Related papers: Voronoi Diagram: The Generator Recognition Problem
Poisson point processes provide a versatile framework for modeling the distributions of random points in space. When the space is partitioned into cells, each associated with a single generating point from the Poisson process, there appears…
Effective transport properties of heterogeneous structures are predicted by geometric microstructural parameters, but these can be difficult to calculate. Here, a boundary element code with a recurrent series method accurately and…
A simple model is explored mainly analytically to calculate and understand the PHS of single and multi-layer thermal neutron detectors and to help optimize the design in different circumstances. Several theorems are deduced that can help…
Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by mathematicians, in two- and three dimensional…
We describe a new algorithm for computing the Voronoi diagram of a set of $n$ points in constant-dimensional Euclidean space. The running time of our algorithm is $O(f \log n \log \Delta)$ where $f$ is the output complexity of the Voronoi…
In this paper, we investigate the optimization of Centroidal Voronoi Tessellations (CVT) under geometric constraints. For this purpose, we minimize a linear combination of the standard CVT energy functional with terms involving geometric…
Representing a scanned map of the real environment as a topological structure is an important research in robotics. %is currently an important research. Since topological representations of maps save a huge amount of map storage space and…
Machine learning (ML) strategies are opening the door to faster computer simulations, allowing us to simulate more realistic colloidal systems. Since the interactions in colloidal systems are often highly many-body, stemming from e.g.…
Voronoi diagrams, and their more general weighted counterpart, power diagrams, are fundamental geometric constructs with wide-ranging applications. Recently, they have gained renewed attention in mesh-based neural rendering. Despite being…
This note describes a simple method to draw random points such that the cells of the corresponding Voronoi tesselation (approximately) satisfy a desired size distribution, for instance, follow a power law. The method is illustrated and…
We present a new particle-merging algorithm for the particle-in-cell method. Based on the concept of the Voronoi diagram, the algorithm partitions the phase space into smaller subsets, which consist of only particles that are in close…
We describe a method for modeling the geometry of porous materials. The approach enables the independent selection of crucial parameters, including porosity, pore size distribution, pore shape, and connectivity. Consequently, it can…
The area query, to find all elements contained in a specified area from a certain set of spatial objects, is a very important spatial query widely required in various fields. A number of approaches have been proposed to implement this…
Electrical grids are geographical and topological structures whose voltage states are challenging to represent accurately and efficiently for visual analysis. The current common practice is to use colored contour maps, yet these can…
Voronoi diagrams are a fundamental geometric data structure for obtaining proximity relations. We consider collections of axis-aligned orthogonal polyhedra in two and three-dimensional space under the max-norm, which is a particularly…
We discuss existing and new computational analysis techniques to classify local atomic arrangements in large-scale atomistic computer simulations of crystalline solids. This article includes a performance comparison of typical analysis…
This paper overviews work on the use of simple chemical reactions to calculate Voronoi diagrams and undertake other related geometric calculations. This work highlights that this type of specialised chemical processor is a model example of…
The transition from ordered to disordered structures in Voronoi tessellation is obtained by perturbing the seeds that were originally identified with two types of lattice in 2D and one type in 3D. The area in 2D and the volume in 3D are…
Tight-frame, a generalization of orthogonal wavelets, has been used successfully in various problems in image processing, including inpainting, impulse noise removal, super-resolution image restoration, etc. Segmentation is the process of…
We present a new open source code for massive parallel computation of Voronoi tessellations(VT hereafter) in large data sets. The code is focused for astrophysical purposes where VT densities and neighbors are widely used. There are several…