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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.
On a Mercator projection the North Pole and South Pole occur at infinity and are therefore never shown. However the full loxodrome on an infinitely high map would consist of infinitely many line segments between the two edges. On a stereographic projection map, a loxodrome is an equiangular spiral whose center is the north or south pole.
Stereographic projection of a pole. The upper sphere is projected on a plane using the stereographic projection. Consider the (x,y) plane of the reference basis; its trace on the sphere is the equator of the sphere. We draw a line joining the South pole with the pole of interest P.
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 ...
The title can be translated as "celestial plane" or "star chart". In this work Ptolemy explored the mathematics of mapping figures inscribed in the celestial sphere onto a plane by what is now known as stereographic projection. This method of projection preserves the properties of circles.