Geometric Hermite Interpolation Based on the Representation of Circular Arcs

摘要

A new heuristic method of geometric Hermite interpolation is presented to construct a planar cubic rational Bezier curve with two points and two unit tangent directions. The integral, which shows the change rate of the curvature, is taken as the energy function to measure the fairness of the parameter curve. Hence the curvature of the new curve is more stable. Since that the energy function of circular arc is minimum, the necessary and sufficient condition for the cubic rational Bezier curve representation of circular arc, instead of the sufficient condition mentioned in Farm's scheme, is applied to construct the planar cubic rational Bezier curve. The energy function of now curve can be less then the one of Farin's curve. The numerical example is presented to illustrate the validity of the algorithm.