52 citations · 270 across the 71 of their papers we have counts for
77 papers
Super Guarding and Dark Rays in Art Galleries
MIT CompGeom Group, Hugo A. Akitaya, Erik D. Demaine +5
We explore an Art Gallery variant where each point of a polygon must be seen by k guards, and guards cannot see through other guards. Surprisingly, even covering convex polygons un…
Polar Zonohedra Edge-Unfold to Nets
Joseph O'Rourke
This note proves that every polar zonohedron has an edge-unfolding to a non-overlapping net.
Every Combinatorial Polyhedron Can Unfold with Overlap
Joseph O'Rourke
Ghomi proved that every convex polyhedron could be stretched via an affine transformation so that it has an edge-unfolding to a net [Gho14]. A net is a simple planar polygon; in pa…
Hamiltonian Quasigeodesics yield Nets
Joseph O'Rourke
This note establishes that every polyhedron that has a Hamiltonian quasigeodesic can be edge-unfolded to a net, and shows that the class of such polyhedra is infinite.
Simple Closed Quasigeodesics on Tetrahedra
Joseph O'Rourke, Costin Vilcu
Pogorelov proved in 1949 that every every convex polyhedron has at least three simple closed quasigeodesics. Whereas a geodesic has exactly pi surface angle to either side at each…
Every Tetrahedron has a 3-vertex Quasigeodesic
Joseph O'Rourke
We prove that every tetrahedron T has a simple, closed quasigeodesic that passes through three vertices of T. Equivalently, every T has a face whose "exterior angles" are at most p…