  We present an algorithm that takes as input a finite point set in Euclidean
space, and performs a perturbation that guarantees that the Delaunay
triangulation of the resulting perturbed point set has quantifiable stability
with respect to the metric and the point positions. There is also a guarantee
on the quality of the simplices: they cannot be too flat. The algorithm
provides an alternative tool to the weighting or refinement methods to remove
poorly shaped simplices in Delaunay triangulations of arbitrary dimension, but
in addition it provides a guarantee of stability for the resulting
triangulation.
