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Full-Text Articles in Physical Sciences and Mathematics
Unfolding Manhattan Towers, Mirela Damian, Robin Flatland, Joseph O'Rourke
Unfolding Manhattan Towers, Mirela Damian, Robin Flatland, Joseph O'Rourke
Computer Science: Faculty Publications
We provide an algorithm for unfolding the surface of any orthogonal polyhedron that falls into a particular shape class we call Manhattan Towers, to a nonoverlapping planar orthogonal polygon. The algorithm cuts along edges of a 4×5×1 refinement of the vertex grid.
Grid Vertex-Unfolding Orthogonal Polyhedra, Mirela Damian
Grid Vertex-Unfolding Orthogonal Polyhedra, Mirela Damian
Computer Science: Faculty Publications
No abstract provided.
Epsilon-Unfolding Orthogonal Polyhedra, Mirela Damian, Robin Flatland, Joseph O'Rourke
Epsilon-Unfolding Orthogonal Polyhedra, Mirela Damian, Robin Flatland, Joseph O'Rourke
Computer Science: Faculty Publications
An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connected, planar piece without overlap (except possibly at boundary points). It is a long unsolved problem to determine whether every polyhedron may be unfolded. Here we prove, via an algorithm, that every orthogonal polyhedron (one whose faces meet at right angles) of genus zero may be unfolded. Our cuts are not necessarily along edges of the polyhedron, but they are always parallel to polyhedron edges. For a polyhedron of n vertices, portions of the unfolding will be rectangular strips which, in the worst case, …