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Convex Polyhedra
General Methods
Shortest Path
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Star Unfolding Convex Polyhedra via Quasigeodesic Loops
Star Unfolding Convex Polyhedra via Quasigeodesic Loops,10.1007/s004540099223x,Discrete & Computational Geometry,Jinichi Itoh,Joseph O’Rourke,Cost
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Star Unfolding Convex Polyhedra via Quasigeodesic Loops
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Citations: 3
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Jinichi Itoh
,
Joseph O’Rourke
,
Costin Vîlcu
We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point. This gives a new general method to unfold the surface of any convex polyhedron P to a simple (nonoverlapping), planar polygon: cut along one
shortest path
from each vertex of P to Q, and cut all but one segment of Q.
Journal:
Discrete & Computational Geometry  DCG
, vol. 44, no. 1, pp. 3554, 2010
DOI:
10.1007/s004540099223x
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Citation Context
(1)
...Four general unfolding algorithms are known for arbitrary convex polyhedra: the source unfolding [15,11],thestarunfolding[4],andtwovariationsthereof[
10
,9].Positiveandnegative results for unfolding nonconvex polyhedra can be found in [5,7,13]...
Erik D. Demaine
,
et al.
Continuous Blooming of Convex Polyhedra
References
(18)
Nonoverlap of the Star Unfolding
(
Citations: 43
)
Boris Aronov
,
Joseph O'rourke
Journal:
Discrete & Computational Geometry  DCG
, vol. 8, no. 1, pp. 219250, 1992
Intrinsic Geometry of Surfaces
(
Citations: 65
)
A. D. Aleksandrov
,
V. A. Zalgaller
Published in 1967.
Metric Combinatorics of Convex Polyhedra: Cut Loci and Nonoverlapping Unfoldings
(
Citations: 11
)
EZRA MILLERAND
,
Igor Pak
Journal:
Discrete & Computational Geometry  DCG
, vol. 39, no. 13, pp. 339388, 2008
On shortest paths in polyhedral spaces
(
Citations: 199
)
Amir Schorr
Conference:
ACM Symposium on Theory of Computing  STOC
, pp. 144153, 1984
An OptimalTime Algorithm for Shortest Paths on a Convex Polytope in Three Dimensions
(
Citations: 9
)
Yevgeny Schreiber
,
Micha Sharir
Journal:
Discrete & Computational Geometry  DCG
, vol. 39, no. 13, pp. 500579, 2008
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Citations
(3)
Continuous Blooming of Convex Polyhedra
Erik D. Demaine
,
Martin L. Demaine
,
Vi Hart
,
John Iacono
,
Stefan Langerman
,
Joseph O’Rourke
Journal:
Graphs and Combinatorics
, vol. 27, no. 3, pp. 363376, 2011
Conical Existence of Closed Curves on Convex Polyhedra
Joseph O'Rourke
,
Costin Vilcu
Journal:
Computing Research Repository  CORR
, vol. abs/1102.0, 2011
On Flat Polyhedra deriving from Alexandrov's Theorem
(
Citations: 1
)
Joseph O'Rourke
Journal:
Computing Research Repository  CORR
, vol. abs/1007.2, 2010