The inclusion of edge diffraction has long been recognized as an improvement to geometrical-acoustics (GA) modeling techniques, particularly for acoustic simulations of complex environments that are represented as collections of finite-sized planar surfaces. One particular benefit of combining edge diffraction with GA components is that the resulting total sound field is continuous when an acoustic source or receiver crosses a specular-zone or shadow-zone boundary, despite the discontinuity experienced by the associated GA component. In interactive acoustic simulations which include only GA components, such discontinuities may be heard as clicks or other undesirable audible artifacts, and thus diffraction calculations are important for high perceptual quality as well as physical realism. While exact diffraction calculations are difficult to compute at interactive rates, approximate calculations are possible and sufficient for situations in which the ultimate goal is a perceptually plausible simulation rather than a numerically exact one. In this paper, we describe an edge-subdivision strategy that allows for fast time-domain edge-diffraction calculations with relatively low error when compared with results from a more numerically accurate solution. The tradeoff between computation time and accuracy can be controlled with a number of parameters, allowing the user to choose the speed that is necessary and the error that is tolerable for a specific modeling scenario.