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See all on WikipediaIn mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection), onto a plane (the projection plane) perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere … See more
The origin of the stereographic projection is not known, but it is believed to have been discovered by Ancient Greek astronomers and used for projecting the celestial sphere to … See more
The first stereographic projection defined in the preceding section sends the "south pole" (0, 0, −1) of the unit sphere to (0, 0), the equator to the See more
Stereographic projection plots can be carried out by a computer using the explicit formulas given above. However, for graphing by hand these formulas are unwieldy. Instead, it … See more
Cartography
The fundamental problem of cartography is that no map from the sphere to the plane can … See moreFirst formulation
The unit sphere S in three-dimensional space R is the set of points (x, y, z) such that x + y + z = 1. Let N = (0, 0, 1) be the "north pole", and let M be the rest of the sphere. The plane z = 0 runs through the center of the … See moreComplex analysis
Although any stereographic projection misses one point on the sphere (the projection point), the … See more• List of map projections
• Astrolabe
• Astronomical clock
• Poincaré disk model, the analogous mapping of the See moreWikipedia text under CC-BY-SA license WEBOct 10, 2021 · Given a point P = (x, y) ≠ N on the unit circle, let s(P) denote the intersection of the line ¯ NP with the x -axis. See Figure 1.3.1. The map s: S1 ∖ {N} → R given by this rule is called stereographic …
WEB4 days ago · Stereographic projections have a very simple algebraic form that results immediately from similarity of triangles. In the above figures, let the stereographic sphere have radius r, and the z-axis positioned as...
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.
Wikipedia · Text under CC-BY-SA licenseProperties of Stereographic Projection - University of Washington
WEBThe two most important properties of Stereographic Projection with center N from a sphere S to a plane F are these: 1. The image of a circle is a circle (or a line). If c is a circle on …
WEBMay 10, 2024 · In the multi-dimensional case, a stereographic projection is a projection of points of the Euclidean space $E_{n+1}$ onto the space $E_n$ complemented by one point at infinity, from a point $P$ …
WEBLearn how to map a sphere onto a plane using stereographic projection, a technique that preserves angles and takes circles into circles. Explore the geometry of circles, …
WEBFor any point P ≠ S P ≠ S on Σ Σ, consider the line (SP) ( S P) in the space. This line intersects Π Π in exactly one point, denoted by P′ P ′. Set S′ = ∞ S ′ = ∞. The map ξs P ↦ P′ ξ s P ↦ P ′ is called the …
WEBStereographic Projection. Stereographic projection maps the sphere (minus the north pole) to the plane. This is a one-to-one mapping that allows us to study the sphere by …
WEBStereographic Projection. Geographers have devised all sorts of projections from the curved surface of a sphere in three-space to flat two-dimensional maps. We have already …
stereographic projection - PlanetMath.org
WEBFeb 10, 2018 · Learn the definition and construction of the stereographic projection, a smooth bijective mapping from the n-dimensional unit sphere to the n …
Stereographic Projections | SpringerLink
WEBDec 14, 2021 · Learn how to project a sphere onto a plane using conformal or area-preserving mapping functions. See examples of Wulff net and Schmitt net applications …
Stereographic Projection - University of Washington
WEBThis is an outline of the basic construction for stereographic projection and a statement of some basic properties. The central projection of 3-space from a point N to a plane onto …
Math 519, Stereographic projection - Department of Mathematics
WEBStereographic projection maps all points on the sphere except the North Pole onto the plane through the equator. If $P(y_1, y_2, \dots, y_n)$ is the point on the sphere and if …
AMS :: Feature Column :: Stereographic Projection
WEBWhat is stereographic projection? Stereographic projection associates to every point P P on the sphere, with one exception, a point P ′ P ′ on the plane. Place the unit sphere x2 …
Stereographic Projection
WEBStereographic projection preserves circles and angles. That is, the image of a circle on the sphere is a circle in the plane and the angle between two lines on the sphere is the …
(IUCr) The stereographic projection - International Union of ...
WEBLearn how to use the stereographic projection to represent the directions and angles of crystal faces on a plane. The pamphlet explains the definition, properties and …
Stereographic Projection - Brown University
WEBWhen the viewing point is at the top of a sphere that rests on the horizontal plane, central projection sends each point of the sphere to a unique point of the plane. This gives a …
1.4: Stereographic Projection - Geosciences LibreTexts
WEBStereographic projection is a powerful method for solving geometric problems in structural geology. Unlike structure contouring and other map-based techniques, it …
Stereographic Projection - an overview | ScienceDirect Topics
WEBJun 15, 1991 · Learn about the stereographic projection, a mapping that projects the sphere on to a plane, from various chapters and articles in ScienceDirect Topics. …
Spotlight on Stereographic Projections - Mathemalchemy
WEBMay 1, 2021 · Stereographic projection is a map from the sphere to the plane. So just like the Mercator map is a way of getting the continents of the globe on a flat piece of paper, …
geometry - Stereographic projection (Theorem that circles on the …
WEBJun 4, 2022 · $S$ is defined to be the stereographic projection, i.e. the function $S:\Sigma\setminus\{N\}\rightarrow\mathbb{R}^2$ satisfying $$ S\big((x,y,z)\big) = …
Understanding the formula for stereographic projection of a point.
WEBFeb 16, 2018 · How do I apply the Stereographic projection to generate the Star Finder templates at different latitudes?
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