  Rational B\'{e}zier functions are widely used as mapping functions in surface
reparameterization, finite element analysis, image warping and morphing. The
injectivity (one-to-one property) of a mapping function is typically necessary
for these applications. Toric B\'{e}zier patches are generalizations of
classical patches (triangular, tensor product) which are defined on the convex
hull of a set of integer lattice points. We give a geometric condition on the
control points that we show is equivalent to the injectivity of every 2D toric
B\'{e}zier patch with those control points for all possible choices of weights.
This condition refines that of Craciun, et al., which only implied injectivity
on the interior of a patch.
