  We present the preliminary measurement of CP-violating asymmetries in
B0->(rhopi)0->pi+pi-pi0 decays using a time-dependent Dalitz plot analysis. The
results are obtained from a data sample of 213 million Y(4S)->BB-bar decays,
collected by the BABAR detector at the PEP-II asymmetric-energy B Factory at
SLAC. This analysis extends the narrow-rho quasi-two-body approximation used in
the previous analysis, by taking into account the interference between the rho
resonances of the three charges. We measure 16 coefficients of the bilinear
form factor terms occurring in the time-dependent decay rate of the B0 meson
with the use of a maximum-likelihood fit. We derive the physically relevant
quantities from these coefficients. We measure the direct CP-violation
parameters Acp = -0.088 +- 0.049 +- 0.013 and C = 0.34 +- 0.11 +- 0.05, where
the first errors are statistical and the second systematic. For the
mixing-induced CP-violation parameter we find S = -0.10 +- 0.14 +- 0.04, and
for the dilution and strong phase shift parameters respectively, we obtain dC =
0.15 +- 0.11 +- 0.03 and dS = 0.22 +- 0.15 +- 0.03. For the angle alpha of the
Unitarity Triangle we measure (113 +27 -17 +-6) deg, while only a weak
constraint is achieved at the significance level of more than two standard
deviations. Finally, for the relative strong phase delta+- between the
B0->rho-pi+ and B0->rho+pi- transitions we find (-67 +28 -31 +- 7) deg, with a
similarly weak constraint at two standard deviations and beyond.
