In time-domain simulations of sound propagation and/or scattering, it is possible to model the geometrical-acoustics (GA) components and the edge-diffraction components separately and combine the results into a "total" impulse response. However, such separate calculations can limit the efficiency and accuracy of the simulations because the two components are not independent. This paper presents an integrated approach for time-domain acoustic modeling in which intermediate values normally utilized only in diffraction calculations are exploited in finding the GA components as well. Specifically, it is shown how to detect the existence of first-order specular reflections and an unobstructed direct-sound path using source and receiver locations specified in edge-aligned cylindrical coordinates. The benefits of the method are described for general modeling cases, as well as for specific source/receiver configurations in which the receiver is located on or near a specular-zone or shadow-zone boundary. Particular attention is paid to the zone-boundary cases, where this method is well suited to ensure continuity of the sound field across the boundary.