An Aliasing Theory of Shadow Mapping

Abstract

Shadow mapping is a popular image-based technique for real-time shadow rendering. Although numerous improvements have been made to help anti-aliasing in shadow mapping, there is a lack of mathematical tools that allow us to quantitatively analyze aliasing errors in its variants. In this paper, we establish an aliasing theory to achieve this goal. A generalized representation of aliasing errors is derived from a pure mathematical point of view. The major highlight of this representation is the ability of quantifying the aliasing error at any position for general view-light configurations. On the contrary, due to the geometric assumptions used in the computational model, previous work analyzes the aliasing only along the view direction in the simplest case where the light and view directions are orthogonal. Subsequently, as a direct application of our theory, we present a comparison of aliasing distributions in a few representative variants of perspective shadow maps. We believe that these theoretical results are useful to better understand shadow mapping, and thus inspire people to develop novel techniques in this area.