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and λ is the longitude, λ 0 is the central meridian, φ is the latitude, and R is the radius of the globe to be projected. The map has area 4 π R 2, conforming to the surface area of the generating globe. The x-coordinate has a range of [−2R √ 2, 2R √ 2], and the y-coordinate has a range of [−R √ 2, R √ 2].
They are written in terms of longitude (λ) and latitude (φ) on the sphere. Define the radius of the sphere R and the center point (and origin) of the projection (λ 0, φ 0). The equations for the orthographic projection onto the (x, y) tangent plane reduce to the following: [1]
In cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. [ 1][ 2][ 3] In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. [ 4][ 5 ...
v. t. e. A projected coordinate system – also called a projected coordinate reference system, planar coordinate system, or grid reference system – is a type of spatial reference system that represents locations on Earth using Cartesian coordinates ( x, y) on a planar surface created by a particular map projection. [ 1]
Equirectangular projection. Equirectangular projection of the world; the standard parallel is the equator (plate carrée projection). Height map of planet Earth at 2km per pixel, including oceanic bathymetry information, normalized as 8-bit grayscale. Because of its easy conversion between x, y pixel information and lat-lon, maps like these are ...
v. t. e. A geographic coordinate system ( GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on Earth as latitude and longitude. [ 1] It is the simplest, oldest and most widely used of the various spatial reference systems that are in use, and forms the basis for most others.
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified by three real numbers: the radial distance r along the radial line connecting the point to the fixed point of origin; the polar angle θ between the radial line and a polar axis; and the ...
Ecliptic latitude or celestial latitude (symbols: heliocentric b, geocentric β ), measures the angular distance of an object from the ecliptic towards the north (positive) or south (negative) ecliptic pole. For example, the north ecliptic pole has a celestial latitude of +90°. Ecliptic latitude for "fixed stars" is not affected by precession.