves using rational Bézier cubic segments. The splines interpolate a sequence of points, tangents and curvatures. In addition each segment has two more geometric shape handles. These are obtained from an analysis of the singular point of the curve. The individual segments are convex, but zero curvature can be assigned at a junction point, hence inflection points can be placed where desired but cannot occur otherwise.