Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Primitives for the manipulation of three-dimensional subdivisions
SCG '87 Proceedings of the third annual symposium on Computational geometry
Representing geometric structures in d dimensions: topology and order
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Subdivisions of n-dimensional spaces and n-dimensional generalized maps
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
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
Nonmanifold Topology Based on Coupling Entities
IEEE Computer Graphics and Applications
On the combinatorial complexity of euclidean Voronoi cells and convex hulls of d-dimensional spheres
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Updating the topology of the dynamic Voronoi diagram for spheres in Euclidean d-dimensional space
Computer Aided Geometric Design
Proximity and applications in general metrics
Proximity and applications in general metrics
Computer-Aided Design
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Voronoi diagrams have been known to have numerous applications in various fields in science and engineering. While the Voronoi diagram for points has been extensively studied in two and higher dimensions, the Voronoi diagram for spheres in three or higher dimensions has not been studied sufficiently. In this paper, we propose an algorithm to construct Euclidean Voronoi diagrams for spheres in 3D. Starting from the ordinary Voronoi diagram for the centers of spheres, the proposed region expansion algorithm constructs the desired diagram by expanding Voronoi regions for one sphere after another via a series of topology operations. Adopted data structure for the proposed algorithm is a variation of radial data structure. While the worst-case time complexity is O(n3 log n) for the whole diagram, its expected time complexity can be much lower.