  The transverse charge density in the pion can be represented as a dispersion
integral of the imaginary part of the pion form factor in the timelike region.
This formulation incorporates information from e+e- annihilation experiments
and allows one to reconstruct the transverse density much more accurately than
from the spacelike pion form factor data alone. We calculate the transverse
density using an empirical parametrization of the timelike pion form factor and
estimate that it is determined to an accuracy of ~10% at a distance b ~ 0.1 fm,
and significantly better at larger distances. The density is found to be close
to that obtained from a zero-width rho meson pole over a wide range and shows a
pronounced rise at small distances. The resulting two-dimensional image of the
fast-moving pion can be interpreted in terms of its partonic structure in QCD.
We argue that the singular behavior of the charge density at the center
requires a substantial presence of pointlike configurations in the pion's
partonic wave function, which can be probed in other high-momentum transfer
processes.
