Valient, M., W., H., de Boer., “Fractional-Disk Soft Shadows”, In: Engel, W. F., et al., “ShaderX3: Advanced Rendering With DirectX And OpenGL”, Charles River Media, November 2004, ISBN 1-58450-357-2.
This article describes a simple, practical, and fairly effective way to approximate soft shadows. The actual implementation is a modification of the percentage closer filtering (PCF). PCF was originally designed to address the aliasing problem inherent in shadow mapping. It also has the welcome side effect of generating soft shadow edges, which resemble simple constant-width penumbrae. In this article we show how a modified PCF algorithm can produce more realistic penumbrae. We use stochastic sampling varied per pixel to obtain reasonable results while using fewer shadow map samples.