Optimal shortest path queries in a simple polygon
Journal of Computer and System Sciences
A new data structure for shortest path queries in a simple polygon
Information Processing Letters
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
Digital Curves in 3D Space and a Linear-Time Length Estimation Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Minimum-length polygons of first-class simple cube-curves
CAIP'05 Proceedings of the 11th international conference on Computer Analysis of Images and Patterns
Shortest paths in a cuboidal world
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Decomposing a simple polygon into trapezoids
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
An environment-aware mobility model for wireless ad hoc network
Computer Networks: The International Journal of Computer and Telecommunications Networking
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Let p and q be two points in a simple polygon Π. An open problem in computational geometry asks to devise a simple linear-time algorithm for computing a shortest path between p and q, which is contained in Π, such that the algorithm does not depend on a (complicated) linear-time triangulation algorithm. This report provides a contribution to the solution of this problem by applying the rubberband algorithm. The obtained solution has ${\cal O}$ (nlogn) time complexity (where the super-linear time complexity is only due to preprocessing, i.e. for the calculation of critical edges) and is, altogether, considerably simpler than the triangulation algorithm. It has applications in 2D pattern recognition, picture analysis, robotics, and so forth.