  A number of methods for studying the large-scale cosmic matter distribution
exist in the literature. One particularly common method employed to define the
cosmic web is to examine the density, velocity or potential field. Such methods
are advantageous since a Hessian matrix can be constructed whose eigenvectors
(and eigenvalues) indicate the principal directions (and strength) of local
collapse or expansion. Technically this is achieved by diagonalizing the
Hessian matrix using a fixed finite grid. The resultant large-scale structure
quantification is thus inherently limited by the grid's finite resolution.
Here, we overcome the obstacle of finite grid resolution by introducing a new
method to determine halo environment using an adaptive interpolation which is
more robust to resolution than the typical "Nearest Grid Point" (NGP) method.
Essentially instead of computing and diagonalizing the Hessian matrix once for
the entire grid, we suggest doing so once for each halo or galaxy in question.
We examine how the eigenvalues and eigenvector direction's computed using our
algorithm and the NGP method converge for different grid resolutions, finding
that our new method is convergent faster. Namely changes of resolution have a
much smaller effect than in the NGP method. We therefore suggest this method
for future use by the community.
