Interpolation of G3 Hermite data by quintic Bézier space curves

The problem of interpolation of G3 Hermite data (end points, Frenet frames, curvatures, and torsions) by quintic space curves is addressed. It is shown that, in general, a family of interpolants to such data exist, dependent on two free parameters (which determine the magnitudes of the end–point derivatives). If the G3 data is sampled from a prescribed analytic curve, the free parameters may be employed to minimize the mid–point discrepancy between the interpolant and the given curve, or to optimize a measure of shape quality, such as the elastic bending energy. Several computed examples are included to show that the G3 quintic interpolants to data derived from a given smooth space curve are capable of achieving excellent approximation accuracy