  We study the moment maps of a smooth projective toric variety. In particular,
we characterize when the moment map coming from the quotient construction is
equal to a weighted Fubini-Study moment map. This leads to an investigation
into polytopes with strict linear precision, and in the process we use results
from and find remarkable connections between Symplectic Geometry, Geometric
Modeling, Algebraic Statistics, and Algebraic Geometry.
