Star unfolding convex polyhedra via quasigeodesic loops

DOI10.1007/s00454-009-9223-xzbMath1194.52008OpenAlexW2109720094MaRDI QIDQ977183

Joseph O'Rourke, Jin-ichi Itoh, Costin Vîlcu

Publication date: 21 June 2010

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-009-9223-x

zbMATH Keywords

shortest pathsquasigeodesicsunfoldingconvex polyhedrastar unfoldingquasigeodesic loop

Mathematics Subject Classification ID

Three-dimensional polytopes (52B10) Convex sets in (2) dimensions (including convex curves) (52A10)

Related Items (10)

Geodesics on the regular tetrahedron and the cube ⋮ Development of curves on polyhedra via conical existence ⋮ Unfoldings and nets of regular polytopes ⋮ Toward unfolding doubly covered \(n\)-stars ⋮ Unfolding cubes: nets, packings, partitions, chords ⋮ Continuous blooming of convex polyhedra ⋮ Affine unfoldings of convex polyhedra ⋮ A Generalization of the Source Unfolding of Convex Polyhedra ⋮ Star unfolding convex polyhedra via quasigeodesic loops ⋮ Star unfolding from a geodesic curve

Cites Work

• Star unfolding convex polyhedra via quasigeodesic loops
• Nonoverlap of the star unfolding
• An optimal-time algorithm for shortest paths on a convex polytope in three dimensions
• Metric combinatorics of convex polyhedra: cut loci and nonoverlapping unfoldings
• Quasigeodesics and farthest points on convex surfaces
• Criteria for farthest points on convex surfaces
• On Shortest Paths in Polyhedral Spaces
• Convex Polyhedra
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