Finding the minimum visible vertex distance between two non-intersecting simple polygons
SCG '86 Proceedings of the second annual symposium on Computational geometry
A linear time algorithm with minimum link paths inside a simple polygon
Computer Vision, Graphics, and Image Processing
On-line construction of the convex hull of a simple polyline
Information Processing Letters
On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
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
Computing the link center of a simple polygon
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
Finding minimal convex nested polygons
Information and Computation
An efficient algorithm for link-distance problems
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Minimum-link paths among obstacles in the plane
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Computational Geometry: Theory and Applications
Approximating Polygons and Subdivisions with Minimum Link Paths
ISA '91 Proceedings of the 2nd International Symposium on Algorithms
Minimum link paths in polygons and related problems
Minimum link paths in polygons and related problems
Efficient piecewise-linear function approximation using the uniform metric: (preliminary version)
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Proceedings of the twelfth annual symposium on Computational geometry
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
Constructing pairwise disjoint paths with few links
ACM Transactions on Algorithms (TALG)
Link Distance and Shortest Path Problems in the Plane
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
Link distance and shortest path problems in the plane
Computational Geometry: Theory and Applications
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We develop a data structure for answering link distance queries between two arbitrary points in a simple polygon. The data structure requires O(n3) time and space for its construction and answers link distance queries in O(log n) time. Our result extends to link distance queries between pairs of segments or polygons. We also propose a simpler data structure for computing a link distance approximately, where the error is bounded by a small additive constant. Finally, we also present a scheme for approximating the link and the shortest path distance simultaneously.