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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 ...
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].
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.
The stereographic projection, also known as the planisphere projection or the azimuthal conformal projection, is a conformal map projection whose use dates back to antiquity. Like the orthographic projection and gnomonic projection, the stereographic projection is an azimuthal projection, and when on a sphere, also a perspective projection .
Tissot's indicatrices illustrate linear, angular, and areal distortions of maps: A map distorts distances (linear distortion) wherever the quotient between the lengths of an infinitesimally short line as projected onto the projection surface, and as it originally is on the Earth model, deviates from 1. The quotient is called the scale factor.
Equal-area projection. In cartography, an equivalent, authalic, or equal-area projection is a map projection that preserves relative area measure between any and all map regions. Equivalent projections are widely used for thematic maps showing scenario distribution such as population, farmland distribution, forested areas, and so forth, because ...
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.
Stereographic projection of the unit sphere from the north pole onto the plane z = 0, shown here in cross section. The unit sphere S 2 in three-dimensional space R 3 is the set of points (x, y, z) such that x 2 + y 2 + z 2 = 1.