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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 ...
Orthographic projection in cartography has been used since antiquity. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective (or azimuthal) projection in which the sphere is projected onto a tangent plane or secant plane. The point of perspective for the orthographic projection is at infinite distance.
v. t. e. 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.
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].
Specifically, stereographic projection from the north pole (0,1) onto the x-axis gives a one-to-one correspondence between the rational number points (x, y) on the unit circle (with y ≠ 1) and the rational points of the x-axis. If ( m / n , 0) is a rational point on the x-axis, then its inverse stereographic projection is the point
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 ...
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]
On a Mercator projection map, any rhumb line is a straight line; a rhumb line can be drawn on such a map between any two points on Earth without going off the edge of the map. But theoretically a loxodrome can extend beyond the right edge of the map, where it then continues at the left edge with the same slope (assuming that the map covers ...