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COMPGEOM
2004
ACM
14 years 2 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
COMPGEOM
1998
ACM
14 years 1 months ago
Constructing Approximate Shortest Path Maps in Three Dimensions
We present a new technique for constructing a data-structure that approximates shortest path maps in IRd . By applying this technique, we get the following two results on approxim...
Sariel Har-Peled
ICRA
1999
IEEE
110views Robotics» more  ICRA 1999»
14 years 1 months ago
Range-Sensor Based Navigation in Three Dimensions
This paper presents a new globally convergent rangesensor based navigation algorithm in three-dimensions, called 3DBug. The 3DBug algorithm navigates a point robot in a three-dime...
Ishay Kamon, Ehud Rivlin, Elon Rimon
COMPGEOM
2006
ACM
14 years 3 months ago
An optimal-time algorithm for shortest paths on a convex polytope in three dimensions
We present an optimal-time algorithm for computing (an implicit representation of) the shortest-path map from a fixed source s on the surface of a convex polytope P in three dime...
Yevgeny Schreiber, Micha Sharir
COMPGEOM
1996
ACM
14 years 1 months ago
Approximating Shortest Paths on a Convex Polytope in Three Dimensions
Sariel Har-Peled, Micha Sharir, Kasturi R. Varadar...