Abstract :
The quadratic geometric Hermite interpolant (GHI), as introduced by Höllig and Koch, is an interpolation scheme with maximal order and smoothness. Existence of the GHI depends on the given data. If the curve f, to be interpolated at ft0 and ft1, is analytic, then nonzero curvature and small h:=t1−t0 guarantee existence. An example of a C∞ curve is given to show that this conclusion does not hold if f is only smooth but not analytic.
