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Optical spaces are mathematical coordinate systems that facilitate the modelling of optical systems as mathematical transformations. An optical space is a mathematical coordinate system such as a Cartesian coordinate system associated with a refractive index. The analysis of optical systems is greatly simplified by the use of optical spaces ...
Another common coordinate system for the plane is the polar coordinate system. [7] A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line).
Geocentric coordinate systems used in geodesy can be divided naturally into two classes: The inertial reference systems, where the coordinate axes retain their orientation relative to the fixed stars or, equivalently, to the rotation axes of ideal gyroscopes. The X-axis points to the vernal equinox. The co-rotating reference systems (also ECEF ...
Coordinate systems in astronomy can specify an object's relative position in three-dimensional space or plot merely by its direction on a celestial sphere, if the object's distance is unknown or trivial. Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate system used on the surface of Earth.
For satellites orbiting the Earth it is normal to use the Equatorial coordinate system. The projection of the Earth's equator onto the celestial sphere is called the celestial equator . Similarly, the projections of the Earth's north and south geographic poles become the north and south celestial poles , respectively.
In the passive transformation (right), point P stays fixed, while the coordinate system rotates counterclockwise by an angle θ about its origin. The coordinates of P ′ after the active transformation relative to the original coordinate system are the same as the coordinates of P relative to the rotated coordinate system.
The Universal Transverse Mercator (UTM) is a map projection system for assigning coordinates to locations on the surface of the Earth.Like the traditional method of latitude and longitude, it is a horizontal position representation, which means it ignores altitude and treats the earth surface as a perfect ellipsoid.
On a Riemannian manifold, a normal coordinate system at p facilitates the introduction of a system of spherical coordinates, known as polar coordinates. These are the coordinates on M obtained by introducing the standard spherical coordinate system on the Euclidean space T p M .