Shadows contribute significantly to the perceived realism of an image, and provide an important depth cue. Rendering high quality, antialiased shadows efficiently is a difficult problem. To antialias shadows, it is necessary to compute partial visibilities, but computing these visibilities using existing approaches is often too slow for interactive applications.
Shadow maps are a widely used technique for real-time shadow rendering. One major drawback of shadow maps is aliasing, because the shadow map data cannot be filtered in the same way as colour textures.
In this thesis, I present variance shadow maps (VSMs). Variance shadow maps use a linear representation of the depth distributions in the shadow map, which enables the use of standard linear texture filtering algorithms. Thus VSMs can address the problem of shadow aliasing using the same highly-tuned mechanisms that are available for colour images. Given the mean and variance of the depth distribution, Chebyshev's inequality provides an upper bound on the fraction of a shaded fragment that is occluded, and I show that this bound often provides a good approximation to the true partial occlusion.
For more difficult cases, I show that warping the depth distribution can produce multiple bounds, some tighter than others. Based on this insight, I present layered variance shadow maps, a scalable generalization of variance shadow maps that partitions the depth distribution into multiple segments. This reduces or eliminates an artifact - "light bleeding" - that can appear when using the simpler version of variance shadow maps. Additionally, I demonstrate exponential variance shadow maps, which combine moments computed from two exponentially-warped depth distributions. Using this approach, high quality results are produced at a fraction of the storage cost of layered variance shadow maps.
These algorithms are easy to implement on current graphics hardware and provide efficient, scalable solutions to the problem of shadow map aliasing
