On determining the shape of matter distributions
  A basic property of objects, like galaxies and halos that form in
cosmological structure formation simulations, is their shape. Here, we
critically investigate shape determination methods that are commonly used in
the literature. It is found that using an enclosed integration volume and
weight factors r^{-2} and r_{ell}^{-2} (elliptical radius) for the contribution
of each particle or volume element in the shape tensor leads to biased axis
ratios and smoothing of details when calculating the local shape as a function
of distance from the center. To determine the local shape of matter
distributions as a function of distance for well resolved objects (typically
more than O(10^4) particles), we advocate a method that (1) uses an ellipsoidal
shell (homoeoid) as an integration volume without any weight factors in the
shape tensor and (2) removes subhalos.
