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GJK Algorithm. The GJK uses supporting point in the Minkowski Difference to get close to the origin point. As it gets close to the Origin point, the GJK stores the supporting point in a set Q. If the set Q encloses the origin, a collision has occurred. Here is a visual representation of the GJK. (Assume M is a Minkowski difference.)
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In general, collision detection is tackled as a computational geometry problem, with the so-called Gilbert, Johnson, and Keerthi (GJK) algorithm being the most adopted solution nowadays. While.
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The Gilbert-Johnson-Keerthi distance algorithm is a method of determining the minimum distance between two convex sets, first published by Elmer G. Gilbert, Daniel W. Johnson, and S. Sathiya Keerthi in 1988.
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GJK is an algorithm for computing the minimal distance between two convex shapes. It cannot be directly used as a collision detection algorithm in games, since it doesn't account for movement. One simple trick in Ericson's book can change that, though. Keep in mind that GJK only requires the geometry's support function to work, it does.
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Correction: GJK is used to find the closest distance between two disjoint convex sets; it cannot find the minimum translation vector of two sets that are already intersecting. The algorithm used for that is called the Expanding Polytope Algorithm (EPA) and you can view it as an extension of GJK.
