\\n\\n
Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\\n\\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
Note: Edited in March 2021
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'IntechOpen is proud to announce that 191 of our authors have made the Clarivate™ Highly Cited Researchers List for 2020, ranking them among the top 1% most-cited.
\n\nThroughout the years, the list has named a total of 261 IntechOpen authors as Highly Cited. Of those researchers, 69 have been featured on the list multiple times.
\n\n\n\nReleased this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\n\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
Note: Edited in March 2021
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In some cases, the requirements for the accuracy of the description must be very high, for example, when modeling the flow around objects or automating technological processes (to ensure specified gaps during assembly of products or reproduction-oriented products on equipment with numerical program control). All this causes to a wide range of geometric modeling methods used in modern technology.
\nTheoretical questions of the geometric modeling method from various aspects were investigated in the works of Russian scientists—Valkova K.I., Ivanova G.S., Kotova I.I., Osipova V.A., Yakunina V.I., Rvacheva V.L. etc.,—and the works of Robert Fergusson, Stephen Coons, Pierre Bezier, Charles Hermite, Isaac Jacob Schoenberg, Carl de Boor, Ken Versprille, Eugene Lee, Steve Ginsberg, and others. Their works contain both classical and computer-oriented methods of assignment, calculation, and reproduction of geometric forms of the designed objects.
\nOf course, such an abundance of methods is focused on the description of the geometric shape of heterogeneous technical objects. To classify the geometric models used in the description of design objects, it is advisable to use the approach, proposed by Semenkov O.I.-Osipov V.A. in [1], which is based on the structure of the synthesis of geometric objects from their constituent elements. This classifier divides all geometric objects (GO) into two large groups—geometric objects of complex technical form and geometric objects of complex technical structure. Objects of the first group are limited to compartments of surfaces, each of which is described by sufficiently complex analytical equations or systems of equations. These include aircraft fuselages, car bodies, ship hulls, turbine blades, etc. The objects of the second group are combined on the basis of set-theoretic operations (union, intersection, negation) are described, as a rule, relatively simple geometric shapes. In Markin [2], we proved that based on the specifics of the solved project tasks, the number of such groups should be increased to four (\nFigure 1\n).
\nClassification of geometric objects by level of complexity: (a) primitives, (b) objects of complex technical structures, (c) objects of complex technical forms, and (d) objects of complex technical form and structure.
The abundance of geometric forms of objects in engineering, construction, design, etc. requires a library of geometric modeling methods adapted to describe the specific features of the shape of geometric objects. Therefore, in addition to the classification of geometric objects, there are classification systems of geometric modeling methods themselves, which can be divided into three classes (\nFigure 2\n).
\nClassification of methods for modeling geometric objects.
\n
Examples of technical objects implemented by sculptural methods: (a) analytical approximation methods; (b) exact methods; kinematic (c) and parametric (d).
The implementation of this method is based on a fairly large library of surface approximation methods using splines, B-splines, NURBS, Koon’s surfaces, Hermite, Lagrange, Bezier, etc.
\n\n
\n
Kinematic
Parametric
Wireframe
Piecewise analytical
Algebra-logical (R-function method)
The method of “decomposition into elements”
The method of constructive geometry of the elementary volume
An illustration of these methods of geometric modeling is shown in \nFigure 3b\n and \nc\n.
\nDeniskin et al. [3] showed that at present the problem of computer representation of the geometric shape of objects of any complexity can be considered sufficiently solved. However, in some design tasks, the requirement of accuracy of the description of the form is not the main one. An example of such tasks is the automation of layout calculations. In modern technology, the quality of the layout (i.e., placing the necessary equipment and payload) largely determines the quality of the design.
\nThe development of technology, primarily transport and, especially, aerospace, increasing the density of the layout makes designers constantly improve the methods of design automation. For illustration, two aircrafts of different eras are shown with approximately the same takeoff mass. (30 tons)—ANT-20 (30 years of the last century—\nFigure 4a\n) and a modern Su-24 (\nFigure 4b\n). At the same time, much more various onboard equipment is installed on a modern aircraft.
\nAircraft about the same takeoff weight of different eras: (a) 30 years of the last century and (b) current.
Many requirements must be complied when designing the layout (both automated and traditional methods)—ensuring maximum density, but with the exception of mutual crossing of the hosted objects—to provide a predetermined position of the center of mass of the composed object and the minimum bulk of communications between placed objects, with the exception of the proximity of incompatible objects (such as “hot at work” and “cold”). An additional requirement is to ensure the ergonomics of the layout (the possibility of installation and maintenance of equipment). It is also necessary to ensure the reliability of the functioning of the assembled equipment, which depends on the levels of vibration, pressure drop, temperature, etc., which in turn is determined by the location of this in the designed vehicle.
\nTaking into account so many of these factors that determine the quality of layout solutions requires either a lot of engineering experience of the developer or the use of information technology in solving this problem. For objects with a high-density layout, even the most careful placement on the drawing does not exclude the possibility of cases of their mutual intersection. To avoid this situation allows the creation of the physical layout, which in scale or life-size simulated layout of a solution. However, despite the attractiveness of physical models, their production is long and expensive. Therefore, the development of methodological, algorithmic, and software processes of automated placement is an actual practical task. Since object placement problems are geometric problems (in geometry they are called positional), their solution should be sought in an extensive library of geometric modeling methods.
\nEven the first experiments of computerization of design process at the decision of separate private problems have shown their high efficiency. Work on the automation of placement was no exception. The first publications in this area belong to the 60 of the last century and are associated with the names of Russian scientists, L.V. Kantorovich and V.A. Zalgaller, on the cutting of materials by linear programming methods. However, the transition from 2D objects to 3D objects and the complexity of the shape of the placed objects from linear strips to real objects of modern technology caused an avalanche of complexity of the mathematical description of the placement process. In our opinion, the main efforts of scientists-geometers were directed to the study of various aspects of the computer description of the form of technical objects, which are alternative to many classical methods of descriptive geometry. Therefore, now there are no problems to describe the geometric shape of objects of almost any complexity with the necessary accuracy.
\nThe development of methods for automated placement of objects according to specified criteria was much less fortunate. In placement problems, it is important not to accurately describe the geometric shape of the objects being placed, as to solve two critical issues:
Detection of cases of mutual intersection of the placed objects.
Generation of options for placing objects in a given space, providing an effective layout. The implementation of the known algorithms of automated placement is based on polygonal models and computational methods of “brute force,” which does not allow them to be implemented in practice for objects of complex structures, even with the modern power of computer equipment.
It can be objected that the use of modern CAD systems allows to carry out modeling of quite complex objects and at the same time to track possible cases of their crossing by means of the CAD system (\nFigure 5\n). But in this case, we are not talking about computer-aided design, but only about checking the layout variant already generated taking into account the experience and intuition of the designer.
\nModeling layout in CAD systems.
The problem of computer representation of geometric objects of any complexity can now be considered sufficiently solved. However, other requirements are imposed on automated layout models, of which the accuracy of the form description is not the main thing. We have to choose which is better—an accurate geometric model, automatic layout of which is impossible, or a coarser geometric model, but allows the possibility of automated layout.
\nIt is known that the most accurate formal description of a three-dimensional object as a geometric body is its identification with the area of space occupied by it (a point set). However, in this formulation, the problem of the formation of a geometric object (GO) can be considered only theoretically. This concept can be used in practice if as the initial element of the set (
The space in this case is called discrete, and the geometric model formed in such a space, respectively, is discrete or voxel model. The term voxel formed from the words volumetric and pixel—elements of the three-dimensional image. Voxels are analogous to pixels in a two-dimensional to three-dimensional space. Voxel models are often used for visualization and analysis of medical and scientific information, as well as in computer graphics (most often in games (\nFigure 6\n)). Polygonal models inside are empty (and often this is enough—why do we, for example, know what is inside a computer character?). Voxel models are completely filling their insides—volumetric voxel cubes, which can contain additional information about the object.
\nVoxel models in medicine ((a) the result of computed tomography) and in computer graphics ((b) in computer games).
The discrete method of geometric modeling (in relation to technical applications) was described in the early 70 years of the last century by the Belarusian scientist, Zozulevich in [4], but in those years it did not spread due to the limited capabilities of computers in memory and performance. Although he and the team of his employees solved certain applied problems using this method, it was impossible to count on the effective use of voxel models with computers of those years with 16-bit architecture and 32–128 kb of RAM.
\nThe basis of such models is an approximate representation of a geometric object in a field or voxel space. For the flat case, the voxel field is a uniform rectangular network
Voxel model of a 2D object.
3D objects are described by a three-dimensional matrix
Voxel model of a 3D object.
The author of the method Prof. Zozulevich D.M. called his method “receptor” by analogy with the receptors of the human brain; each of which can be either excited or not. Other names of this method are also known—“matrix,” “binary,” “enumeration of space elements,” etc. In its geometric essence, the receptor (voxel) method is a special case of the analytical approximation method, which is used to describe three-dimensional objects that include complex surfaces of the second and higher orders. Since computational processing of such surfaces is difficult, they are approximated by areas of surfaces of lower order (planes, cylinders, etc.).
\nResearch and development of voxel geometric models for various applications was carried out in the works of Russian scientists Gorelik AG, Gerasimenko YP, Klishin VV, Romance YA, Pashchenko OB, and Toloka AV, as well as a number of foreign authors—Gargantini I, Requcha AAG, Si Thu Lin, Nyi Nyi Htun, Kyi Min Han, Ye Win Tun, and a several others.
\nHere, it should be noted that very close in research ideology of Nazarova KM, Ratkova SI, etc., in which as basic object shape is not classic receptor in the form of a cube or parallelepiped, and more complex shapes—for example hexahedron.
\nThe voxel method has both advantages and disadvantages. The main advantage is the homogeneity of computational algorithms and a very simple detection of cases of intersection of objects with each other.
\nThe obvious disadvantages include the discreteness of the model and the need for large amounts of computer memory for its implementation. However, now the increase of computer memory to any volume is neither technical nor economic.
\nAnother drawback is that the voxel geometric model is never primordial. Placed and already placed products are described by the designer, usually parametric geometric models (i.e., specifying the type of object and its parameters—a sphere with radius
Setting parameters of geometric objects in traditional drawings (a) and computer modeling (b).
Stages of construction of voxel model of an electric drill: (a) initial drawing, (b) solid model from CAD system, and (c) voxel model.
Consider the problem of placing additional equipment in the technical compartment of the vehicle (the problem of pre-assembly). This problem is often found in the practice of design and from a geometric point of view is reduced to the problem of analyzing the geometric shape of empty spaces among previously placed objects.
\nWe will solve the problem of additional placement in the following statement—there is a closed area (e.g., the technical compartment of the aircraft) with the equipment already partially placed in it (\nFigure 11a\n). There is a set of equipment that needs to be “repositioned” (\nFigure 11b\n). The possibilities of “additional placement” are determined by the shape and size of still unfilled spaces between already composed objects.
\nTechnical compartment of the aircraft: (a) “redeployable” and equipment (b).
For a person, such a task “re-arrangement” of objects will seem quite easy—he can easily “by eye” determine how several volumes relate to each other and which object fits in another and which does not. To do this, he mentally classifies the object by shape (almost a ball, almost a cylinder) and then mentally correlates their sizes. Unfortunately, this operation of pattern recognition, which is so simple for a person, is of considerable complexity even for modern computers.
\nThe most important issue is the class of geometric objects allowed to be placed. Typically, from a geometric point of view, such equipment is either primitives or a combination of primitives. Assume that the objects to be placed are a composition of primitives that describe the shape of the instrumentation quite well (this can be seen in \nFigure 11b\n). The technical literature provides data that the composition of primitives effectively describes 95% of the instrument equipment.
\nThe advantage of the voxel geometric model is the ability to identify empty spaces in the layout for subsequent placement of objects not yet placed in them. If there is an empty space among the assembled objects, then on the corresponding section of the voxel matrix it is relatively easy to identify as “clumps” of zero voxels. For this purpose, an algorithm was developed to determine the center of a certain free area (flat) and its dimensions.
\nTo do this, scan the rows and columns to identify the largest cluster of inextricably located receptors and identify their centers. To analyze the individual cross section of the object, we use the transition from the geometric shape of the object (in the form of a discrete set of receptors) to the “feature space” adopted in the theory of pattern recognition. Such a feature space for us will be the hodograph of the function of the radius of the vector from the center of the section (\nFigure 12\n):
\nConstruction of the hodograph of the radius-vector function (a) and analysis of the unfilled area of space (case-polygon) (b).
where
After constructing the function
On the real results of the analysis of the hodograph function, naturally superimposed “noise” due to the discreteness of the description of the component objects. An example of such real hodographs of a plane slice of the objects being assembled, statistically identified as slices of “polygon,” “cylinder,” and “sphere,” are shown in \nFigure 13a\n–\nc\n, respectively.
\nView of the hodograph of the slice function from for the polygon (a), sphere (b), and cylinder (c).
An illustration of the software implementation of this method is presented in \nFigure 14\n. The obtained results are implemented in the framework of a graphical shell written in C#. If we have a desire to place in this area not a parallelepiped of the maximum size, but, for example, a sphere of a certain radius, then it becomes a full participant of the scene, and after pressing the “analysis” button, a new definition of the configuration of unfilled spaces occurs.
\nDetermination of the configuration of empty spaces: (a) visualization of space, (b) output of data on the size and position of the free area, and (c) assessment of the possibility of inscribing different shapes.
The solution of the task was carried out within the framework of the dissertation research by Situ Lin (Republic of the Union of Myanmar), a postgraduate student of MAI and described in [5].
\nThe purpose of designing the channel surface is the delivery of a certain trajectory of a material carrier (liquid, gas, electrical energy from one point (entry point) of the technical product to another (exit point)). In this case, one of the tasks of the layout is to solve the problems of tracing, i.e., designing communications between already placed objects. Such problems are quite difficult to formalize and difficult to solve because of their inherent multi-extreme nature.
\nA special and much more complex type of trace is called “solid” trace, that is, such a case when the dimensions (connecting elements) of the trace are comparable to the dimensions of the components. In practice, this is the design of pipelines, air ducts, and other elements of transport systems (\nFigure 15\n).
\nAn example of laying the trace: (a) electric furnace and (b) the air duct channel of the car.
To solve this problem, two main approaches to tracing are used, which are determined by the metric used. A metric is a rule that determines the distance between two points in a given space. The first approach is to use the Euclidean metric. In this case, the trace is drawn in the direction of the shortest distance between the entry and exit points (\nFigure 16a\n), and the length of the trace is determined by the Pythagorean theorem.
\nDesigning trace with different metrics.
The second approach is to use the Manhattan metric, in which the trace is drawn in the direction of the coordinate axes (\nFigure 16b\n). In this case the trace is much longer than using the Euclidean metric, but the approach itself provides additional mathematical possibilities for the design of the trace. It is used for tracing large integrated circuits and printed circuit boards; this metric is used by industrial automated tracing systems P-CAD, ТороR, and others. A typical example of the result of wiring in such programs is shown in \nFigure 16c\n. From this figure it can be seen that the tracing in such systems is carried out either by the Manhattan metric or at 45° angles.
\nIn our opinion, the problems of trace design according to the Manhattan metric are the most developed in the theory of geometric modeling of traces. This is due to the extreme practical importance of solving these problems in the automated wiring of printed circuit boards and large integrated circuits. Fundamental in this field are the theoretical studies of Russian scientists Abraitis LB, Bazilevich RP, Petrenko AP, Tetelbaum AY, Selyutina VA and others, as well as foreign scientists EW Dijkstra, Judea Pearl, Ira Pohl, Daniel Delling, Peter E Hart, etc.
\nHowever, the use of the Manhattan metric is unacceptable for channel design, since due to viscous friction, the sharp bends of the channel make it difficult to move liquid or gas through the channel, turning the flow energy into heat. The current line that determines the direction of travel through the channel is called the main guide line (GNL). It is the axis of the channel and is given either by the equation of the spatial curve or by a discrete set of points. However, tasking this parameter alone is not enough—it is necessary to specify the shape and area of individual cross sections of the channel (\nFigure 17\n). By controlling the position of the GNL and the shapes and sizes of the cross sections, we can provide the specified designer characteristics of the flow of liquid or gas through the channel.
\nGeometric parameters that determine the shape of the channel.
Let us complicate the task of designing. If earlier the channel was first designed according to the specified characteristics and then it was already placed, then we are trying to design a channel with the specified characteristics, “inscribed” in an already existing layout. Let there be a rectangular area with dimensions
Finding a rational path between two endpoints A and B in a 2D formulation without taking into account the size of the trace and the restrictions on smoothness.
From \nFigure 18\n it can be seen that there are quite a lot of options for its passage. At first glance, of all the traces in \nFigure 18\n, the one that is shorter will be better. However, it is known from design practice that hydraulic losses are minimal not in the short but in the main channel. Additional requirements are possible, for example, to provide a specified gap between the channel and other elements of the layout.
\nA significant problem in solving the tracing problem is to avoid obstacles, which are already composed objects or communications between them. The big advantage of the voxel approach is the ease of detecting an obstacle by voxel code (0 or 1). The simplest approach is to ignore obstacles before encountering them. Such an algorithm would look something like this: choose the direction to move toward the target, and move until the target is reached and the direction is free to move (\nFigure 19\n). Given that the transverse area of the channel can repeatedly exceed the size of one voxel, it is possible that a valid trace option in this layout situation is not at all.
\nThe principle of obstacle avoidance in the construction of voxel method.
The known trace algorithms closest to our approach are described in the following [6, 7]:
Dijkstra’s algorithm
Algorithm A* “A the asterisk”
The simplest approach implemented in these algorithms is to ignore obstacles before encountering them. The structure of the choice of direction of movement is determined by the rule to move back to choose a different direction in accordance with the strategy of the traversal.
\nThis allows us to argue that these algorithms contain elements of artificial intelligence (AI), since the solution is chosen according to the predicative principle of “If”-“Then.”
\nIn the works of Dijkstra EW, Donald Ervin Knuth, Thomas H Cormen, etc., various obstacle avoidance strategies (heuristics) based on both random search and artificial intelligence algorithms are analyzed. Each of them has both its limitations and areas of preferred application. Examples of different trace algorithms are shown in \nFigure 20a\n. \nFigure 20a\n shows that although the well-known Dijkstra algorithm was able to pave the way from the start to the end points, it did not do it rationally, making an extremely many unnecessary movements and repeatedly unnecessarily changing the direction of travel.
\nExamples of tracing when bypassing various obstacles in 2D staging.
Voxel algorithm A* operates in a more reasonable way (\nFigure 20b\n) and is commonly used to find the optimal shortest path. But this algorithm is not able to take into account the given gap (δ-neighborhood)—the route may pass too close to the areas of prohibition. Thus, the search for the path of the trace by the algorithm A* gives the best results but does not always provide a solution to the problem. In addition, the algorithm A* is not able to design trajectories with a given degree of smoothness, since such a task has never been set before.
\nAs it was already noted earlier, the strongest side of the algorithm A*, which led to its choice by us as a prototype, is the possibility of optimal and heuristic trajectory search. The literature shows that in many cases heuristic search works better than other search strategies. The heuristic function of the algorithm determines the choice of the search direction to the target vertex. If the heuristic function is valid (that is, does not exceed the minimum cost of the graph to the target vertex), then the algorithm A* is guaranteed to find the shortest path. The modified algorithm A* uses a set of heuristics that provide for multidirectional search. The search for direction is conducted not as usually on 4 and 8 directions (respectively in a plane and space (\nFigure 21a\n and \nb\n)) and in 8 directions, if the construction of the channel occurs in the plane and 26 adjacent vertices in the design of the spatial channel (\nFigure 21c\n and \nd\n).
\nIncreasing the directions of the path search in the original and modified algorithms.
To implement the proposed trace algorithm, the Advanced Pathfinder System (APS) program was written in Microsoft Visual Studio 2010, using the C# programming language. The solution of the task was carried out within the framework of the dissertation research by Nyi Nyi Htun (Republic of the Union of Myanmar), a postgraduate student of MAI and described in [8]. With this program, you can:
Use the improved algorithm A* and find a rational trace between two points in 2D and 3D spaces, taking into account the areas of prohibitions.
Carry out smoothing of the trace received at the previous stage either on any set radius or on the maximum possible radius with the subsequent check of accomplishment of a condition that the minimum radius is not less than the set
Ensure that the trace passes at the specified minimum distance δ from already placed objects and areas of prohibition.
Testing showed significantly higher performance of our modified algorithms than the original one. It should be recognized that the described program, which implements the voxel method of body tracing, is not integrated into any existing CAD system, so the geometric information is entered into the program in parametric form. This reduces the performance of the build process. Integration of this program with any CAD system in the form of a separate built-in calculation module is an actual technical task.
\nWhen designing the SC, the question on estimation of the effective area of solar panels arises, taking into account their inevitable shading by each other and other structural elements of the spacecraft SC (\nFigure 22\n). All this significantly limits the functionality of the SC. When designing SC or ground-mounted solar power plants, we have to decide on the area of solar panels—if there are a small number of panels, then the solar energy absorption will be small, and if there are too many, they will work inefficiently, shading each other (not to mention the additional costs for them and increasing the mass of the entire SC). Therefore, the solution of this question can be considered as an optimization problem of mathematical programming.
\nPartial shading of solar panels in space on the International Space Station (ISS).
Voxel geometric models do not require complex formulas or logical constructions for their implementation. However, their practical implementation has its own specific complexity. In addition to the need to convert the initial parametric model specified by the constructor into a receptor model, the complexity is conditioned by the need to take into account the position and value of each voxel (out of many millions in the voxel matrix), as well as to create a mechanism for visualizing the results. The solution of the task was carried out within the framework of the dissertation research by Kui Min Khan (Republic of the Union of Myanmar), a postgraduate student of MAI and described in [9].
\nAn essential feature of our approach is that we will not use the classical voxel matrix (filled with “0” and “1”) in the calculations, but a
Representation of SC by multi-digit voxel matrix.
Using a multi-digit voxel geometric model allows you to proceed directly to the calculations of shading. We will move a slice of the voxel matrix with thickness of 1 voxel (\nFigure 24a\n) as a cutting plane along the coordinate plane from the beginning to the end of the voxel matrix (\nFigure 24b\n).
\nSingle-layer slice of the voxel matrix (a), moving this slice along the voxel matrix (b).
In \nFigure 25a\n, it can be seen that on each slice we can put each specific voxel in accordance with either “1” (if it coincides with the body of the SC) or “2” (if it coincides with solar panels). If there is no match with any elements of the SC, the value of the voxel on the slice remains the initially set value of “0.” Looking at a single-layer slice of the voxel matrix from the direction of the energy flow
Single-layer slice of the receptor matrix (a), the view of this slice toward the flow (b).
In this calculation model, there are situations when along the thickness of the solar panel may be not one, but several layers of the voxel matrix (for example, 4 layers), resulting in the unreasonable increase of the effective area of solar panels by four times. It is also necessary to exclude unreasonable repeat account of already screened objects. To do this, we introduce an additional code “3” in the voxel matrix, which will exclude the account of the areas of the corresponding voxels. The essence of the model change is that once absorbed part of the energy flow should no longer be taken into account. Therefore, starting with some slice of the voxel matrix, everything that follows this slice, the element with the code “2,” is forcibly filled with the prohibiting code “3,” which does not allow the use of voxels with this code in any calculations.
\nHowever, the shading of solar panels in the
On the basis of the geometric model described above, a software package was created, implemented in the C# language, allowing to simulate the effective area of solar concentrators. At the same time, a graphical shell is developed that visualizes the calculation process and the calculated parameters of the effective area.
\nThe work of the software package is as follows. After entering the information about the geometric dimensions of the station and solar panels (in parametric form), a layer-by-layer scan of the sections begins. A 2D matrix is formed in each layer, the form of which was previously shown in \nFigure 24b\n, from the 3D matrix, in which our entire object (SC) is immersed. In each section (slice) of the voxel matrix, the areas of the current section of the solar panels, the effective (cumulative) sectional area of the solar panels, and the cumulative sectional area of the body of the space station are calculated (although this parameter has no practical value for us). \nFigure 26a\n shows that the cutting plane of voxel matrix has not yet reached the model of SC, so all the sectional areas are zero.
\nScanning stages of 3D model SC with inclined position for calculation of sectional areas of solar panels and SC body.
\n\nFigure 26b\n shows that the cutting plane already passes on the SC itself, crossing both the solar panels and the SC body, so specific calculated values are obtained in each section of slice area, which will be visualized in the corresponding program windows. And finally, Figure
The advantage of the voxel method is the simplicity of determining many geometric parameters and solving many geometric problems of processing three-dimensional objects. However, when using voxel model, the shape of the object is described approximately. The desire to increase the accuracy of the description in
To determine the appropriate accuracy of the representation of 3D objects voxel matrix as a test example, consider the most unfavorable for the accuracy of the description of the case of the ball. Let us assume that a ball with a radius of 500 mm is inscribed in a voxel matrix with a variable number of voxel, which varies in the range from 1000 to 25,000 (\nFigure 27a\n).
\nResults of calculation of the error of the shape description by the voxel matrix.
For \nFigure 27b\n, the results of the calculation of the value of the most probable absolute error depending on the number of voxels for this matrix with dimensions 1 m × 1 m × 1 m are given. It can be seen from this graph that the error of the voxel model shape description is expected to depend on the voxel size, which, in turn, is determined by the number of voxels in the matrix. There is a threshold (in our case it is about 5000 voxels), with a decrease in which the absolute accuracy of the description of the form is sharply reduced. In [10] it is shown that for the most typical sizes of technical objects, even with a not very high number of voxels (about 5000 on each axis), the relative accuracy of the description remains quite high (below 0.05%), which is quite enough for most technical applications.
\nSince receptor models are discrete by definition, the discussion of the results raises the question not only about the accuracy of their description but also about the computational resources required for their implementation. Studies show that with a seemingly huge number of computational operations, they are performed surprisingly quickly. This is probably due to the homogeneity of the calculations and the use of only the RAM of the computer for their execution. The time of computer processing of voxel models is determined by both the hardware capabilities of the computer and the parameters of a particular scene—the number of voxels and the number of objects already placed. In \nFigure 28\n the estimation of processor time in solving the problem of recognition of a flat area with a fixed number of voxels (1000 × 1000) is given. \nFigure 28\n shows that the CPU time is still relatively small (fractions of a second), even for a medium-power computer. For a spatial scene, the time to obtain a solution increases by about an order of magnitude, but still remains acceptable for interactive mode. But it should be borne in mind that for voxel geometric models are possible methods of decomposition and parallelization of calculations, which will significantly speed up the calculation time.
\nCPU time required to determine empty spaces depending on the number of objects already placed.
Evaluation of the accuracy and performance of the channel design between obstacles in the test example using a voxel matrix size 1 m × 1 m × 1 m is shown in \nFigure 29\n. They also show acceptable practice accuracy and simulation time.
\nCalculated characteristics of voxel geometric model accuracy in designing a channel between obstacles.
Discrete methods of geometric modeling, which include voxel, can effectively track the cases of intersection of simulated objects in space, which makes it advisable to use them in automated layout problems. Voxel models allow you to create intelligent algorithms for automated placement. This eliminates the need to use multiple methods of search of accommodation options.
\nThe unsolved problem of using voxel geometric models in the problems of automated layout is their integration into modern CAD systems, which limits their widespread introduction into the practice of computer-aided design.
\nWireless mesh network is a network which comprises various wireless nodes with access points. Each node in the network acts as a forwarding node to transfer the data. Since the network is decentralized, forwarding of data is possible only to the neighboring node. This results in the network structure simple and easy. WMN makes the people connected with the Internet who work at remote areas and operating business. This chapter throws light on WMN architecture, layer functionalities, various other networking standards, and applications.
Wireless mesh network is the architecture which provides less mobility with low cost within a radio range. WMN is an infrastructure which is a network of routers minus cabling between the nodes. It consists of radio nodes which need not to be cabled to a wired port like the conventional wireless access points. Shortest hops are predicted to transmit the data toward large distance [1]. Nodes between the source and destination act as a forwarding node which works cooperatively in making decisions in route prediction based on the topology and forwarding the data. Wireless mesh network provides stability when compared to the rest of the network topologies rather than the node addition or deletion in the network. In infrastructure mesh network, the data forwarding and receiving are via gateway, whereas in the rest of the network, it is through pair of nodes [2].
The frequency of link breakage is higher in the case of wireless mesh networks when there is a high mobility which results in low performance in communication of information [3, 4].
Wireless mesh networks are categorized into three types based on the functionality of the nodes in the network:
Infrastructure mesh architecture
Mesh architecture based on clients
Hybrid mesh architecture
Mesh routers together act as a wireless back bone for infrastructure mesh architecture. Client node is passive in mesh infrastructure via Ethernet links; conventional clients with Ethernet interfaces can be connected to mesh routers.
If the traditional network and the mesh router are operating under the same radio range, then it is easy for the mesh network to communicate with the mesh router. Alternatively, if the radio ranges differ, the nodes will communicate to the base station so that with the help of Ethernet, it can be further communicated to the mesh routers. Figure 1 shows the mesh architecture for infrastructure-based network.
Mesh architecture for infrastructure-based network.
Mesh architecture based on client is the one in which the client nodes are connected from peer to peer. Each node can act as a routing node to transfer the data. Here, the client performs the role of mesh routing by acting in the forwarding of the data packets.
Figure 2 shows the architecture of mesh based on clients. In this we can see that the network with no router is connected to it, and rather all clients are interconnected to perform data transfer.
Mesh architecture based on clients.
In hybrid mesh architecture, usually the mesh nodes/router acts as a back bone of the entire network operation. With the help of network mesh router, it performs routing and forwarding of data packets toward its destination [5] which is shown in Figure 3.
Hybrid mesh architecture.
Dynamic self-configuration and self-organization
Adaptation
Fault tolerance and robustness
Low-cost
Integration and interoperability
The infrastructure-based wireless mesh network is a decentralized network without a centralized management or with no centralized server which is more expensive. These methods are more reliable and efficient as each node has to transmit to the next node. Here, nodes act as router to transmit the data to its peers which are located far even it is a single hop. Wireless mesh network should be stable, i.e., there should not be high mobility. If node failure occurs due to any hardware problem or any other, the neighbor node will perform rerouting with the help of routing protocols.
Mesh network may comprise of mobile devices or stationary devices. Some of the applications of mesh networks which deserve communication are:
Battlefield surveillance
Tunnels
Mobile video applications
Emergency situations
Tunnels
Real time car racing, etc.
Voice over Internet Protocol (VoIP) is the main application of wireless mesh networks. In order to provide quality of service (QoS), wireless mesh network is used in telecommunication for voice communication. In current scenario, some of the applications where wireless mesh has been used include:
Military forces in the USA are using wireless mesh networks to connect their devices for field operations.
In residences, electric smart meters have been implemented to transfer the reading from one point to another (say as, from home to centralized office) to eliminate the man power.
Wireless mesh network is used in one laptop per child program, in which it makes the students to share their files even when they are not connected with the Internet or with any physical connections.
From 2010 onward, Wi-Fi-enabled mesh routers are available in the market which is installable even in homes or at small workplace. Google Home, Google on Hub, and Google Wi-Fi are various Wi-Fi wireless mesh networks.
Iridium constellation with 66 satellites works under mesh network. This topology connects various wireless links with other satellite. Voice calls can be communicated via mesh networks between one satellite and another across constellations without transferring the signal to the ground station. Latency is highly reduced by avoiding the signal transfer to the nearby mesh instead of transferring to ground station.
The working principle of wireless mesh network is the same as that of the packets that travel around the wired internet data transfer between one node and another toward the destination [6]. This is implemented with the help of dynamic routing algorithm. It is possible by making each node communicate its routing information to other nodes within the network. With the received information, each node will decide whether to forward or to keep the data for itself. It is based on the functionality of the routing protocol. It is necessary for any routing algorithm to ensure that routing is done by predicting the shortest path between the source and destination. Figure 4 shows the architecture of wireless mesh network.
Architecture of wireless mesh network.
Wireless mesh network can be connected with the existing network to provide effective communication. In traditional network comprises of various wired nodes, hotspots to communicate with the users, whereas in wireless mesh networks, the network is established with the help of various numbers of wireless nodes to communicate with each other.
The wireless nodes used in wireless mesh networks play same role as wireless routers. Various Wi-Fi communication IEEE standards like IEEE 802.11a, 802.11b, and 802.11 g are used for wireless mesh communication. Nodes in the network are capable of predicting the shortest path from the available path between source and destination. Addition and deletion of nodes and the routes will be updated then and there whenever there is a change in the network infrastructure. Dynamic routing is the capability of the node to predict the shortest available path between source and destination [6].
The cost of designing the network is lesser for fewer numbers of nodes even for large network coverage.
Wireless mesh network shows better performance even for large number of nodes in the network.
Wireless mesh networks relay on various Wi-Fi standards.
It is useful for Non-line-of-sight (NLoS) network.
It is self-configuring and self-healing.
Easy to install and uninstall which makes network more adaptable with less or more number of nodes.
In wireless LAN, there may be a chance that the information may be returned to the wired access point. Getting back the information to access is called backhaul. Small networks can be handled without any special configuration, whereas in larger network, backhaul nodes are required to retrieve the information from wired access node.
Factors that influence the performance of wireless mesh networks include:
Architecture
Topology
Data pattern and traffic
Density of the nodes
Number of channels used by the nodes in the network
Transmission power
Mobility of the nodes
In order to develop the protocols, we need to clearly understand the relationship between the above factors and the capacity of WMNs and is given in Figure 5.
Layer structure of WMN.
Wireless mesh networks are capable of multiple data rates simultaneously. It is achieved with the help of various modulation techniques and coding rates. Link adaption provides adaptive error resilience. High-speed data transmission is achieved with orthogonal frequency-division multiple access (OFDMA) and ultra-wideband (UWB) techniques.
Wireless communication system is provided with smart antenna for the purpose of increasing the capacity and to overcome the co-channel interference, fading, multi-antenna systems, etc. But it is tedious for designing the same for wireless mesh networks though it is available with the existing system. Unoccupied spectrum can be utilized by proper frequency planning with the help of WMN. Frequency agile/cognitive radio is used in order to utilize the unused spectrum.
As most of the radio components, RF band, various channel modulations, and access modes are programmable in such a way that it can be implemented in a software for working under cognitive radio range. It will be easier if further updating is to be carried out.
With the available physical test beds, the software platform is not much appropriate to provide desired solution. But still it can able to make advance changes in physical layer techniques which suit better for wireless communications.
MAC layer in WMN plays a unique role when compared to various other wireless networks:
In WMN, communication is focused on more than one hop rather than single hop with the help of MAC.
Multipoint to multipoint communication is possible with the help of distributed MAC.
Self-healing and self-organization of node are the prime requirements of WMN for better performance.
Communication between the node and the node which are located far (multihop distances) from the source node should be proper for providing better stability.
Even less mobility influences the system performance of MAC.
MAC protocol is designed in such a fashion that WMN can work simultaneously with both single and with multiple channels.
Though various routing protocols are available for ad hoc networks, it cannot be directly used for wireless mesh networks. It is still a big research to perform modifications of the available protocol to be adopted for WMN. There are the same salient features that WMN should provide with which are:
Various performance metrics
Scalability
Robustness
Energy-efficient routing algorithm suits for mesh network
Various routing algorithms in ad hoc network are available with any one of the above features, but not with all which makes it difficult to adopt with the mesh network. Some of the routing concepts for mesh network are as follows.
In MR-LQSR, a metric called weighted cumulative expected transmission time (WCETT) is used for measuring the system performance. In WCETT, link quality and minimum number of hop counts are considered as a system metric which results in better throughput and less delay.
The objective of multipath routing is to provide load balancing and fault tolerance. Between the source and destination, multiple paths are predicted. When the shortest path link breaks, it can be easily switched over to other available paths. This results in better system performance by reducing the waiting time for computing the path at the time of fault. It also improves throughput and reduces end-to-end delay and fault tolerance. Still complexity exists with the multipath routing as it has to keep record of multipath always even if there is no breakage or fault.
Hierarchical routing protocols show better performance when there is dense number of nodes in the network. This is due to fast setup procedure, reduced overheads, and shortest routing path. Complexity is higher on maintaining the hierarchy and directly relates to the performance of the system.
It is a unique routing scheme in which it forwards the packets with the knowledge on the position of the node which is being communicated instead of the topology-based method. Geographical routing algorithm (single-path greedy routings) finds difficulty in delivering the data, if the path is available between source and the destination as data forwarding with the help of current location information.
Data delivery is guaranteed by using planar-graph-based geographic routing algorithms but results in more overhead information.
A large number of transport protocols are available for ad hoc networks, and WMNs depend on those transport layer protocols. Till date, there is no transport protocol that has been proposed specifically for WMNs. We know that ad hoc network is also not mature. It also has various unresolved issues. This suggests further research in this area.
WMN supports enormous applications which include:
Internet access
Distributed information storage and sharing
Information exchange across multiple wireless networks
Various research works have been carried out under these domains but focusing on modifying the existing application layer protocol by adapting various features for the mesh application layer protocol [7].
WMNs have their merits and drawbacks too. There are some issues to be concentrated for improving the network performance which include connectivity, radio range, interoperability, compatibility, etc.
The weak area of WMN is security. Strong research is demanded due to the absence of centralized authority or key management for assuring security to provide fully trusted system.
The common issues in WMNs are channel capacity expansion, scalability, and quality of service [8].
The nodes in WMN are self-configurable and self-healable. Such self- configuring nodes are better which improves the system performance, whereas self-healing makes the network to reconfigure if there are any addition and deletion of nodes in the network. Due to the huge number of nodes and data, there will be a high fault tolerance and degradation in performance. Integration of existing network leads to more complexity. By eradicating these drawbacks, the performance of WMN can be enhanced.
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