  Simulation methods for the decays $ B \to {\pi}^+ {\pi}^- V$, where $V$ is a
$1^{--}$ vector-meson, are presented in detail. Emphasis is put on the use of
the helicity formalism and the use of effective Lagrangians. We show the
importance of ${{\rho}^{0}}-{\omega}$ mixing in enhancing the direct $CP$
violation (DCPV) when the pion-pion invariant mass is near the mass of the
$\omega$.
