In article <C8CKz5.5E3@liverpool.ac.uk> email@example.com (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.