  The excluded area between a pair of two-dimensional hard particles with given
relative orientation is the region in which one particle cannot be located due
to the presence of the other particle. The magnitude of the excluded area as a
function of the relative particle orientation plays a major role in the
determination of the bulk phase behaviour of hard particles. We use principal
component analysis to identify the different types of excluded area
corresponding to randomly generated two-dimensional hard particles modeled as
non-self-intersecting polygons and star lines (line segments radiating from a
common origin). Only three principal components are required to have an
excellent representation of the value of the excluded area as a function of the
relative particle orientation. Independently of the particle shape, the minimum
value of the excluded area is always achieved when the particles are
antiparallel to each other. The property that affects the value of the excluded
area most strongly is the elongation of the particle shape. Principal component
analysis identifies four limiting cases of excluded areas with one to four
global minima at equispaced relative orientations. We study selected particle
shapes using Monte Carlo simulations.
