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» Shortest Path Problems on a Polyhedral Surface
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COMPGEOM
2004
ACM
15 years 3 months ago
New results on shortest paths in three dimensions
We revisit the problem of computing shortest obstacle-avoiding paths among obstacles in three dimensions. We prove new hardness results, showing, e.g., that computing Euclidean sh...
Joseph S. B. Mitchell, Micha Sharir
DCG
2008
93views more  DCG 2008»
14 years 9 months ago
Metric Combinatorics of Convex Polyhedra: Cut Loci and Nonoverlapping Unfoldings
Let S be the boundary of a convex polytope of dimension d + 1, or more generally let S be a convex polyhedral pseudomanifold. We prove that S has a polyhedral nonoverlapping unfold...
Ezra Miller, Igor Pak
PAMI
2010
222views more  PAMI 2010»
14 years 8 months ago
Minimal Surfaces Extend Shortest Path Segmentation Methods to 3D
—Shortest paths have been used to segment object boundaries with both continuous and discrete image models. Although these techniques are well defined in 2D, the character of the...
Leo Grady
COMPGEOM
2010
ACM
15 years 2 months ago
Finding shortest non-trivial cycles in directed graphs on surfaces
Let D be a weighted directed graph cellularly embedded in a surface of genus g, orientable or not, possibly with boundary. We describe algorithms to compute a shortest non-contrac...
Sergio Cabello, Éric Colin de Verdiè...
COSIT
1995
Springer
103views GIS» more  COSIT 1995»
15 years 1 months ago
On the Determination of the Optimum Path in Space
: Various algorithms have been proposed for the determination of the optimum paths in line networks. Moving in space is a far more complex problem, where research has been scarce. ...
Emmanuel Stefanakis, Marinos Kavouras