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Journal articles on the topic 'Coordinates'
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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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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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Eckermann, Stephen. "Hybrid σ–p Coordinate Choices for a Global Model." Monthly Weather Review 137, no. 1 (January 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 reduce stratospheric errors in models due to vertical truncation effects in the computation of the pressure gradient force over steep terrain. When implemented in a global model, the new coordinates significantly reduce vorticity and divergence errors at all altitudes in idealized simulations. In forecasting experiments with a global model, the new coordinates slightly reduce the stability of the semi-implicit time scheme. Resetting the reference pressure in the scheme to ∼800 hPa solves the problem for every coordinate except the Sangster–Arakawa–Lamb hybrid, which remains intrinsically less stable than the others. Impacts of different coordinates on forecast skill are neutral or weakly positive, with the new hybrid coordinates yielding slight improvements relative to earlier hybrid choices. This essentially neutral impact indirectly endorses the wide variety of hybrid coordinate choices currently used in NWP and climate models, with the proviso that these tests do not address the impact over longer time scales or on data assimilation.
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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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Shanurov, G. A., and A. D. Manilova. "Mobile scanning complex positioning accuracy depending on the coordinate systems used." Geodesy and Cartography 919, no. 1 (February 20, 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 of similar investigations, but applied to a local area, limited by a mobile scanning complex surveying area. The accuracy of the mobile scanning complex coordinates is characterized by the mobile scanning complex coordinates errors cofactor matrix. It turned out that the local site sequential coordinate transformation procedure from one coordinate system to another coordinate system does not introduce any distortion into the mobile scanning complex coordinates.
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Tian, Haoxin, Xipeng Fang, Yubin Lan, Chenyang Ma, Huasheng Huang, Xiaoyang Lu, Dehua Zhao, Hanchao Liu, and Yali Zhang. "Extraction of Citrus Trees from UAV Remote Sensing Imagery Using YOLOv5s and Coordinate Transformation." Remote Sensing 14, no. 17 (August 26, 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 coordinate transformation. A high-precision orthophoto map of a citrus orchard was drawn from UAV remote sensing images. The YOLOv5 model was subsequently used to train the remote sensing dataset to efficiently identify the fruit trees and extract tree pixel coordinates from the orchard orthophoto map. According to the geographic information contained in the orthophoto map, the pixel coordinates were converted to UTM coordinates and the WGS84 coordinates of citrus trees were obtained using Gauss–Krüger inverse calculation. To simplify the coordinate conversion process and to improve the coordinate conversion efficiency, a coordinate conversion app was also developed to automatically implement the batch conversion of pixel coordinates to UTM coordinates and WGS84 coordinates. Results show that the Precision, Recall, and F1 Score for Scene 1 (after weeding) reach 0.89, 0.97, and 0.92, respectively; the Precision, Recall, and F1 Score for Scene 2 (before weeding) reach 0.91, 0.90 and 0.91, respectively. The accuracy of the orthophoto map generated using UAV remote sensing images is 0.15 m. The accuracy of converting pixel coordinates to UTM coordinates by the coordinate conversion app is reliable, and the accuracy of converting UTM coordinates to WGS84 coordinates is 0.01 m. The proposed method is capable of automatically obtaining the WGS84 coordinates of citrus trees with high precision.
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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 displacement components of latitudinal coordinate dy and longitudes is similar to the straight lines. The relationship of graphics between point displacement components of longitudinal coordinate dx and latitudinal coordinate dy, and the geodetic height is similar to the straight lines.
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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 displacement components of latitudinal coordinate dy and longitudes is similar to the straight lines. The relationship of graphics between point displacement components of longitudinal coordinate dx and latitudinal coordinate dy, and the geodetic height is similar to the straight lines.
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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 (June 2, 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 effectively used in modelling braking and traction dynamics. One of the objectives of this investigation is to demonstrate that by using track coordinate systems that can have an arbitrary motion, the trajectory coordinates can be used as the basis for developing computer algorithms for modelling braking and traction conditions. To this end, a set of six generalized trajectory coordinates is used to define the configuration of each rigid body in the railroad vehicle system. This set of coordinates consists of an arc length that represents the distance travelled by the body, and five relative coordinates that define the configuration of the body with respect to its track coordinate system. The independent non-linear state equations of motion associated with the trajectory coordinates are identified and integrated forward in time in order to determine the trajectory coordinates and velocities. The results obtained in this study show that when the track coordinate systems are allowed to have an arbitrary motion, the resulting set of trajectory coordinates can be used effectively in the study of braking and traction conditions. The results obtained using the trajectory coordinates are compared with the results obtained using the absolute Cartesian-coordinate-based formulations, which allow modelling braking and traction dynamics. In addition to this numerical validation of the trajectory coordinate formulation in braking scenarios, an experimental validation is also conducted using a roller test rig. The comparison presented in this study shows a good agreement between the obtained experimental and numerical results.
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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'; x2', y2', z2'; x3', y3', z3'; x4', y4', z4') in a hypothetical coordinate system (X', Y', Z') and the coordinates of the same points (x1, y1, z1; x2, y2, z2; x3, y3, z3; x4, y4, z4) in the coordinate system (X, Y, Z) to which the point clouds need to be transformed. Determination of constants a1, a2, a3, d, b1, b2, b3, e, c1, c2, c3, f through a system of equations. After determining the constants, the coordinates of points (x', y', z') in the hypothetical coordinate system (X', Y', Z') are calculated using equations where each equation expresses the coordinates of points (x', y', z') in terms of coordinates of points (x, y, z) in the coordinate system (X, Y, Z) and the determined constants. After performing the calculations, point clouds can be merged into a single coordinate system using the computed coordinates (x', y', z'). This methodology allows for the successful transformation of coordinate systems for point clouds in geophysical research. Findings. Analytical regularities have been established based on known coordinates of four points in both coordinate systems, allowing for the efficient transformation of a point cloud from one coordinate system to another. The originality. For the first time, precise analytical dependencies have been established that enable the efficient transformation of point clouds from one coordinate system to another using known coordinates of four points in both systems. Practical implementation. The obtained dependencies enable the efficient transformation of point clouds from one coordinate system to another using known coordinates of four points in both systems.
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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 (December 20, 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 article presents the the results of calculations of changes of coordinates of the same point in GSK-2011 and SC-95 in six-degree zones of Gauss projection. It was found that in each region values of the shifts changed to small ones. Therefore, it is possible to convert the coordinates of the points by the simplified formulae. For recalculation from the coordinates of GSK-2011 in SK-95 or local coordinate system (WCS) of the administrative district it is necessary to find the origin of coordinates, scale value and rotation of the coordinate axes. The error of the conversion shall not exceed 0,001 m. The coordinates of the initial point of the local coordinate system relative to the central meridian of the local coordinate system shall be added in the list of parameters of the transition from local coordinate system to the state one.
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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 the element type and inertial reference based.
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Rader, C. M. "Generating rectangular coordinates in polar coordinate order." IEEE Signal Processing Magazine 22, no. 6 (November 2005): 178–80. http://dx.doi.org/10.1109/msp.2005.1550199.
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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 (August 7, 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. Adjustments to the position coordinates were performed using Topcon Tools v8.2.3 software at a 1mm standard deviation. The adjusted coordinates of LISAG_KUMASI were used as the reference points to compute the positions of the LiSAGNet CORS in differential mode by using 24 hour data for 11 consecutive days. The GPS data covered DoY 284 to DoY 295 in 2021. The final positions of the CORS, computed by this approach, indicate some differences from the officially published coordinates of the same CORS, confirming the suspicion of inhomogeneity in the source coordinates used in determining the coordinates of the local CORS. Furthermore, a test network, consisting of five COR stations, was designed and used to address the coordinate inconsistencies in the officially published coordinates. Using the officially published coordinates as reference inputs, the ROVER I station was fixed by three different CORSs, thus resulting in average coordinate variabilities of 2.78m and 0.80m in the northing (N) and easting (E) directions, respectively. Through substitution, the coordinates computed in this study as reference inputs, namely, the ROVER I station, were fixed by the same three CORSs, thus resulting in a coordinate variability of 0.002m and 0.006m in the northing (N) and easting (E) directions, respectively. The analysis revealed inconsistencies and inhomogeneity in terms of the officially published coordinates. It is, therefore, recommended that the officially published coordinates of the CORS be replaced by the adjusted homogeneous and consistent values determined through the approach adopted in this study.
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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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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 (July 8, 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 the prediction of three-dimensional coordinates of space points. Findings The average measurement error of three-dimensional coordinates of space points at three-dimensional coordinate measuring system based on dual-PSD based on GA-BP neural network is relatively small. This method does not require considering the lens distortion and the non-linearity of PSD. It has simple structure and high precision and is suitable for three-dimensional coordinate measurement of space points. Originality/value A new three-dimensional coordinate measurement algorithm by optimizing BP neural network based on GA is proposed to predict three-dimensional coordinates of space points formed on three-dimensional coordinate measuring system based on dual-PSD.
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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 that, the directional accuracy by using the MapGis measurement frame point pixel coordinates is higher than that by using PhotoShop measurement;
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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 (November 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 reach 1 m. For a group of stations global coordinates transformation into a local reference frame leads to the effect of coordinate stabilization and increases their relative precision in the time series. As a result of such procedure, the level of maximum coordinate discrepancies between the methods decreased to 46%. Moreover, one of the methods of calculating coordinates has improved its convergence with the other methods by 80%. Based on the Euclidean distance method, the quality of the raw data for each station was evaluated. Thus, there is a group of 8 stations, for which the convergence of coordinates in different methods are approximately at the same level, and 2-3 times better than for the other 2 stations.
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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 defined on the differential manifold. Second, the method of local linear iterative alignment is used to align the manifold’s local coordinates into the manifold’s global coordinate. The experimental results presented in this paper show that the errors of noniterative alignment are considerably large and can be reduced to almost zero within the first two iterations. The large errors of noniterative/linear alignment verify the nonlinear nature of alignment and justify the necessity of iterative alignment.
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Wu, Shuai. "A Method for Calculating the Band Change of Gauss Projection Coordinates." Academic Journal of Science and Technology 5, no. 1 (March 8, 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 coordinates (x, y) and the geodetic coordinates (L, (B)), that is, the forward and reverse calculation formulas of Gauss projection. With the help of Gauss projection as a communication "bridge", the coordinate transformation calculation is studied from geodetic coordinate transformation, and its advantages and disadvantages are compared with other methods. Based on the 1954 Beijing coordinate system and 1980 Xi'an coordinate system commonly used in China, a geodetic coordinate conversion system is compiled using C # language, and the forward and inverse calculation of Gaussian projection is realized.
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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 (October 10, 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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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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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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Zängl, Günther. "An Adaptive Vertical Coordinate Formulation for a Nonhydrostatic Model with Flux-Form Equations." Monthly Weather Review 135, no. 1 (January 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 coordinate is used to emulate a hybrid isentropic system. Idealized tests in which the coordinate surfaces are artificially moved reveal that the ensuing spurious motions are small enough to be negligible in realistic applications. Mountain wave tests demonstrate that the hybrid coordinate remains numerically stable under strong forcing. However, the model layer distribution established with the hybrid isentropic coordinate is not optimal for representing the dynamics of breaking gravity waves because the vertical distance between the model levels tends to be too large in the wave breaking region. On the other hand, real case studies demonstrate that the hybrid coordinate significantly improves the representation of the tropopause because of enhanced vertical resolution in the tropopause region.
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Nesnov, Dmitriy. "Area of correct space coordination by normal conic coordinates." Geometry & Graphics 11, no. 3 (December 26, 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 example, a field with a rectilinear source is more convenient to refer to cylindrical coordinates, and a field with a point source - to spherical coordinates. Basically, the use of field theory in the study of physical processes by methods of applied geometry is limited to two classical curvilinear systems, although their presentation in arbitrary curvilinear coordinates is known. We will distinguish between global and local coordinate systems. The global system, as well as the coordinates of a point in this system, will be denoted by x, y, z. She is unchanging. The local system, as well as the coordinates of a point in this system, will be denoted by t, u, v. Local system variable. At each point in space belonging to the area of existence of the system, the local coordinate system is defined
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BOONSERM, PETARPA, and MATT VISSER. "BUCHDAHL-LIKE TRANSFORMATIONS FOR PERFECT FLUID SPHERES." International Journal of Modern Physics D 17, no. 01 (January 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 generalize our previous theorems, in isotropic coordinates we shall encounter a variant of the so-called "Buchdahl transformation," and in other coordinate systems (such as Gaussian polar coordinates, Synge isothermal coordinates, and Buchdahl coordinates) we shall find a number of more complex "Buchdahl-like transformations" and "solution-generating theorems" that may be used to investigate and classify the general-relativistic static perfect fluid sphere. Finally, by returning to general diagonal coordinates and making a suitable ansatz for the functional form of the metric components, we place the Buchdahl transformation in its most general possible setting.
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NAKAMURA, AKIRA. "SOME NOTES ON PARALLEL COORDINATE GRAMMARS." International Journal of Pattern Recognition and Artificial Intelligence 09, no. 05 (October 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 some properties of parallel coordinate grammars and examines a relationship between the sequential coordinate grammars and parallel ones.
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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 (December 8, 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 coordinate transform technique. Different from other techniques previously developed, no assumption in boundary condition at magnetic axis is used. This is consistent with the fact that there is no physical boundary at the magnetic axis. A flux coordinate system with poloidal coordinate chosen as the geometric poloidal angle is proposed. It conquers the difficulty in no definition of poloidal coordinate in flux coordinates at separatrix because of the singularity at x-point(s) in a divertor configuration. It also simplifies the process for computing poloidal flux coordinate during the iteration for solving the nonlinear GS equation. Non-uniform grids can be applied in both radial and poloidal coordinates, which allows it to increase the spacial resolution near x-point(s) in a divertor configuration. Based on the model proposed in this paper, a new Flux coordinates based EQuilibrium solver (FEQ) in tokamaks is developed. The numerical solutions from this code agree well with both the analytic Solov’ev solution and the numerical one from the EFIT code for a divertor configuration in the EAST tokamak. This code can be applied for simulating different equilibria with prescribed shape, pressure and current profiles, i.e. including both limiter and divertor configurations, positive triangularity and negative triangularity, different β, arbitrary magnetic shear profile etc. It provides a powerful and convenient fixed-boundary inverse equilibrium solver including both magnetic axis and separatrix in the solution for tokamak researches.
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Kilner, Steven J., and David L. Farnsworth. "Parabolic coordinates." Mathematical Gazette 105, no. 563 (June 21, 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 more easily studied.
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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 (May 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 general relativity and to prescribe the equations of motion for a quadrupole in a coordinate system adapted to its motion and then transform them to the laboratory coordinates. An example is given of another unusual feature: a quadrupole which is free of dipole terms in polar coordinates has dipole terms in Cartesian coordinates. It is shown that dipoles, electric dipoles, quadrupoles and electric quadrupoles can be defined without reference to a metric and in a coordinates-free manner. This is particularly useful given their complicated coordinate transformation.
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BINI, DONATO, LUCA LUSANNA, and BAHRAM MASHHOON. "LIMITATIONS OF RADAR COORDINATES." International Journal of Modern Physics D 14, no. 08 (August 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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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 (October 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 Leksell unit does occur but is rare. The magnitude of such slippage is typically within the error of the stereotactic system and coordinate reading. The authors noted that coordinate setting slippage is significantly correlated with patient weight.
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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 (January 16, 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 barycentric coordinates that describe the positions of points on a plane concerning the vertices of a given planar triangle; analogously, spherical area coordinates (SACs) describe the positions of points on a sphere concerning the vertices of a given spherical triangle. In particular, the global coordinate system is obtained by decomposing the globe into several identical triangular regions, constructing local coordinates for each region, and then combining them. Once the SACs have been established, the coordinate isolines form a new class of global grid systems. This kind of grid system has some useful properties: the grid cells exhaustively cover the globe without overlapping and have the same shape, and the grid system has a congruent hierarchical structure and simple relationship with traditional coordinates. These beneficial characteristics are suitable for organizing, representing, and analyzing spatial data.
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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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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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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 software for coordinate transformations in terms of single-stage and multi-stage transitions between ellipsoidal coordinates of different systems.
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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 and the same coordinates be used for both the kinematics and dynamics of a specific problem;3)adopt IAU recommendations specifying reference systems and time scales to be used in ephemeris astronomy.
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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 (March 29, 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 coordinate systems. The algorithm of the generalized reduced gradient (OPG) method is given. A study has been conducted on the transformation of coordinate systems of starting points from SK1 to SK2 using the OPG method. The requirement for the value of the mean square error (SQR) of determining the position of the starting points when converting them from one coordinate system to another is justified. Results: a check was performed on the possibility of applying the obtained transformation parameters to recalculate the coordinates of points from the local SC to the city SC. Based on the verification of the obtained transformation parameters, the possibility of using them to recalculate the coordinates of points located at a distance of about 1,5 km was revealed. The need for additional research on the application of the generalized reduced gradient method to solve coordinate system transformation problems has been identified. Practical significance: the necessity of transformation of coordinate systems in the field of construction of buildings and structures is shown. The possibility of applying the generalized reduced gradient method to transform coordinate systems is presented. Using this method will allow you to convert the coordinates of the starting points from the local coordinate system to the coordinate system of the city with geodetic support for the construction of buildings and structures of various categories.
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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 (January 8, 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 coordinates based on ELM is proposed, so the target location of the end-effector is obtained. The path of the joint is determined by polynomial path partition and Descartes path planning method. The path is modified by Gaussian filtering method, and the peak value of path obtained by planning is filtered out, and the path correction is realized. Finally, the virtual simulation test is carried out in Unity3D. The planned coordinate curve has Poisson-like distribution and approximately around the target coordinate curve, and local error and correction error are within 2 cm and 0.1 cm, respectively. The coordinate curve obtained by combining planning and correction has a better effect.
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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 (January 8, 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 coordinates based on ELM is proposed, so the target location of the end-effector is obtained. The path of the joint is determined by polynomial path partition and Descartes path planning method. The path is modified by Gaussian filtering method, and the peak value of path obtained by planning is filtered out, and the path correction is realized. Finally, the virtual simulation test is carried out in Unity3D. The planned coordinate curve has Poisson-like distribution and approximately around the target coordinate curve, and local error and correction error are within 2 cm and 0.1 cm, respectively. The coordinate curve obtained by combining planning and correction has a better effect.
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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 (October 28, 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 or simultaneously equal to zero. Therefore, this study attempts to put forth an optimum coordinate conversion technique between space rectangular and curvilinear coordinates. The data used are coordinates of points which include the space rectangular coordinates and their equivalent curvilinear coordinates. They were observed and processed in Nigeria using Doppler 9 software by African Doppler Survey (ADOS) and they were confirmed to be of first order accuracy and hence of high quality. The data processing involved the design of the optimum techniques equations, coding of the algorithms and necessary computations to obtain results. Analyzing the results obtained, it can be inferred that the designed optimum model has successfully carried out the conversion between space rectangular and curvilinear coordinates. Therefore, the optimum technique model is recommended for use for the conversions from Space rectangular coordinates to Geocentric, Geodetic, Reduced coordinates and vice versa.
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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 (October 28, 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 or simultaneously equal to zero. Therefore, this study attempts to put forth an optimum coordinate conversion technique between space rectangular and curvilinear coordinates. The data used are coordinates of points which include the space rectangular coordinates and their equivalent curvilinear coordinates. They were observed and processed in Nigeria using Doppler 9 software by African Doppler Survey (ADOS) and they were confirmed to be of first order accuracy and hence of high quality. The data processing involved the design of the optimum techniques equations, coding of the algorithms and necessary computations to obtain results. Analyzing the results obtained, it can be inferred that the designed optimum model has successfully carried out the conversion between space rectangular and curvilinear coordinates. Therefore, the optimum technique model is recommended for use for the conversions from Space rectangular coordinates to Geocentric, Geodetic, Reduced coordinates and vice versa.
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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 (October 1, 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 computation concerning regression parameters estimation and hypothesis testing. To enhance interpretation of regression parameters, the orthogonal coordinates and their relation with orthonormal and centred log-ratio coordinates are presented. Further we discuss the quality of prediction in different coordinate system. It is shown that the mean squared error (MSE) for orthonormal coordinates is less or equal to the MSE for log-transformed data. Finally, an illustrative real-world example from geology is presented.
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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 (February 1, 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 differences between 7 coordinate sets, we used parameters based on the Euclidean distance between these coordinate samples. The difference analysis of all pair combinations for 7 coordinate sets was carried out by 3D radius vectors, individual coordinate axes, and individual observation stations. The calculations showed that the positioning accuracy and precision depended not only on the coordinate calculation method but also on the selected reference frame. Methods using the international terrestrial reference frame (ITRF) provide station positions with regular deviations of <2 mm and individual deviations up to 5 cm. Methods using the regional and "point" reference frames have regular discrepancies for individual coordinates up to 2 cm and maximum deviations up to 1 m. Converting XYZ coordinates to UVW with the local reference frame reduces the difference between UVW sets by at least 25%. Due to the spatial orientation relative to the studied stations, the X (U) coordinate is reproduced 2-3 times with smaller deviations than other coordinates. The average deviation level of coordinate sets can be an indicator of the quality of conditions for receiving a GNSS signal at one station. We have identified the station group that has a coordinate deviation level several times lower than other stations. Doi: 10.28991/CEJ-2023-09-02-04 Full Text: PDF
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Gaur, Rudeep, and Matt Visser. "Cosmology in Painlevé-Gullstrand coordinates." Journal of Cosmology and Astroparticle Physics 2022, no. 09 (September 1, 2022): 030. http://dx.doi.org/10.1088/1475-7516/2022/09/030.
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Abstract Cosmology is most typically analyzed using standard co-moving coordinates, in which the galaxies are (on average, up to presumably small peculiar velocities) “at rest”, while “space” is expanding. But this is merely a specific coordinate choice; and it is important to realise that for certain purposes other, (sometimes radically, different) coordinate choices might also prove useful and informative, but without changing the underlying physics. Specifically, herein we shall consider the k= 0 spatially flat FLRW cosmology but in Painlevé-Gullstrand coordinates — these coordinates are very explicitly not co-moving: “space” is now no longer expanding, although the distance between galaxies is still certainly increasing. Working in these Painlevé-Gullstrand coordinates provides an alternate viewpoint on standard cosmology, and the symmetries thereof, and also makes it somewhat easier to handle cosmological horizons. With a longer view, we hope that investigating these Painlevé-Gullstrand coordinates might eventually provide a better framework for understanding large deviations from idealized FLRW spacetimes. We illustrate these issues with a careful look at the Kottler and McVittie spacetimes.
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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 use of a solution of a hyperbolic system of equations. In particular, the mapping between the principal lines and Cartesian coordinates is given in parametric form with the characteristic coordinates as parameters.
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Halimy, N. A. A., and N. J. Trilaksono. "Analysis of the influence hybrid mass coordinate on WRF-ARW models to the turbulence simulation of Batik airlines aviation (case study October 24, 2017)." IOP Conference Series: Earth and Environmental Science 893, no. 1 (November 1, 2021): 012032. http://dx.doi.org/10.1088/1755-1315/893/1/012032.
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Abstract The influence of hybrid sigma coordinate is better to represent turbulence in America than basic sigma coordinate. Therefore, it is necessary to search the effect of these coordinates on turbulence simulations in Indonesia due to the analysis of different atmospheric conditions from America. In this research, two experiments are performed using two different vertical coordinates with a case study flight turbulence from Batik Airlines on October 24, 2017. The two different vertical coordinates are the hybrid sigma coordinate and basic sigma coordinate. The data used are NCEP-FNL, Himawari-8 satellite image data, and sounding data. Based on the result of this research, simulation using hybrid sigma coordinate shows isentropic lines that have the potential turbulence during and after turbulence event. Richardson number value about 0.1 – 0.2 and intensity of the energy dissipation rate is 0.06 m 2/3s-1. According to the Richardson number value and intensity of the energy dissipation rate, the hybrid sigma coordinate simulation shows turbulence potential more significant than the basic sigma coordinate.
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Lee, Wooyoung, Minchul Lee, Myoungho Sunwoo, and Kichun Jo. "Fast Online Coordinate Correction of a Multi-Sensor for Object Identification in Autonomous Vehicles." Sensors 19, no. 9 (April 29, 2019): 2006. http://dx.doi.org/10.3390/s19092006.
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Multi-sensor perception systems may have mismatched coordinates between each sensor even if the sensor coordinates are converted to a common coordinate. This discrepancy can be due to the sensor noise, deformation of the sensor mount, and other factors. These mismatched coordinates can seriously affect the estimation of a distant object’s position and this error can result in problems with object identification. To overcome these problems, numerous coordinate correction methods have been studied to minimize coordinate mismatching, such as off-line sensor error modeling and real-time error estimation methods. The first approach, off-line sensor error modeling, cannot cope with the occurrence of a mismatched coordinate in real-time. The second approach, using real-time error estimation methods, has high computational complexity due to the singular value decomposition. Therefore, we present a fast online coordinate correction method based on a reduced sensor position error model with dominant parameters and estimate the parameters by using rapid math operations. By applying the fast coordinate correction method, we can reduce the computational effort within the necessary tolerance of the estimation error. By experiments, the computational effort was improved by up to 99.7% compared to the previous study, and regarding the object’s radar the identification problems were improved by 94.8%. We conclude that the proposed method provides sufficient correcting performance for autonomous driving applications when the multi-sensor coordinates are mismatched.
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IUKHNO, Alona, Dmytro SOPOV, and Dmytro HOPTSII. "PERFORMANCE OF ENGINEERING SURVEYS AS AN INTEGRAL PART OF LAND AND CADASTRE WORKS IN PREPARATION OF LAND PLOTS FOR REGISTRATION IN THE BASE OF THE STATE LAND CADASTER." Ukrainian Journal of Applied Economics 6, no. 3 (September 2, 2021): 273–80. http://dx.doi.org/10.36887/2415-8453-2021-3-37.
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Performing engineering surveys is a mandatory part of the development of technical documentation on land management. Surveys allow to confirm the accuracy of the performed geodetic or topographic survey. In particular, the accuracy of determining the geodetic coordinates of the turning points of the boundaries of the land, to link the turning points of the boundaries of the land to the geodetic points of the State Geodetic Network of Ukraine. The main purpose of the article is to reflect the main components of engineering surveys as part of land cadastral works in preparation of land for registration in the database of the State Land Cadastre. The coordinate basis for land management is the State Geodetic Reference Coordinate System USK-2000, the geodetic basis for land management – points of the State Geodetic Network 1-3 classes, points of geodetic networks of compaction 4 class, 1 and 2 categories, points of the surveying network. The coordinates of the points of the State Geodetic Network of Ukraine, geodetic networks of condensing and turning points of the boundaries of geospatial objects are determined by rectangular coordinates (x, y) in the Gauss-Krueger projection in the USC-2000 coordinate system or local coordinate systems. related to the USC-2000 coordinate system. The control of the differential field of coordinate corrections when working with the use of RTK technologies is carried out at least at the two nearest points of DGM and GMZ, the coordinates of which are obtained from the administrator of the geodetic data bank. The difference in the values of the coordinates of control points should not exceed 0.1 m in cities of regional importance, 0.2 m - in other cities and towns, 0.3 m - in rural areas and 0.5 m - outside the settlements. Keywords: engineering surveys, State Geodetic Network of Ukraine, land cadastral works, coordinate system, State Land Cadastre.
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Obidenko, V. I. "The methodology of geodetic supporting Russian Federation digital economy." Geodesy and Cartography 954, no. 12 (January 20, 2020): 42–55. http://dx.doi.org/10.22389/0016-7126-2019-954-12-42-55.
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In the article the researches on developing modern methodology of supporting the national program “Digital economy of the Russian Federation” with geospatial data and, first of all, its base component, the systems of coordinate support are presented. As the main sentences of upgrading coordinate support it is offered to pass to kinematic model of evolution of coordinates in the state coordinate system GSK-2011 completely. The coordinates in this model are to be given to the consumer not on some separate instants (an initial epoch of installation of a coordinate system, an epoch of the last adjustment etc.), but for the current date, using a federal network of differential geodetic stations as the main tool for implementing this methodology. In order to avoid inconveniences of application the reference system for practical operations (as the coordinates are time-dependent), it is offered to use the additional coordinate system, “fixed” to an appropriate tectonic plate, spun round Euler’s pole within the state reference system GSK-2011.