Vertex-Unfoldings of Simplicial Manifolds

Vertex-Unfoldings of Simplicial Manifolds

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by Erik D. Demaine , David Eppstein , Jeff Erickson , George W. Hart , Joseph O'Rourke

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13 - 3 self

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@MISC{Demaine_vertex-unfoldingsof,
    author = {Erik D. Demaine and David Eppstein and Jeff Erickson and George W. Hart and Joseph O'Rourke},
    title = {Vertex-Unfoldings of Simplicial Manifolds},
    year = {}
}

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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.

Citations

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51	Folding and unfolding in computational geometry - O'Rourke - 2000
30	Dissections: Plane and Fancy - Frederickson - 1997
29	Unfolding some classes of orthogonal polyhedra - Biedl, Demaine, et al. - 1998
22	Ununfoldable polyhedra with convex faces - Bern, Demaine, et al. - 2003
14	Kuo - Ununfoldable Polyhedra - Bern, Demaine, et al.
2	Vertex-unfoldings of simplicial polyhedra - Demaine, Eppstein, et al. - 2001
1	The Cat in the Hat Comes Back. Beginner Books. Random House - Seuss - 1958