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

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Dr. C.D. Wright

Posts: 2
Registered: 12/8/04
Re: General 3D 'jigsaw puzzle'
Posted: Jun 10, 1993 5:54 AM
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Joseph O'Rourke (orourke@sophia.smith.edu) wrote:
: In article <C8CKz5.5E3@liverpool.ac.uk> cdw10@liverpool.ac.uk (Dr. C.D. Wright) writes:
: > In response to the following, there has been some work done
: > on the "Jackstraws" problem, which is quite similar. This
: > asks, given a collection of compact manifolds in R^n, can
: > they be separated to infinity one at a time. I don't know
: > any references - [...]

: There is a nice new advance on this problem by Snoeyink
: and Stofi: "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. They also establish the same negative result with
: "translated" replaced by "translated and rotated." There is a
: stunning video associated with the paper.

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. I don't know where he published it - I was sharing
a house with him at the time, but didn't pay a lot of attention
to where he sent it. I don't have a lot of time to spend on
this, but I'll try to find something about it.

Colin Wright.






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