Computational geometry: an introduction
Computational geometry: an introduction
Visibility of disjoint polygons
Algorithmica
Linear time algorithms for visibility and shortest path problems inside simple polygons
SCG '86 Proceedings of the second annual symposium on Computational geometry
Rectilinear Shortest Paths and Minimum Spanning Trees in the Presence of Rectilinear Obstacles
IEEE Transactions on Computers
Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Planning, geometry, and complexity of robot motion
Planning, geometry, and complexity of robot motion
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Rectilinear shortest paths through polygonal obstacles in O(n(logn)2) time
SCG '87 Proceedings of the third annual symposium on Computational geometry
An O(n2) shortest path algorithm for a non-rotating convex body
Journal of Algorithms
The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
On the complexity of reachability and motion planning questions (extended abstract)
SCG '85 Proceedings of the first annual symposium on Computational geometry
Rectilinear shortest paths with rectangular barriers
SCG '85 Proceedings of the first annual symposium on Computational geometry
Planning the shortest path for a disc in O(n2log n) time
SCG '85 Proceedings of the first annual symposium on Computational geometry
An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
Data Structures and Algorithms
Data Structures and Algorithms
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
On shortest paths in polyhedral spaces
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Retraction: A new approach to motion-planning
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Movement Problems for 2-Dimensional Linkages
Movement Problems for 2-Dimensional Linkages
Computational geometry.
Optimal shortest path queries in a simple polygon
SCG '87 Proceedings of the third annual symposium on Computational geometry
Shortest path queries among weighted obstacles in the rectilinear plane
Proceedings of the eleventh annual symposium on Computational geometry
Proceedings of the fourteenth annual symposium on Computational geometry
Computing shortest paths with comparisons and additions
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate distance oracles for graphs with dense clusters
Computational Geometry: Theory and Applications
Shortest paths with arbitrary clearance from navigation meshes
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Navigation queries from triangular meshes
MIG'10 Proceedings of the Third international conference on Motion in games
A nearly optimal algorithm for finding L1shortest paths among polygonal obstacles in the plane
ESA'11 Proceedings of the 19th European conference on Algorithms
Computing shortest paths amid pseudodisks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Approximate distance oracles for graphs with dense clusters
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Mathematical and Computer Modelling: An International Journal
Shortest path problem in rectangular complexes of global nonpositive curvature
Computational Geometry: Theory and Applications
A near-optimal algorithm for shortest paths among curved obstacles in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
Computing shortest paths among curved obstacles in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We present a practical algorithm for finding minimum-length paths between points in the Euclidean plane with (not necessarily convex) polygonal obstacles. Prior to this work, the best known algorithm for finding the shortest path between two points in the plane required &OHgr;(n2 log n) time and O(n2) space, where n denotes the number of obstacle edges. Assuming that a triangulation or a Voronoi diagram for the obstacle space is provided with the input (if is not, either one can be precomputed in O(n log n) time), we present an O(kn) time algorithm, where k denotes the number of “islands” (connected components) in the obstacle space. The algorithm uses only O(n) space and, given a source point s, produces an O(n) size data structure such that the distance between s and any other point x in the plane (x) is not necessarily an obstacle vertex or a point on an obstacle edge) can be computed in O(1) time. The algorithm can also be used to compute shortest paths for the movement of a disk (so that optimal movement for arbitrary objects can be computed to the accuracy of enclosing them with the smallest possible disk).