Axis aligned torus collision detection

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I am looking to detect the collision (test for intersection) of axis aligned torus and other axis aligned shapes:

  1. Torus and box.
  2. Torus and cylinder.
  3. Torus and another torus.

There exist algorithms to calculate this for other simple objects (sphere, cylinder, box), however I cannot find the way to do this with torus.

If such algorithm (test) exists, or the only possibility is to approximate torus with some other shapes?