This paper presents a novel approach to compute high quality and noise-free soft shadows using exact visibility computations. This work relies on a theoretical framework allowing to group lines according to the geometry they intersect. From this study, we derive a new algorithm encoding lazily the visibility from a polygon. Contrary to previous works on from-polygon visibility, our approach is very robust and straightforward to implement. We apply this algorithm to solve exactly and efficiently the visibility of an area light source from any point in a scene. As a consequence, results are not sensitive to noise, contrary to soft shadows methods based on area light source sampling. We demonstrate the reliability of our approach on different scenes and configurations.