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Artykuły w czasopismach na temat „Coordinates”

Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 25 lipca 2025

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1

Funahashi, Shintaro. "Coordinate Transformation from Retinotopic Coordinates to Craniotopic Coordinates." Equilibrium Research 57, no. 4 (1998): 353–68. http://dx.doi.org/10.3757/jser.57.353.

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2

Shrestha, Kalyan Gopal. "An Approach to Determine Coordinate Transformation Parameter for Nepal GPS Network." Journal on Geoinformatics, Nepal 10 (June 30, 2011): 9–13. http://dx.doi.org/10.3126/njg.v10i0.23187.

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The Surveying and Mapping community now has the benefit of 3-dimensional coordinates at the centimeter level, through the Global Positioning System (GPS). The reference frame for GPS, World Geodetic System of 1984 (WGS84), within which a user ascertains these coordinates is essentially geocentric. All coordinated data and mapping in Nepal are based on a non-geocentric coordinate system known as the Everest Datum of 1830. This paper tries to present a practical approach to define transformation parameters between the two coordinate systems for Nepal.

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3

Eckermann, Stephen. "Hybrid σ–p Coordinate Choices for a Global Model". Monthly Weather Review 137, № 1 (2009): 224–45. http://dx.doi.org/10.1175/2008mwr2537.1.

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Abstract A methodology for choosing a hybrid σ–p (sigma–pressure) vertical coordinate of the Simmons–Strüfing form for a global model is presented. The method focuses on properties of the vertical derivative of the terrain-following coefficient, which affect the smoothness and shape of layer thickness profiles and determines the coordinate’s monotonicity over variable terrain. The method is applied to characterize and interrelate existing hybrid coordinate choices in NWP and climate models, then to design new coordinates with specific properties. Offline tests indicate that the new coordinates

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4

Botsiura, Olesia, Iryna Zadorozhna, and Igor Zakharov. "MEASUREMENT UNCERTAINTY EVALUATION OF THE OBJECT PLANIMETRIC COORDINATES USING THE RHO-THETA METHOD." Metrology and instruments, no. 2 (December 13, 2024): 05. https://doi.org/10.30837/2663-9564.2024.2.05.

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Determining the planimetric coordinates of an object is a topical task of coordinate metrology, which finds application in cartography, geodesy, location and navigation. The article considers the features of measurement uncertainty evaluation the coordinatesof an object on a plane using the rho-theta method. The measurement model is substantiated. Expressions for estimating the numerical values of coordinates and their combined standard uncertaintiesare obtained. Expressions for estimating expanded uncertainties using the kurtosis methodare found. The uncertainty budgets for measuring the plan

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Zhang, Xian Min, Ya Liu, Gang Li, and Fei Xia. "Study and Application on Airport Clearance Based on Secant Method in Gauss Projection Algorithm for Inverse Solution." Advanced Materials Research 790 (September 2013): 669–72. http://dx.doi.org/10.4028/www.scientific.net/amr.790.669.

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This article adopts WGS-84 Coordinate, applying the Secant Method successive approximation to solve geographic coordinates according to the Gauss-Krueger formula, realizing the transformation from plane rectangular coordinates to geographic coordinates, using the coordinate translation and rotation formula to achieve the transformation between the airport coordinate and Gauss plane rectangular coordinates, thus geographic coordinate, gauss plane rectangular coordinates and the airport coordinate can change into each other.

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6

Shanurov, G. A., and A. D. Manilova. "Mobile scanning complex positioning accuracy depending on the coordinate systems used." Geodesy and Cartography 919, no. 1 (2017): 13–17. http://dx.doi.org/10.22389/0016-7126-2017-919-1-13-17.

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Inertial coordinate system and geodetic (terrestrial) coordinate system are used in processing of results of topographic survey, carried out with a mobile scanning complex. Mobile scanning complex geodetic coordinates, in turn, are presented in geodetic three-dimensional rectangular coordinate system form, in geodetic ellipsoidal coordinate system form and in the form of coordinates on a geodetic projection plane. The results of research, carried out earlier [4–7], suggest that the coordinate transformation on large areas distorts geodetic points coordinates. The article presents the results o

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7

Tian, Haoxin, Xipeng Fang, Yubin Lan, et al. "Extraction of Citrus Trees from UAV Remote Sensing Imagery Using YOLOv5s and Coordinate Transformation." Remote Sensing 14, no. 17 (2022): 4208. http://dx.doi.org/10.3390/rs14174208.

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Obtaining the geographic coordinates of single fruit trees enables the variable rate application of agricultural production materials according to the growth differences of trees, which is of great significance to the precision management of citrus orchards. The traditional method of detecting and positioning fruit trees manually is time-consuming, labor-intensive, and inefficient. In order to obtain high-precision geographic coordinates of trees in a citrus orchard, this study proposes a method for citrus tree identification and coordinate extraction based on UAV remote sensing imagery and co

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8

Radov, Stanislav, Serhii Rotte, Maksym Soboliev, Valentyna Lytvyn, and Alina Volontyr. "High-precision coordinate transformation algorithm for equidistant transverse cylindrical projection." Geodesy, cartography and aerial photography 101,2025, no. 101 (2025): 26–34. https://doi.org/10.23939/istcgcap2025.101.026.

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The aim of the present study is to design an algorithm for direct and inverse transformation of geodetic coordinates and flat rectangular coordinates of equiintermediate transverse cylindrical projection, based on the use of geocentric coordinate ellipses. Methods. General scientific methods of abstraction, analysis, synthesis, and mathematical modeling have been deployed to substantiate the coordinate transformation algorithm. Results. The proposed study has developed an accurate algorithm for equiintermediate transverse cylindrical projection, which uses geocentric coordinate ellipses, namel

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9

Jin, Li Xin, Lian Jun Wang, and Song Lin Yang. "Movement and Deformation Rules of Gauss Coordinates Based on Ellipsoid Expanded Modal." Advanced Materials Research 368-373 (October 2011): 2211–15. http://dx.doi.org/10.4028/www.scientific.net/amr.368-373.2211.

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This paper studies on deducing the analytic formulae on Gauss coordinates displacement before or after the increase of major radius of ellipsoid expanded modals, which is based on the partial derivatives of geodetic coordinates in Gauss coordinates deducing from direct solution formulae of the Gauss projection coordinates in conjunction with differential coefficient formulae and variable of geodetic coordinates. On this theoretical foundation, analyzing the relationships between Gauss coordinates displacement and other mathematical parameter . The relationship of graphics between point displac

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10

Jin, Li Xin, Lian Jun Wang, and Song Lin Yang. "Displace Regulation of Gauss Coordinates Based on Ellipsoid Expanded Modal." Applied Mechanics and Materials 105-107 (September 2011): 1333–37. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.1333.

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This paper studies on deducing the analytic formulae on Gauss coordinates displacement before or after the increase of major radius of ellipsoid expanded modals, which is based on the partial derivatives of geodetic coordinates in Gauss coordinates deducing from direct solution formulae of the Gauss projection coordinates in conjunction with differential coefficient formulae and variable of geodetic coordinates. On this theoretical foundation, analyzing the relationships between Gauss coordinates displacement and other mathematical parameter . The relationship of graphics between point displac

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11

Mellace, C., A. P. Lai, A. Gugliotta, N. Bosso, T. Sinokrot, and A. A. Shabana. "Experimental and numerical investigation of railroad vehicle braking dynamics." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 223, no. 3 (2009): 255–67. http://dx.doi.org/10.1243/14644193jmbd129.

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One of the important issues associated with the use of trajectory coordinates in railroad vehicle dynamic algorithms is the ability of such coordinates to deal with braking and traction scenarios. In these algorithms, track coordinate systems that travel with constant speeds are introduced. As a result of using a prescribed motion for these track coordinate systems, the simulation of braking and/or traction scenarios becomes difficult or even impossible. The assumption of the prescribed motion of the track coordinate systems can be relaxed, thereby allowing the trajectory coordinates to be eff

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12

Romanenko, A. "Theoretical foundations of point cloud coordinate system transformation." Collection of Research Papers of the National Mining University 74 (September 2023): 46–57. http://dx.doi.org/10.33271/crpnmu/74.046.

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Purpose. To provide theoretical foundations and develop mathematical models for the efficient transformation of coordinate systems for point clouds in geophysical research; the scientific analysis is aimed at developing algorithms and establishing necessary dependencies for the reliable integration of data obtained at different time points into a unified coordinate system, opening up prospects for further study and analysis of processes in geophysical research. The methods.The calculation is carried out using the following steps. Determination of known coordinates of four points (x1', y1', z1'

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13

Vinogradov, A. V. "Establishment of local coordinate systems in the transition to the geodetic system of coordinates of GSK-2011." Geodesy and Cartography 929, no. 11 (2017): 2–10. http://dx.doi.org/10.22389/0016-7126-2017-929-11-2-10.

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Pretty before long there will be transition to the geodetic system of coordinates of GSK-2011. For the transition period it is necessary to develop a method of recalculating coordinates from one system to another. The existing methods of recalculating coordinates are designed for recalculating coordinate points of state geodetic networks (GGS) and geodetic local networks (GSS). For small areas (administrative districts, populated areas) simplified methods are more acceptable. You need to choose the resampling methods that can be applied in small businesses, performing surveying works. The arti

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14

Zhao, Yun Peng, and Nan Li. "Research on Coordinate System Transformation in Flexible Rope FEA." Advanced Materials Research 753-755 (August 2013): 1785–89. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.1785.

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This paper focuses on the transform relationships between each element and between elements with inertial system under different attitude coordinate system in the finite element multi-body system mechanical analysis of the flexible rope process. It mainly research the attitude coordinate transformation matrix between the of flexible rope Micro-element and inertial system under the four coordinate system which are the direction cosine coordinates, finite rotation four element coordinates, Euler angle coordinate and Cardan angle coordinates, and the relationship between the connecting base on th

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15

Abukari, Osman Mohammed, Akwasi Afrifa Acheampong, Samuel Osah, and John Ayer. "Homogenizing coordinates through the use of the active CORS in Ghana." South African Journal of Geomatics 12, no. 2 (2023): 129–44. http://dx.doi.org/10.4314/sajg.v12i.2.2.

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In this study, the course towards determining the homogeneous three-dimensional (3D) coordinates of the newly established active Continuously Operating Reference Station (CORS), based on ITRF2014 in Ghana, is revealed. The aim is to address coordinate inconsistencies and inhomogeneity in the published positions of the new active CORS in Ghana. In order to attain homogeneity, the coordinates of two primary control points, GCS 305 and GCS 306, were obtained using AUSPOS online services via email. These were subsequently used as reference stations to compute the position of the LISAG_KUMASI CORS.

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16

Song, Sha Jia, and Neng He. "Digital Image Processing and Coordinate Transformation for Vic-3D System." Applied Mechanics and Materials 333-335 (July 2013): 1002–6. http://dx.doi.org/10.4028/www.scientific.net/amm.333-335.1002.

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This paper discusses the problem about the processing of the images collected by Vic-3D measurement system and the coordinate transformation between the pixel coordinate and plane coordinate. Correlation analysis on image information is carried out by using Matlab. Template matching method is used to get the pixel coordinates of the marked part on the images. Based on affine transformation and least square method, I transform the pixel coordinates of the marked part on the images into the plane coordinates.

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17

Lu, Xiaohong, Yongquan Wang, Jie Li, Yang Zhou, Zongjin Ren, and Steven Y. Liang. "Three-dimensional coordinate measurement algorithm by optimizing BP neural network based on GA." Engineering Computations 36, no. 6 (2019): 2066–83. http://dx.doi.org/10.1108/ec-09-2018-0410.

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Purpose The purpose of this paper is to solve the problem that the analytic solution model of spatial three-dimensional coordinate measuring system based on dual-position sensitive detector (PSD) is complex and its precision is not high. Design/methodology/approach A new three-dimensional coordinate measurement algorithm by optimizing back propagation (BP) neural network based on genetic algorithm (GA) is proposed. The mapping relation between three-dimensional coordinates of space points in the world coordinate system and light spot coordinates formed on dual-PSD has been built and applied to

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18

Rader, C. M. "Generating rectangular coordinates in polar coordinate order." IEEE Signal Processing Magazine 22, no. 6 (2005): 178–80. http://dx.doi.org/10.1109/msp.2005.1550199.

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19

Liu, De Li, Nan Lin, and Ya Shuang Zhang. "Digital Aerial Photo Orientation within the Different Algorithm Analysis." Advanced Materials Research 610-613 (December 2012): 3680–84. http://dx.doi.org/10.4028/www.scientific.net/amr.610-613.3680.

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Scanning digital aerial images as data source, using PhotoShop software and MapGis software measurement pixel coordinates of the 8frame point on photo , according to the camera parameters file provided fiducial mark on the image plane coordinate system coordinates the theory, using affine transformation method and bilinear transformation method, calculated the interior orientation parameters. Basing on this parameter calculates residual error of frame point coordinate, analyse and compare residual error which obtained by two kinds of measurement frame point pixel coordinates .Research shows th

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20

Kenigsberg, D. V., Yu M. Salamatina, O. A. Prokhorov, and S. I. Kuzikov. "Convergence of daily mean coordinates of precise positioning methods." IOP Conference Series: Earth and Environmental Science 929, no. 1 (2021): 012014. http://dx.doi.org/10.1088/1755-1315/929/1/012014.

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Abstract As part of the research of modern movements of the Earth’s crust, an analysis of 7 high-precision methods for calculating GNSS positions was carried out for the convergence of their daily mean coordinates. Based on Euclidean distances, regular and maximal discrepancies between coordinates of different methods are given. According to the coordinates in the ITRF, 5 methods are stood out with regular coordinate discrepancies <1 mm, and individual maximum discrepancies up to 30 mm. The other two methods have regular discrepancies in coordinates up to 2 cm, and the maximum differences r

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21

Zhang, Sumin, Zhengming Ma, and Zengrong Zhan. "Nonlinear Alignment and Its Local Linear Iterative Solution." Mathematical Problems in Engineering 2016 (2016): 1–14. http://dx.doi.org/10.1155/2016/7196043.

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In manifold learning, the aim of alignment is to derive the global coordinate of manifold from the local coordinates of manifold’s patches. At present, most of manifold learning algorithms assume that the relation between the global and local coordinates is locally linear and based on this linear relation align the local coordinates of manifold’s patches into the global coordinate of manifold. There are two contributions in this paper. First, the nonlinear relation between the manifold’s global and local coordinates is deduced by making use of the differentiation of local pullback functions de

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22

PILOT, CHRISTOPHER, and SUBHASH RAJPOOT. "A SUPERSPACE OF (1, 1/2)+(1/2, 1) FERMIONIC COORDINATES." International Journal of Modern Physics A 05, no. 19 (1990): 3801–9. http://dx.doi.org/10.1142/s0217751x90001628.

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A superspace is constructed in which the elements of the superspace consist of the four Minkowski space-time coordinates and a set of vector-spinor coordinates that belong to the irreducible (1, 1/2)+(1/2, 1) representation of the Lorentz group. It is shown that a translation in the vector-spinor coordinates leads to a vector-spinor coordinate dependent translation in the space-time coordinate xμ. The super covariant derivatives are also constructed.

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23

Wu, Shuai. "A Method for Calculating the Band Change of Gauss Projection Coordinates." Academic Journal of Science and Technology 5, no. 1 (2023): 263–68. http://dx.doi.org/10.54097/ajst.v5i1.5662.

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In geodesy, many surveying projects are carried out on the plane, which requires the transformation of geodetic coordinates, the element on the ellipsoid, into plane coordinates, and each independent coordinate system has new contradictions due to zoning. Based on the basic geometric parameters and the mathematical description of the earth ellipsoid, this paper introduces the principle of Gauss projection method. Since Gauss Krueger projection is currently used in China, this paper introduces the principle and method of Gauss projection, and deduces the correlation between the Gauss plane coor

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24

Meng, Qing Wu, and Lu Meng. "Influencing of Coordinate Transformation on Based CGCS2000 on Topographic Map with Large Scales." Applied Mechanics and Materials 522-524 (February 2014): 1207–10. http://dx.doi.org/10.4028/www.scientific.net/amm.522-524.1207.

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Using three dimensional coordinate transformation model with 7 parameters the coordinate transformation parameters are solved. Comparing the coordinates of the kilometer grid point on topographic maps in Beijing54, Xian80 and Urban Independent Coordinate System with the observation coordinates of same point inCGCS2000, Through watching their coordinate changes the moving changes regularity on topographic maps are discovered between Beijing54 and CGCS2000, between Xian 80 and CGCS2000, Urban Independent Coordinate System and CGCS2000

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25

Zängl, Günther. "An Adaptive Vertical Coordinate Formulation for a Nonhydrostatic Model with Flux-Form Equations." Monthly Weather Review 135, no. 1 (2007): 228–39. http://dx.doi.org/10.1175/mwr3298.1.

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Abstract The concept of adaptive vertical coordinates is used to upgrade conventional terrain-following σ coordinates to arbitrary hybrid coordinates. Compared with previous approaches for implementing adaptive coordinates, the method presented here combines unrestricted applicability to nonhydrostatic models with the capability to integrate the atmospheric equations in flux form. The coordinate is based on a three-dimensional field carrying the vertical position of the coordinate surfaces, which is made time dependent by introducing a prognostic equation. As a specific example, the adaptive c

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26

Nesnov, Dmitriy. "Area of correct space coordination by normal conic coordinates." Geometry & Graphics 11, no. 3 (2023): 3–11. http://dx.doi.org/10.12737/2308-4898-2023-11-3-3-11.

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The field theory is widely represented in spherical and cylindrical coordinate systems, since the mathematical apparatus of these coordinate systems is well studied. Field sources with more complex structures require new approaches to their study. The purpose of this study is to determine the correct coordination of space by normal conic coordinates. This is necessary in subsequent studies, the task of which will be to simplify the expressions for the characteristics of the field by introducing a special coordination of space, which reflect the shape of the source and/or sink of the field. For

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27

BOONSERM, PETARPA, and MATT VISSER. "BUCHDAHL-LIKE TRANSFORMATIONS FOR PERFECT FLUID SPHERES." International Journal of Modern Physics D 17, no. 01 (2008): 135–63. http://dx.doi.org/10.1142/s0218271808011912.

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In two previous articles [Phys. Rev. D71 (2005) 124307 (gr-qc/0503007) and Phys. Rev. D76 (2006) 0440241 (gr-qc/0607001)] we have discussed several "algorithmic" techniques that permit one (in a purely mechanical way) to generate large classes of general-relativistic static perfect fluid spheres. Working in Schwarzschild curvature coordinates, we used these algorithmic ideas to prove several "solution-generating theorems" of varying levels of complexity. In the present article we consider the situation in other coordinate systems. In particular, in general diagonal coordinates we shall general

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28

Johannes, Jacobus Myburgh, and Johannes Luwes Nicolaas. "Optimised coordinate generation for Arduino-based focus and motion control system for deployment in time-lapse photography." TELKOMNIKA (Telecommunication, Computing, Electronics and Control) 21, no. 2 (2023): 431–40. https://doi.org/10.12928/telkomnika.v21i2.22198.

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This paper demonstrated the design and implementation of a unique algorithm used to generate interim coordinates for focus transitions in time-lapse photography. Through a prototype design methodology, the unique algorithm was developed to function within the limitations imposed by a low-cost 8-bit microcontroller for the development of a cost-effective focus and motion control system for deployment in photographic higher education. Through conceptualization and virtualization in MathLab and comparison with values generated in simulated real-world use-case, the proposed algorithm was test

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29

NAKAMURA, AKIRA. "SOME NOTES ON PARALLEL COORDINATE GRAMMARS." International Journal of Pattern Recognition and Artificial Intelligence 09, no. 05 (1995): 753–61. http://dx.doi.org/10.1142/s0218001495000304.

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In a coordinate grammar, the rewriting rules replace sets of symbols having given coordinates by sets of symbols whose coordinates are given functions of the coordinates of the original symbols. Usually, at each step of a derivation, only one rule is applied and only one instance of its left hand side is rewritten. This type is referred to sequential grammars. As a counterpart of this grammar, parallel coordinate grammars are defined as generalized parallel isometric grammars. In the parallel grammars, the rewriting rule are used in parallel in a derivation application. The paper discusses som

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30

Meng, Qing Wu, and Lu Meng. "Research of Transformation Models between Urban Independent Coordinates and CGCS2000 Coordinates." Applied Mechanics and Materials 522-524 (February 2014): 1202–6. http://dx.doi.org/10.4028/www.scientific.net/amm.522-524.1202.

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In case of no errors of known coincidence points coordinates the plane coordinate transformation model equation with four parameters and the plane coordinate transformation model equation with six parameters are derived, this algorithm needs not composed normal equation from error equation, which is verified by examples about transformation between the urban plane coordinate and CGCS2000 plane coordinate. Finally the some beneficial conclusions have been got.

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31

Karpinskyi, Yurii, Danylo Kin, Ihor Kuryliak, and Nikita Rotachov. "METHOD TRANSFORMATION OF COORDINATES FROM THE ARCHIVE SYSTEM (VARASH-42) TO THE CURRENT SYSTEM (LCS-56) USING QGIS." Urban development and spatial planning, no. 86 (May 31, 2024): 397–410. http://dx.doi.org/10.32347/2076-815x.2024.86.397-410.

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This article proposes a technique for transforming coordinates from an archival coordinate system into an active one using affine transformation using the finite element method in the QGIS geoinformation environment using a transformation field in the NTv2 format. The purpose of the work is to develop a method of transforming coordinates from the archival system into the one operating in Ukraine using the GRID model of the transformation field in the form of NTv2 format and QGIS software using the example of the Varash-42 coordinate system, derived from CS-42, and LCS-56, derived from UCS-2000

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Gratus, J., and T. Banaszek. "The correct and unusual coordinate transformation rules for electromagnetic quadrupoles." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2213 (2018): 20170652. http://dx.doi.org/10.1098/rspa.2017.0652.

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Despite being studied for over a century, the use of quadrupoles have been limited to Cartesian coordinates in flat space–time due to the incorrect transformation rules used to define them. Here the correct transformation rules are derived, which are particularly unusual as they involve second derivatives of the coordinate transformation and an integral. Transformations involving integrals have not been seen before. This is significantly different from the familiar transformation rules for a dipole, where the components transform as tensors. It enables quadrupoles to be correctly defined in ge

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33

JIANG, Xinhao, and Youwen SUN. "FEQ: a new flux coordinates based equilibrium solver including both magnetic axis and separatrix." Plasma Science and Technology 24, no. 1 (2021): 015105. http://dx.doi.org/10.1088/2058-6272/ac363e.

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Abstract Accurate tokamak plasma equilibrium solution in flux coordinates is crucial for many stability and transport studies. Different approaches for dealing with singularities in solving the nonlinear Grad–Shafranov (GS) equation in flux coordinates or also known as straight field line coordinates are proposed in this paper. The GS equation is solved by iterating the position of grids directly in flux coordinates, and hence, no additional errors are introduced due to mapping process for a convergent solution. The singularity at magnetic axis in flux coordinates is removed by using a novel c

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34

Foote, Robert L., Bruce E. Pollock, Michael J. Link, Yolanda I. Garces, and Robert W. Kline. "Leksell Gamma Knife coordinate setting slippage: how often, how much?" Journal of Neurosurgery 101, no. 4 (2004): 590–93. http://dx.doi.org/10.3171/jns.2004.101.4.0590.

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Object. The aim of this study was to determine the incidence and magnitude of coordinate setting slippage during gamma knife surgery (GKS). Methods. Thirty-six consecutive patients undergoing GKS with a Leksell unit between June and December 2000 had their coordinates (right and left x-, y-, and z-coordinates; 1548 coordinates; 258 isocenters) and gamma angles checked after the delivery of treatment to each isocenter to determine whether the coordinate settings had slipped and, if so, which settings and the magnitude of the slippage. Conclusions. Coordinate setting slippage during GKS with a L

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Lei, Kin, Dongxu Qi, and Xiaolin Tian. "A New Coordinate System for Constructing Spherical Grid Systems." Applied Sciences 10, no. 2 (2020): 655. http://dx.doi.org/10.3390/app10020655.

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In astronomy, physics, climate modeling, geoscience, planetary science, and many other disciplines, the mass of data often comes from spherical sampling. Therefore, establishing an efficient and distortion-free representation of spherical data is essential. This paper introduces a novel spherical (global) coordinate system that is free of singularity. Contrary to classical coordinates, such as Cartesian or spherical polar systems, the proposed coordinate system is naturally defined on the spherical surface. The basic idea of this coordinate system originated from the classical planar barycentr

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36

Feng, Rongquan, and Hongfeng Wu. "A Mean Value Formula for Elliptic Curves." Journal of Numbers 2014 (August 25, 2014): 1–5. http://dx.doi.org/10.1155/2014/298632.

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It is proved in this paper that, for any point on an elliptic curve, the mean value of x-coordinates of its n-division points is the same as its x-coordinate and that of y-coordinates of its n-division points is n times that of its y-coordinate.

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Kilner, Steven J., and David L. Farnsworth. "Parabolic coordinates." Mathematical Gazette 105, no. 563 (2021): 226–36. http://dx.doi.org/10.1017/mag.2021.51.

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An important first step in understanding or solving a problem can be the selection of coordinates. Insight can be gained from finding invariants within a class of coordinate systems. For example, an important feature of rectangular coordinates is that the Euclidean distance between two points is an invariant of a change to another rectangular system by a rigid motion, which consists of translations, rotations and reflections. Indeed, the form of the distance function is an invariant. In calculus courses, students learn about polar coordinates, so that useful curves can be simply expressed and

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BINI, DONATO, LUCA LUSANNA, and BAHRAM MASHHOON. "LIMITATIONS OF RADAR COORDINATES." International Journal of Modern Physics D 14, no. 08 (2005): 1413–29. http://dx.doi.org/10.1142/s0218271805006961.

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The construction of a radar coordinate system about the world line of an observer is discussed. Radar coordinates for a hyperbolic observer as well as a uniformly rotating observer are described in detail. The utility of the notion of radar distance and the admissibility of radar coordinates are investigated. Our results provide a critical assessment of the physical significance of radar coordinates.

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Gustafsson, Björn, and Jaak Peetre. "Notes on projective structures on complex manifolds." Nagoya Mathematical Journal 116 (December 1989): 63–88. http://dx.doi.org/10.1017/s0027763000001690.

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Consider a Riemann surface X equipped with a projective structure, that is, a covering of X with coordinate neighborhoods U and corresponding (holomorphic) local coordinates {t} such that in the intersection U ∩ U′ of any two such coordinate neighborhoods U and U′ change of local coordinates is mediated by a fractional linear transformation

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40

Nepoklonov, Vicktor, Mayya Maximova, and Ivan Sukharev-Krylov. "Monitoring of spatial data coordinate basis integrity using coordinate transformations." E3S Web of Conferences 310 (2021): 03009. http://dx.doi.org/10.1051/e3sconf/202131003009.

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The modern spatial data coordinate basis (SDCB) is built taking into account the variety of existing and used today geodetic networks, models of physical fields of the Earth, cartographic models, as well as coordinate systems (СS). One of the requirements for SDCB from the standpoint of system analysis is the requirement of integrity, which presupposes the unity of the determination of coordinates, that is, the consistency of the results of determining the coordinates of the same points in different CSs. The article is devoted to the monitoring of the accuracy characteristics of the available

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Brumberg, V. A. "Relativistic Aspects of Reference Systems and Time Scales." Highlights of Astronomy 9 (1992): 133–39. http://dx.doi.org/10.1017/s1539299600008856.

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Mindful of the fact that any time and space coordinates of General Relativity Theory (GRT) are not, in general, physically meaningful and measurable quantities, one may choose between three possibilities in applying GRT to ephemeris astronomy: 1)avoid coordinates completely, i.e., construct coordinate-independent theories of light propagation and solar system body motion involving the removal of all coordinate-dependent quantities from the present system of astronomical constants;2)use any coordinate system to describe observational procedures and to solve dynamics problems, provided that one

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Schenyavskaya, Lyudmila, Grittel' Shevchenko, and Polina Kovalenko. "Development of a methodology for determining the parameters of the transformation of coordinate systems based on the first-order nonlinear programming method when accompanying the construction of buildings and structures." Proceedings of Petersburg Transport University 21, no. 1 (2024): 47–60. http://dx.doi.org/10.20295/1815-588x-2024-01-47-60.

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Objective: to analyze the advantages and disadvantages of existing nonlinear programming methods for solving problems of coordinate system transformation (SC). To consider the need to convert the coordinates of points from local SC to urban. To determine the possibility of using the generalized reduced gradient method to transform the coordinates of points located both at a distance between points of about 150 m and at a distance of about 1.5 km. Methods: the theoretical foundations of this method are revealed. Information is provided on the procedure for performing transformations of coordina

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Suara, Gafar, and Timothy Oluwadare Idowu. "Optimum Techniques for the Conversion of Space Rectangular and Curvilinear Coordinates." European Journal of Engineering Research and Science 4, no. 10 (2019): 147–51. http://dx.doi.org/10.24018/ejers.2019.4.10.1588.

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Conversion between space rectangular (X, Y, Z) and curvilinear (φ, λ, h) coordinates is an important task in the field of Surveying, geodesy, positioning, navigation, mapping etc. Different techniques which include iterative methods, non-iterative techniques and closed form algebraic methods have been applied over the years to carry out the coordinate conversion. However, the results obtained using these techniques are deficient in one way or the other due to the inherent limitations such as inability to produce results for curvilinear coordinates when the values of X, Y and Z are subsequently

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Suara, Gafar, and Timothy Oluwadare Idowu. "Optimum Techniques for the Conversion of Space Rectangular and Curvilinear Coordinates." European Journal of Engineering and Technology Research 4, no. 10 (2019): 147–51. http://dx.doi.org/10.24018/ejeng.2019.4.10.1588.

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Conversion between space rectangular (X, Y, Z) and curvilinear (?, ?, h) coordinates is an important task in the field of Surveying, geodesy, positioning, navigation, mapping etc. Different techniques which include iterative methods, non-iterative techniques and closed form algebraic methods have been applied over the years to carry out the coordinate conversion. However, the results obtained using these techniques are deficient in one way or the other due to the inherent limitations such as inability to produce results for curvilinear coordinates when the values of X, Y and Z are subsequently

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Fišerová, Eva, Sandra Donevska, Karel Hron, Ondřej Bábek, and Kristýna Vaňkátová. "Practical Aspects of Log-ratio Coordinate Representations in Regression with Compositional Response." Measurement Science Review 16, no. 5 (2016): 235–43. http://dx.doi.org/10.1515/msr-2016-0029.

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AbstractRegression analysis with compositional response, observations carrying relative information, is an appropriate tool for statistical modelling in many scientific areas (e.g. medicine, geochemistry, geology, economics). Even though this technique has been recently intensively studied, there are still some practical aspects that deserve to be further analysed. Here we discuss the issue related to the coordinate representation of compositional data. It is shown that linear relation between particular orthonormal coordinates and centred log-ratio coordinates can be utilized to simplify the

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Li, Suhua, Jiacheng Xie, Xuewen Wang, Fang Ren, Xin Zhang, and Qingbao Bao. "Path Planning of Hydraulic Support Pushing Mechanism Based on Extreme Learning Machine and Descartes Path Planning." Symmetry 13, no. 1 (2021): 97. http://dx.doi.org/10.3390/sym13010097.

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As a floating system connecting hydraulic support and scraper conveyor, the path planning of pushing mechanism is of great significance for their coordinated movement. In this paper, a method for path planning of hydraulic support pushing mechanism based on extreme learning machine (ELM) and Descartes path planning is proposed. According to the motion characteristics of moving mechanism, it is transformed into industrial robot model, based on the characteristics of the coordinates of the key points on the ear seat of the scraper conveyor when advancing, a prediction method of the key points co

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Li, Suhua, Jiacheng Xie, Xuewen Wang, Fang Ren, Xin Zhang, and Qingbao Bao. "Path Planning of Hydraulic Support Pushing Mechanism Based on Extreme Learning Machine and Descartes Path Planning." Symmetry 13, no. 1 (2021): 97. http://dx.doi.org/10.3390/sym13010097.

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As a floating system connecting hydraulic support and scraper conveyor, the path planning of pushing mechanism is of great significance for their coordinated movement. In this paper, a method for path planning of hydraulic support pushing mechanism based on extreme learning machine (ELM) and Descartes path planning is proposed. According to the motion characteristics of moving mechanism, it is transformed into industrial robot model, based on the characteristics of the coordinates of the key points on the ear seat of the scraper conveyor when advancing, a prediction method of the key points co

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Kuzikov, Sergey, D. V. Kenigsberg, Yuliya Salamatina, and O. A. Prokhorov. "Comparison of Methods for Computing Highly Accurate Daily GNSS Positions." Civil Engineering Journal 9, no. 2 (2023): 305–18. http://dx.doi.org/10.28991/cej-2023-09-02-04.

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In Central Asia, the level of geodynamic displacements of the Earth's crust does not significantly exceed the accuracy of their measurement methods. Therefore, we need to choose the most accurate methods of calculating coordinates for cosmogeodetic stations. In this work, based on the data of 8 days of GPS measurements at 10 stations, 7 sets of average daily geocentric XYZ coordinates were calculated using different methods. To determine the positions, we used 3 calculation methods in the GAMIT/GLOBK program, 2 methods in the Bernese GNSS software, and 2 web services. To estimate the differenc

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Alexandrov, Sergei, Elena Lyamina, and Prashant Date. "A Method of Calculating Principal Stress Trajectories in Powder and Porous Materials Obeying a Piece-wise Linear Yield Criterion." MATEC Web of Conferences 220 (2018): 01002. http://dx.doi.org/10.1051/matecconf/201822001002.

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The present paper deals with the system of equations comprising the pyramid yield criterion together with the stress equilibrium equations under plane strain conditions. The stress equilibrium equations are written relative to a coordinate system in which the coordinate curves coincide with the trajectories of the principal stress directions. The general solution of the system is found giving a relation connecting the two scale factors for the coordinate curves. This relation is used for developing a method for finding the mapping between the principal lines and Cartesian coordinates with the

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Larry D, Edmonds. "An Alternate Presentation of a Generalization of the Lorentz Transformation to Allow Acceleration of a Coordinate System." International Journal of Physics Research and Applications 8, no. 6 (2025): 178–210. https://doi.org/10.29328/journal.ijpra.1001127.

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The traditional version of the Lorentz transformation is used to relate the coordinates of an event (a point in space-time) between different inertial coordinate systems in the absence of any gravitational effects. It is limited to those cases in which both reference frames are inertial, so they have a constant velocity relative to each other. By utilizing postulates regarding the equivalence between coordinates measured in an accelerating reference frame and coordinates measured in a reference frame instantaneously at rest with the accelerating frame, together with the traditional version of

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