Map Folding

• Main Author: Nishat, Rahnuma Islam
• Other Authors: Whitesides, Sue H.
• Language: English; en
• Published: 2013
• Subjects: Paper Folding; Computational Geometry; Map Folding; Linear Orderings
• Online Access: http://hdl.handle.net/1828/4565

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. === Graduate === 0984