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The Earth and Its Coordinate System
Published in Terry A. Slocum, Robert B. McMaster, Fritz C. Kessler, Hugh H. Howard, Thematic Cartography and Geovisualization, 2022
Terry A. Slocum, Robert B. McMaster, Fritz C. Kessler, Hugh H. Howard
Finally, we introduce the field of geodesy, the science of understanding and measuring Earth's size and shape. Approximately 2,000 years ago, the Greek Eratosthenes was able to calculate the circumference of Earth as 40,500 kilometers (25,170 miles), a figure not far from our present-day value of 40,075 kilometers (24,906 miles). Determining the correct shape of Earth has proved more problematic, as it wasn't until about 300 years ago that Sir Isaac Newton suggested that Earth is an oblate spheroid or ellipsoid, bulging at the Equator due to centrifugal force. This ellipsoid concept extends to the reference ellipsoid as a solid body that more accurately defines Earth's shape than a simple spherical assumption. Advances in satellite technology have led to the concept that Earth is not a smooth, mathematically definable surface (as described by the reference ellipsoid) but due to differences in gravitational forces, can be modeled as a geoid—a shape that Earth would take on if the world's oceans were allowed to flow over the land, adjusting to the gravitational differences across its surface and creating a single undisturbed water body. A reference ellipsoid and a geoid are components that comprise a geodetic datum. A geodetic datum establishes the origin for latitude and longitude values as well as elevation and can be divided into a horizontal and vertical datum. More specifically, a horizontal datum is based on a reference ellipsoid that establishes the origin for latitude and longitude values for Earth's address system. On the other hand, a vertical datum is defined by the geoid, which establishes mean sea level and thus elevations across Earth's surface. One example of a geodetic datum that is used in the United States is the North American Datum 1983 (NAD83).
Global Navigation Satellite Systems (GNSS)
Published in Leonid Nadolinets, Eugene Levin, Daulet Akhmedov, Surveying Instruments and Technology, 2017
Leonid Nadolinets, Eugene Levin, Daulet Akhmedov
A further three angles of rotation φx, φy, φz and a scaling factor m (see Figure 6.15) may have to be added so that the complete transformation formula contains seven parameters. The geodetic datum specifies the location of a local three-dimensional Cartesian coordinate system with regard to the global system.
An integrated solution for reducing ill-conditioning and testing the results in non-linear 3D similarity transformations
Published in Inverse Problems in Science and Engineering, 2018
Some direct LS methods are developed under the rotational invariant situation (DLS, QBA, PGH, and PSH) and some under small rotational angles (DBW, DMB). Hence, while all of them can be used in geodetic datum transformation, some of them cannot in photogrammetry, remote sensing and computer-vision (DBW, DMB). Under rotational variant situations, we should be only employed LLS methods in the 3D-ST. In this paper, DLS (being one of the non-iterative methods) and LLS methods have also been compared to each other on the simulated data in the numerical example part of the paper and success of the LLS with respect to DLS has been demonstrated, as well. It is observed that the other non-iterative methods (PSH, PGH, and QBA) give the equivalence results to ones of LLS for the data used in the paper. LLS do not require iteration when the three methods are used to compute initial values of LLS. But, all non-iterative methods do need LLS for quality analysis, testing and improving their results in all circumstances (rotational invariant and variant structures).
3D-GIS Parametric Modelling for Virtual Urban Simulation Using CityEngine
Published in Annals of GIS, 2022
Ibrahim M. Badwi, Hisham M. Ellaithy, Hidi E. Youssef
The 2D-GIS data was prepared using the AutoCAD and ArcGIS 10.8 programs; the geodatabase consists of layers representing residential buildings, roads, walkways, schools, commercial markets, mosques, service buildings, parking areas, green spaces, and playgrounds. The geodatabase was projected based on the Egyptian Transverse Macerator Coordinate System (ETM), according to the Geodetic Datum, Helmert Ellipsoid 1906. Figure 15 shows the flowchart of the procedural modelling using CityEngine.-
The location of the Pink and White Terraces of Lake Rotomahana, New Zealand
Published in Journal of the Royal Society of New Zealand, 2019
The location of Hochstetter’s Station 21, derived from the above three plot lines, is within the triangle centred at, or close to, the following point (NZ Geodetic Datum 2000: NZ Transverse Mercator Projection, generated from the coordinate conversion tool at the website of Land Information New Zealand): latitude 38°16′00.9″S; longitude 176°25′48.3″E (Topo50 grid ref: E1900100 N5759000).