Geometry of the Cosmic Web: Minkowski Functionals from the Delaunay
  Tessellation
  We present a novel method for computing the Minkowski Functionals from
isodensity surfaces extracted directly from the Delaunay tessellation of a
point distribution. This is an important step forward compared to the previous
cosmological studies when the isodensity surface was built in the field on a
uniform cubic grid and therefore having a uniform spatial resolution. The
density field representing a particular interest in cosmology is the density of
galaxies which is obtained from the highly nonuniform distribution of the
galaxy positions. Therefore, the constraints caused by the spatially uniform
grid put severe limitations on the studies of the geometry and shapes of the
large-scale objects: superclusters and voids of galaxies. Our technique
potentially is able to eliminate most of these limitations. The method is
tested with some simple geometric models and an application to the density
field from an N-body simulation is shown.
