Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Voronoi diagrams over dynamic scenes
Discrete Applied Mathematics
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)
Algorithmic geometry
Swap conditions for dynamic Voronoi diagrams for circles and line segments
Computer Aided Geometric Design
Voronoi-based interpolation with higher continuity
Proceedings of the sixteenth annual symposium on Computational geometry
Voronoi diagram of a circle set from Voronoi diagram of a point set: topology
Computer Aided Geometric Design
Voronoi diagram of a circle set from Voronoi diagram of a point set: geometry
Computer Aided Geometric Design
Collision Detection Optimization in a Multi-particle System
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Crystal Voronoi Diagram and Its Applications to Collision-Free Paths
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Continuous range search based on network Voronoi diagram
International Journal of Grid and Utility Computing
Region-expansion for the Voronoi diagram of 3D spheres
Computer-Aided Design
Computer-Aided Design
Euclidean Voronoi diagram of 3D balls and its computation via tracing edges
Computer-Aided Design
Multicriteria tunnel computation
CGIM '08 Proceedings of the Tenth IASTED International Conference on Computer Graphics and Imaging
Quasi-worlds and quasi-operators on quasi-triangulations
Computer-Aided Design
Three-dimensional beta-shapes and beta-complexes via quasi-triangulation
Computer-Aided Design
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
Reduction of the search space in the edge-tracing algorithm for the voronoi diagram of 3d balls
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Euclidean voronoi diagrams of 3d spheres: their construction and related problems from biochemistry
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Visualization and analysis of protein structures using euclidean voronoi diagram of atoms
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
DEM interpolation from contours using medial axis transformation
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part I
Visualization for the Physical Sciences
Computer Graphics Forum
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The problem of dynamic maintenance of a Voronoi diagram for a set of spheres moving independently in d-dimensional space is addressed in this paper. The maintenance of this Voronoi diagram for spheres moving along 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 the topological event in the Euclidean metric is derived as a solution of a system of non-linear algebraic equations. The criterion is given in the form of polynomial algebraic equations dependent on the coordinates and trajectories of the moving spheres. These equations are solved using numerical methods. Application of the method to study the structure of a system of polydisperse spheres in a three-dimensional Euclidean space is briefly discussed.