Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Complexity and real computation
Complexity and real computation
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
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
Root comparison techniques applied to computing the additively weighted Voronoi diagram
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Voronoi Diagram of a Circle Set Constructed from Voronoi Diagram of a Point Set
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Voronoi diagrams of semi-algebraic sets
Voronoi diagrams of semi-algebraic sets
The predicates of the Apollonius diagram: Algorithmic analysis and implementation
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
| Hi-index | 0.00 |
Circles are frequently used for modelling the growth of particle aggregates through the Johnson-Mehl tessellation, that is a special instance of the Voronoi diagram of circles. Voronoi diagrams allow one to answer proximity queries after locating a query point in the Voronoi zone it belongs to. The dual graph of the Voronoi diagram is called the Delaunay graph. In this paper, we first show a necessary and sufficient condition of connectivity of the Voronoi diagram of circles. Then, we show how the Delaunay graph of circles (the dual graph of the Voronoi diagram of circles) can be computed exactly, and in a much simpler way, by computing the eigenvalues of a two by two matrix. Finally, we present how the Voronoi diagram of circles can be used to model the growth of particle aggregates. We use the Poisson point process in the Voronoi diagram of circles to generate the Johnson-Mehl tesselation. The Johnson-Mehl model is a Poisson Voronoi growth model, in which nuclei are generated asynchronously using a Poisson point process, and grow at the same radial speed. Growth models produce spatial patterns as a result of simple growth processes and their visualization is important in many technical processes.