  The relativistic point-form formalism that we proposed for the study of the
electroweak structure of few-body bound states is applied to calculate the
elastic form factors of spin-1 mesons, such as the rho meson, within
constituent-quark models. We treat electron-meson scattering as a
Poincare-invariant coupled-channel problem for a Bakamjian-Thomas mass operator
and extract the meson current from the resulting invariant 1-photon-exchange
amplitude. Wrong cluster properties inherent in the Bakamjian-Thomas framework
are seen to cause spurious contributions in the current. These contributions,
however, can be separated unambiguously from the physical ones and we end up
with a meson current with all required properties. Numerical results for the
rho-meson form factors are presented assuming a simple harmonic-oscillator
bound-state wave function. The comparison with other approaches reveals a
remarkable agreement of our results with those obtained within the covariant
light-front scheme proposed by Carbonell et al. [Phys. Rep. 300, 215 (1998)].
