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The description of the algorithm isn't quite right. It only works for convex polyhedra (or, in theory, polytopes in N dimensions). And "enhanced" versions of the algorithm which use edge information, not just a point cloud, are used in practice, because they're much faster.
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: Amusingly, that paper cites my posting to comp.graphics.algorithms as identifying the problem. The Steven Cameron paper cited in the article has some of the answers. That needs a better cite; the link is to the IEEE repository, which is, annoyingly, a pay site. --[[User:Nagle|John Nagle]] 04:35, 20 June 2007 (UTC)
Probably a redirect from [[GJK algorithm]] should be added.
-- [[User:Vftdan|Vftdan]] ([[User talk:Vftdan|talk]]) 18:55, 24 April 2022 (UTC)
== Nice pictures ==
Some pictures were added. But they show collisions, not distances. GJK is normally a distance algorithm for non-intersecting polyhedra, but there are extensions for "negative distance", i.e. interpenetration.
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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