Vertex-unfoldings of simplicial manifolds

Discrete Geometry: In Honor of W. Kuperberg's 60th Birthday (András Bezdek, editor), Marcel-Dekker, 2003, pp. 215-228.

Proceedings of the 18th Annual ACM Symposium on Computational Geometry, 237-243, 2002.

arXiv:cs.CG/0110054

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• This is an updated version of "Vertex-unfoldings of simplicial polyhedra".

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.

Publications - Jeff Erickson (jeffe@cs.uiuc.edu) 23 Jun 2003