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Stereographic projection is conformal, meaning that it preserves the angles at which curves cross each other (see figures). On the other hand, stereographic projection does not preserve area; in general, the area of a region of the sphere does not equal the area of its projection onto the plane. The area element is given in (X, Y) coordinates by
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.
The stereographic projection, which is conformal, can be constructed by using the tangent point's antipode as the point of perspective. r(d) = c tan d / 2R ; the scale is c/(2R cos 2 d / 2R ). [36] Can display nearly the entire sphere's surface on a finite circle. The sphere's full surface requires an infinite map.
In normal aspect, pseudoconical projections represent the central meridian as a straight line, other meridians as complex curves, and parallels as circular arcs. Azimuthal In standard presentation, azimuthal projections map meridians as straight lines and parallels as complete, concentric circles. They are radially symmetrical.
For example, stereographic projection of a sphere onto the plane augmented with a point at infinity is a conformal map. One can also define a conformal structure on a smooth manifold, as a class of conformally equivalent Riemannian metrics .
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 ...
A gigantic and creepy eyeball projection has appeared in Las Vegas, thoroughly unsettling residents of the area. The Madison Square Garden (MSG) Sphere at the Venetian Resort in Las Vegas has LED ...
Gall stereographic projection of the world. 15° graticule. Gall stereographic projection with 1,000 km indicatrices of distortion. The Gall stereographic projection, presented by James Gall in 1855, is a cylindrical projection. It is neither equal-area nor conformal but instead tries to balance the distortion inherent in any projection.