Vertex-unfoldings of simplicial manifolds

We present an algorithm to unfold any triangulated 2-manifold (in particular, any simplicial polyhedron) into a non-overlap-linebreak ping, 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.

• Publication year

  2001

• Venue

  SCG '02

• Publication date

  2001-10-27

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1145/513400.513429arXiv cs/0110054
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Folding and unfolding

  2002cited by this paper
• Vertex-Unfoldings of Simplicial Polyhedra

  2001cited by this paper
• Ununfoldable polyhedra with convex faces

  1999cited by this paper
• Ununfoldable polyhedra

  1999cited by this paper
• Folding and Unfolding in Computational Geometry

  1998cited by this paper
• Unfolding some classes of orthogonal polyhedra

  1998cited by this paper
• Drawing Planar Partitions II: HH-Drawings

  1998cited by this paper
• Computational Geometry in C by Joseph O'Rourke

  1998cited by this paper
• Dissections: Plane and Fancy

  1997cited by this paper
• The Cat in the Hat Comes Back

  1996cited by this paper
• Computational Geometry in C.

  1995cited by this paper

• Ununfoldable polyhedra with 6 vertices or 6 faces

  2021cites this paper
• String Mechanism for Polyhedral Pop-up Card Design

  2021cites this paper
• Acutely Triangulated, Stacked, and Very Ununfoldable Polyhedra

  2020cites this paper
• LineUp

  2019influential citation
• Vertex Unfoldings of Orthogonal Polyhedra: Positive, Negative, and Inconclusive Results

  2018cites this paper
• Realization of Simply Connected Polygonal Linkages and Recognition of Unit Disk Contact Trees

  2015cites this paper
• Unfolding Rectangle-Faced Orthostacks

  2012cites this paper
• A Topologically Convex Vertex-Ununfoldable Polyhedron

  2011cites this paper
• Vertex unfoldings of tight polyhedra

  2011influential citation
• Common Unfoldings of Polyominoes and Polycubes

  2010cites this paper
• Not being (super)thin or solid is hard: A study of grid Hamiltonicity

  2009cites this paper
• Two New Classes of Hamiltonian Graphs

  2007cites this paper
• Two New Classes of Hamiltonian Graphs: (Extended Abstract)

  2007cites this paper
• A Survey of Folding and Unfolding in Computational Geometry

  2007cites this paper
• Hinged Dissections Exist

  2007cites this paper
• Epsilon-Unfolding Orthogonal Polyhedra

  2006cites this paper
• Unfolding and Reconstructing Polyhedra

  2006cites this paper
• Grid Vertex-Unfolding Orthogonal Polyhedra

  2005influential citation
• Reconfigurations of polygonal structures

  2005cites this paper
• Single‐Strip Triangulation of Manifolds with Arbitrary Topology

  2004cites this paper
• Hamiltonian cycles in sparse vertex-adjacency duals

  2004cites this paper
• Grid Vertex-Unfolding Orthostacks

  2004cites this paper
• Vertex-unfoldings of triangulated polyhedra

  2002cites this paper
• Folding and unfolding

  2002cites this paper
• Polyhedron man: Spreading the word about the wonders of crystal‐like geometric forms

  2001cites this paper