3 papers
cs.CG2026
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.
cs.CG2026
Partitioning Regular Polygons into Circular Pieces I: Convex Partitions
Mirela Damian, Joseph O'Rourke
We explore an instance of the question of partitioning a polygon into pieces, each of which is as ``circular'' as possible, in the sense of having an aspect ratio close to 1. The a…
cs.CG2025
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…