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Re: General 3D 'jigsaw puzzle'
Posted:
Jun 10, 1993 5:54 AM


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, 247256. 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.



