7 papers · 1 filter
Overlapping Unfoldings of Cones and Convex Polyhedra
MIT CompGeom Group, Hugo A. Akitaya, Erik D. Demaine +4
Research on Dürer's problem focuses on edge unfoldings of convex polyhedra that avoid overlap. We invert the goal and find unfoldings that overlap at some point to any given thick…
Finding Closed Quasigeodesics on Convex Polyhedra
Erik D. Demaine, Adam C. Hesterberg, Jason S. Ku
A closed quasigeodesic is a closed curve on the surface of a polyhedron with at most of surface on both sides at all points; such curves can be locally unfolded straigh…
Escaping a Polygon
Zachary Abel, Hugo Akitaya, Erik D. Demaine +4
Suppose an escaping player ("human") moves continuously at maximum speed in the interior of a region, while a pursuing player ("zombie") moves continuously at maximum speed …
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…
Minimum Plane Bichromatic Spanning Trees
Hugo A. Akitaya, Ahmad Biniaz, Erik D. Demaine +3
For a set of red and blue points in the plane, a minimum bichromatic spanning tree (MinBST) is a shortest spanning tree of the points such that every edge has a red and a blue endp…
Tiling with Three Polygons is Undecidable
Erik D. Demaine, Stefan Langerman
We prove that the following problem is co-RE-complete and thus undecidable: given three simple polygons, is there a tiling of the plane where every tile is an isometry of one of th…