  We determine the energy-dependent amplitude for elastic {\pi}{\pi} P-wave
scattering in isospin-1 by computing part of the discrete energy spectrum of
QCD in finite cubic boxes. We observe a rapidly rising phase shift that can be
well described by a single {\rho} resonance. The spectrum is obtained from
hadron correlators computed using lattice QCD with light quark masses
corresponding to m{\pi} ~ 400 MeV. Variational analyses are performed with
large bases of hadron interpolating fields including, as well as fermion
bilinears that resemble q-qbar constructions, also operators that resemble
pairs of pions with definite relative and total momentum. We compute the
spectrum for a range of center-of-mass momenta and in various irreducible
representations of the relevant symmetry group. Hence we determine more than
thirty values of the isospin-1 P-wave scattering phase shift in the elastic
region, mapping out its energy dependence in unprecedented detail.
