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The most popular techniques for interactive rendering of hard shadows are shadow maps and shadow volumes. Shadow maps work well in regions that are completely in light or in shadow but result in objectionable artifacts near shadow boundaries. In contrast, shadow volumes generate precise shadow boundaries but require high fill rates. In this paper, we propose the method of silhouette maps, in which a shadow depth map is augmented by storing the location of points on the geometric silhouette. This allows the shader to construct a piecewise linear approximation to the true shadow silhouette, improving the visual quality over the piecewise constant approximation of conventional shadow maps. We demonstrate an implementation of our approach running on programmable graphics hardware in real-time.