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We present a new algorithm for interactive generation of hard-edged, umbral shadows in complex environments with a moving light source. Our algorithm uses a hybrid approach that combines the image quality of object-precision methods with the efficiencies of image-precision techniques. We present an algorithm for computing a compact potentially visible set (PVS) using levels-of-detail (LODs) and visibility culling. We use the PVSs computed from both the eye and the light in a novel cross-culling algorithm that identifies a reduced set of potential shadow-casters and shadow-receivers. Finally, we use a combination of shadow-polygons and shadow maps to generate shadows. We also present techniques for LOD-selection to minimize possible artifacts arising from the use of LODs. Our algorithm can generate sharp shadow edges and reduces the aliasing in pure shadow map approaches. We have implemented the algorithm on a three-PC system with NVIDIA GeForce 4 cards. We achieve 7--25 frames per second in three complex environments composed of millions of triangles.