  An exact calculation of electromagnetic scattering from a perfectly
conducting parabolic cylinder is employed to compute Casimir forces in several
configurations. These include interactions between a parabolic cylinder and a
plane, two parabolic cylinders, and a parabolic cylinder and an ordinary
cylinder. To elucidate the effect of boundaries, special attention is focused
on the "knife-edge" limit in which the parabolic cylinder becomes a half-plane.
Geometrical effects are illustrated by considering arbitrary rotations of a
parabolic cylinder around its focal axis, and arbitrary translations
perpendicular to this axis. A quite different geometrical arrangement is
explored for the case of an ordinary cylinder placed in the interior of a
parabolic cylinder. All of these results extend simply to nonzero temperatures.
