Making Polygons by Simple Folds and One Straight Cut

We give an efficient algorithmic characterization of simple polygons whose edges can be aligned onto a common line, with nothing else on that line, by a sequence of all-layers simple folds. In particular, such alignments enable the cutting out of the polygon and its complement with one complete stra...

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Bibliographic Details
Published inComputational Geometry, Graphs and Applications Vol. 7033; pp. 27 - 43
Main Authors Demaine, Erik D., Demaine, Martin L., Hawksley, Andrea, Ito, Hiro, Loh, Po-Ru, Manber, Shelly, Stephens, Omari
Format Book Chapter
LanguageEnglish
Published Germany Springer Berlin / Heidelberg 2011
Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Algorithms & data structures
Convex Hull
Convex Polygon
Discrete mathematics
Graphics programming
Polygonal Line
Simple Polygon
Steiner Point
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ISBN9783642249822
3642249825
ISSN0302-9743
1611-3349
DOI10.1007/978-3-642-24983-9_4

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Summary:We give an efficient algorithmic characterization of simple polygons whose edges can be aligned onto a common line, with nothing else on that line, by a sequence of all-layers simple folds. In particular, such alignments enable the cutting out of the polygon and its complement with one complete straight cut. We also show that these makeable polygons include all convex polygons possessing a line of symmetry.
ISBN:9783642249822
3642249825
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-24983-9_4