#### CSC274b

Spring 2000

Ileana Streinu

#
Lecture 17

#### Thursday, March 28, 2000

Eric Demaine's
talk.

## Folding and Cutting Paper

### Erik Demaine

Department of Computer Science

University of Waterloo

Take a sheet of paper, fold it flat, and make one complete straight cut. What
shapes can the unfolded pieces make? The earliest reference to this idea is a
1721 Japanese puzzle book, in which a Japanese crest is made by this method.
Houdini used folding and cutting for a magic trick before he became a famous
escape artist. This talk discusses our work on the fold-and-cut problem: given
a collection of line segments (i.e., a plane graph), find a flat folding of the
plane so that precisely those line segments are folded to a common line, along
which we can cut to make the desired shapes.

I will describe two algorithms that we have developed to solve this problem for
any collection of line segments: convex and nonconvex polygons, multiple
disjoint polygons, adjoining polygons, nested polygons, and even floating line
segments and points. The first algorithm (joint work with Martin Demaine and
Anna Lubiw) is based on the straight skeleton. The second algorithm (joint
work with Marshall Bern, David Eppstein, and Barry Hayes) is based on disk
packing.

Last modified March 28, 2000.