Paper by Erik D. Demaine

Reference:

Oswin Aichholzer, Erik D. Demaine, Jeff Erickson, Ferran Hurtado, Mark Overmars, Michael A. Soss, and Godfried T. Toussaint, “Reconfiguring Convex Polygons”, in Proceedings of the 12th Annual Canadian Conference on Computational Geometry (CCCG 2000), Fredericton, New Brunswick, Canada, August 16–18, 2000, pages 17–20.

BibTeX

@InProceedings{CCCG2000c,
  AUTHOR        = {Oswin Aichholzer and Erik D. Demaine and Jeff Erickson and
                   Ferran Hurtado and Mark Overmars and Michael A. Soss and
                   Godfried T. Toussaint},
  TITLE         = {Reconfiguring Convex Polygons},
  BOOKTITLE     = {Proceedings of the 12th Annual Canadian Conference on
                   Computational Geometry (CCCG 2000)},
  BOOKURL       = {http://www.cs.unb.ca/conf/cccg/},
  MONTH         = {August 16--18},
  YEAR          = 2000,
  ADDRESS       = {Fredericton, New Brunswick, Canada},
  PAGES         = {17--20},

  award         = {Invited to a special issue of \emph{Computational Geometry: Theory and Applications}.},
  length        = {4 pages; 25 minutes},
  webpages      = {linkage},
  dblp          = {https://dblp.org/rec/conf/cccg/AichholzerDEHOST00},
  ee            = {http://www.cccg.ca/proceedings/2000/42.ps.gz},
  comments      = {This paper is also available from the
                   <A HREF="http://www.cs.unb.ca/conf/cccg/eProceedings/">
                   electronic proceedings</A> as
                   <A HREF="http://www.cs.unb.ca/conf/cccg/eProceedings/42.ps.gz">http://www.cs.unb.ca/conf/cccg/eProceedings/42.ps.gz</A>.},
  papers        = {ConvexPolygonsCGTA},
  unrefereed    = 1,
}

Abstract:

We prove that there is a motion from any convex polygon to any convex polygon with the same counterclockwise sequence of edge lengths, that preserves the lengths of the edges, and keeps the polygon convex at all times. Furthermore, the motion is “direct” (avoiding any intermediate canonical configuration like a subdivided triangle) in the sense that each angle changes monotonically throughout the motion. In contrast, we show that it is impossible to achieve such a result with each vertex-to-vertex distance changing monotonically.

Comments:

This paper is also available from the electronic proceedings as http://www.cs.unb.ca/conf/cccg/eProceedings/42.ps.gz.

Length:

The paper is 4 pages and the talk is 25 minutes.

Availability:

The paper is available in PostScript (144k).

See information on file formats.

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Related papers:

ConvexPolygonsCGTA (Reconfiguring Convex Polygons)

Related webpages:

Carpenter's Rule Theorem