Coordinate Systems

Coordinate systems describe positions in space with one or more numbers. Coordinates can specify position as distance along a route, distance and direction from an origin, the intersection of two axes on a plane, the intersection of three axes in space, the intersection of spherical or ellipsoidal angles on the surface of the Earth, range circle or sphere intersections, a combination of vertical height and horizontal angles, or location with respect to celestial objects at a specified date and time.

Coordinate systems are sometimes called absolute methods of specifying location, as opposed to relative methods such as street addresses or proximity to landmarks. For the most part, coordinate systems can be converted, with some degree of uncertainty, from one coordinate system to another.

One of the most common coordinate systems used in geography is that of longitude, latitude, and altitude with respect to a specified horizontal and vertical datum. The spherical or ellipsoidal system of longitude and latitude angles is difficult to use for distance, direction, shape, or area estimation because longitude and latitude are not orthogonal to each other, are not equally scaled, and do not maintain a fixed relationship between their angular and distance dimensions on Earth. The Earth Centered, Earth Fixed X, Y, Z system (ECEF) defines a three-dimensional (3D) orthogonal coordinate system with the center of mass of Earth as the origin. ECEF makes vector distances and directions easy to compute in space but does not define any Earth surface and so cannot be used to compute distances and directions over an Earth surface.

To facilitate wayfinding, navigation, mapping, surveying, pointing to place, and the easy and accurate computation of distance, directions, and area, coordinate systems map portions of the Earth on a flat surface. Some coordinate systems implicitly describe point positions, while others describe areas on a surface or volumes in space. Coordinate systems are defined for local surveys, engineering drawings, regional surveying, country mapping, designation of international borders, continental and global mapping and modeling of climate change, plate tectonics, seismic activity, and exploration and mapping in space.

Surveyors and engineers often consider regions spanning less than 20 km (kilometers) to be reasonably approximated by a flat plane on which distances and directions are not appreciably influenced by the curvature of the Earth. Within 20 km, the distance difference between a line on a flat plane and the surface of an ellipsoid is less than 1 cm (centimeter). Local plane coordinate systems are defined by a point of beginning (POB), with arbitrary X and Y values, and a base line (BL) defining the rotation of the local system. Coordinates are given for other points in the system through X and Y coordinates or distances and directions with respect to the POB and BL. If the POB and BL in the local system are known with respect to another coordinate system, it is often possible to convert from a local plane coordinate system to other regional or global systems.

Small countries, provinces, states, departments, or groups of counties are often mapped and surveyed with respect to coordinate systems that are based on map projections and projection parameters. These systems allow approximate distance and direction estimates to be made with the X and Y, or easting and northing coordinates for points. More exact values of distance and direction can be computed using correction values based on the position of points and lines within the projection system. The State Plane Coordinate Systems of the United States, the British National Grid, the Costa Rican National [Page 580]Grids, and the Qatar National Grid are examples. The British and Qatar national grids are based on Transverse Mercator projections, the Costa Rican grids are Lambert Conformal Conics, and the U.S. State Plane System is based on almost an equal number of Lambert Conformal Conic and Transverse Mercator grids and a single Oblique Mercator projection used for southeastern Alaska.

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