Communications of the ACM - Robots: intelligence, versatility, adaptivity
Motorcycle graphs and straight skeletons
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Dudeney Dissection of Polygons
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Straight Skeletons for General Polygonal Figures in the Plane
COCOON '96 Proceedings of the Second Annual International Conference on Computing and Combinatorics
Hinged dissection of polyominoes and polyforms
Computational Geometry: Theory and Applications - Special issue: The 11th Candian conference on computational geometry - CCCG 99
Locked and unlocked chains of planar shapes
Proceedings of the twenty-second annual symposium on Computational geometry
Proceedings of the twenty-fourth annual symposium on Computational geometry
Straight Skeletons of Three-Dimensional Polyhedra
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Straight skeletons of three-dimensional polyhedra
Proceedings of the twenty-fifth annual symposium on Computational geometry
Generating realistic roofs over a rectilinear polygon
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Skeletal representations of orthogonal shapes
Graphical Models
Realistic roofs over a rectilinear polygon
Computational Geometry: Theory and Applications
| Hi-index | 0.00 |
This paper presents a general family of 3D hinged dissections for polypolyhedra, i.e., connected 3D solids formed by joining several rigid copies of the same polyhedron along identical faces. (Such joinings are possible only for reflectionally symmetric faces.) Each hinged dissection consists of a linear number of solid polyhedral pieces hinged along their edges to form a flexible closed chain (cycle). For each base polyhedron P and each positive integer n, a single hinged dissection has folded configurations corresponding to all possible polypolyhedra formed by joining n copies of the polyhedron P. In particular, these results settle the open problem posed in [7] about the special case of polycubes (where P is a cube) and extend analogous results from 2D [7].Along the way, we present hinged dissections for polyplatonics (where P is a platonic solid) that are particularly efficient: among a type of hinged dissection, they use the fewest possible pieces.