92 citations · 129 across the 11 of their papers we have counts for
9 papers · 1 filter
Continuous Flattening of All Polyhedral Manifolds using Countably Infinite Creases
Zachary Abel, Erik D. Demaine, Martin L. Demaine +4
We prove that any finite polyhedral manifold in 3D can be continuously flattened into 2D while preserving intrinsic distances and avoiding crossings, answering a 19-year-old open p…
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 …
Negative Instance for the Edge Patrolling Beacon Problem
Zachary Abel, Hugo A. Akitaya, Erik D. Demaine +5
Can an infinite-strength magnetic beacon always ``catch'' an iron ball, when the beacon is a point required to be remain nonstrictly outside a polygon, and the ball is a point alwa…
Infinite All-Layers Simple Foldability
Hugo A. Akitaya, Cordelia Avery, Joseph Bergeron +3
We study the problem of deciding whether a crease pattern can be folded by simple folds (folding along one line at a time) under the infinite all-layers model introduced by [Akitay…
Rigid Foldability is NP-Hard
Hugo Akitaya, Erik D. Demaine, Takashi Horiyama +3
In this paper, we show that deciding rigid foldability of a given crease pattern using all creases is weakly NP-hard by a reduction from Partition, and that deciding rigid foldabil…
Symmetric Assembly Puzzles are Hard, Beyond a Few Pieces
Erik D. Demaine, Matias Korman, Jason S. Ku +6
We study the complexity of symmetric assembly puzzles: given a collection of simple polygons, can we translate, rotate, and possibly flip them so that their interior-disjoint union…
Folding Flat Crease Patterns with Thick Materials
Jason S. Ku, Erik D. Demaine
Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in fold…
Filling a Hole in a Crease Pattern: Isometric Mapping from Prescribed Boundary Folding
Erik D. Demaine, Jason S. Ku
Given a sheet of paper and a prescribed folding of its boundary, is there a way to fold the paper's interior without stretching so that the boundary lines up with the prescribed bo…