Continuous fields and discrete samples: reconstruction through Delaunay tessellations

Here we introduce the Delaunay Density Estimator Method. Its purpose is ren dering a fully volume-covering reconstruction of a density field from a set of discrete data points sampling this field. Reconstructing density or int ensity fields from a set of irregularly sampled data is a recurring key iss ue in operations on astronomical data sets, both in an observational contex t as well as in the context of numerical simulations. Our technique is base d upon the stochastic geometric concept of the Delaunay tessellation genera ted by the point set. We shortly describe the method, and illustrate its vi rtues by means of an application to an N-body simulation of cosmic structur e formation. The presented technique is a fully adaptive method: automatica lly it probes high density regions at maximum possible resolution, while lo w 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 filam ents and walls. The prominence of such features at a range of resolution le vels within a hierarchical clustering scenario as the example of the standa rd CDM scenario is shown to be impressively recovered by our scheme.