Paper by Erik D. Demaine

Reference:

Erik D. Demaine, David Eppstein, Jeff Erickson, George W. Hart, and Joseph O'Rourke, “Vertex-Unfolding of Simplicial Manifolds”, in Proceedings of the 18th Annual ACM Symposium on Computational Geometry (SoCG 2002), Barcelona, Spain, June 5–7, 2002, pages 237–243.

BibTeX

@InProceedings{VertexUnfolding_SoCG2002,
  AUTHOR        = {Erik D. Demaine and David Eppstein and Jeff Erickson and
                   George W. Hart and Joseph O'Rourke},
  TITLE         = {Vertex-Unfolding of Simplicial Manifolds},
  BOOKTITLE     = {Proceedings of the 18th Annual ACM Symposium on
                   Computational Geometry (SoCG 2002)},
  BOOKURL       = {http://www-ma2.upc.es/~geomc/events/socg2002/socg2002.html},
  ADDRESS       = {Barcelona, Spain},
  MONTH         = {June 5--7},
  YEAR          = 2002,
  PAGES         = {237--243},

  doi           = {https://dx.doi.org/10.1145/513400.513429},
  dblp          = {https://dblp.org/rec/conf/compgeom/DemaineEEHO02},
  award         = {Invited to special issue of \emph{Discrete \& Computational Geometry}.},
  papers        = {VertexUnfolding_Kuperberg2002; VertexUnfolding2},
  length        = {7 pages},
}

Abstract:

We present an algorithm to unfold any triangulated 2-manifold (in particular, any simplicial polyhedron) into a non-overlapping, connected planar layout in linear time. The manifold is cut only along its edges. The resulting layout is connected, but it may have a disconnected interior; the triangles are connected at vertices, but not necessarily joined along edges. We extend our algorithm to establish a similar result for simplicial manifolds of arbitrary dimension.

Length:

The paper is 7 pages.

Availability:

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Related papers:

VertexUnfolding2 (Vertex-Unfoldings of Simplicial Manifolds)