Barycentric coordinates computation in homogeneous coordinates

The recent developments in collaborative search, acquisition, and tracking have hoisted the geographical barrier. The network between unmanned aerial vehicles (UAVs) and wireless sensor networks (WSNs) is one such collaboration, which comprises battery-powered static sensor nodes that act as sources and sinks and UAVs that act as relays. This collaborative network presents with opportunities and advantages, but at the same time, configuration of such networks is an arduous task. The WSN nodes are characterized by constant depleting power. Their network itself requires constant management and reconfiguration. These requisites can be slaked through the formation of an efficient data dissemination algorithm, which acclimates according to the network state. Considering this, a data dissemination approach is presented in this paper, which constructs a virtual topology predicated on the charge of WSN nodes utilizing software-defined networks (SDNs) through UAVs. The topology is constantly monitored and reconfigured when required. The aerial nodes are equipped with multiple-input multiple-output (MIMO) antennas in order to facilitate simultaneous communication with the ground nodes, the base station, and the SDN controller. An efficient sleep timer and backoff counter strategies are also utilized by the proposed approach. The SDN controller facilitates the topology formation and maintenance of a sleep timer and a backoff counter. The proposed model is compared with clustered hierarchical layouts and hexagonal cell layouts through the network simulations. The results suggest significant improvements in the proposed model for various metrics, such as lifetime, delay, latency, delivery ratio, and throughput in comparison with the existing solutions.High radio frequency (RF) coverage, high altitude, high throughput, heavy payload, less operating time, ease of use, and low cost are the basic requirements of UAV-CONOPS. Chemical, Biological, Radiological, and Nuclear Reconnaissance (CBRN)-CONOPS whose major purpose is the containment of hazards are also turning towards UAV networks. Cellular network-based air-to-ground links and unmanned aircraft system (UAS)-backbone systems, communication aware sensor distribution, etc are some of the promising aspects of the UAV systems. 2,3 The crucial step towards UAV networks is the development of sustainable multi-UAV environments. National regulations, routing, path planning, quality of service (QoS), integration with Global Information Grid (GIG), mobility control, coordination, and standardization are the steps required for efficient migration towards flying networks (multi-UAV). 4,5 The complexity of the multi-UAV ad hoc networks makes data dissemination also a challenging prospect. Latency, delay, antenna type, timing, etc come into play when we are talking about a network that is so fast moving and dynamic. 6 Multi-UAVs collaborate to achieve common objectives. It is evident that the collaborative UAV and the ground networks together can perform complex tasks. Some of these tasks...

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“…55 Intuitively, the idea of sectors comes from the UAV maneuver angels. To perform this mapping, the Barycentric coordinate system is applied.…”

Section: Uavs-coordinated Wsnsmentioning

confidence: 99%

“…To perform this mapping, the Barycentric coordinate system is applied. 55 Intuitively, the idea of sectors comes from the UAV maneuver angels. Points (x i , y i ), (x j , y j ) define two consecutive UAV turning points.…”

Section: Uavs-coordinated Wsnsmentioning

confidence: 99%

Efficient data management and control over WSNs using SDN‐enabled aerial networks

Sayeed

Kumar

Sharma

2019

Int J Communication

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“…In order to create a continuous coordinate system for the triangular grid that enables us to uniquely address any point of the triangular grid, we combine discrete triangular coordinate systems from Reference [22] (see also Figure 1 for some examples) with the barycentric coordinate system (BCS), discovered by Möbius (see References [1,23]).…”

Section: Preliminariesmentioning

confidence: 99%

A Continuous Coordinate System for the Plane by Triangular Symmetry

Nagy¹,

Abuhmaidan²

2019

Symmetry

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The concept of the grid is broadly used in digital geometry and other fields of computer science. It consists of discrete points with integer coordinates. Coordinate systems are essential for making grids easy to use. Up to now, for the triangular grid, only discrete coordinate systems have been investigated. These have limited capabilities for some image-processing applications, including transformations like rotations or interpolation. In this paper, we introduce the continuous triangular coordinate system as an extension of the discrete triangular and hexagonal coordinate systems.The new system addresses each point of the plane with a coordinate triplet. Conversion between the Cartesian coordinate system and the new system is described. The sum of three coordinate values lies in the closed interval [−1, 1], which gives many other vital properties of this coordinate system. Symmetry 2019, 11, 191 2 of 17 of the grid. In Figure 1a, the first coordinate value is ascending right-upwardly, the second values are ascending into the right-downward direction, and the third one is ascending into the left-upward direction [7,8]. We should mention that this system could be seen as the extension of the oblique coordinate system using two independent integer values [9] by concerning the third value to obtain zero-sum for every triplet. The digital distance based on the neighborhood relation is computed in Reference [9]. Since the vectors describing the grid are not orthogonal, some geometric descriptions based on Cartesian coordinates are not very clear. However, to simplify the expressions of the constrained three-dimensional coordinate system is recommended. We should also mention that 0-sum triplets allowing real numbers were used in Reference [8] to describe rotations (that may not map the hexagonal grid to itself). In this way, a useful digitization operator is found. Her's system was mentioned and used in References [10,11] for various imaging-related disciplines.Symmetry 2019, 11, 191 3 of 17

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“…Rewriting the Eq. (6), we obtain = (7) where It can be shown that a system of homogeneous linear equations = is equivalent to the extended cross-product, actually outer-product [19] [20]. In general, solutions of the both cases = and = , i.e.…”

Section: Projective Notation and Geometry Algebramentioning

confidence: 99%

Proceedings of the 2017 Federated Conference on Computer Science and Information Systems

Awad¹,

Andrzej²

2017

Annals of Computer Science and Information Systems

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-There are many practical applications based on the Least Square Error (LSE) approximation. It is based on a square error minimization "on a vertical" axis. The LSE method is simple and easy also for analytical purposes. However, if data span is large over several magnitudes or non-linear LSE is used, severe numerical instability can be expected.The presented contribution describes a simple method for large span of data LSE computation. It is especially convenient if large span of data are to be processed, when the "standard" pseudoinverse matrix is ill conditioned. It is actually based on a LSE solution using orthogonal basis vectors instead of orthonormal basis vectors. The presented approach has been used for a linear regression as well as for approximation using radial basis functions.

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Barycentric coordinates computation in homogeneous coordinates

Cited by 57 publications

References 6 publications

Efficient data management and control over WSNs using SDN‐enabled aerial networks

Efficient data management and control over WSNs using SDN‐enabled aerial networks

A Continuous Coordinate System for the Plane by Triangular Symmetry

Proceedings of the 2017 Federated Conference on Computer Science and Information Systems

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