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The creation of a map projection involves two steps: Selection of a model for the shape of the Earth or planetary body (usually choosing between a sphere or ellipsoid). Because the Earth's actual shape is irregular, information is lost in this step. Transformation of geographic coordinates (longitude and latitude) to Cartesian (x, y) or polar (r, θ) plane coordinates. In large-scale maps ...
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 ...
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 ...
For exact latitude and longitude translations Geohash is a spatial index of base 4, because it transforms the continuous latitude and longitude space coordinates into a hierarchical discrete grid, using a recurrent four-partition of the space. To be a compact code it uses base 32 and represents its values by the following alphabet, that is the "standard textual representation".
Formulas for the Web Mercator are fundamentally the same as for the standard spherical Mercator, but before applying zoom, the "world coordinates" are adjusted such that the upper left corner is (0, 0) and the lower right corner is ( , ): [7] where is the longitude in radians and is geodetic latitude in radians. [8] Because the Mercator projects the poles at infinity, a map using the Web ...
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 ...
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.