Paper by Erik D. Demaine

Reference:

Mirela Damian, Erik D. Demaine, Robin Flatland, and Joseph O'Rourke, “Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement”, Graphs and Combinatorics, volume 33, number 5, 2017, pages 1357–1379.

BibTeX

@Article{Genus2Unfolding_GC,
  AUTHOR        = {Mirela Damian and Erik D. Demaine and Robin Flatland and Joseph O'Rourke},
  TITLE         = {Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement},
  JOURNAL       = {Graphs and Combinatorics},
  journalurl    = {http://www.springer.com/mathematics/numbers/journal/373},
  VOLUME        = 33,
  NUMBER        = 5,
  YEAR          = 2017,
  PAGES         = {1357--1379},

  papers        = {DeltaUnfolding_GC},
  doi           = {https://dx.doi.org/10.1007/s00373-017-1849-5},
  dblp          = {https://dblp.org/rec/journals/gc/DamianDFO17},
  comments      = {This paper is also available from <A HREF="http://dx.doi.org/10.1007/s00373-017-1849-5">SpringerLink</A> and as <A HREF="https://arXiv.org/abs/1611.00106">arXiv:1611.00106</A>.},
}

Abstract:

We show that every orthogonal polyhedron of genus g ≤ 2 can be unfolded without overlap while using only a linear number of orthogonal cuts (parallel to the polyhedron edges). This is the first result on unfolding general orthogonal polyhedra beyond genus-0. Our unfolding algorithm relies on the existence of at most 2 special leaves in what we call the “unfolding tree” (which ties back to the genus), so unfolding polyhedra of genus 3 and beyond requires new techniques.

Comments:

This paper is also available from SpringerLink and as arXiv:1611.00106.

Availability:

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Related papers:

DeltaUnfolding_GC (Unfolding Orthogonal Polyhedra with Quadratic Refinement: The Delta-Unfolding Algorithm)