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This paper presents a new method to compute exact from-polygon visibility, as well as a possible application to the calculation of high quality ambient occlusion. The starting point of this work is a theoretical framework which allows to group lines together according to the geometry they intersect. By applying this study in the context of from-polygon visibility, we derive an analytical definition which permits us to group the view rays according to the first geometry they encounter. Our new algorithm encodes lazily the visibility from a polygon. In contrast to the previous works on from-polygon visibility, our approach is very robust. For each point in the scene, the algorithm efficiently calculates the exact fragments of visible geometry. By combining this information with a analytical definition of ambient occlusion, we achieve results that are not sensitive to noise or other visual imperfections, contrary to ambient occlusion methods which are based either on sampling or visibility approximations.