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
Swap conditions for dynamic Voronoi diagrams for circles and line segments
Computer Aided Geometric Design
Generalized voronoi diagrams and geometric searching.
Generalized voronoi diagrams and geometric searching.
Dynamic Additively Weighted Voronoi Diagrams in 2D
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
The Voronoi Diagram of Circles and Its Application to the Visualization of the Growth of Particles
Transactions on Computational Science III
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Presented in this paper is an algorithm to compute the exact Voronoi diagram of circle set from the Voronoi diagram of point set. In particular, the topology aspect of the algorithm is presented here. The circles are located in a two dimensional Euclidean space, the radii of circles are not necessarily equal, and the circles are allowed to intersect. Even though the time complexity is O(n2), the algorithm turns out to be fast and robust. The algorithm uses the topology of the point set Voronoi diagram as an initial solution, and finds the correct topology of the Voronoi diagram of circle set from its point set counterpart. Hence, the algorithm is as stable as point set Voronoi diagram algorithm.