Abstract
A novel method allowing to compute density, velocity and other fields in cosmological N--body simulations with unprecedentedly high spatial resolution is described. It is based on the tessellation of the three-dimensional manifold representing cold dark matter in six-dimensional phase space. The density, velocity and other fields are computed by projecting the tessellation on configuration space. The application of this technique to cosmological N--body simulations in LambdaCDM cosmology reveals a far more elaborate cosmic web then dot plots or self--adaptive SPH. In addition, this method allows to uniquely define physical voids and identify and study the caustic surfaces directly.
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