Strictly speaking, neither the Laplace equation nor the biharmonic
equation provides a local interpolation scheme.
Depending on the
topology of the grid point cloud, the change in any of the Dirichlet
values may have an impact on all 
. The insertion of
additional grid points also affects the values on grid points already
present. The mutual
influence (the coupling) of two points, however, does decay
with increasing distance.
The Laplace equation yields a monotonous interpolation scheme, whereas the
biharmonic equation tends to produce ``overshoots'' at local maxima.
For these reasons, both point-cloud interpolation
methods are available in VORONOI and can be used alternatively
to fit the requirements of the problem at hand.