c) Equal-area stereonets are used in structural geology because they present b ) The north pole of the stereonet is the upper point where all lines of longitude. Background information on the use of stereonets in structural analysis The above is an equal area stereonet projection showing great circles as arcuate lines. Page 1. mm. WIDTH. Blunt. TUT. HT. T itillinn.
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If the same plane was rotated about a vertical axis in the stereonet center, they would then retain their dip, but have a different strike. Typically university geology and engineering students are expected create stereonets by hand. The point 1 and 2 are best fit line points for the poles that lies about stersonet center of the diagram.
Planar Gnomonic Orthographic Stereographic. The transparent sheet is rotated and the central angle is read along the common meridian to both points P 1 and P 2. Where it is defined, the mapping is smooth and bijective. The numbers in the upper right quadrant represent potential strike line positions from degree, in 10 degree increments see below diagram. All lines in the plane, when transformed to circles on the sphere by the eqjal of stereographic projection, meet at the projection point.
G On a new sheet of paper plot the following two lines. The strike and dips are given to the left. Intersecting lines are transformed to circles that intersect transversally at two points in the sphere, one of which is the projection point. The x-axis horizontal and y-axis vertical coordinates of a latitude-longitude measurement can be calculated using the following formula:.
Stereographic projection – Wikipedia
Complex variables and applications. Albers Equidistant Lambert conformal. J On a new page, plot the following line 40 and then find the family of lines points on the stereonet that stereoent 20 degrees away. In the figure, the area-distorting property of the stereographic projection can be seen by comparing a grid sector near the center of the net with one at the far right or left. The great circle is divided in to degrees like degree protractor because maps are designed based on same azimuthal bearing directional vectors.
It was originally known as the planisphere projection.
In order to do this, rotate the two pole points until they fall qrea the same great circle. Two points P 1 and P 2 are drawn on a transparent sheet tacked at the origin of a Wulff net.
The stereographic projection gives an alternative parametrization of the unit circle:. The stereographic projection presents the quadric hypersurface as eqjal rational hypersurface. Together, they describe the sphere as an oriented surface or two-dimensional manifold.
Where that line passes through the stereonet project plane is where the line plots the dark green dot. If you are a mineralogist, you will use the top half of the spherical projection for crystallographic analysis. Basic Algebraic Geometry I. For someone who is steeeonet in geology or structural geology, it is highly recommended to use paper and pencil over software.
The equal-area lower-hemisphere projection defined by the Lambert azimuthal equal-area projection is also used, especially when the plot is to be subjected to subsequent statistical analysis such as density contouring.
One of its stereondt important uses was the representation of celestial charts. Stereographic projection is conformal, meaning that it preserves the angles at which curves cross each other see figures. Along the common great circle containing the two poles count in degree increments half of the angle found in D above.
Stereoet the stereographic projection also lets us visualize planes as points in the disk.
They are hemisphere surface paths from one line being rotated about another line the pole of rotationboth passing through the hemisphere center.
In this context the stereographic projection is often referred to as the equal-angle lower-hemisphere projection. Similar remarks hold about the real projective atereonetbut the intersection relationships are different there. That is the angle desired.
For example, from intersection point 3 upwards towards NW direction of the great circle intersection of plane A. In practice, the projection is carried out by computer or by hand using a special kind of graph paper called a stereographic netshortened to stereonetor Wulff net.
On the other hand, stereographic projection does not preserve area; in general, the area of a region of the sphere does not equal the area of its projection onto the plane. The point you arrive represents a line perpendicular to the plane you started with, i. The stereographic projection has been used to map spherical panoramas. In crystallographythe orientations of crystal axes and faces in three-dimensional space are a central geometric concern, for example in the interpretation of X-ray and electron diffraction patterns.
This facilitates an elegant and useful notion of infinity for the complex numbers and indeed an entire theory of meromorphic functions mapping to the Riemann sphere. It is believed that already the map created in by Gualterius Lud  was in stereographic projection, as were later the maps of Jean RozeRumold Mercatorand many others. The above diagram shows the same plane in two positions.
It could represent a principal stress for a conjugate fault pair.