A quantitative evaluation model of ancient military defense efficiency based on spatial strength—take Zhejiang of the Ming Dynasty as an example by Yinggang Wang, Lifeng Tan, Zao Zhang, Huanjie Liu, Jiayi Liu, Yukun Zhang, Mengqi Mu

“…It determines the control points of defense groups, quantifies the defense group area with a Voronoi diagram, and classifies and assigns the entropy value to the deployment data of guard forts in historical data. …”
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Automatic reconstruction of skeletal structures from TLS forest scenes by A. Schilling, H.-G. Maas

“…Second, each component is processed separately: A 2D skeleton is obtained via the Voronoi Diagram and refined. Subsequently, a component is segmented into subsets of points depending on their proximity to skeleton nodes. …”
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Collision Avoidance for a Selective Compliance Assembly Robot Arm Manipulator Using Topological Path Planning by Josias G. Batista, Geraldo L. B. Ramalho, Marcelo A. Torres, Anderson L. Oliveira, Daniel S. Ferreira

“…In our experiments, our proposal presented better results for applications in industrial robotic manipulators when compared to the probabilistic roadmap method (PRM) and TPP*, a particular case of TPP that is similar to the generalized Voronoi diagram (GVD).…”
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A Data-Driven Framework for Analyzing Spatial Distribution of the Elderly Cardholders by Using Smart Card Data by Zhicheng Shi, Xintao Liu, Jianhui Lai, Chengzhuo Tong, Anshu Zhang, Wenzhong Shi

“…The center points of clusters are utilized to construct a Voronoi diagram. Third, a quasi-gravity model is proposed to reveal the elderly mobility between regions, using the public facilities index. …”
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A Time-constrained Network Voronoi Construction and Accessibility Analysis in Location-based Service Technology by W. Yu, T. Ai

“…Accessibility analysis usually requires special models of spatial location analysis based on some geometric constructions, such as Voronoi diagram (abbreviated to VD). There are many achievements in classic Voronoi model research, however suffering from the following limitations for location-based services (LBS) applications. (1) It is difficult to objectively reflect the actual service areas of facilities by using traditional planar VDs, because human activities in LBS are usually constrained only to the network portion of the planar space. (2) Although some researchers have adopted network distance to construct VDs, their approaches are used in a static environment, where unrealistic measures of shortest path distance based on assumptions about constant travel speeds through the network were often used. (3) Due to the computational complexity of the shortest-path distance calculating, previous researches tend to be very time consuming, especially for large datasets and if multiple runs are required. …”
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Study on machining performance of fixed-abrasive lap-grinding plate with random grid structure by Xingtai SHI, Lei GUO, Xiaohui LIU, Qichao JIN, Zhenxian CHEN, Jingxiang LÜ, Jiaqing WANG

“…To meet the increasing requirements on material removal efficiency, surface quality, and subsurface damage in the ultra-precision grinding process, a textured-fixed abrasive plate (T-FAP) with random grid structure based on the Voronoi Diagram is proposed. The abrasive tool is fabricated by using UV-curable resin and micro-level alumina abrasive grains. …”
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Multi-Objective 3D Airspace Sectorization Problem Using NSGA-II with Prior Knowledge and External Archive by Weining Zhang, Minghua Hu, Jianan Yin, Haobin Li, Jinghan Du

“…Specifically, it clusters flights and generates initial sectors using a Voronoi diagram. To further optimize sector shape, the concept of dynamic density is introduced to evaluate the controller workload, based on which a sector optimization model is constructed. …”
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Numerical simulation of the failure process of reinforced concretestructures based on the rigid body spring method by Zhao Chao, Zhong Xingu, Liu Bo, Zhang Tianyu, Shi Weihua

“…Considering that continuous numerical methods cannot accurately describe the physical characteristics of cracks and discontinuous numerical methods cannot reflect structural stiffness,a rigid body spring model is proposed in this paper to analyze the failure process of reinforcement concrete(RC) structures.In the proposed method,concrete is simulated by the rigid body spring model based on Voronoi diagram random generated mesh.Reinforcement is modeled as a series of bar elements and the bond-slip characteristics between reinforcing steel and concrete are also considered by introducing special linkage elements.The spring stiffness of concrete is determined from the uniaixal stress-strain curve of concrete,and the shear failure behavior of concrete is judged by the Mohr-Coulomb criterion.A home-made program based on FORTRAN Language is developed and used to analyze the failure processes of a Z-type component under direct shear loading and a RC beam under two-point loading.The comparison of numerical results and experimental results show that the proposed method can simulate cracking behavior of RC structures precisely,and can provide the physical characteristics of cracks.The ultimate strengths and load-deflection response of the test beam predicted by the proposed method are in good agreement with the experimental results,which means the proposed method is feasible and effective.…”
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The Repair Strategy for Event Coverage Holes Based on Mobile Robots in Wireless Sensor and Robot Networks by Yaoming Zhuang, Chengdong Wu, Hao Wu, Hao Chu, Yuan Gao, Li Li

“…The conventional network repair methods based on the geometric graph theory such as Voronoi diagram method are unable to meet the conditions of flexible surveillance tasks and severe multi-restraint scenarios. …”
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ASAMS: An Adaptive Sequential Sampling and Automatic Model Selection for Artificial Intelligence Surrogate Modeling by Carlos A. Duchanoy, Hiram Calvo, Marco A. Moreno-Armendáriz

“…In each iteration, this framework uses a grid search algorithm to determine the best candidate models and perform a leave-one-out cross-validation to calculate the performance of each sampled point. A Voronoi diagram is applied to partition the sampling region into some local cells, and the Voronoi vertexes are considered as new candidate points. …”
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Computational geometry through the information lens by Pătrașcu, Mihai

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Decorating 3D models with Poisson vector graphics by Liu, Yongjin, Wang, Wencheng, Qin, Hong, He, Ying, Fu, Qian, Hou, Fei, Sun, Qian, Xin, Shiqing

“…To render PVG on meshes efficiently, we develop a Poisson solver based on harmonic B-splines, which could be constructed using geodesic Voronoi diagram. Our Poisson solver is a local solver for rendering with more flexibility and versatility. …”
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Laser simulator: a novel search graph-based path planning approach by Ali, Mohammed A. H., Mailah, Musa

“…In addition, a comparative study on the laser simulator approach, A* algorithm, Voronoi diagram with fast marching and PointBug algorithms was performed to show the benefits and drawbacks of the proposed approach. …”
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Voronoi classified and clustered data constellation: A new 3D data structure for geomarketing strategies by Azri, Suhaibah, Ujang, Uznir, Abdul Rahman, Alias

“…These analyses are performed based on encoded neighbour information of the Voronoi diagram that is extracted from the data structure. …”

Urban Area Characterization and Structure Analysis: A Combined Data-Driven Approach by Remote Sensing Information and Spatial–Temporal Wireless Data by Xiangyu Chen, Kaisa Zhang, Gang Chuai, Weidong Gao, Zhiwei Si, Yijian Hou, Xuewen Liu

“…In this paper, a novel urban data analysis method combining spatiotemporal wireless network data and remote sensing data was proposed. First, a Voronoi-diagram-based method was used to divide the urban remote sensing images into zones. …”
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Fast Marching Techniques for Teaming UAV’s Applications in Complex Terrain by Santiago Garrido, Javier Muñoz, Blanca López, Fernando Quevedo, Concepción A. Monje, Luis Moreno

“…Next, a first 2D geometric path perpendicular to the Voronoi diagram of the Gaussian distribution is calculated, obtained by skeletonization. …”
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Analysis of Endonasal Endoscopic Transsphenoidal (EET) surgery pathway and workspace for path guiding robot design by Suwiphat Chalongwongse, Sorayouth Chumnanvej, Jackrit Suthakorn

“…Delaunay triangulation and Voronoi diagram were utilized to determine the cloud position of the gathered data for EET workspace. …”
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Parallel Raster Scan for Euclidean Distance Transform by Juan Carlos Elizondo-Leal, José Gabriel Ramirez-Torres, Jose Hugo Barrón-Zambrano, Alan Diaz-Manríquez, Marco Aurelio Nuño-Maganda, Vicente Paul Saldivar-Alonso

“…Distance transform (DT) and Voronoi diagrams (VDs) have found many applications in image analysis. …”
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AN AUTOMATIC OPTICAL AND SAR IMAGE REGISTRATION METHOD USING ITERATIVE MULTI-LEVEL AND REFINEMENT MODEL by C. Xu, H. G. Sui, D. R. Li, K. M. Sun, J. Y. Liu

“…Thirdly, a uniform level set segmentation model for optical and SAR images is presented to segment conjugate features, and Voronoi diagram is introduced into Spectral Point Matching (VSPM) to further enhance the matching accuracy between two sets of matching points. …”
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Constant-work-space algorithms for geometric problems by Tetsuo Asano, Wolfgang Mulzer, Günter Rote, Yajun Wang

“…Actually, we show that the former result carries over to the Delaunay triangulation, and hence the Voronoi diagram. This also means that we can compute the largest empty circle of a planar point set in quadratic time and constant work-space. …”
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