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In this paper, we present a new shadow mapping technique that improves upon the quality of perspective and uniform shadow maps. Our technique uses a perspective transform specified in light space which allows treating all lights as directional lights and does not change the direction of the light sources. This gives all the benefits of the perspective mapping but avoids the problems inherent in perspective shadow mapping like singularities in post-perspective space, missed shadow casters etc. Furthermore, we show that both uniform and perspective shadow maps distribute the perspective aliasing error that occurs in shadow mapping unequally over the available depth range. We therefore propose a transform that equalizes this error and gives equally pleasing results for near and far viewing distances. Our method is simple to implement, requires no scene analysis and is therefore as fast as uniform shadow mapping.