  We show how generalized quark distributions in the nucleon describe the
density of polarized quarks in the impact parameter plane, both for
longitudinal and transverse polarization of the quark and the nucleon. This
density representation entails positivity bounds including chiral-odd
distributions, which tighten the known bounds in the chiral-even sector. Using
the quark equations of motion, we derive relations between the moments of
chiral-odd generalized parton distributions of twist two and twist three. We
exhibit the analogy between polarized quark distributions in impact parameter
space and transverse momentum dependent distribution functions.
