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A general integral finite-difference time-domain (FDTD) formulation on cubical grids for the modeling of electrically inhomogeneous media of arbitrary shape is derived. The simple cubical structure is maintained and no modifications of the integral paths are necessary. Instead, a three-dimensional tensor relationship between the average electric flux density and electric field is determined beforehand and used during the simulation to account for discontinuities in the neighborhood of sloped interfaces. The accuracy of the method is confirmed by comparisons with analytical solutions.