Map Folding

Rahnuma Islam Nishat, Sue Whitesides
2013 Canadian Conference on Computational Geometry  
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
more » ... 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.
dblp:conf/cccg/NishatW13 fatcat:d3cf5qfqmbcrzmni3z6rgihu74