Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Near-quadratic bounds for the L1 Voronoi diagram of moving points
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Data structures for mobile data
Journal of Algorithms
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Voronoi Diagrams of Moving Points in the Plane
WG '91 Proceedings of the 17th International Workshop
A Two-Dimensional Kinetic Triangulation with Near-Quadratic Topological Changes
Discrete & Computational Geometry
Kinetic and dynamic data structures for closest pair and all nearest neighbors
ACM Transactions on Algorithms (TALG)
Kinetic stable Delaunay graphs
Proceedings of the twenty-sixth annual symposium on Computational geometry
Convex Distance Functions In 3-Space Are Different
Fundamenta Informaticae
Kinetic stable Delaunay graphs
Proceedings of the twenty-sixth annual symposium on Computational geometry
A kinetic triangulation scheme for moving points in the plane
Computational Geometry: Theory and Applications
The Geometric Stability of Voronoi Diagrams with Respect to Small Changes of the Sites
Proceedings of the twenty-seventh annual symposium on Computational geometry
Proceedings of the twenty-seventh annual symposium on Computational geometry
Stability of Delaunay-type structures for manifolds: [extended abstract]
Proceedings of the twenty-eighth annual symposium on Computational geometry
Kinetic data structures for all nearest neighbors and closest pair in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
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The best known upper bound on the number of topological changes in the Delaunay triangulation of a set of moving points in ℜ2 is (nearly) cubic, even if each point is moving with a fixed velocity. We introduce the notion of a stable Delaunay graph (SDG in short), a dynamic subgraph of the Delaunay triangulation, that is less volatile in the sense that it undergoes fewer topological changes and yet retains many useful properties of the full Delaunay triangulation. SDG is defined in terms of a parameter ± 0, and consists of Delaunay edges pq for which the (equal) angles at which p and q see the corresponding Voronoi edge epq are at least ±. We prove several interesting properties of SDG and describe two kinetic data structures for maintaining it. Both structures use O*(n) storage. They process O*(n2) events during the motion, each in O*(1) time, provided that the points of P move along algebraic trajectories of bounded degree; the O*(·) notation hides multiplicative factors that are polynomial in 1/± and polylogarithmic in n. The first structure is simpler but the dependency on 1/± in its performance is higher.