Paper by Erik D. Demaine
- 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.
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
- This paper is also available from the electronic proceedings as http://www.cs.unb.ca/conf/cccg/eProceedings/42.ps.gz.
- The paper is 4 pages and the talk is 25 minutes.
- The paper is available in PostScript (144k).
- See information on file formats.
- [Google Scholar search]
- Related papers:
- ConvexPolygonsCGTA (Reconfiguring Convex Polygons)
- Related webpages:
- Carpenter's Rule Theorem
See also other papers by Erik Demaine.
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Last updated February 24, 2021 by