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PSA: Collision Detection is an optimization problem and GJK is Frank-Wolfe


A different perspective on the collision detection problem.

It was discovered in 1988, and nowadays all the cool kids use it or some variant as a basis for collision detection, for example, PhysX, Bullet, Chaos, Jolt, and Rubikon. It is unclear whether Gilbert, Johnson, or Keerthi derived the algorithm from FW or maybe the connection is so trivial to people working in optimization that it is pointless to mention. This motivates tracking a larger active set: if it included the boundary segment nearest the origin, projecting onto it would give the exact solution.

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optimization problem

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Frank-Wolfe

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GJK