What type of projection is stereographic?
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane. The projection is defined on the entire sphere, except at one point: the projection point. Where it is defined, the mapping is smooth and bijective.
What is the purpose of stereographic projection?
Stereographic projection is a technique for displaying the angular properties of a plane faced object on a single drawing or diagram. Directions as well as planes may be shown and any desired angle can be measured directly from the projection using a graphical technique.
How do you calculate stereographic projection?
The stereographic projection of the circle is the set of points Q for which P = s-1(Q) is on the circle, so we substitute the formula for P into the equation for the circle on the sphere to get an equation for the set of points in the projection. P = (1/(1+u2 + v2)[2u, 2v, u2 + v2 – 1] = [x, y, z].
How do you find the inverse of a stereographic projection?
Let S1 the unit circle centered at the origin and the pole p=(0,1). The stereographic projection is the homeomorphism φ:S1∖{p}→R1. In order to find a formula for φ, note that the point of the semi-straight line px are of the form p+t((x,y)−p) with t>0 and (x,y)∈S1.
What is stereographic projection in geology?
Stereographic projection is a method used in crystallography and structural geology to depict the angular relationships between crystal faces and geologic structures, respectively. Here we discuss the method used in crystallography, but it is similar to the method used in structural geology.
What is stereographic projection in structural geology?
Stereographic projection is a powerful method for solving geometric problems in structural geology. Unlike structure contouring and other map-based techniques, it preserves only the orientation of lines and planes with no ability to preserve position relationships.
What is great circle in stereographic projection?
The line of intersection between the plane and the sphere will then represent a circle, and this circle is formally known as a great circle. Except for the field of crystallography, where upper-hemisphere projection is used, geologists use the lower part of the hemisphere for stereographic projections, as shown in Fig.