Map Folding
نویسندگان
چکیده
A crease pattern is an embedded planar graph on a piece of paper. An m×n map is a rectangular piece of paper with a crease pattern that partitions the paper into an m×n regular grid of unit squares. If a map has a configuration such that all the faces of the map are stacked on a unit square and the paper does not self-intersect, then it is flat foldable, and the linear ordering of the faces is called a valid linear ordering. Otherwise, the map is unfoldable. In this paper, we show that given a linear ordering of the faces of an m×n map, we can decide in linear time whether it is a valid linear ordering, which improves the quadratic time algorithm of Morgan. We also define a class of unfoldable 2 × n mountain-valley patterns for every n ≥ 5.
منابع مشابه
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The idea of the ray diagram was introduced by David Charlton, and further elaborated by Yoyo Zhou, in the context of an open problem session held as part of an MIT class 6.885 on Geometric Folding Algorithms in Fall 2007. I thank the participants of that open problem session for helpful early discussions about 2 × n map folding. I would also like to thank Eric Liu for his close help in the earl...
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