  A basis shape locus takes as input data a zero/nonzero pattern in an $n
\times k$ matrix, which is equivalent to a presentation of a transversal
matroid. The locus is defined as the set of points in the Grassmannian of $k$
planes in $\mathbb{R}^n$ which are the row space of a matrix with the
prescribed zero/nonzero pattern. We show that this locus depends only on the
transversal matroid, not on the specific presentation. When a transversal
matroid is a positroid, the closure of its basis shape locus is the associated
positroid variety. We give a sufficient, and conjecturally necessary, condition
for when a transversal matroid is a positroid. Finally, we discus applications
to two programs for computing scattering amplitudes in $\mathcal{N} = 4$ SYM
theory: one trying to prove that projections of certain positroid cells
triangulate the amplituhedron, and another using Wilson loop diagrams.
