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For the distance between two convex polyhedra, there are four main cases - vertex/vertex, vertex/edge, vertex/face, and edge/edge, plus the ambiguous cases edge/face and face/face, where the objects are parallel and there is no unique closest-points vector. See the Cameron paper. The ambiguous cases are troublesome. In practice, in physics engines, they come up frequently, since as objects come to rest they tend to settle into a face/face configuration. This can lead to roundoff error problems in collision detection and is often a [[statically indeterminate]] system in a physics engine. --[[User:Nagle|John Nagle]] ([[User talk:Nagle|talk]]) 03:46, 15 February 2011 (UTC)
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