Map Folding
Date
2013-04-29
Authors
Nishat, Rahnuma Islam
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Abstract
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 thesis, 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 or not. We also define a class of unfoldable 2 × n crease patterns for every
n ≥ 5.
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Keywords
Paper Folding, Computational Geometry, Map Folding, Linear Orderings