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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.
PROJ (formerly PROJ.4) is a library for performing conversions between cartographic projections.The library is based on the work of Gerald Evenden at the United States Geological Survey (USGS), [2] but since 2019-11-26 is an Open Source Geospatial Foundation (OSGeo) project maintained by the PROJ Project Steering Committee (PSC).
Stereographic projection of the world north of 30°S. 15° graticule. The stereographic projection with Tissot's indicatrix of deformation.. 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.
It is possible to choose any projection plane parallel to the equator (except the South pole): the figures will be proportional (property of similar triangles). It is usual to place the projection plane at the North pole. Definition The pole figure is the stereographic projection of the poles used to represent the orientation of an object in space.
A stereographic projection of a Clifford torus performing a simple rotation Topologically a rectangle is the fundamental polygon of a torus, with opposite edges sewn together. In geometric topology , the Clifford torus is the simplest and most symmetric flat embedding of the Cartesian product of two circles S 1
The Hopf fibration can be visualized using a stereographic projection of S 3 to R 3 and then compressing R 3 to a ball. This image shows points on S 2 and their corresponding fibers with the same color. For unit radius another choice of hyperspherical coordinates, (η, ξ 1, ξ 2), makes use of the embedding of S 3 in C 2.
In cases where there are two possibilities among a, b, and c (such as a or b), the letter e is used. (In these cases, centering entails that both glides occur.) To summarize: a, b, or c glide translation along half the lattice vector of this face. n glide translation along half a face diagonal.
The stereographic projection provides a coordinate system for the sphere in which conformal flatness is explicit, as the metric is proportional to the flat one. In general relativity conformally flat manifolds can often be used, for example to describe Friedmann–Lemaître–Robertson–Walker metric. [5]