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2D concave-concave polygon collision detection

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I am using a variation on a static quadtree for broad-phase pruning, but I'm not sure how to handle concave-concave collision detection. Obviously I first split the concave polygons into several convex sub-polygons, but now I want to avoid doing m*n convex-convex intersection tests. I was thinking that I could implement a bounding-box hierarchy to contain my object - first 1 big AABB, which contains 2 smaller AABBs, that contain 2 even smaller ones etc., until at the final level, each AABB would only contain one convex sub-polygon. To test if a given point is inside the object, it would 1st check the largest AABB, and if it was inside, it would check the two contained AABB's, and so on, checking only the sub-AABB's of the AABB's it intersects. I guess what I'm asking is, is there a faster/more elegant/better method? And what are the draw-backs of this method? Keep in mind the concave polygons will be potentially huge and very complex, rotating and moving all the time, and it is likely they will cluster together into a pile, however, even that pile will keep on moving-rotating (everything is basically in space, and the clustering will be due to gravitational attraction between the objects). Thanks, and toodles.

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