A non-iterative method and its application to planar geometries in homogeneous media is presented. The method is extendable to the cases of quasi-planar structures and/or layered-media problems. The fast direct algorithm (FDA)/steepest descent path (SDP) takes advantage of the fact that the induced currents on planar and quasi-planar geometries interact with each other within a very limited solid angle. Thus, all the degrees of freedom required to solve a `truly 3D' geometry are not required for a planar or quasi-planar geometry, and this situation can be exploited to develop efficient solution algorithms.