球極平面投影 - 维基百科，自由的百科全书
网页球極平面投影 （stereographic projection），在 幾何學 裏，是一種將圓球面 投影 至平面的 映射。. 在 構造地質學 裏，稱為 球面立體投影 或 球面投影。. 除了投影點以外，這投影在整個球面都有定義。. 在這定義域裏，這映射具有 光滑性 、 雙射性 和 共形性。. 共 ...
Stereographic Projection -- from Wolfram MathWorld
网页2024年8月22日 · 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...
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.
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. This type of mapping is either conformal in that it preserves the angles at which different curves meet or it is area-preserving in that two sectors with the same area on the sphere have the same areas ...
Stereographic Projection
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 \(P\) on the sphere of radius \(r\) is mapped to the point \(X\) in the horizontal plane by projecting \(P\) along the line connecting it to the south pole, \(S\text{.}\)
网页Stereographic Projection. David Kruzel and Yilong Zhang. April 23, 2022. This semester, we focus on stereographic projection, which is a bijective map from the unit sphere in R3 with the north point removed S2 n fNg to the. z = 0 plane. The map is conformal and sends circles on the spheres to circles or the lines on the plane.
Stereographic projection - Encyclopedia of Mathematics
网页2024年5月10日 · Stereographic projection establishes a correspondence not only between the points of the sphere and the plane, but also between points outside the sphere and circles on the plane. For a point outside the sphere, the polar plane intersects the …
Stereographic Projection - an overview | ScienceDirect Topics
网页1991年6月15日 · A stereographic projection, or more simply a stereonet, is a powerful method for displaying and manipulating the 3-dimensional geometry of lines and planes (Davis and Reynolds 1996). The orientations of lines and planes can be plotted relative to the center of a sphere, called the projection sphere, as shown at the top of Fig. 2-7 .
网页Stereographic projection is one way of making maps, and it preserves angles. It has been used since ancient times for this purpose, and its basic geometrical properties were known even then. 1. The projection. The basic idea is very simple. We apply ordinary perspective to a sphere embedded in three dimensions in a particular way.
Properties of Stereographic Projection - University of Washington
网页The 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 S, then the image of c is a circle if N is not on c or is a line if …
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