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Most previous soft shadow algorithms have either suffered from aliasing, been too slow, or could only use a limited set of shadow casters and/or receivers. Therefore, we present a strengthened soft shadow volume algorithm that deals with these problems. Our critical improvements include robust penumbra wedge construction, geometry-based visibility computation, and also simplified computation through a four-dimensional texture lookup. This enables us to implement the algorithm using programmable graphics hardware, and it results in images that most often are indistinguishable from images created as the average of 1024 hard shadow images. Furthermore, our algorithm can use both arbitrary shadow casters and receivers. Also, one version of our algorithm completely avoids sampling artifacts which is rare for soft shadow algorithms. As a bonus, the four-dimensional texture lookup allows for small textured light sources, and, even video textures can be used as light sources. Our algorithm has been implemented in pure software, and also using the GeForce FX emulator with pixel shaders. Our software implementation renders soft shadows at 0.5--5 frames per second for the images in this paper. With actual hardware, we expect that our algorithm will render soft shadows in real time. An important performance measure is bandwidth usage. For the same image quality, an algorithm using the accumulated hard shadow images uses almost two orders of magnitude more bandwidth than our algorithm.