5 papers
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…
Rerouting Curves on Surfaces
Timo Brand, Stefan Felsner, Henry Förster +8
We study the problem of reconfiguring a crossing-free embedding of a graph on a surface, with edges represented as curves, into another crossing-free embedding of the same graph on…
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…