Practical logarithmic shadow maps

Abstract

Computer games and simulators are among the most demanding real-time computer graphics applications. In these applications, shadows greatly contribute to the visual realism and provide important depth cues. However, computing high-quality shadows at interactive rates in a complex and dynamic environment remains a challenging problem. In this paper, we restrict ourselves to generating hard shadows from point light sources. One of the popular techniques for interactive shadow generation is shadow mapping [Williams 1978]. A major disadvantage of shadow maps is that they are prone to aliasing artifacts if they have inadequate resolution. Aliasing error can be classified as perspective or projection aliasing [Stamminger and Drettakis 2002]. Current practical shadow mapping solutions reduce perspective aliasing by reparameterizing the shadow map to allocate more resolution to the undersampled regions of a scene [Stamminger and Drettakis 2002; Wimmer et al. 2004]. These algorithms use the 4× 4 projective transformation matrices available on current GPUs to obtain a non-uniform parameterization. The optimal shadow mapping parameterization, however, involves logarithmic transformations. Since perspective and logarithmic functions can diverge significantly, approximations with projective transformations can require much higher shadow map resolution to avoid perspective aliasing.