Stereographic projection - Wikipedia
网页In 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.
1.3: Stereographic Projection - Mathematics LibreTexts
网页2021年10月10日 · Given a point P = (x, y) ≠ N P = (x, y) ≠ N on the unit circle, let s(P) s (P) denote the intersection of the line NP¯ ¯¯¯¯¯¯¯ N P ¯ with the x x -axis. See Figure 1.3.1. The map s:S1 ∖ {N} → R s: S 1 ∖ {N} → R given by …
Stereographic Projection -- from Wolfram MathWorld
网页2024年8月22日 · A map projection obtained by projecting points on the surface of sphere from the sphere's north pole to point in a plane tangent to the south pole (Coxeter 1969, p. 93). In such a projection, great circles are mapped to circles, and loxodromes become logarithmic spirals.
网页From a technical standpoint, stereographic projection is distinguished by these two properties: It preserves the angle between paths. It takes circles on the sphere into circles on the plane, except that it takes circles through P into lines.
Stereographic Projection - Geometry of
网页The relationship between the sphere and the Klein disk is given by stereographic projection, which is illustrated in Figure 7.2.1. A point P P on the sphere of radius r r is mapped to the point X X in the horizontal plane by projecting P P along the line connecting it to the south pole, S. S.
Stereographic Projections - SpringerLink
网页2021年12月14日 · Stereographic projections are geometrical mapping functions to project a sphere that contains directional features of interest onto a plane.
Stereographic projection - Encyclopedia of Mathematics
网页2024年5月10日 · 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 $P$ of the sphere $S_n$ …
Chapter 6 : Stereographic Projection - Brown University
网页Stereographic 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 been studying one of the most useful mapping techniques, central projection from a viewing point to a horizontal plane.
Feature Column :: Stereographic Projection - AMS
网页What 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 +y2+z2 = 1 x 2 + y 2 + z 2 = 1 in 3D, and put on top of it the …
Math 519, Stereographic projection - University of …
网页Stereographic 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 $(z_1, z_2, \dots, z_{n-1})$ is its image then \[ z_1 = \frac{y_1}{1-y_n}, \quad z_2 = \frac{y_2}{1-y_n}, \quad \dots\quad z_{n-1} = \frac{y_{n-1}}{1-y_n}.