C-shaped G~2 Hermite interpolation by rational cubic Bezier curve with conic precision

摘要

We present a simple method for C-shaped G~2 Hermite interpolation by a rational cubic Bezier curve with conic precision. For the interpolating rational cubic Bezier curve, we derive its control points according to two conic Bezier curves, both matching the G~1 Hermite data and one end curvature of the given G~2 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 Bezier curves are the same when the given G~2 Hermite data are sampled from a conic. Both the control points and weights of the resulting rational cubic Bezier curve are expressed in explicit form.