Circles are frequently used for modelling the growth of particle aggregates through the Voronoi diagram of circles, that is a special instance of the Johnson-Mehl tessellation. The Voronoi diagram of a set of sites is a decomposition of space into proximal regions. The proximal region of a site is the locus of points closer to that site than to any other one. Voronoi diagrams allow one to answe...

A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample from the posterior, which contains information about the unobserved Voronoi tessellation and the mode...

Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata — finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting, excited, refractory and precipitate. A resting cell excites if it has at least one excited neighbour; the cell precipitates if a ratio of excited cells in its neigh...

We developed a model of macromolecular interfaces based on the Voronoi diagram and the related alpha-complex, and we tested its properties on a set of 96 protein-protein complexes taken from the Protein Data Bank. The Voronoi model provides a natural definition of the interfaces, and it yields values of the number of interface atoms and of the interface area that have excellent correlation coef...

To support the need for interactive spatial analysis, it is often necessary to rethink the data structures and algorithms underpinning applications. This paper describes the development of an interactive environment in which a number of different Voronoi models of space can be manipulated together in real time, to (1) study their behaviour, (2) select appropriate models for specific analysis ta...

The Voronoi-based 9-intersection model (V9I) is a modified version of the original point-set-based 9-intersection model. The modification is made by replacing the complement (exterior) of an entity with its Voronoi region. It is shown in this paper that it is possible to solve the three major problems associated with the original 9-intersection model with the new V9I model.

In this paper, we review the computational aspects of a multiscale dissipative particle dynamics model for complex fluid simulations based on the feature-rich geometry of the Voronoi tessellation. The geometrical features of the model are critical since the mesh is directly connected to the physics by the interpretation of the Voronoi volumes of the tessellation as coarse-grained fluid clusters...