  Here we introduce the Delaunay Density Estimator Method. Its purpose is
rendering a fully volume-covering reconstruction of a density field from a set
of discrete data points sampling this field. Reconstructing density or
intensity fields from a set of irregularly sampled data is a recurring key
issue in operations on astronomical data sets, both in an observational context
as well as in the context of numerical simulations. Our technique is based upon
the stochastic geometric concept of the Delaunay tessellation generated by the
point set. We shortly describe the method, and illustrate its virtues by means
of an application to an N-body simulation of cosmic structure formation. The
presented technique is a fully adaptive method: automatically it probes high
density regions at maximum possible resolution, while low density regions are
recovered as moderately varying regions devoid of the often irritating
shot-noise effects. Of equal importance is its capability to sharply and
undilutedly recover anisotropic density features like filaments and walls. The
prominence of such features at a range of resolution levels within a
hierarchical clustering scenario as the example of the standard CDM scenario is
shown to be impressively recovered by our scheme.
