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Graphs and Combinatorics

, Volume 27, Issue 3, pp 363–376 | Cite as

Continuous Blooming of Convex Polyhedra

  • Erik D. Demaine
  • Martin L. Demaine
  • Vi Hart
  • John Iacono
  • Stefan Langerman
  • Joseph O’Rourke
Proceedings Paper

Abstract

We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming.

Keywords

Unfolding Folding Collision-free motion 

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Copyright information

© Springer 2011

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • Martin L. Demaine
    • 1
  • Vi Hart
    • 2
  • John Iacono
    • 3
  • Stefan Langerman
    • 4
  • Joseph O’Rourke
    • 5
  1. 1.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA
  2. 2.
  3. 3.Department of Computer Science and EngineeringPolytechnic Institute of NYUBrooklynUSA
  4. 4.Maître de recherches du F.R.S.-FNRS, Départment d’InformatiqueUniversité Libre de BruxellesBrusselsBelgium
  5. 5.Department of Computer ScienceSmith CollegeNorthamptonUSA

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