Abstract: In this paper we abandon the regular structure of shadow maps. Instead, we transform the visible pixels P(x, y, z) from screen space to the image plane of a light source P'(x', y', z'). The (x', y') are then used as sampling points when the geometry is rasterized into the shadow map. This eliminates the resolution issues that have plagued shadow maps for decades, e.g., jagged shadow boundaries. Incorrect self-shadowing is also greatly reduced, and semi-transparent shadow casters and receivers can be supported. A hierarchical software implementation is outlined.