scholarly journals A New Coordinate System for Constructing Spherical Grid Systems

2020 ◽  
Vol 10 (2) ◽  
pp. 655
Author(s):  
Kin Lei ◽  
Dongxu Qi ◽  
Xiaolin Tian
Keyword(s):  
Coordinate System ◽  
Spatial Data ◽  
Spherical Surface ◽  
Planetary Science ◽  
Barycentric Coordinates ◽  
Global Coordinate System ◽  
Simple Relationship ◽  
Grid System ◽  
Grid Systems ◽  
Spherical Data

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.

scholarly journals THE TRANSFORM BETWEEN GEOGRAPHIC COORDINATES AND LOCATION CODES OF APERTURE 4 HEXAGONAL GRID SYSTEM

2017 ◽  
Vol XLII-2/W7 ◽  
pp. 161-167 ◽  
Author(s):  
R. Wang ◽  
J. Ben ◽  
Y. Li ◽  
L. Du
Keyword(s):  
Spatial Data ◽  
Data Model ◽  
Geospatial Data ◽  
Grid System ◽  
Hexagonal Grid ◽  
Encoding Scheme ◽  
Global System ◽  
Grid Systems ◽  
Grid Codes ◽  
Global Grid

Discrete global grid system is a new data model which supports the fusion processing of multi-source geospatial data. In discrete global grid systems, all cell operations can be completed by codes theoretically, but most of current spatial data are in the forms of geographic coordinates and projected coordinates. It is necessary to study the transform between geographic coordinates and grid codes, which will support data entering and getting out of the systems. This paper chooses the icosahedral hexagonal discrete global system as a base, and builds the mapping relationships between the sphere and the icosahedron. Then an encoding scheme of planar aperture 4 hexagonal grid system is designed and applied to the icosahedron. Basing on this, a new algorithm of transforms between geographic coordinates and grid codes is designed. Finally, experiments test the accuracy and efficiency of this algorithm. The efficiency of code addition of HLQT is about 5 times the efficiency of code addition of HQBS.

scholarly journals A Universal Generating Algorithm of the Polyhedral Discrete Grid Based on Unit Duplication

2019 ◽  
Vol 8 (3) ◽  
pp. 146 ◽  
Author(s):  
Li Meng ◽  
Xiaochong Tong ◽  
Shuaibo Fan ◽  
Chengqi Cheng ◽  
Bo Chen ◽  
...  
Keyword(s):  
Coordinate System ◽  
Grid Cell ◽  
Triangular Grid ◽  
Grid System ◽  
Rectangular Coordinate System ◽  
Factors Affecting ◽  
Grid Systems ◽  
Starting Point ◽  
Rectangular Coordinates ◽  
Discrete Grid

Based on the analysis of the problems in the generation algorithm of discrete grid systems domestically and abroad, a new universal algorithm for the unit duplication of a polyhedral discrete grid is proposed, and its core is “simple unit replication + effective region restriction”. First, the grid coordinate system and the corresponding spatial rectangular coordinate system are established to determine the rectangular coordinates of any grid cell node. Then, the type of the subdivision grid system to be calculated is determined to identify the three key factors affecting the grid types, which are the position of the starting point, the length of the starting edge, and the direction of the starting edge. On this basis, the effective boundary of a multiscale grid can be determined and the grid coordinates of a multiscale grid can be obtained. A one-to-one correspondence between the multiscale grids and subdivision types can be established. Through the appropriate rotation, translation and scaling of the multiscale grid, the node coordinates of a single triangular grid system are calculated, and the relationships between the nodes of different levels are established. Finally, this paper takes a hexagonal grid as an example to carry out the experiment verifications by converting a single triangular grid system (plane) directly to a single triangular grid with a positive icosahedral surface to generate a positive icosahedral surface grid. The experimental results show that the algorithm has good universality and can generate the multiscale grid of an arbitrary grid configuration by adjusting the corresponding starting transformation parameters.

Shoulder Joint Motion Analysis of Daily Living Activities Using a Global Coordinate System

2013 ◽  
Vol 50 (10) ◽  
pp. 840-844
Author(s):  
Yukiya INOUE ◽  
Mayumi KIHARA ◽  
Junko YOSHIMURA ◽  
Naoki YOSHIDA ◽  
Kenji MATSUMOTO ◽  
...  
Keyword(s):  
Coordinate System ◽  
Motion Analysis ◽  
Shoulder Joint ◽  
Daily Living ◽  
Global Coordinate System ◽  
Joint Motion ◽  
Daily Living Activities

Technique for relation global reference system and local realization of global reference system by continuously operated reference stations

2020 ◽  
Vol 962 (8) ◽  
pp. 24-37
Author(s):  
V.E. Tereshchenko
Keyword(s):  
Coordinate System ◽  
Russian Federation ◽  
Reference System ◽  
Main Part ◽  
Precise Point Positioning ◽  
Global Coordinate System ◽  
Coordinate Systems ◽  
Novosibirsk Region ◽  
The Russian Federation

The article suggests a technique for relation global kinematic reference system and local static realization of global reference system by regional continuously operated reference stations (CORS) network. On the example of regional CORS network located in the Novosibirsk Region (CORS NSO) the relation parameters of the global reference system WGS-84 and its local static realization by CORS NSO network at the epoch of fixing stations coordinates in catalog are calculated. With the realization of this technique, the main parameters to be determined are the speed of displacement one system center relativly to another and the speeds of rotation the coordinate axes of one system relatively to another, since the time evolution of most stations in the Russian Federation is not currently provided. The article shows the scale factor for relation determination of coordinate systems is not always necessary to consider. The technique described in the article also allows detecting the errors in determining the coordinates of CORS network in global coordinate system and compensate for them. A systematic error of determining and fixing the CORS NSO coordinates in global coordinate system was detected. It is noted that the main part of the error falls on the altitude component and reaches 12 cm. The proposed technique creates conditions for practical use of the advanced method Precise Point Positioning (PPP) in some regions of the Russian Federation. Also the technique will ensure consistent PPP method results with the results of the most commonly used in the Russian Federation other post-processing methods of high-precision positioning.

Consistent co-rotational framework for Euler-Bernoulli and Timoshenko beam-column elements under distributed member loads

2021 ◽  
pp. 136943322098663
Author(s):  
Yi-Qun Tang ◽  
Wen-Feng Chen ◽  
Yao-Peng Liu ◽  
Siu-Lai Chan
Keyword(s):  
Coordinate System ◽  
Stiffness Matrix ◽  
Traditional Method ◽  
Local Coordinate System ◽  
Frame Structures ◽  
Global Coordinate System ◽  
Single Element ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Geometric Stiffness

Conventional co-rotational formulations for geometrically nonlinear analysis are based on the assumption that the finite element is only subjected to nodal loads and as a result, they are not accurate for the elements under distributed member loads. The magnitude and direction of member loads are treated as constant in the global coordinate system, but they are essentially varying in the local coordinate system for the element undergoing a large rigid body rotation, leading to the change of nodal moments at element ends. Thus, there is a need to improve the co-rotational formulations to allow for the effect. This paper proposes a new consistent co-rotational formulation for both Euler-Bernoulli and Timoshenko two-dimensional beam-column elements subjected to distributed member loads. It is found that the equivalent nodal moments are affected by the element geometric change and consequently contribute to a part of geometric stiffness matrix. From this study, the results of both eigenvalue buckling and second-order direct analyses will be significantly improved. Several examples are used to verify the proposed formulation with comparison of the traditional method, which demonstrate the accuracy and reliability of the proposed method in buckling analysis of frame structures under distributed member loads using a single element per member.

scholarly journals Visual-Inertial Odometer-Based Global High Precision Indoor Human Navigation in a University Library

2019 ◽  
Vol 1 ◽  
pp. 1-2
Author(s):  
Shinpei Ito ◽  
Akinori Takahashi ◽  
Ruochen Si ◽  
Masatoshi Arikawa
Keyword(s):  
Coordinate System ◽  
High Precision ◽  
Real World ◽  
Indoor Navigation ◽  
Experimental Result ◽  
Coordinate Space ◽  
Central Position ◽  
Global Coordinate System ◽  
Prototype System ◽  
3D Environments

<p><strong>Abstract.</strong> AR (Augmented Reality) could be realized as a basic and high-level function on latest smartphones with a reasonable price. AR enables users to experience consistent three-dimensional (3D) spaces co-existing with 3D real and virtual objects with sensing real 3D environments and reconstructing them in the virtual world through a camera. The accuracy of sensing real 3D environments using an AR function, that is, visual-inertial odometer, of a smartphone is extremely higher than one of a GPS receiver on it, and can be less than one centimeter. However, current common AR applications generally focus on “small” real 3D spaces, not large real 3D spaces. In other words, most of the current AR applications are not designed for uses based on a geographic coordinate system.</p><p>We proposed a global extension of the visual-inertial odometer with an image recognition function of geo-referenced image markers installed in real 3D spaces. Examples of geo-referenced image markers can be generated from analog guide boards existing in the real world. We tested this framework of a global extension of the visual-inertial odometer embedded in a smartphone on the first floor in the central library of Akita University. The geo-referenced image markers such as floor map boards and book categories sign boards were registered in a database of 3D geo-referenced real-world scene images. Our prototype system developed on a smartphone, that is, iPhone XS, Apple Inc., could first recognized a floor map board (Fig. 1), and could determine the 3D precise distance and direction of the smartphone from the central position of the floor map board in a local 3D coordinate space with the origin point as the central positon of the board. Then, the system could convert the relative precise position and the relative direction of the smartphone’s camera in a local coordinate space into a global precise location and orientation of it. A subject was walking the first floor in the building of the library with a world tracking function of the smartphone. The experimental result shows that the error of tracking a real 3D space of a global coordinate system was accumulated, but not bad. The accumulated error was only about 30 centimeters after the subject’s walking about 30 meters (Fig. 2). We are now planning to improve our prototype system in the accuracy of indoor navigation with calibrating the location and orientation of a smartphone based sequential recognitions of multiple referenced scene image markers which have already existed for a general user services of the library before developing this proposed new services. As the conclusion, the experiment’s result of testing our prototype system was impressive, we are now preparing a more practical high-precision LBS which enables a user to be navigated to the exact location of a book of a user’s interest in a bookshelf on a floor with AR and floor map interfaces.</p>

scholarly journals Updating of digital topographic maps in the new national spatial coordinate system: case Fergana valley in Uzbekistan

2021 ◽  
Vol 4 ◽  
pp. 1-5
Author(s):  
Dilbarkhon Fazilova ◽  
Hasan Magdiev
Keyword(s):  
Coordinate System ◽  
Spatial Data ◽  
Information Technologies ◽  
Satellite System ◽  
Topographic Maps ◽  
The North ◽  
New Information ◽  
Global Navigation Satellite ◽  
Geodetic Coordinate System ◽  
Geocentric Coordinate System

Abstract. The classical geodetic coordinate system (CS42) in Uzbekistan uses the Krasovsky ellipsoid. The implementation of new information technologies, such as the Global Navigation Satellite System, became the basis for the development of a new national open geocentric coordinate system. This paper describes the development of a distortion grid for transforming horizontal spatial data from the local geodetic datum CS42 to a geocentric datum WGS84 for 1:100000 scale maps of the Fergana Valley in Uzbekistan. A first version of the distortion grid file has been created for transforming between CS42 and WGS84 for the whole territory of the country. The significant influence of the longitudinal drift of the region has been confirmed. The grid was used to transform topographic maps at a scale of 1:100000 for the Fergana Valley. Changing the map datum has shifted the grid of coordinate systems by 70 m in the East and 7 m in the North.

Rolling Condition and Gyroscopic Moments in Curve Negotiations

2012 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Martin B. Hamper ◽  
James J. O’Shea
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
The Body ◽  
Contact Forces ◽  
Body Motion ◽  
Global Coordinate System ◽  
Gyroscopic Moment ◽  
Absolute Angular Velocity ◽  
Pure Rolling ◽  
The Stability

In vehicle system dynamics, the effect of the gyroscopic moments can be significant during curve negotiations. The absolute angular velocity of the body can be expressed as the sum of two vectors; one vector is due to the curvature of the curve, while the second vector is due to the rate of changes of the angles that define the orientation of the body with respect to a coordinate system that follows the body motion. In this paper, the configuration of the body in the global coordinate system is defined using the trajectory coordinates in order to examine the effect of the gyroscopic moments in the case of curve negotiations. These coordinates consist of arc length, two relative translations and three relative angles. The relative translations and relative angles are defined with respect to a trajectory coordinate system that follows the motion of the body on the curve. It is shown that when the yaw and roll angles relative to the trajectory coordinate system are constrained and the motion is predominantly rolling, the effect of the gyroscopic moment on the motion becomes negligible, and in the case of pure rolling and zero yaw and roll angles, the generalized gyroscopic moment associated with the system degrees of freedom becomes identically zero. The analysis presented in this investigation sheds light on the danger of using derailment criteria that are not obtained using laws of motion, and therefore, such criteria should not be used in judging the stability of railroad vehicle systems. Furthermore, The analysis presented in this paper shows that the roll moment which can have a significant effect on the wheel/rail contact forces depends on the forward velocity in the case of curve negotiations. For this reason, roller rigs that do not allow for the wheelset forward velocity cannot capture these moment components, and therefore, cannot be used in the analysis of curve negotiations. A model of a suspended railroad wheelset is used in this investigation to study the gyroscopic effect during curve negotiations.

Applications of the Global Coordinate System

2011 ◽  
Author(s):  
Yves Balasko
Keyword(s):  
Coordinate System ◽  
Critical Points ◽  
Global Coordinate System ◽  
Coordinate Systems ◽  
Analytical Characterization ◽  
Equilibrium Manifold ◽  
System P ◽  
Definition Of

The global coordinate system for the equilibrium manifold follows from: (1) the determination of the unique fiber F(b) through the equilibrium (ρ‎, ω‎) where b = φ‎((ρ‎, ω‎) = (ρ‎, ρ‎ · ρ‎1, …, ρ‎ · ρ‎m); and (2) the determination of the location of the equilibrium (ρ‎, ω‎) within the fiber F(b) viewed as a linear space of dimension (ℓ − 1)(m − 1) and, therefore, parameterized by (ℓ − 1)(m − 1) coordinates. If there is little leeway in determining the fiber F(b) through the equilibrium (ρ‎, ω‎), there are different ways of representing the equilibrium (ρ‎, ω‎) within its fiber F(b). This leads to the definition of coordinate systems (A) and (B) for the equilibrium manifold. This chapter defines these two coordinate systems and applies them to obtain an analytical characterization of the critical equilibria, i.e., the critical points of the natural projection.

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