  The Newton polygon of the implicit equation of a rational plane curve is
explicitly determined by the multiplicities of any of its parametrizations. We
give an intersection-theoretical proof of this fact based on a refinement of
the Kushnirenko-Bernstein theorem. We apply this result to the determination of
the Newton polygon of a curve parameterized by generic Laurent polynomials or
by generic rational functions, with explicit genericity conditions. We also
show that the variety of rational curves with given Newton polygon is
unirational and we compute its dimension. As a consequence, we obtain that any
convex lattice polygon with positive area is the Newton polygon of a rational
plane curve.

Algebraic Geometry;Combinatorics