Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Voronoi diagrams over dynamic scenes
Discrete Applied Mathematics
Approximation of generalized Voronoi diagrams by ordinary Voronoi diagrams
CVGIP: Graphical Models and Image Processing
Delaunay triangulations in three dimensions with finite precision arithmetic
Computer Aided Geometric Design
Approximating polyhedra with spheres for time-critical collision detection
ACM Transactions on Graphics (TOG)
Swap conditions for dynamic Voronoi diagrams for circles and line segments
Computer Aided Geometric Design
Robust and Fast Algorithm for a Circle Set Voronoi Diagram in a Plane
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Remembering Conflicts in History Yields Dynamic Algorithms
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Dynamically maintaining a hierarchical planar Voronoi diagram approximation
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
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The problem of dynamic maintenance of the Voronoi diagram for a set of spheres moving independently in d-dimensional space is addressed in this paper. The maintenance of the generalized Voronoi diagram of spheres, moving alone the given trajectories, requires the calculation of topological events, that occur when d + 2 spheres become tangent to a common sphere. The criterion for determination of such a topological event for spheres in the Euclidean metric is presented. This criterion is given in the form of polynomial algebraic equations dependent on the coordinates and trajectories of the moving spheres. These equations are normally solved using numerical methods.