A Disk-Packing Algorithm for an Origami Magic Trick (1998) [11 citations — 7 self]
http://theory.lcs.mit.edu/~edemaine/papers/OSME200
http://db.uwaterloo.ca/~eddemain/papers/OSME2001b/
http://www.ics.uci.edu/~eppstein/pubs/BerDemEpp-Fu
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author = {Marshall Bern and Erik Demaine and M. Bern and Barry Hayes and E. Demaine and David Eppstein and B. Hayes},
title = {A Disk-Packing Algorithm for an Origami Magic Trick},
booktitle = {In Proceedings of the 3rd International Meeting of Origami Science, Math, and Education},
year = {1998},
pages = {32--42}
}
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Abstract:
We present an algorithm for a magic trick. Given a polygon with holes P , our algorithm determines a folding of a rectangular sheet of paper such that a single straight cut suffices to cut out P . Keywords: Computational Geometry, Paperfolding, Polygon. 1 Introduction The great Harry Houdini was one of the first to perform the following magic trick: fold a sheet of paper so that a single straight cut produces a cut-out of a rabbit, a dog, or whatever else one likes. Whereas Houdini only published a method for a five-pointed star [11] (a method probably known to Betsy Ross [10]), Martin Gardner [9] posed the question of cutting out more complex shapes. Demaine and Demaine [5] stated this question more formally: given a polygon with holes P (possibly with more than one connected component) and a rectangle R large enough to contain P , find a "flat folding" of R such that the cross-section of the folding with a perpendicular plane is the boundary of P . More intuitively, a single str...
Citations
| 59 | A new and simple algorithm for quality 2-dimensional mesh generation – Ruppert - 1993 |
| 43 | Linear-size nonobtuse triangulation of polygons – Bern, Mitchell, et al. - 1995 |
| 31 | A computational algorithm for origami design – Lang - 1996 |
| 28 | An Upper Bound for Conforming Delaunay Triangulations – Edelsbrunner, Tan - 1993 |
| 26 | Polynomial-size nonobtuse triangulation of polygons – Bern, Eppstein - 1992 |
| 24 | Quadrilateral meshing by circle packing – Bern, Eppstein |
| 10 | Computing extreme origami bases – Demaine, Demaine - 1997 |
| 10 | Paper Cutting – Gardner - 1995 |
| 8 | The complexity of origami – Bern, Hayes - 1996 |
| 8 | Faster circle packing with application to nonobtuse triangulation – Eppstein |
| 5 | Folding and one straight cut suce – Demaine, Demaine, et al. - 1999 |
| 3 | Folding and cutting paper. Revised papers from the – Demaine, Demaine, et al. - 1998 |
| 2 | On the mathematics of origamis. Congressus Numerantium 100 – Hull - 1994 |
