How to find 2D grid cells swept by a moving circle?

Posted by Nevermind on Game Development See other posts from Game Development or by Nevermind
Published on 2011-06-22T14:11:02Z Indexed on 2011/06/22 16:31 UTC
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c#

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collision-detection

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algorithm

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grid

I'm making a game based on a 2D grid, with some cells passable and some not. Dynamic objects can move continuously, independent of the grid, but need to collide with impassable cells.

I wrote an algorithm to trace a ray against the grid, that gives me all cells that ray intersects. However, actual object are not point-sized; I'm currently representing them as circles. But I can't figure out an effective algorithm to trace a moving circle. Here's a picture of what I need: enter image description here

The numbers show in what order the circle collides with grid cells. Does anybody know the algorithm to find these collisions? Preferably in C#.

Update The circle can be bigger than a single grid cell.

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