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Continuous collision detection

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I'm trying to make a 2D physics engine, and for the hit detection I'm currently using SAT. Currently all objects are stationary and the collision detection is discrete, but I'm trying to implement a continuous collision detection. I did some research and found out there's "swept SAT", but from what I understand it can only predict the collision between moving objects that are not rotating (but can't predict the collision between two moving rotating objects). However, I also found out about Minkowski collision detection and that it can work for continuous collision detection for moving rotating objects, but I didn't really do much research into it because I already have SAT. I was wondering if there's a way to predict whether and when two moving rotating objects will collide with SAT, or if I should try to implement the Minkowski collision detection (also, how hard is it compared to SAT?).


Thank you

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