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Topic: General 3D 'jigsaw puzzle'
Replies: 3   Last Post: Jun 10, 1993 11:25 AM

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Joseph O'Rourke

Posts: 38
Registered: 12/3/04
Re: General 3D 'jigsaw puzzle'
Posted: Jun 10, 1993 9:32 AM
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In article <> (Dr. C.D. Wright) writes:
>Joseph O'Rourke ( wrote:
>: There is a nice new advance on this problem by Snoeyink
>: and Stolfi: "Objects that cannot be taken apart by two hands,"
>: 9th ACM Symp. Comp. Geom., 1993, 247-256. They show that a
>: collection of convex objects in 3D cannot always be partitioned into
>: two sets such that each can be translated to infinity without hitting
>: the other.
>Perhaps I wasn't clear enough, but that isn't a new result.
>Bob Dawson constructed a collection of 12 convex objects that
>can only be taken apart by explosion, and he did this in 1985
>or 1986.

It is a new result. Dawson's paper is in Math. Mag. 57(1):27-30
(1984). He constructed a collection of convex objects arranged so that
no single object could be translated without disturbing the others. It
turns out that 21 years earlier, Fejes-Toth and Heppes established a
somewhat stronger result.
But for both of their examples, it is still possible to
separate the objects if one permits moving a collection of several
objects at once in unison. And it is this that Snoeyink and Stolfi
showed is not always possible.

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