Voronoi Diagram Research Articles

Accelerating structure search using atomistic graph-based classifiers.

We introduce an atomistic classifier based on a combination of spectral graph theory and a Voronoi tessellation method. This classifier allows for the discrimination between structures from different minima of a potential energy surface, making it a useful tool for sorting through large datasets of atomic systems. We incorporate the classifier as a filtering method in the Global Optimization with First-principles Energy Expressions (GOFEE) algorithm. Here, it is used to filter out structures from exploited regions of the potential energy landscape, whereby the risk of stagnation during the searches is lowered. We demonstrate the usefulness of the classifier by solving the global optimization problem of two-dimensional pyroxene, three-dimensional olivine, Au12, and Lennard-Jones LJ55 and LJ75 nanoparticles.

Inverse design of functionally graded porous structures with target dynamic responses

Although functionally graded porous structures (FGPS) have been studied comprehensively due to their excellent mechanical and functional properties, the design process of FGPS with target stress response still dependent on continuous trial and error, which is not only time-consuming but also heavily relies on experience and intuition. This study proposes a novel inverse design framework of 2D FGPS with targeted dynamic stress-strain responses via a combination of conditional diffusion model and a residual neural network. Unlike traditional binary pixel representations, this approach utilizes nuclei position maps and color mapping technique to represent the structure configurations and cell wall thicknesses to improve the efficiency and performance of the model. Firstly, various functionally graded porous structures were constructed by employing Voronoi diagram techniques, and finite element simulations were conducted to calculate the nonlinear responses subjected to dynamic loadings. A dataset comprising 2100 FGPS and corresponding nonlinear stress-strain responses was established. Then, an inverse design framework is formulated by integrating a generator that uses a diffusion model to synthesize structures conditioned on specific target responses, with a predictor that employs a residual neural network to assess the responses of these structures. Finally, to demonstrate the effectiveness of the approach, the performance of the predictor and generator was thoroughly investigated. Structures with various target stress-strain responses were generated through the proposed method, and validated by finite element analysis. A detailed impact experiment was also carried out to verify the effectiveness of the proposed methods. The result shows that the framework can effectively generate new structures with objective nonlinear responses. This work offers a fast and efficient way to design FGPS that meet specific performance objectives.

Many-sided Poisson–Voronoi cells with only Gabriel neighbors

Let pnG be the probability for a planar Poisson–Voronoi cell to be n-sided and have only Gabriel neighbors. Using an exact coordinate transformation followed by scaling arguments and a mean-field type calculation, we obtain the asymptotic expansion of log⁡pnG in the limit of large n. We determine several statistical properties of a many-sided cell obeying this ‘Gabriel condition.’ In particular, the cell perimeter, when parametrized as a function τ(θ) of the polar angle θ, behaves as a Brownian bridge on the interval 0⩽θ⩽2π . We point out similarities and differences with related problems in random geometry.

Utilizing Voronoi Tessellations to Determine Radial Density Profiles

We have developed a novel method of determining 2D radial density profiles for astronomical systems of discrete objects using Voronoi tessellations. This Voronoi-based method was tested against the standard annulus-based method on five simulated systems of objects, following known Hubble density profiles of varying parameters and sizes. It was found that the Voronoi-based method returned radial density fits with lower uncertainties on the fitting parameters across all five systems compared to the annulus-based method. The Voronoi-based method also consistently returned more accurate estimates of the total number of objects in each system than the annulus-based method, and this accuracy increased with increasing system size. Finally, the Voronoi-based method was applied to two observed globular cluster systems around brightest cluster galaxies ESO 444-G046 and 2MASX J13272961-3123237 and the results were compared to previous results for these galaxies obtained with the annulus-based method. Again, it was found that the Voronoi-based method returned fits with lower uncertainties on the fitting parameters, and the total number of globular clusters returned are within errors of the annulus-based method estimates, however also with lower uncertainties.

Voronoi Tessellation as a Tool for Predicting the Formation of Deep Eutectic Solvents.

Deep eutectic solvents (DESs) have attracted increasing attention in recent years due to their broad applicability in different fields, but their computer-aided discovery, which avoids a time-consuming trial-and-error investigation, is still lagging. In this paper, a set of nine DESs, composed of choline chloride as a hydrogen-bond acceptor and nine functionalized phenols as hydrogen bond donors, is simulated by using classical molecular dynamics to investigate the possible formation of a DES. The tool of the Voronoi tessellation analysis is employed for producing an intuitive and straightforward representation of the degree of mixing between the different components of the solutions, therefore permitting the definition of a metric quantifying the propensity of the components to produce a uniform solution. The computational findings agree with the experimental results, thus confirming that the Voronoi tessellation analysis can act as a lightweight yet powerful approach for the high-throughput screening of mixtures in the optics of the new DES design.

CURE: A Hierarchical Framework for Multi-Robot Autonomous Exploration Inspired by Centroids of Unknown Regions

In this paper, a novel multi-robot autonomous exploration approach CURE is proposed based on dynamic Voronoi diagrams and centroids of unknown connected regions. Compared with existing approaches, the novelty of this work is twofold: 1) Dynamic Voronoi diagram is used for partition of the space being explored to improve the efficiency of multi-robot exploration, and then a new parameter-insensitive utility function is elaborately designed to evaluate the information of centroids, which helps guide the robot to explore unknown regions. 2) A hierarchical framework consisting of global and local exploration windows for detecting centroids is designed, wherein the global exploration window is activated to find centroids to guide the robot exploration when there are no centroids in any one local exploration window. We validate the feasibility and exploration efficiency of the proposed approach in various complex simulation scenarios and challenging real-world tasks. All test results show that the exploration time consumption and path cost are reduced by up to 50.7% and 34.4%, respectively, compared with an advanced RRT-based multi-robot exploration approach. (Supplementary video link: https://youtu.be/P5jXKlGQOec) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the efficient multi-robot autonomous exploration problem. In some applications such as target search and disaster rescue, the information about the environment is totally unknown to the robots, and thus they are required to explore unknown environments autonomously. In this case, it is necessary to improve the efficiency of multi-robot exploration due to the time limitation of the task and the battery capacity. In this paper, a hierarchical framework is proposed to improve the efficiency of multi-robot autonomous exploration. Each robot only needs to explore the Voronoi partition it is responsible for and is guided to the unknown region by the centroid detected in the global and local exploration windows. Overall, the proposed approach can dramatically reduce the exploration time and path cost.

A review of coordinated multi-robot exploration

Abstract A multiple robots system provides advantages over a single robot when it comes to exploring an unfamiliar area. Due to its applications in localization and mapping, search and rescue, etc. This technology has attracted a lot of study interest. The main challenge is properly distributing target points among several robots so that they can each investigate a separate section of the environment simultaneously and ensure the shortest possible total exploration time. However, more work still needs to be done to incorporate research issues in a real setting, such as how to eliminate duplicate exploration areas by giving robots multiple target locations or how to avoid unanticipated barriers in new situations. The allocation algorithms, motion planning techniques, and exploration strategies used in multi-robot collaboration (CME) are reviewed in this paper. Additionally, it provides an explanation of the methods research teams employ to optimize traditional whale optimization algorithm (WOA), how they enhance exploration performance and speed, and a comparative analysis of these methods. We also discussed a cooperative exploration method based on dynamic Voronoi partitioning. However, we also need some obstacle avoidance algorithms to help understand the gaps and issues that will need to be solved in the upcoming years, namely how to handle unexpected impediments in unfamiliar surroundings. Lastly, a summary of potential future lines of inquiry and uses is given.

Multi-Robot Collaborative Hunting in Cluttered Environments With Obstacle-Avoiding Voronoi Cells

Multi-Robot Collaborative Hunting in Cluttered Environments With Obstacle-Avoiding Voronoi Cells

Voronoi cells in random split trees

Voronoi cells in random split trees

Accessibility to palliative care services in Colombia: an analysis of geographic disparities

ObjectivesDue to the increase in the prevalence of non-communicable diseases and the Colombian demographic transition, the necessity of palliative care has arisen. This study used accessibility and coverage indicators to measure the geographic barriers to palliative care.MethodsPopulation-based observational study focused on urban areas and adult population from Colombia, which uses three measurements of geographic accessibility to services: a) density of palliative care services per 100,000 inhabitants, b) analysis of geographic distribution by territorial nodes of the country, and c) spatial analysis of palliative care services using Voronoi diagrams. ArcGIS Pro software was used to map services’ locations and identify geographic disparities.ResultsA total of 504 palliative care services were identified, of which 77% were primary health care services. The density of palliative care services in Colombia is 1.8 primary care services per 100,000 inhabitants and 0.4 specialized services per 100,000 inhabitants. The average palliative care coverage is 41%, two regions of the country have a coverage below 30%. Twenty-eight percent of the services provide care for a population greater than 50,000 inhabitants within their coverage area, exceeding the acceptable limit by international standards.ConclusionsPalliative care services are concentrated in three main regions (Bogotá D.C., the Center, and the Caribbean) and are limited in the Orinoquia and Amazonia nodes. Density of specialized palliative care services is extremely low and there are regions without palliative services for adults with palliative needs.

Voronoi Diagram-based USBL Outlier Rejection for AUV Localization

USBL systems are essential for providing accurate positions of autonomous underwater vehicles (AUVs). On the other hand, the accuracy can be degraded by outliers because of the environmental conditions. A failure to address these outliers can significantly impact the reliability of underwater localization and navigation systems. This paper proposes a novel outlier rejection algorithm for AUV localization using Voronoi diagrams and query point calculation. The Voronoi diagram divides data space into Voronoi cells that center on ultra-short baseline (USBL) data, and the calculated query point determines if the corresponding USBL data is an inlier. This study conducted experiments acquiring GPS and USBL data simultaneously and optimized the algorithm empirically based on the acquired data. In addition, the proposed method was applied to a sensor fusion algorithm to verify its effectiveness, resulting in improved pose estimations. The proposed method can be applied to various sensor fusion algorithms as a preprocess and could be used for outlier rejection for other 2D-based location sensors.

Applications of Voronoi Diagrams in Multi-Robot Coverage: A Review

In recent decades, multi-robot region coverage has played an important role in the fields of environmental sensing, target searching, etc., and it has received widespread attention worldwide. Due to the effectiveness in segmenting nearest regions, Voronoi diagrams have been extensively used in recent years for multi-robot region coverage. This paper presents a survey of recent research works on region coverage methods within the framework of the Voronoi diagram, to offer a perspective for researchers in the multi-robot cooperation domain. First, some basic knowledge of the Voronoi diagram is introduced. Then, the region coverage issue under the Voronoi diagram is categorized into sensor coverage and task execution coverage problems, respectively, considering the sensor range parameter. Furthermore, a detailed analysis of the application of Voronoi diagrams to the aforementioned two problems is provided. Finally, some conclusions and potential further research perspectives in this field are given.

Gradient anisotropic design of Voronoi porous structures

Gradient and anisotropic design have proved to be two effective approaches for customizing lightweight porous parts in recent years due to their outstanding performances comparing to the uniform porous ones, such as high specific strength, specific surface areas and high energy and shock absorption capacities, etc. However, it is still challenging to integrate both gradient and anisotropy into a same porous part, while making it profile adaptable simultaneously. In this paper, a novel gradient anisotropic design method of Voronoi porous structures for parts customization is proposed driven by the stress field of a part in a specific application scenario. Firstly, the stress field is decomposed into a stress scalar field and a stress direction field. The former is mapped into the Voronoi site distribution by a weighted random sampling algorithm that globally controls the gradient of the mechanical properties, while the latter is applied to adjust the shapes and orientations of the Voronoi cells for tailoring the anisotropy locally. Then, a lightweight gradient anisotropic Voronoi porous (GAVP) part is customized based on a Voronoi cell growth strategy with preferred directions, making the porous part highly profile adaptable. Finally, the influences of the design parameters on the mechanical properties of the GAVP parts are analyzed in detail, and the proposed design method is further validated experimentally and numerically. The results show that the integration of gradient and anisotropy significantly enhances the mechanical properties of a GAVP part compared to the corresponding gradient porous or anisotropic porous ones, because our GAVP structure modeling method realize a more optimal allocation of material locally, which makes the stress distribution much more even.

Evaluation of the Spatial Arrangement of Rabbit Hepatocytes Based on Voronoi Tessellation Following Exposure to Zinc Oxide Nanoparticles.

Zinc oxide nanoparticles have been utilized in different fields over the last decades. These nanoparticles can pose significant risks to various organs such as the liver. This study aimed to evaluate the effects of zinc oxide nanoparticles on liver histology, serum biochemistry, and spatial arrangement of the hepatocytes in the female New Zealand white rabbit. The rabbits received 1, 5, and 10 mg/kg of the zinc oxide nanoparticles (ZnO NPs) intraperitoneally once every 3 days for 28 days. The serum levels of the aspartate aminotransferase, alanine aminotransferase, alkaline phosphatase and zinc were assessed 48 hr following the first administration. The histopathological changes and Voronoi tessellation were evaluated after the last administration. Our findings showed that the ZnO NPs significantly increased the serum levels of aspartate aminotransferase, alanine aminotransferase, alkaline phosphatase, and zinc. The histopathological findings showed ballooning degeneration, and sinusoidal congestion in ZnO NPs administrated groups. The Voronoi tessellation diagrams also confirmed that ZnO NPs changed the regular spatial arrangement of hepatocytes to random and cluster patterns. In conclusion, the ZnO NPs alter the liver spatial arrangement and induce hepatic pathological changes that may affect liver function in rabbits.

FE modeling to generate composite RVEs with high volume fractions and various shapes of inclusions

This work proposes a novel multi-step dynamic FE compression method to generate Representative Volume Elements (RVEs) of composites containing a variety of inclusions. This method is actualized through a sequential and four-stage procedure: (1) Sparse and periodic inclusions exhibiting a predefined orientation distribution are generated by implementing a modified random sequential adsorption algorithm, (2) Sparse inclusions undergo biaxial compression into the region of the targeted RVE via a dynamic FE analysis, (3) Periodic inclusions are compressed into the region utilizing a dynamic FE analysis with periodic boundary conditions, and (4) Positions and orientations of the compressed inclusions are extracted and the RVE in computer-aided design format is then generated. The proposed method confers advantages from four distinct perspectives: (1) applicability to various inclusion geometries, including ellipses, lobules, polygons, kidneys and stars, (2) ability to generate periodic RVEs of composites with high inclusion volume fractions (up to 80.0% for circular inclusions), (3) simple and straightforward numerical implementation without explicitly considering inclusion intersection check and (4) capacity to predefine inclusion orientation distribution. Statistical analyses utilizing multiple spatial descriptors, i.e., inclusion orientation angle, local volume fraction, Voronoi cell area, nearest-neighbor distance and orientation, second order intensity function, radial distribution function and two-point probability function, confirm randomness of inclusion distribution in the generated RVEs. The elastic properties and damage behaviors of composites via the FE homogenization method are predicted based on the generated RVEs and are compared with those of available experimental data, the literature and the mean-field homogenization models to demonstrate effectiveness of the proposed multi-step dynamic FE compression method.

Dynamic Construction of Spherical Raster Voronoi Diagrams Based on Ordered Dilation

Dynamic Construction of Spherical Raster Voronoi Diagrams Based on Ordered Dilation

Path Planning of a Mobile Robot Based on the Improved Rapidly Exploring Random Trees Star Algorithm

With the increasing utilization of sampling-based path planning methods in the field of mobile robots, the RRT* algorithm faces challenges in complex indoor scenes, including high sampling randomness and slow convergence speed. To tackle these issues, this paper presents an improved RRT* path-planning algorithm based on the generalized Voronoi diagram with an adaptive bias strategy. Firstly, the algorithm leverages the properties of the generalized Voronoi diagram (GVD) to obtain heuristic paths, and a sampling region with target bias is constructed, increasing the purposefulness of the sampling process. Secondly, the node expansion process incorporates an adaptive bias strategy, dynamically adjusting the step size and expanding direction. This strategy allows the algorithm to adapt to the local environment leading to improved convergence speed. To ensure the generation of smooth paths, the paper employs the cubic spline curve interpolation algorithm for trajectory optimization to ensure that the mobile robotic can obtain the best trajectory. Finally, the proposed algorithm is experimentally compared with existing algorithms, including the RRT* and Informed-RRT* algorithms, to verify the feasibility and stability.

Two-phase model for inverse Hall–Petch effect in nanocrystalline thin film: Atomistic simulation study

This work presents two methods to improve the understanding of the mechanical behavior of nanocrystalline thin films. Firstly, a simple two-phase model is proposed to explain the inverse Hall–Petch effect. The model suggests that the nanocrystalline material consists of the grain-boundary and the grain interior with different mechanical properties. Secondly, a computational method is developed to create more realistic grain boundaries in simulations of polycrystals. Traditionally created grain boundaries by Voronoi tessellation are too dense and do not accurately reflect the reality and the experimental results. The strength of the nanocrystalline aluminum thin film is simulated using molecular dynamics. The grain size dependence of the elastic modulus, ultimate tensile stress, and engineering yield strength is demonstrated. The experimental values of modulus and strength are approximately 6 times smaller probably due to the presence of porosity in the real sample. An approach is developed to introduce porosity in the simulated samples at the grain boundaries and in the grain interior to reduce this discrepancy. The modeled value of modulus for a grain size of 40 nm without porosity is 67GPa, whereas, with 50% grain-boundary porosity and 20% intra-granular porosity it is 30GPa. For the ultimate tensile strength, we get 3GPa and 1.4GPa for samples without porosity and with porosity, respectively. The simulated values of modulus with porosity are still 4 times higher and the values of strength are about 2 times higher than the experimental ones. The amount of porosity in our method can be adjusted to fit the experimental values; however, high values of porosity cause the mechanical instability of the simulated samples.

A GIS-Based Fuzzy Model to Detect Critical Polluted Urban Areas in Presence of Heatwave Scenarios

This research presents a new method for detecting urban areas critical for the presence of air pollutants during periods of heatwaves. The proposed method uses a geospatial model based on the construction of Thiessen polygons and a fuzzy model based on assessing, starting from air quality control unit measurement data, how concentrations of air pollutants are distributed in the urban study area during periods of heatwaves and determine the most critical areas as hotspots. The proposed method represents an optimal trade-off between the accuracy of the detection of critical areas and the computational speed; the use of fuzzy techniques for assessing the intensity of concentrations of air pollutants allows evaluators to model the assessments of critical areas more naturally. The method is implemented in a GIS-based platform and has been tested in the city of Bologna, Italy. The resulting criticality maps of PM10, NO2, and PM2.5 pollutants during a heatwave period that occurred from 10 to 14 July 2023 revealed highly critical hotspots with high pollutant concentrations in densely populated areas. This framework provides a portable and easily interpretable decision support tool which allows you to evaluate which urban areas are most affected by air pollution during heatwaves, potentially posing health risks to the exposed population.

Visual simulation of opal using bond percolation through the weighted Voronoi diagram and the Ewald construction

Visual simulation of opal using bond percolation through the weighted Voronoi diagram and the Ewald construction