  The $\phi(\kpp)\sim \kpp$ relation is called polarization structure. By
density functional calculations, we study the polarization structure in
ferroelectric perovskite PbTiO$_3$, revealing (1) the $\kpp$ point that
contributes most to the electronic polarization, (2) the magnitude of
bandwidth, and (3) subtle curvature of polarization dispersion. We also
investigate how polarization structure in PbTiO$_3$ is modified by compressive
inplane strains. The bandwidth of polarization dispersion in PbTiO$_3$ is shown
to exhibit an unusual decline, though the total polarization is enhanced. As
another outcome of this study, we formulate an analytical scheme for the
purpose of identifying what determine the polarization structure at arbitrary
$\kpp$ points by means of Wannier functions. We find that $\phi(\kpp)$ is
determined by two competing factors: one is the overlaps between neighboring
Wannier functions within the plane {\it perpendicular} to the polarization
direction, and the other is the localization length {\it parallel} to the
polarization direction. Inplane strain increases the former while decreases the
latter, causing interesting non-monotonous effects on polarization structure.
Finally, polarization dispersion in another paradigm ferroelectric BaTiO$_3$ is
discussed and compared with that of PbTiO$_3$.
