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Flight Planning
Published in Yasmina Bestaoui Sebbane, Multi-UAV Planning and Task Allocation, 2020
As it is difficult to control aircraft precisely enough to follow the minimum-distance path without risk of colliding with obstacles, many skeleton-based road map approaches have been taken. The Voronoi approach builds a skeleton that is maximally distant from the obstacles and finds the minimum-distance path that follows this skeleton. This algorithm is a 2D algorithm, complete but not optimal. Voronoi diagram is a special kind of decomposition of a metric space determined by distances to a specified discrete set of objects in the space [240]. Given a set of points S, the corresponding Voronoi diagram is generated, and each point P has its own Voronoi cell which consists of all points closer to P than any other points. The border points between polygons are the collection of the points with the distance to shared generators [28].
Introduction
Published in Vlad P. Shmerko, Svetlana N. Yanushkevich, Sergey Edward Lyshevski, Computer Arithmetics for Nanoelectronics, 2018
Vlad P. Shmerko, Svetlana N. Yanushkevich, Sergey Edward Lyshevski
Given a set S of n points, called sites, the Voronoi diagram of S is a partition (decomposition) of space into regions (cells), such that each region consists of all points that are closer to one site than to any other. Voronoi diagrams are useful for modeling spatial structures, location optimization, and fractal generation. Most of the early work on Voronoi diagrams was motivated by crystallography. The objective in this respect was the study of regions arising from regularly placed sites. Molecular system consists of a number of distinct molecules. Equilibrium and other properties of the system depend on the spatial distribution of the sites, which can be conveniently represented by dividing the space between them according to the nearest-neighbor rule. The nearest-neighbor rule (the crystal growth model) forces the Voronoi regions to be convex polyhedra.
Orienteering and Coverage
Published in Yasmina Bestaoui Sebbane, Intelligent Autonomy of Uavs, 2018
In the coverage of a circle using a network of UAVs considered as mobile sensors with non-identical maximum velocities, the goal is to deploy the UAVs on the circle such that the largest arrival time from the mobile sensor network to any point on the circle is minimized. This problem is motivated by the facts that in practice the assumption of UAVs with identical moving speed often cannot be satisfied, and events taking place in the mission domain only last for a finite time period. When the sensing range of mobile sensors is negligible with respect to the length of a circle, reduction of the largest arrival time from a sensor network to the points on the circle will increase the possibility of capturing the events taking place on the circle before they fade away. To drive the sensors to the optimal locations such that the overall sensing performance of the sensor network is optimized, gradient descent coverage control laws based on Voronoi partition are developed for mobile sensors with limited sensing and communication capabilities to minimize a locational optimization function. A Voronoi diagram is a subdivision of a Euclidean space according to a given finite set of generating points such that each generating point is assigned a Voronoi cell containing the space which is closer to this generating point than to any other.
‘Turbulent’ shear flow of solids under high-pressure torsion
Published in Philosophical Magazine, 2023
Yan Beygelzimer, Alexander Filippov, Yuri Estrin
In addition to the velocity distributions, it is also instructive to use the Voronoi and Delaunay diagrams. A Voronoi diagram for a set of points (particles) on a plane is a tessellation of the plane into regions where each point is closer to all points within that region than to any point of the set outside of it. A Delaunay diagram is a triangulation of the same set of points such that for any triangle all points, except those at its apexes, are situated outside of its circumcircle. The Voronoi diagram permits identification of the symmetry of the neighbourhood of any point, while Delaunay triangulation, which is dual to the Voronoi mesh, enables visual construction of a lattice at any step of a numerical experiment. Figure 1 displays a typical instantaneous snapshot of a system represented by the Voronoi and Delaunay constructions. One can readily recognize a subdivision of the system into domains and chains of defects with fivefold and sevenfold symmetry axes located at domain boundaries (coloured blue and orange, respectively). A blow-up in the insert presents an enlarged view of the Delaunay lattice where some of the defects are highlighted by pentagons for clarity.
Understanding small-scale COVID-19 transmission dynamics with the Granger causality test
Published in Archives of Environmental & Occupational Health, 2023
Carolina Romero García, Álvaro Briz-Redón, Adina Iftimi, Manuel Lozano, José De Andrés, Giovanni Landoni, Massimiliano Zanin
A Voronoi diagram is a partition of a planar region into polygons close to a given set of locations. For instance, given two locations in the region, denoted by P and Q, the Voronoi cell associated with P consists of all points in that region that are closer to P than to Q. Analogously, the Voronoi cell associated with Q includes all points of the region that are closer to Q than to P. This case, considering two locations, is easily generalizable to a context of three or more locations. Specifically, the Voronoi cell associated with a location is formed by those points in the region closer to the corresponding location than to any of the other locations considered. In practice, a Voronoi diagram can be used to divide a study area into multiple polygons associated (by proximity) with specific points of interest. Therefore, instead of using an administrative division of the study area, one may analyze the spatial distribution of a disease measuring the incidence at the cell level, for a given Voronoi diagram. In this study, primary care facilities and subway stations have been used to obtain two different Voronoi diagrams of the study area. This allows performing a functional network analysis based on these locations and assessing their potential effect on disease transmission.
Seismic Performance of Historical Buildings Based on Discrete Element Method: An Adobe Church
Published in Journal of Earthquake Engineering, 2020
Nuno Mendes, Sara Zanotti, José V. Lemos
The numerical model was prepared in the 3DEC software (ITASCA, 2015), which is based on the DEM. In the DEM, the masonry units are modeled through blocks that interact with each other by contact interfaces. In general, the masonry units are expanded to include the thickness of the joints. As a consequence of this procedure, the adobe units were modeled by blocks of 0.715×0.315×0.215 m and the joints have zero thickness. The rubble masonry of the base course was simulated by Voronoi polygons, taking as reference the real morphology of the masonry. A Voronoi diagram is, from a mathematical point of view, a partitioning of a plan into regions based on the distance to points in a specific subset of the plan. Given a set of points, it is possible to construct a Voronoi diagram drawing equidistant lines between the points considered, in order to define the regions of points closer to each one of the original points. This dataset of points, called the Voronoi points, adopted to construct the Voronoi polygons, are the centroid of the stone that constitutes the sectional morphology of the rubble masonry (Torres and Castaño, 2007).