  Superellipse sector particles (SeSPs) are segments of superelliptical curves
that form a tunable set of hard-particle shapes for granular and colloidal
systems. SeSPs allow for continuous parameterization of corner sharpness,
aspect ratio, and particle curvature; rods, circles, rectangles, and staples
are examples of shapes SeSPs can model. We compare three computational
processes: pair-wise Monte Carlo simulations that look only at
particle-particle geometric constraints, Monte Carlo simulations that look at
how these geometric constraints play out over extended dispersions of many
particles, and Molecular Dynamics simulations that allow particles to interact
to form random loose and close packings. We investigate the dependence of
critical random loose and close packing fractions on particle parameters,
finding that both values tend to increase with opening aperture (as expected)
and, in general, decrease with increasing corner sharpness. The identified
packing fractions are compared with the mean-field prediction of the Random
Contact Model. We find deviations from the model's prediction due to
correlations between particle orientations. The complex interaction of spatial
proximity and orientational alignment is explored using a generalized
Spatio-Orientational Distribution Area (SODA) plot. Higher density packings are
achieved through particles assuming a small number of preferred configurations
which depend sensitively on particle shape and system preparation.
