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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 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.
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 plate carrée (French, for flat square), [3] is the special case where is zero. This projection maps x to be the value of the longitude and y to be the value of the latitude, [4] and therefore is sometimes called the latitude/longitude or lat/lon (g) projection.
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 ...
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 projection is conventionally defined as: where λ is the longitude from the central meridian in degrees, φ is the latitude, and R is the radius of the globe used as the model of the earth for projection. For longitude given in radians, remove the π 180° factors.
The map projection and the Geographic coordinate system (GCS, latitude and longitude) date to the Hellenistic period, proliferating during the Enlightenment Era of the 18th century. However, their use as the basis for specifying precise locations, rather than latitude and longitude, is a 20th century innovation.