  Efficient shape morphing techniques play a crucial role in the approximation
of partial differential equations defined in parametrized domains, such as for
fluid-structure interaction or shape optimization problems. In this paper, we
focus on Inverse Distance Weighting (IDW) interpolation techniques, where a
reference domain is morphed into a deformed one via the displacement of a set
of control points. We aim at reducing the computational burden characterizing a
standard IDW approach without significantly compromising the accuracy. To this
aim, first we propose an improvement of IDW based on a geometric criterion
which automatically selects a subset of the original set of control points.
Then, we combine this new approach with a dimensionality reduction technique
based on a Proper Orthogonal Decomposition of the set of admissible
displacements. This choice further reduces computational costs. We verify the
performances of the new IDW techniques on several tests by investigating the
trade-off reached in terms of accuracy and efficiency.
