5 papers
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…
Deltahedral Domes over Equiangular Polygons
MIT CompGeom Group, Hugo A. Akitaya, Erik D. Demaine +6
A polyiamond is a polygon composed of unit equilateral triangles, and a generalized deltahedron is a convex polyhedron whose every face is a convex polyiamond. We study a variant w…
Quasigeodesics on the Cube
MIT CompGeom Group, Hugo A. Akitaya, Erik D. Demaine +10
A quasigeodesic is a curve on the surface of a convex polyhedron that has surface to each side at every point. In contrast, a geodesic has exactly to each side and so…