Abstract: We present Convolution Shadow Maps, a novel shadow representation that affords efficient arbitrary linear filtering of shadows. Traditional shadow mapping is inherently non-linear w.r.t. the stored depth values, due to the binary shadow test. We linearize the problem by approximating shadow test as a weighted summation of basis terms. We demonstrate the usefulness of this representation, and show that hardware-accelerated anti-aliasing techniques, such as tri-linear filtering, can be applied naturally to Convolution Shadow Maps. Our approach can be implemented very efficiently in current generation graphics hardware, and offers real-time frame rates.