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Broad Phase Self-Intersection

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I have a problem, and without delving into the background, let me describe it abstractly. I have a bunch of lines/surfaces (2d or 3d, id like it to be general) with a certain thickness. The vertices of these surfaces have a certain position, and a certain target position. I want this geometry to approach its target position, without penetrating eachother or itself. The good thing is that this are inertialess and completely deformable geometries, so there is no need to statisfy the laws of motion or other contraints. An naive implementation would be: -move vertices towards target position in a step smaller than its associated thickness -push all intersecting things apart -repeat until the situation converges (possibility not at each's target position) However, i want to apply some broad phase culling to the intersection process. But i dont really have a clue how to go about it. it may take many steps to move something completely towards its target position, and any structures involved would need to be updateable lightning fast. One technique im not familiar with is hash-based collision. Would that be something for me? Other thoughts?

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Spatial hashing seems like the obvious choice.

You can find something to get you started here.

Also, depending on the nature of your problem, you could take a look at the spatial hash tiling algorithm by Mark Overmars.

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