Arbitrary compact shapes
"Casimir Forces between Arbitrary Compact Objects,"
T. Emig, N. Graham, R. L. Jaffe, and M. Kardar, Phys. Rev. Lett. 99, 170403 (2007)
Generalizes the multi-pole expansion from electrostatics to fluctuating sources
Full results are available for (frequency-dependent) dielectrics, as well as metals
Can be generalized to arbitrary compact shapes:
The shape and material properties are encoded in the scattering properties of the object.