Computational geometry: an introduction
Computational geometry: an introduction
Introduction to Solid Modeling
Introduction to Solid Modeling
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Approximation of generalized Voronoi diagrams by ordinary Voronoi diagrams
CVGIP: Graphical Models and Image Processing
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
Molecular surfaces on proteins via beta shapes
Computer-Aided Design
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Region-expansion for the Voronoi diagram of 3D spheres
Computer-Aided Design
Apollonius tenth problem via radius adjustment and Möbius transformations
Computer-Aided Design
Euclidean Voronoi diagram of 3D balls and its computation via tracing edges
Computer-Aided Design
Large-scale fixed-outline floorplanning design using convex optimization techniques
Proceedings of the 2008 Asia and South Pacific Design Automation Conference
Medial axis computation for planar free-form shapes
Computer-Aided Design
An O(n2log n) time algorithm for computing shortest paths amidst growing discs in the plane
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
3D hyperbolic Voronoi diagrams
Computer-Aided Design
Quasi-worlds and quasi-operators on quasi-triangulations
Computer-Aided Design
UFO: unified convex optimization algorithms for fixed-outline floorplanning
Proceedings of the 2010 Asia and South Pacific Design Automation Conference
A fast algorithm for constructing approximate medial axis of polygons, using Steiner points
Advances in Engineering Software
Using Voronoi diagrams to solve a hybrid facility location problem with attentive facilities
Information Sciences: an International Journal
Fuzzy Voronoi diagram for disjoint fuzzy numbers of dimension two
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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Presented in this paper is a sweepline algorithm to compute the Voronoi diagram of a set of circles in a two-dimensional Euclidean space. The radii of the circles are non-negative and not necessarily equal. It is allowed that circles intersect each other, and a circle contains others. The proposed algorithm constructs the correct Voronoi diagram as a sweepline moves on the plane from top to bottom. While moving on the plane, the sweepline stops only at certain event points where the topology changes occur for the Voronoi diagram being constructed. The worst-case time complexity of the proposed algorithm is O((n+m)log n), where n is the number of input circles, and m is the number of intersection points among circles. As m can be O(n^2), the presented algorithm is optimal with O(n^2 log n) worst-case time complexity.