On G 2 continuous cubic spline interpolation

In this paper the interpolation by G 2 continuous planar cubic Bézier spline curves is studied. The interpolation is based upon the underlying curve points and the end tangent directions only, and could be viewed as an extension of the cubic spline interpolation to the curve case. Two boundary, and two interior points are interpolated per each spline section. It is shown that under certain conditions the interpolation problem is asymptotically solvable, and for a smooth curve f the optimal approximation order is achieved. The practical experiments demonstrate the interpolation to be very satisfactory.