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Registering a line within a grid

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I''m trying to do a piball game, and I''ve got basic collisions working fine, but I want to partition things into a grid to cut down on collision checks. Each line will have to register itself in all grid squares that it goes through. Using the Bresenham algorithm doesn''t work because it''ll jump along diagonals without getting the squares above or beside the original square. I found a modified algorithm that provides more coverage, but still doesn''t fully cover the line, because it''s really trying to cover a line from the middle of the start square to the middle of the end square, instead of a line that starts anywhere within the start, etc. Can someone point me in a good direction for this?

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