Paper by Erik D. Demaine

Reference:

Erik D. Demaine and Joseph S. B. Mitchell, “Reaching Folded States of a Rectangular Piece of Paper”, in Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG 2001), Waterloo, Ontario, Canada, August 13–15, 2001, pages 73–75.

BibTeX

@InProceedings{PaperReachability_CCCG2001,
  AUTHOR        = {Erik D. Demaine and Joseph S. B. Mitchell},
  TITLE         = {Reaching Folded States of a Rectangular Piece of Paper},
  BOOKTITLE     = {Proceedings of the 13th Canadian Conference on Computational
                   Geometry (CCCG 2001)},
  BOOKURL       = {http://compgeo.math.uwaterloo.ca/~cccg01},
  ADDRESS       = {Waterloo, Ontario, Canada},
  MONTH         = {August 13--15},
  YEAR          = 2001,
  PAGES         = {73--75},

  WEBPAGES      = {folding},
  LENGTH        = {3 pages},
  dblp          = {https://dblp.org/rec/conf/cccg/DemaineM01},
  COMMENTS      = {This paper is also available from the
                   <A HREF="http://compgeo.math.uwaterloo.ca/~cccg01/proceedings/">
                   electronic proceedings</A> as
                   <A HREF="http://compgeo.math.uwaterloo.ca/~cccg01/proceedings/short/eddemaine-33029.ps.gz">http://compgeo.math.uwaterloo.ca/~cccg01/proceedings/short/eddemaine-33029.ps.gz</A>.
                   <P>
                   <A HREF="../../photos/PaperReachability_Hart_August2001/">Photos of Victoria Hart folding a crane by our algorithm <IMG ALIGN=CENTER SRC="victoria_small.jpg"></A>
                   },
  PAPERS        = {PaperReachability_CCCG2004},
  unrefereed    = 1,
  ee            = {http://www.cccg.ca/proceedings/2001/eddemaine-33029.ps.gz},
}

Abstract:

We prove that any folded state of a rectangular piece of paper (a continuous isometric non-self-intersecting mapping of the paper into space) can be reached by a continuous folding process, starting from the unfolded state, while at all times being a valid folding. In our model, the paper cannot properly cross itself, but can touch itself, as in a flat folding.

Comments:

This paper is also available from the electronic proceedings as http://compgeo.math.uwaterloo.ca/~cccg01/proceedings/short/eddemaine-33029.ps.gz.

Photos of Victoria Hart folding a crane by our algorithm

Length:

The paper is 3 pages.

Availability:

The paper is available in PostScript (118k) and gzipped PostScript (45k).

See information on file formats.

[Google Scholar search]

Related papers:

PaperReachability_CCCG2004 (Continuous Foldability of Polygonal Paper)

Related webpages:

Folding and Unfolding