  Collective-density variables have proved to be a useful tool in the
prediction and manipulation of how spatial patterns form in the classical
many-body problem. Previous work has employed properties of collective-density
variables along with a robust numerical optimization technique to find the
classical ground states of many-particle systems subject to radial pair
potentials in one, two and three dimensions. That work led to the
identification of ordered and disordered classical ground states. In this
paper, we extend these collective-coordinate studies by investigating the
ground states of directional pair potentials in two dimensions. Our study
focuses on directional potentials whose Fourier representations are non-zero on
compact sets that are symmetric with respect to the origin and zero everywhere
else. We choose to focus on one representative set which has exotic
ground-state properties: two circles whose centers are separated by some fixed
distance. We obtain ground states for this "two-circle" potential that display
large void regions in the disordered regime. As more degrees of freedom are
constrained the ground states exhibit a collapse of dimensionality
characterized by the emergence of filamentary structures and linear chains.
This collapse of dimensionality has not been observed before in related
studies.
