Continuous Fields and Discrete Samples: Reconstruction through Delaunay Tessellations

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.