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Collision detection

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Hello, I'm having trouble with collision detection. I'm sorry if this is not right forum for this. I have 2D geometries and I should move one geometry to specified direction until it collides with another geometry. Here's a drawing about that (red geometry is just a preview of the original geometry after move): Free Image Hosting at www.ImageShack.us I have searched for collision detection algorithms, but haven't found good enough. Many of the algorithms are for 3D. I'm sure there's relatively simple algorithm which solves my problem.

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The first thing that comes to mind for that particular example is swept SAT. You would need to decompose the objects into convex polygons (you'd have to sacrifice some accuracy with respect to the curved portions of the shapes), and then perform multiple swept SAT tests to determine the first time of intersection.

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