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Therefore, more generally, a map projection is any method of flattening a continuous curved surface onto a plane. [citation needed] The most well-known map projection is the Mercator projection. [7]: 45 This map projection has the property of being conformal. However, it has been criticized throughout the 20th century for enlarging regions ...
The stereographic projection has been used to map spherical panoramas, starting with Horace Bénédict de Saussure's in 1779. This results in effects known as a little planet (when the center of projection is the nadir ) and a tube (when the center of projection is the zenith ).
In normal aspect, pseudoazimuthal projections map the equator and central meridian to perpendicular, intersecting straight lines. They map parallels to complex curves bowing away from the equator, and meridians to complex curves bowing in toward the central meridian.
The Mercator projection (/ m ər ˈ k eɪ t ər /) is a conformal cylindrical map projection first presented by Flemish geographer and mapmaker Gerardus Mercator in 1569. In the 18th century, it became the standard map projection for navigation due to its property of representing rhumb lines as straight lines.
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 .
Web Mercator is a spherical Mercator projection, and so it has the same properties as a spherical Mercator: north is up everywhere, meridians are equally spaced vertical lines, angles are locally correct (assuming spherical coordinates), and areas inflate with distance from the equator such that the polar regions are grossly exaggerated.
The stereographic projection maps the -sphere onto -space with a single adjoined point at infinity; under the metric thereby defined, {} is a model for the -sphere. In the more general setting of topology , any topological space that is homeomorphic to the unit n {\displaystyle n} -sphere is called an n ...
Stereographic projection of a 3-sphere (again removing the north pole) maps to three-space in the same manner. (Notice that, since stereographic projection is conformal, round spheres are sent to round spheres or to planes.) A somewhat different way to think of the one-point compactification is via the exponential map. Returning to our picture ...