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Generally, a coordinate system is a system that uses one or more numbers, or coordinates, to locate the position of any point uniquely, line, place, or object concerning some reference system.
For example, the location of any place is obtained by placing its coordination on a map. That is what the global positioning system does since it is impossible to have a precisely defined address for each and everything in the world.
Types of Coordinate System:
The Coordinate system is a fundamental idea of defining the location in any system, and thus this system is altered according to the needs of the field. Here are a few prominent ones.
The simplest one is a Cartesian coordinate system, named for the 17th-century mathematician and philosopher René Descartes. A Cartesian coordinate system is simply a grid formed by placing two measurement scales or axes, one horizontal (X-axis) and one vertical (Y-axis). The point at which both X and Y values are zero is called the coordinate system's origin.
This is the case with the 2-Dimensional system. When higher dimensions are used, a greater number of scales came into the picture. Below is an example of 3 -Dimensional and 4- Dimensional Cartesian coordinate system.
A polar coordinate system is a two-dimensional coordinate system. Each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The polar coordinate system is an alternate coordinate system where the two variables are r and θ, instead of X and Y.
The polar grid is denoted as a series of concentric circles radiating out from the pole. A distance measured from the pole is called Radius (r). A ray from the pole in the reference direction is called the Polar axis. The reference point of the polar graph is known as Pole.
An angle measured from the polar axis, usually counter-clockwise, is called Angular coordinate (θ). This is only a 2-D system because we have only two coordinates.
The polar coordinate system is extended, resulting in the Cylindrical and the Spherical Coordinate system.
The Cylindrical-coordinate system involves an additional Z-axis as the one in the 3-D cartesian system. Giving coordinates as (r , θ, Z ).
The Spherical coordinate system is a 3-D extension of the Polar Coordinate system, which uses two angle coordinates (θ, φ) and one distance coordinate (ρ or r) to locate a point, that is (ρ, θ, φ) coordinates.
These are a few of the very important and widely used coordinate systems. The systems mentioned above are used in mathematics, Physics, and mostly for research purposes a few more are mentioned below.
Here, the coordinate lines may be curved. These coordinates can be derived from a set of Cartesian coordinates using a locally invertible transformation (a one-to-one map) at each point.
Coordinates here are defined as a set of d coordinates q = (q1, q2, ..., QD) in which the coordinate surfaces all meet at right angles.
A skew coordinate system is a curvilinear coordinate system where the coordinate surfaces are not orthogonal, in contrast to orthogonal coordinates.
This system represents a point in the plane by the logarithm of the distance from the origin and an angle measured from a reference line intersecting the origin.
It is a coordinate system in which a point's location is specified by reference to a simplex (a triangle for points in a plane, a tetrahedron for points in three-dimensional space, etc.). The barycentric coordinates of a point can be interpreted as masses placed at the simplex vertices, such that the point is the center of mass (or barycentre) of these masses.
Here, the direction in which your hand closes to make a fist in the direction of a positive rotation around an axis signified by the extended right-hand thumb.
Here, the direction in which your hand closes to make a fist in the direction of a positive rotation around an axis signified by the extended left-hand thumb.
Other than the systems mentioned above, a coordinate system is used to locate points on Earth.
A geographic coordinate system is a 3-dimensional reference system that locates points on the Earth's surface. The unit of measure is usually decimal degrees. A point has two coordinates: latitude and longitude. Latitude and longitude measure angles.
Latitude is defined as the angle formed by the intersection of a line perpendicular to the Earth's surface at a point and the Equator's plane. Latitude values range from -90 to +90 degrees.
A meridian, or line of longitude, is formed by a plane that passes through the point and the North and South poles.
A geographic coordinate system has the following components:
Author: Sayalee Kahandal for ThinkRobotics