Finding the visibility graph of a simple polygon in time proportional to its size
SCG '87 Proceedings of the third annual symposium on Computational geometry
Optimal shortest path queries in a simple polygon
SCG '87 Proceedings of the third annual symposium on Computational geometry
Minimum-link paths among obstacles in the plane
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
An algorithm for generalized point location and its applications
Journal of Symbolic Computation
The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
Shortest paths among obstacles in the plane
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Efficient computation of geodesic shortest paths
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Kinetic collision detection for simple polygons
Proceedings of the sixteenth annual symposium on Computational geometry
Visibility queries in a polygonal region
Computational Geometry: Theory and Applications
Planar rectilinear shortest path computation using corridors
Computational Geometry: Theory and Applications
Finding a rectilinear shortest path in R2using corridor based staircase structures
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Information and Computation
Computing shortest paths amid pseudodisks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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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The problem of determining the Euclidean shortest path between two points in the presence of m simple polygonal obstacles is studied. An O( m2 logn + nlogn ) algorithm is developed, where n is the total number of points in the obstacles. A simple O(E+T) algorithm for determining the visibility graph is also shown, where E is the number of visibility edges and T is the time for triangulating the point set. This is extended to a O(Es + nlogn) algorithm for the shortest path problem where Es is bounded by m2.