  A numerical scheme is described for accurately accommodating oblique,
non-aligned, boundaries, on a three-dimensional cartesian grid. The scheme
gives second-order accuracy in the solution for potential of Poisson's equation
using compact difference stencils involving only nearest neighbors.
Implementation for general "Robin" boundary conditions and for boundaries
between media of different dielectric constant for arbitrary-shaped regions is
described in detail. The scheme also provides for the interpolation of field
(potential gradient) which, despite first-order peak errors immediately
adjacent to the boundaries, has overall second order accuracy, and thus
provides with good accuracy what is required in particle-in-cell codes: the
force. Numerical tests on the implementation confirm the scalings and the
accuracy.
