Abstract: We present a novel shadow map parameterization to reduce perspective aliasing artifacts for both point and directional light sources. We derive the aliasing error equations for both types of light sources in general position. Using these equations we compute tight bounds on the aliasing error. From these bounds we derive our shadow map parameterization, which is a simple combination of a perspective projection with a logarithmic transformation. We formulate several types of logarithmic perspective shadow maps (LogPSMs) by replacing the parameterization of existing algorithms with our own. We perform an extensive error analysis for both LogPSMs and existing algorithms. This analysis is a major contribution of this paper and is useful for gaining insight into existing techniques. We show that compared with competing algorithms, LogPSMs can produce significantly less aliasing error. Equivalently, for the same error as competing algorithms, LogPSMs can produce significant savings in both storage and bandwidth. We demonstrate the benefit of LogPSMs for several models of varying complexity.