The class of problems to which the Finite-Difference Time-Domain (FDTD) method can be applied is extended through the use of near and far-field projection techniques. These methods are developed by applying the equivalence principle to a surface within the FDTD problem space. Algorithms are found to project the equivalent electric and magnetic currents on this surface to any point in space either in the time or the frequency domains. A summary of extensive validation and error checking results is presented which shows the routines to be robust and accurate to within a few percent. As a result, the FDTD approach can be applied to a number of previously impractical problems.