SCG '85 Proceedings of the first annual symposium on Computational geometry
Visibility Queries in Simple Polygons and Applications
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Computing Homotopic Shortest Paths Efficiently
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Walking your dog in the woods in polynomial time
Proceedings of the twenty-fourth annual symposium on Computational geometry
Divide-and-conquer for Voronoi diagrams revisited
Proceedings of the twenty-fifth annual symposium on Computational geometry
Homotopic Fréchet distance between curves or, walking your dog in the woods in polynomial time
Computational Geometry: Theory and Applications
Computing homotopic shortest paths efficiently
Computational Geometry: Theory and Applications
Approximate convex decomposition of polygons
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
Divide-and-conquer for Voronoi diagrams revisited
Computational Geometry: Theory and Applications
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The geodesic diameter of polygonal domains
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Shortest paths with arbitrary clearance from navigation meshes
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Testing a rotation axis to drain a 3D workpiece
Computer-Aided Design
Exact workspace boundary by extremal reaches
Proceedings of the twenty-seventh annual symposium on Computational geometry
Optimal paths for mutually visible agents
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Shortest non-crossing walks in the plane
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Tracing compressed curves in triangulated surfaces
Proceedings of the twenty-eighth annual symposium on Computational geometry
Computational and structural advantages of circular boundary representation
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Fast approximate convex decomposition using relative concavity
Computer-Aided Design
Dividing a Territory Among Several Vehicles
INFORMS Journal on Computing
Field D* path-finding on weighted triangulated and tetrahedral meshes
Autonomous Agents and Multi-Agent Systems
Approximate partitioning of 2D objects into orthogonally convex components
Computer Vision and Image Understanding
Reprint of: Memory-constrained algorithms for simple polygons
Computational Geometry: Theory and Applications
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Let P be a simple polygon with N vertices, each being assigned a weight ∈ {0,1}, and let C, the weight of P, be the added weight of all vertices. We prove that it is possible, in O(N) time, to find two vertices a,b in P, such that the segment ab lies entirely inside the polygon P and partitions it into two polygons, each with a weight not exceeding 2C/3. This computation assumes that all the vertices have been sorted along some axis, which can be done in O(Nlog N) time. We use this result to derive a number of efficient divide-and-conquer algorithms for: 1. Triangulating an N-gon in O(Nlog N) time. 2. Decomposing an N-gon into (few) convex pieces in O(Nlog N) time. 3. Given an O(Nlog N) preprocessing, computing the shortest distance between two arbitrary points inside an N-gon (i.e., the internal distance), in O(N) time. 4. Computing the longest internal path in an N-gon in O(N2) time. In all cases, the algorithms achieve significant improvements over previously known methods, either by displaying better performance or by gaining in simplicity. In particular, the best algorithms for Problems 2,3,4, known so far, performed respectively in O(N2), O(N2), and O(N4) time.