Planar Drawings of Origami Polyhedra

Demaine, Erik D. and Demaine, Martin L. (1998) Planar Drawings of Origami Polyhedra. In: Graph Drawing 6th International Symposium, GD’ 98, August 13-15, 1998, Montréal, Canada , pp. 438-440 (Official URL: http://dx.doi.org/10.1007/3-540-37623-2_36).

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Abstract

This work studies the structure of origami bases via graph drawings of origami polyhedra. In particular, we propose a new class of polyhedra, called extreme-base polyhedra, that capture the essence of “extreme” origami bases. We develop a linear-time algorithm to find the “natural” straight-line planar drawing of these polyhedra. This algorithm demonstrates a recursive structure in the polyhedra that was not apparent before, and leads to interesting fractals.

Item Type:Conference Paper
Additional Information:10.1007/3-540-37623-2_36
Classifications:M Methods > M.999 Others
P Styles > P.720 Straight-line
G Algorithms and Complexity > G.999 Others
ID Code:286

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References

E.M. Demaine and M.L. Demaine. Planar drawings of origami polyhedra. Technical Report Cs-98-17, University of Waterloo, August 1998.

E.G. Noik. A survey of presentation emphasis techniques for visualizing graphs. In Proc. Graphics Interface, Banff, Canada, May 1994, 225-233.

M. Bern and B. Hayes. The comlexity of flat origami. In SODA, Atlanta, Jan. 1996, 175-183.