  The reconstruction of density and velocity fields is of central importance to
the interpretation of $N$-body simulations. We propose a phase-space extension
of the Delaunay tessellation field estimator (DTFE) that tracks the dark matter
fluid in phase-space. The new reconstruction scheme removes several artifacts
from the conventional DTFE in multi-stream regions, while preserving the
adaptive resolution in high-density regions and yielding continuous fields. The
estimator also removes tessellation artifacts of a previously proposed
phase-space reconstruction scheme.
