Here we describe the DTFE method for reconstructing fully self-adaptive volume-covering continuous density, velocity and other dynamical fields from a set of irregularly distributed ``tracer'' points. The DTFE method uses a point set's Voronoi tessellation for density estimation, and its Delaunay tessellation as multidimensional interpolation
interval for the velocity fields and resulting density fields. The key virtues of the method are its ability to preserve the anisotropic and hierarchical nature of spatial patterns in point distributions. DTFE was developed for the purpose of analyzing the process of cosmic structure formation.
Two important aspects of cosmic structure formation and evolution through gravitational instability are that it 1) involves a hierarchical process in which small scale objects emerge before they merge into larger features and that it 2) proceeds through a sequel of increasingly anisotropic planar and filamentary configurations before reaching final collapse and virialization into a compact halo. Two major sources of information on the structure formation process are the observed spatial distribution and peculiar velocities of galaxies and the theoretical modelling of the process by N-body computer simulations. Both involve dataset with irregularly distributed spatial point sets. For a proper theoretical interpretation
of the information they contain, such datasets ideally should be processed such that 1) one can reconstruct volume-covering density, velocity and other dynamical fields in a fully self-adaptive and filter-independent fashion, 2) retains the full hierarchical substructure present in the dataset, 3) at each scale of the hierarchy reproduces the anisotropy of the structural features, preserving their shape without any filter dilution.
The presentation will discuss its application to the 2dFGRS and SDSS galaxy redshift surveys, the application to the analysis of density, velocity and other dynamical fields in large N-body simulations of structure formation.