Static Intersection Test Between OBB and Sphere

in

Like many OBB-to-any checks, this test can be greatly simplified by just rotating the sphere into the OBB's coordinate system, effectively making it a AABB to sphere test:

/// <summary>Test whether an oriented box and a sphere intersect each other</summary>
/// <param name="boxTransform">Orientation and position of the box</param>
/// <param name="boxExtents">Extents of the box to be tested</param>
/// <param name="sphereCenter">Center of the sphere relative to the box' center</param>
/// <param name="sphereRadius">Radius of the sphere</param>
/// <returns>True if the sphere overlaps with the oriented box</returns>
public static bool CheckContact(
  Matrix boxTransform, Vector3 boxExtents,
  Vector3 sphereCenter, float sphereRadius
) {

  // Translate the sphere into box coordinates 
  Vector3 local = new Vector3(
    Vector3.Dot(sphereCenter, boxTransform.Right),
    Vector3.Dot(sphereCenter, boxTransform.Up),
    Vector3.Dot(sphereCenter, boxTransform.Forward)
  );

  // Now it's a simple aabb check
  return AabbSphereCollider.CheckContact(
    -boxExtents, boxExtents, sphereCenter, sphereRadius
  );

}

The AabbSphereCollider class used to perform the final collision test can be found in the article Static Intersection Test Between AABB and Sphere.