C-shaped G2G2 Hermite interpolation by rational cubic Bézier curve with conic precision

•The method reproduces a conic arc if the input data come from such a conic curve.•The method can reproduce a ‘whole’ conic curve even if it has singularities.•The Bézier control points have well understood geometrical meaning.•The final rational Bézier control points and weights are given in explicit form.•Each of the tangential angles of the given tangent vectors can be arbitrary up to π.

We present a simple method for C-shaped G2G2 Hermite interpolation by a rational cubic Bézier curve with conic precision. For the interpolating rational cubic Bézier curve, we derive its control points according to two conic Bézier curves, both matching the G1G1 Hermite data and one end curvature of the given G2G2 Hermite data, and the weights are obtained by the two given end curvatures. The conic precision property is based on the fact that the two conic Bézier curves are the same when the given G2G2 Hermite data are sampled from a conic. Both the control points and weights of the resulting rational cubic Bézier curve are expressed in explicit form.