  In the paper, the planar polynomial geometric interpolation of data points is
revisited. Simple sufficient geometric conditions that imply the existence of
the interpolant are derived in general. They require data points to be convex
in a certain discrete sense. Since the geometric interpolation is based
precisely on the known data only, one may consider it as the parametric
counterpart to the polynomial function interpolation. The established result
confirms the H\"{o}llig-Koch conjecture on the existence and the approximation
order in the planar case for parametric polynomial curves of any degree stated
quite a while ago.
