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The forward projection transforms spherical coordinates into planar coordinates. The reverse projection transforms from the plane back onto the sphere. The formulae presume a spherical model and use these definitions: is the longitude of the location to project; is the latitude of the location to project; are the standard parallels (north and south of the equator) where the scale of the ...
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. However, it differs from global latitude/longitude in that it divides earth ...
A cylindrical map projection is specified by formulae linking the geographic coordinates of latitude φ and longitude λ to Cartesian coordinates on the map with origin on the equator and x -axis along the equator.
The projection transforms from latitude and longitude to map coordinates x and y via the following equations: [5] where θ is an auxiliary angle defined by and λ is the longitude, λ0 is the central meridian, φ is the latitude, and R is the radius of the globe to be projected. The map has area 4 πR2, conforming to the surface area of the generating globe. The x -coordinate has a range of ...
The formulas for the spherical orthographic projection are derived using trigonometry. 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 (λ0, φ0). The equations for the orthographic projection onto the (x, y) tangent plane reduce to the following: [1] Latitudes beyond the range of ...
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] Projection is a necessary step in creating a two-dimensional ...
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. Although latitude and longitude form a coordinate tuple like a cartesian ...
The transverse Mercator map projection (TM, TMP) is an adaptation of the standard Mercator projection. The transverse version is widely used in national and international mapping systems around the world, including the Universal Transverse Mercator. When paired with a suitable geodetic datum, the transverse Mercator delivers high accuracy in zones less than a few degrees in east-west extent.