Amanatides and Wu's “A Fast Voxel Traversal..” http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.42.3443&rep=rep1&type=pdf is great for stepping through a grid along a ray, however it only works for infinitely thin rays – I'm trying to sweep a circle through a grid, and I can't find any similar algorithm for swept-circles.
AFAICT there should be some way to adapt Amanatides+Wu so that it visits all the grid cells touched by a “fat ray”. On paper it seems like it should be sufficient to cast two rays and then visit …