Sciweavers

DCG
2008

Grid Vertex-Unfolding Orthogonal Polyhedra

13 years 11 months ago
Grid Vertex-Unfolding Orthogonal Polyhedra
An edge-unfolding of a polyhedron is produced by cutting along edges and flattening the faces to a net, a connected planar piece with no overlaps. A grid unfolding allows additional cuts along grid edges induced by coordinate planes passing through every vertex. A vertexunfolding permits faces in the net to be connected at single vertices, not necessarily along edges. We show that any orthogonal polyhedra of genus zero has a grid vertex-unfolding. (There are orthogonal polyhedra that cannot be vertex-unfolded, so some type of "gridding" of the faces is necessary.) For any orthogonal polyhedron P with n vertices, we describe an algorithm that vertex-unfolds P in O(n2 ) time. Enroute to explaining this algorithm, we present a simpler vertex-unfolding algorithm that requires a 3
Mirela Damian, Robin Y. Flatland, Joseph O'Rourke
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where DCG
Authors Mirela Damian, Robin Y. Flatland, Joseph O'Rourke
Comments (0)