Vertex-unfoldings of simplicial manifolds

Authors:
Erik D. Demaine;David Eppstein;Jeff Erickson;George W. Hart;Joseph O'Rourke
Affiliations:
MIT, Cambridge, MA;University of California, Irvine CA;University of Illinois at Urbana-Champaign;http://www.georgehart.com;Smith College, Northampton, MA
Venue:
Proceedings of the eighteenth annual symposium on Computational geometry
Year:
2002

Citing 3
Cited 5

Computational Geometry in C

Computational Geometry in C
Ununfoldable polyhedra with convex faces

Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Folding and Unfolding in Computational Geometry

JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry

When can a net fold to a polyhedron?

Computational Geometry: Theory and Applications - Special issue: The 11th Candian conference on computational geometry - CCCG 99
Not being (super)thin or solid is hard: A study of grid Hamiltonicity

Computational Geometry: Theory and Applications
When can a net fold to a polyhedron?

Computational Geometry: Theory and Applications - Special issue: The 11th Candian conference on computational geometry - CCCG 99
Grid vertex-unfolding orthogonal polyhedra

STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Grid vertex-unfolding orthostacks

JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.