  We introduce a technique that simplifies the problem of imposing jump
conditions on interfaces that are not aligned with a computational grid in the
context of the Correction Function Method (CFM). The CFM offers a general
framework to solve Poisson's equation in the presence of discontinuities to
high order of accuracy, while using a compact discretization stencil. A key
concept behind the CFM is enforcing the jump conditions in a least squares
sense. This concept requires computing integrals over sections of the
interface, which is a challenge in 3-D when only an implicit representation of
the interface is available (e.g., the zero contour of a level set function).
The technique introduced here is based on a new formulation of the least
squares procedure that relies only on integrals over domains that are amenable
to simple quadrature after local coordinate transformations. We incorporate
this technique into a fourth order accurate implementation of the CFM, and show
examples of solutions to Poisson's equation computed in 2-D and 3-D.
