Voronoi Diagram Research Articles

Computing differential operators of the particle velocity in moving particle clouds using tessellations

We propose finite-time measures to compute the divergence, the curl and the velocity gradient tensor of the point particle velocity for two- and three-dimensional moving particle clouds. For this purpose, a tessellation of the particle positions is performed to assign a volume to each particle. We introduce a modified Voronoi tessellation which overcomes some drawbacks of the classical construction. Instead of the circumcenter we use the center of gravity of the Delaunay cell for defining the vertices. Considering then two subsequent time instants, the dynamics of the volume can be assessed. Determining the volume change of tessellation cells yields the divergence of the particle velocity. Reorganizing the various velocity coefficients allows computing the curl and even the velocity gradient tensor. The helicity of particle velocity can be likewise computed and swirling motion of particle clouds can be quantified. First we assess the numerical accuracy for randomly distributed particles. We find a strong Pearson correlation between the divergence computed with the modified tessellation, and the exact value. Moreover, we show that the proposed method converges with first order in space and time in two and three dimensions. Then we consider particles advected with random velocity fields with imposed power-law energy spectra. We study the number of particles necessary to guarantee a given precision. Finally, applications to fluid and inertial particles advected in three-dimensional fully developed isotropic turbulence show the utility of the approach for real world applications to quantify self-organization in particle clouds and their vortical or even swirling motion.

Competing mechanisms govern the thermal rectification behavior in semi-stochastic polycrystalline graphene with graded grain-size distribution

Thermal rectifiers are devices that have different thermal conductivities in opposing directions of heat flow. The realization of practical thermal rectifiers relies significantly on a sound understanding of the underlying mechanisms of asymmetric heat transport, and two-dimensional materials offer a promising opportunity in this regard owing to their simplistic structures together with a vast possibility of tunable imperfections. However, the in-plane thermal rectification mechanisms in 2D materials like graphene having directional gradients of grain sizes have remained elusive. In fact, understanding the heat transport mechanisms in polycrystalline graphene, which are more practical to synthesize than large-scale single-crystal graphene, could potentially allow a unique opportunity, in principle, to combine with other defects and designs for effective optimization of thermal rectification. In this work, we investigate the thermal rectification behavior in periodic atomistic models of polycrystalline graphene whose grain arrangements were generated semi-stochastically to have different gradient grain-density distributions along the in-plane heat flow direction. We employ the centroidal Voronoi tessellation technique to generate realistic grain boundary structures for graphene, and the non-equilibrium molecular dynamics simulations method is used to calculate the thermal conductivities and rectification values. Additionally, detailed phonon characteristics and propagating phonon spatial energy densities are analyzed based on the fluctuation-dissipation theory to elucidate the competitive interplay between two underlying mechanisms, namely, (1) propagating phonon coupling and (2) temperature-dependence of thermal conductivity that determine the degree of asymmetric heat flow in graded polycrystalline graphene.

Balancing graph Voronoi diagrams with one more vertex

AbstractLet be a graph with unit‐length edges and nonnegative costs assigned to its vertices. Given a list of pairwise different vertices , the prioritized Voronoi diagram of with respect to is the partition of in subsets so that, for every with , a vertex is in if and only if is a closest vertex to in and there is no closest vertex to in within the subset . For every with , the load of vertex equals the sum of the costs of all vertices in . The load of equals the maximum load of a vertex in . We study the problem of adding one more vertex at the end of in order to minimize the load. This problem occurs in the context of optimally locating a new service facility (e.g., a school or a hospital) while taking into account already existing facilities, and with the goal of minimizing the maximum congestion at a site. There is a brute‐force algorithm for solving this problem in time on ‐vertex ‐edge graphs. We prove a matching time lower bound–up to sub‐polynomial factors–for the special case where and , assuming the so called Hitting Set Conjecture of Abboud et al. On the positive side, we present simple linear‐time algorithms for this problem on cliques, paths and cycles, and almost linear‐time algorithms for trees, proper interval graphs and (assuming to be a constant) bounded‐treewidth graphs.

Optimal locating and sizing of charging stations for large‐scale areas based on GIS data and grid partitioning

AbstractThis research proposes an optimisation model for identifying the optimal locations and sizes of public charging stations for large‐scale areas based on geographic information system (GIS) data and grid partitioning. A grid partitioning technique is utilised to generate subareas and investigate the demand for electric vehicle (EV) chargers calculated based on the number of EVs in each subarea. The optimal locations are formulated as a maximum covering location problem and solved by integer programming to ensure that all vehicle access subareas, according to the GIS data, are covered by charging stations. The sizes of charging stations are formulated as a knapsack problem and solved by the EV‐charge point ratio to guarantee each subarea has the appropriate number of chargers. The Voronoi diagram is integrated to estimate vehicle density and improve visualisation. The model is extended to include potential power loss reduction by adjusting the distribution of chargers in relation to the proximity to electrical substations. The developed methodology has been implemented by the whole country area of Thailand, which covers an area of approximately 510,000 km2. The study results are represented in a map blueprint that is very useful in strategic planning to support the so‐called EV30@30 government policy's ambitious national target of 2,050,000 units of EVs in 2030.

An efficient 3-approximation algorithm for the Steiner tree problem with the minimum number of Steiner points and bounded edge length.

We present improved algorithms for the Steiner tree problem with the minimum number of Steiner points and bounded edge length. Given n terminal points in a 2D Euclidean plane and an edge length bound, the problem asks to construct a spanning tree of n terminal points with minimal Steiner points such that every edge length of the spanning tree is within the given bound. This problem is known to be NP-hard and has practical applications such as relay node placements in wireless networks, wavelength-division multiplexing(WDM) optimal network design, and VLSI design. The best-known deterministic approximation algorithm has O(n3) running time with an approximation ratio of 3. This paper proposes an efficient approximation algorithm using the Voronoi diagram that guarantees an approximation ratio of 3 in O(n log n) time. We also present the first exact algorithm to find an optimal Steiner tree for given three terminal points in constant time. Using this exact algorithm, we improve the 3-approximation algorithm with better performance regarding the number of required Steiner points in O(n log n) time.

Voronoi discretization to improve the meshless local Petrov–Galerkin method in 3D-computational fracture mechanics

Purpose1) The OE-MLPG penalty meshfree method is developed to solve cracked structure.(2) Smartening the numerical meshfree method by combining the particle swarm optimization (PSO) optimization algorithms and Voronoi computational geometric algorithm. (3). Selection of base functions, finding optimal penalty factor and distribution of appropriate nodal points to the accuracy of calculation in the meshless local Petrov–Galekrin (MLPG) meshless method.Design/methodology/approachUsing appropriate shape functions and distribution of nodal points in local domains and sub-domains and choosing an approximation or interpolation method has an effective role in the application of meshless methods for the analysis of computational fracture mechanics problems, especially problems with geometric discontinuity and cracks. In this research, computational geometry technique, based on the Voronoi diagram (VD) and Delaunay triangulation and PSO algorithm, are used to distribute nodal points in the sub-domain of analysis (crack line and around it on the crack plane).FindingsBy doing this process, the problems caused by too closeness of nodal points in computationally sensitive areas that exist in general methods of nodal point distribution are also solved. Comparing the effect of the number of sentences of basic functions and their order in the definition of shape functions, performing the mono-objective PSO algorithm to find the penalty factor, the coefficient, convergence, arrangement of nodal points during the three stages of VD implementation and the accuracy of the answers found indicates, the efficiency of V-E-MLPG method with Ns = 7 and ß = 0.0037–0.0075 to estimation of 3D-stress intensity factors (3D-SIFs) in computational fracture mechanics.Originality/valueThe present manuscript is a continuation of the studies (Ref. [33]) carried out by the authors, about; feasibility assessment, improvement and solution of challenges, introduction of more capacities and capabilities of the numerical MLPG method have been used. In order to validate the modeling and accuracy of calculations, the results have been compared with the findings of reference article [34] and [35].

Topology optimization of shell structures in architectural design

Free-form architectural design has gained significant interest in modern architectural practice. Due to their visually appealing nature and inherent structural efficiency, free-form shells have become increasingly popular in architectural applications. Recently, topology optimization has been extended to shell structures, aiming to generate shell designs with ultimate structural efficiency. However, despite the huge potential of topology optimization to facilitate new design for shells, its architectural applications remain limited due to complexity and lack of clear procedures. This paper presents four design strategies for optimizing free-form shells targeting architectural applications. First, we propose a topology-optimized ribbed shell system to generate free-form rib layouts possessing improved structure performance. A reusable and recyclable formwork system is developed for their effective and sustainable fabrication. Second, we demonstrate that topology optimization can be combined with funicular form-finding techniques to generate a rich variety of elegant designs, offering new design possibilities. Third, we offer cost-effective design solutions using modular components for free-form shells by combining surface planarization and periodic constraint. Finally, we integrate topology optimization with user-defined patterns on free-form shells to facilitate aesthetic expression, exemplified by the Voronoi pattern. The presented strategies can facilitate the usage of topology optimization in shell designs to achieve high-performance and innovative solutions for architectural applications.

A novel method for inverting coseismic 3D surface deformation using InSAR considering the weight influence of the spatial distribution of GNSS points

The combination of InSAR and GNSS data can provide more accurate measurements of coseismic 3D surface deformations, which are crucial in determining earthquake source parameters. Currently, the methods for inverting coseismic 3D surface deformations by integrating GNSS and InSAR data using the strain model (SM) (e.g., Simultaneous and integrated strain tensor estimation from geodetic measurements to obtain 3D displacement maps (SISTEM), SM-VCE) simply select GNSS points based on a certain number or distance, without considering the weight influence of the spatial distribution of G NSS points on the InSAR and GNSS data fusion results. To address this issue, this paper proposes a new method that uses Voronoi diagrams analyze the contribution of GNSS points to the deformation at target points. In this paper, GNSS points with high contribution can be used to construct observation value equations and optimize the internal weight of GNSS data. The proposed approach characterizes the contribution of GNSS data to target points by analyzing the changes in the Delaunay triangulation area formed before and after the target points are added to the GNSS data. Simulation experiments reveal that the proposed method outperforms conventional methods in accuracy and completeness. The proposed method is then applied to map the coseismic 3D surface deformations of the 2020 Mw6.5 Monte Cristo Range earthquake and find that the maximum deformation in the east–west, north–south, and vertical directions is about 13 cm, 11 cm, and 24 cm, respectively.

Simulation of Microscopic Fracture Behavior in Nanocomposite Ceramic Tool Materials

In this paper, the microstructures of nanocomposite ceramic tool materials are represented through Voronoi tessellation. A cohesive element model is established to perform the crack propagation simulation by introducing cohesive elements with fracture criteria into microstructure models. Both intergranular and transgranular cracking are considered in this work. The influences of nanoparticle size, microstructure type, nanoparticle volume content and interface fracture energy are analyzed, respectively. The simulation results show that the nanoparticles have changed the fracture pattern from intergranular mode in single-phase materials to intergranular–transgranular–mixed mode. It is mainly the nanoparticles along grain boundaries that have an impact on the fracture pattern change in nanocomposite ceramic tool materials. Microstructures with smaller nanoparticles, in which there are more nanoparticles dispersed along matrix grain boundaries, have higher fracture toughness. Microstructures with a nanoparticle volume content of 15% have the most obvious transgranular fracture phenomenon and the highest critical fracture energy release rate. A strong interface is useful for enhancing the fracture toughness of nanocomposite ceramic tool materials.

Persistent homology based goodness-of-fit tests for spatial tessellations

Motivated by the rapidly increasing relevance of virtual material design in the domain of materials science, it has become essential to assess whether topological properties of stochastic models for a spatial tessellation are in accordance with a given dataset. Recently, tools from topological data analysis such as the persistence diagram have allowed to reach profound insights in a variety of application contexts. In this work, we establish the asymptotic normality of a variety of test statistics derived from a tessellation-adapted refinement of the persistence diagram. Since in applications, it is common to work with tessellation data subject to interactions, we establish our main results for Voronoi and Laguerre tessellations whose generators form a Gibbs point process. We elucidate how these conceptual results can be used to derive goodness of fit tests, and then investigate their power in a simulation study. Finally, we apply our testing methodology to a tessellation describing real foam data.

Energy aware optimal routing model for wireless multimedia sensor networks using modified Voronoi assisted prioritized double deep Q‐learning

SummaryThe energy hole problem is critical in Wireless Multimedia Sensor Network (WMSN), wherein the nodes closer to the sink node will expire sooner than the outer sub‐regions. Because they transmit their packet and forward the outer sub‐regions packet to the sink. Hence, a hole arises near the sink node after a very short time. Thus, an energy‐aware optimal routing model is introduced in this research using Modified Voronoi‐assisted prioritized double deep Q‐learning (PDDQL). Initially, the sensor nodes are deployed using the Voronoi cell structure that splits the entire region of interest into different Voronoi polygons. However, the Voronoi diagram will not always predict an efficient route because of the nodes at a Voronoi edge or vertex outside the transmission range. To tackle this issue, a new Voronoi diagram is proposed that depends on the maximum horizontal transmission range to remove the portion of Voronoi edges uncovered by the sensor node. After the deployment, a PDDQL algorithm is used to select the Relay Nodes based on their remaining energy. The proposed PDDQL determines an alternate route to transmit the packet if an energy hole problem has occurred in WMSN. The analysis of a proposed routing protocol based on the assessment measures like packet delivery ratio, average residual energy, number of alive nodes, and average end‐to‐end delay accomplished the value of 198.33 (ms), 2.05 (J), 100, and 0.85, respectively.

Estimating individual exposure to predation risk in group-living baboons, Papio anubis.

In environments with multiple predators, vulnerabilities associated with the spatial positions of group-living prey are non-uniform and depend on the hunting styles of the predators. Theoretically, coursing predators follow their prey over long distances and attack open areas, exposing individuals at the edge of the group to predation risk more than those at the center (marginal predation). In contrast, ambush predators lurk unnoticed by their prey and appear randomly anywhere in the group; therefore, isolated individuals in the group would be more vulnerable to predators. These positions of vulnerability to predation are expected to be taken by larger-bodied males. Moreover, dominant males presumably occupy the center of the safe group. However, identifying individuals at higher predation risk requires both simultaneous recording of predator location and direct observation of predation events; empirical observations leave ambiguity as to who is at risk. Instead, several theoretical methods (predation risk proxies) have been proposed to assess predation risk: (1) the size of the individual 'unlimited domain of danger' based on Voronoi tessellation, (2) the size of the 'limited domain of danger' based on predator detection distance, (3) peripheral/center position in the group (minimum convex polygon), (4) the number and direction of others in the vicinity (surroundedness), and (5) dyadic distances. We explored the age-sex distribution of individuals in at-risk positions within a wild baboon group facing predation risk from leopards, lions, and hyenas, using Global Positioning System collars. Our analysis of the location data from 26 baboons revealed that adult males were consistently isolated at the edge of the group in all predation risk proxies. Empirical evidence from previous studies indicates that adult male baboons are the most frequently preyed upon, and our results highlights the importance of spatial positioning in this.

Improving flood forecasting in Narmada river basin using hierarchical clustering and hydrological modelling

The purpose of the study was to use hierarchical clustering and Thiessen polygon algorithms to identify the significant rain gauge stations for flood forecasting at Sardar Sarovar Dam. Rainfall data from 2010 to 2018 was utilized to analyze the catchment region between Omkareshwar Dam and Sardar Sarovar Dam. The study identified two clusters of rain gauge stations with similar rainfall patterns and divided the study area into seventeen regions using Thiessen polygons. The land use map showed that the study area was mostly covered by crop lands, and the soil map divided the area into three types of sedimentary claystone soil. A hydrological model, Hydrologic Engineering Center – Hydrologic Modelling System (HEC-HMS), was used for rainfall-runoff modeling, and the computed runoff was compared with observed gauge discharge and inflow of Sardar Sarovar Dam. Regression analysis was performed to assess the performance of the model, and the results showed a good correlation between observed rainfall and estimated runoff values for 2012 and 2016. The study concludes that the existing rain gauge network is sufficient for flood forecasting, and the developed model along with the Thiessen polygon method can provide more accurate predictions of flow. The study highlights the importance of selecting suitable rain gauge stations for reliable flood forecasting in flood-prone basins. The study findings can be useful for future runoff prediction and flood forecasting in the study area.

A Study on the Normalized Delineation of Airspace Sectors Based on Flight Conflict Dynamics

The study of airspace sector demarcation can help controllers to deal with complex air situations, provide reference for air traffic control services, reduce the workload of controllers, and ensure safe and efficient airspace operation. Based on complex network theory, this paper proposes a sector division method based on a mean shift clustering algorithm and a Voronoi diagram. Firstly, a flight conflict network is constructed based on the structural characteristics of the airborne flight situation, combined with the three-dimensional velocity barrier method and the aircraft protected area model. Secondly, six network topology indexes, such as the total node degree, average point strength and network density, are selected to construct the flight-situation-assessment index system, and the busy and idle time segments of the airspace are divided according to the comprehensive network indexes; finally, based on the historical flight data, the airborne aircraft in the busy and idle time segments are clustered using the mean shift clustering algorithm and the Voronoi diagram method, respectively, so as to obtain a sector division scheme. The simulation results show that this method can equalize the network topology indexes and provide a reference for the scientific allocation of controllers’ energy.

Vortex dynamics in rotating Rayleigh–Bénard convection

We investigate the spatial distribution and dynamics of the vortices in rotating Rayleigh–Bénard convection in a reduced Rayleigh number range $1.3\le Ra/Ra_{c}\le 83.1$ . Under slow rotations ( $Ra\approx 80\,Ra_{c}$ ), the vortices are distributed randomly, which is manifested by the size distribution of the Voronoi cells of the vortex centres being a standard $\varGamma$ distribution. The vortices exhibit Brownian-type horizontal motion in the parameter range $Ra\gtrsim 10\,Ra_{c}$ . The probability density functions of the vortex displacements are, however, non-Gaussian at short time scales. At modest rotating rates ( $4\,Ra_{c}\le Ra\lesssim 10\,Ra_{c}$ ), the centrifugal force leads to radial vortex motions, i.e. warm cyclones (cold anticyclones) moving towards (outwards from) the rotation axis. The horizontal scale of the vortices decreases with decreasing $Ra/Ra_c$ , and the size distribution of their Voronoi cells deviates from the $\varGamma$ distribution. In the rapidly rotating regime ( $1.6\,Ra_{c}\le Ra\le 4\,Ra_{c}$ ), the vortices are densely distributed. The hydrodynamic interaction of neighbouring vortices results in the formation of vortex clusters. Within clusters, cyclones exhibit inverse-centrifugal motion as they submit to the outward motion of the strong anticyclones, and the radial velocity of the anticyclones is enhanced. The radial mobility of isolated vortices, scaled by their vorticity strength, is shown to be a simple power function of the Froude number. For all flow regimes studied, we show that the number of vortices with a lifespan greater than $t$ decreases exponentially as $\exp ({-t/{\tau }})$ for large time, where $\tau$ represents the characteristic lifetime of long-lived vortices.

A dislocation density-based crystal plasticity damage model for rolling contact fatigue of gradient grained structures

A dislocation density-based crystal plasticity damage model is presented for a numerical study on the spalling behavior of gradient grained structures under rolling contact fatigue loading. The topology of the gradient grained structure is constructed using Voronoi tessellations. The fatigue damage is coupled into a dislocation density-based crystal plasticity model where the evolutions of the dislocation density and fatigue damage are considered. The process of spalling is characterized by the evolution of fatigue damage in the polycrystalline structures. The evolutions of contact pressure, stresses, dislocation density, plastic strain, and fatigue damage of gradient grained structures with regard to rolling cycles are investigated. Moreover, the effect of the gradient form and residual stress on the rolling contact fatigue behavior is studied. The simulation results reveal that the gradient grained structures and the residual stress influence the rolling contact fatigue resistance.

Air Quality Prediction using Voronai-Based Spatial Temporal Sequence Similarity with Conjugate Gradient Enabled Sparse Autoencoder Deep Learning

Air Quality Prediction (AQP) remains a difficult task because of multidimensional nonlinear spatiotemporal features. To solve this issue, an Improved Sparse Autoencoder with Deep Learning (ISAE-DL) and Enriched ISAE-DL (EISAE-DL) models were developed with the combination of concentric circle-based clustering, Artificial Neural Network (ANN), Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM) followed by the ISAE for AQP. In EISAE-DL, concentric circle-based clustering uses Manhattan distance to efficiently split the locations into four regions using its center and cluster the spatially and temporally similar candidate locations. But it was considered a fixed structure and may struggle to find variations in several data points. Also, it accommodate clusters with regular and circular patterns, whereas irregular and non-circular cluster patterns were not handled. Similarly, the ANN inference was often offended or ignored because of complex meteorological characteristics. Hence, this paper proposes a Voronoi-based spatial-temporal sequence similarity with the Conjugate gradient-enabled SAE-DL (VCSAE-DL) model for effective AQP. First, a Voronoi clustering is performed by creating the Voronoi diagram for analogous candidate location clustering. Then, the resultant clusters of location data along with the PM2.5 and other meteorological data are given to the Improved ANN (IANN), and the target stations are given to the LSTM to capture the spatiotemporal relationship features and temporal features, respectively. Also, CNN is used to extract relationships between terrain and air quality features. These extracted features are fused in the merge layer and transferred to the ISAE for final prediction of air quality. Finally, the test outcomes demonstrate that the VCSAE-DL achieves better prediction performance compared to the existing AQP models.

Enhancing runoff simulation precision in the critical zone through spatiotemporal interpolation of areal rainfall with matrix decomposition

AbstractModelling hydrological process in the critical zone not only contributes to a better understanding of interactions across different Earth surface spheres but also holds significant practical implications for water resource management and disaster prevention. Rainfall‐runoff simulation in critical zones is particularly challenging due to the amalgamation of temporal and spatial complexity, rainfall variability, and data limitations. As a pivotal input variable of hydrological models, accurate estimation of areal rainfall is critical to successful runoff simulation. However, most estimation methods ignore temporal information, thereby increasing uncertainty in rainfall estimation and constraining the precision of rainfall‐runoff simulation. In this study, the matrix decomposition‐based estimation method (F‐SVD), which considers the spatial and temporal correlation of the rainfall process is employed to estimate areal rainfall. The superiority of the method in producing two‐dimensional rainfall information is evaluated through its application in runoff simulation with the Xin'anjiang model. The simulation results of selected flood events in the Jianxi basin in southeast China, spanning from 2009 to 2019, are compared with those of two widely used rainfall estimation methods, namely Arithmetical Mean (AM) and Thiessen Polygons (TP). The results show that (1) F‐SVD not only produces the highest Pearson correlation coefficient between rainfall and runoff series but also reduces the number of flood events with abnormal rainfall‐runoff relationships; (2) the Xin'anjiang model based on F‐SVD achieves the highest Nash‐Sutcliffe efficiency and lowest Relative Error, and performs best in simulating peak flow and its occurrence time as compared to AM and TP. This study contributes to a finer characterization of watershed rainfall distribution, enhancing the accuracy and sharpness of runoff simulation. It provides reliable data support for critical zone research and offers a scientific foundation for rationally allocating and managing water resources.

Lightweight design of Knee-Ankle-Foot Orthotic Devices using Voronoi patterns for Additive Manufacturing

Traditionally fabricated knee-ankle-foot orthosis (KAFO) device that is used to aid in the mobility user is uncomfortable. Problems such as weight and enclosure in almost all the part of the leg make it strenuous and humid for the user to wear for a long time. Furthermore, in the traditional production method, it can take up to a week to fabricate. The aim of this study is to redesign the knee-ankle-foot-orthosis by using the application of topology optimization in order to reduce the material used on the product and to make it lightweight. The parameters of the KAFO were determined by using indirect method; similar to traditional method. The modelling and analysis of the KAFO is completed by using CAD and CAE software. Optimization of the product is performed by redesigning the shape and applying topology optimization function. It is able to reduce the maximum stress of the product by 22.56% and the volume by 4.33%. Application of the Voronoi pattern further reduces the mass of the KAFO and produces more organic looks to the product. SLS Lisa Pro 3D printer is used to produce the KAFO in a period of less than a week. This prove to be a viable alternative for producing customized KAFO.

Pathways of hydrogen atom diffusion at fcc Cu: Σ9 and Σ5 grain boundaries vs single crystal

The diffusion of H-atoms is relevant for innumerous physical–chemical processes in metals. A detailed understanding of diffusion in a polycrystalline material requires the knowledge of the activation energies (ΔEa’s) for diffusion at different defects. Here, we report a study of the diffusion of H-atoms at the Σ9 and Σ5 grain boundaries (GBs) of fcc Cu that are relevant for practical applications of the material. The complete set of possible diffusion pathways was determined for each GB and we compared the ΔEa at bulk fcc Cu with the landscape of ΔEa’s at these defects. We found that while a number of diffusion pathways at the GBs have high tortuosity, there are also many paths with very low tortuosity because of specific structural features of the interstitial GB sites. These data show that the diffusion of H-atoms at these GBs is highly directional but can be fast because at certain paths the ΔEa can be as low as 0.05 eV. The lowest energy paths for diffusion of H-atoms through the whole GB models are ΔEa = 0.05 eV for the Σ9 and ΔEa = 0.20 eV at Σ5 which compare with ΔEa = 0.42 eV for the bulk fcc crystal. This shows that H-atoms will be able to diffuse very fast at these defects. With the Laguerre–Voronoi tessellation method, we studied how the local atomic structure of the interstitial sites of the GBs leads to different ΔEa’s for diffusion of H-atoms. We found that the volume expansions and the coordination numbers alone cannot account for the magnitude of the ΔEa’s. Hence, we developed a symmetry quantifying parameter that measures the deviation of symmetry of the GB sites from that of the bulk octahedral site and hence accounts for the distortion at the GB site. Only when this parameter is introduced together with the volume expansions and the coordination numbers, it is possible to correlate the local structure with the ΔEa’s and to obtain descriptors of diffusion. The complete set of data shows that the extrapolation of diffusion data for H-atoms between different types of GBs is non-trivial and should be done with care.