What is stereographic projection in crystallography?
Stereographic projection is a method used in crystallography and structural geology to depict the angular relationships between crystal faces and geologic structures, respectively. We orient the crystal such that the pole to the (001) face (the c axis) is vertical and points to the North pole of the sphere.
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].
What type of projection is stereographic?
The stereographic projection is a one-to-one mapping of the extended plane onto the sphere S. The sphere S is called the Riemann sphere. The stereographical projection has the property that the angles between two (differentiable) curves in C and the angle between their images on S are equal.
What is the difference between spherical projection and stereographic projection?
The north pole is the spherical image of the point ∞ at infinity. The stereographic projection is a one-to-one mapping. The sphere S is called the Riemann sphere. The stereographical projection has the property that the angles between two (differentiable) curves in C and the angle between their images on S are equal.
What is stereographic net?
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane. In practice, the projection is carried out by computer or by hand using a special kind of graph paper called a stereographic net, shortened to stereonet, or Wulff net.
Where would the pole to a horizontal plane will plot on a stereonet?
As long as the pole is 90o to strike, it will contain all of the information in the associated great circle. We refer to this point as the pole to bedding (or any other planar feature). Poles to horizontal planes will plot at the centre of the stereonet; poles to vertically dipping planes at the perimeter.
How do you find the stereographic projection of a crystal?
The stereographic projection then appears on the equatorial plane. In the right hand-diagram we see the stereographic projection for faces of an isometric crystal. Note how the ρangle is measured as the distance from the center of the projection to the position where the crystal face plots.
What is stereographic projection?
The stereographic projection is a projection of points from the surface of a sphere on to its equatorial plane. The projection is defined as shown in Fig. 1. If any point P on the surface of the sphere is joined to the south pole S and the line PS cuts the equatorial plane at p, then p is the stereographic projection of P.
What is a stereographic net?
A stereographic net is simply a stereographic projection of the lines of latitude and longitude of a sphere on to a central plane. The most obvious form of stereographic net is shown in Fig. 12.
What is the stereographic projection of a great circle?
A great circle in a general position is shown in Fig. 4, and it is clear that its stereographic projection is a circle of radius greater than that of the primitive. It intersects the latter in two points at opposite ends of a diameter of the primitive.