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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.
Direct projection of 3-sphere into 3D space and covered with surface grid, showing structure as stack of 3D spheres (2-spheres) In mathematics, a hypersphere or 3-sphere is a 4-dimensional analogue of a sphere, and is the 3-dimensional n-sphere. In 4-dimensional Euclidean space, it is the set of points equidistant from a fixed central point.
A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane.
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 .
For example, one sphere that is described in Cartesian coordinates with the equation x 2 + y 2 + z 2 = c 2 can be described in spherical coordinates by the simple equation r = c. (In this system—shown here in the mathematics convention—the sphere is adapted as a unit sphere, where the radius is set to unity and then can generally be ignored ...
A checkered sphere, without (left) and with (right) UV mapping (Using 3D XYZ space or 2D UV space). In the example to the right, a sphere is given a checkered texture in two ways. On the left, without UV mapping, the sphere is carved out of three-dimensional checkers tiling Euclidean space.
Stereographic projection of complex numbers and onto the points and of the Riemann sphere - connect () with A or B by a line and determine the intersection with the sphere. In mathematics , the Riemann sphere , named after Bernhard Riemann , [ 1 ] is a model of the extended complex plane (also called the closed complex plane ): the complex ...
A family of map projections that includes as special cases Mollweide projection, Collignon projection, and the various cylindrical equal-area projections. 1932 Wagner VI: Pseudocylindrical Compromise K. H. Wagner: Equivalent to Kavrayskiy VII vertically compressed by a factor of /. c. 1865: Collignon