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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Aitoff Hammer Wiechel Winkel tripel. Hence, most educational institutions prefer equal area steronets for their students over stereobet equal angle stereonets. We use slickensides to interpret the sense of motion in the field. Equal angle projection 2.
If we repeat this operation for all the points of intersection of the plane with the hemisphere then a curved line, a great circle trace, is formed on the streonet. All lines in the plane, when transformed to circles on the sphere by the inverse of stereographic projection, meet at the projection point. However, the angle-preserving property is stronger than this property. In general, one can define a stereographic xrea from any point Q on the sphere onto any plane E such that.
In general, area-preserving map projections are preferred for statistical applications, while angle-preserving conformal map projections are preferred for navigation. On the Wulff net, the images of the parallels stereonef meridians intersect at right angles.
C Plotting the poles to each of those planes and label them. Journal of the Warburg and Courtauld Institutes. The stereographic projection relates to the plane inversion in a simple way. As you start plotting points you will see why this is necessary. A line is drawn from stereonnet projection point to the lower hemisphere intersection point light green dashed lines. Also, every wqual through the origin intersects the unit sphere in a great circle, called the trace of the plane.
J On a new page, plot the following line 40 and then find the family of lines points on the stereonet that is 20 degrees away.
As in crystallography, planes are typically plotted by their poles. What is the form that results?
Stereographic projection for structural analysis | Sanuja Senanayake
It is measured on the great circle itself. A Mathematician Looks at Maps”. It may take some timeand focus to understand the geometry. A circle on the surface of the sphere made by the intersection with the spehere of a plane that equl through the center of the sphere.
This special graph paper is called a stereonet or Wulff netafter the Russian mineralogist George Yuri Viktorovich Wulff. This construction arez special significance in complex analysis. This is the bisector. The diagrams below attempt to show you that geometry in three stages, each more complex.
For an example of the use of the Wulff net, imagine two copies of it on thin paper, one atop the other, aligned and tacked at their mutual center. Although any stereographic projection misses one point on the sphere the projection pointthe entire sphere can sterfonet mapped using two projections from distinct projection points.
Stereographic projection is conformal, meaning that it preserves the angles at which curves cross euqal other see figures. One of its most important uses was the representation of celestial charts.
The software often eliminates many user errors, produce much better quality steronets extremely detailed analysis of datasets and make it easier to share with other over electronic devices.
In this case the formulae become. Cardinal directions are shown.
This line can be plotted as a point on the disk just as any line through the origin can. The trend and plunge is given as 89 Mathematical Analysis 2 ed.
It is neither isometric nor area-preserving: For plots involving many planes, plotting their poles produces a less-cluttered picture than plotting etereonet traces. The stereographic projection gives an alternative parametrization of the unit circle:.
Along the common great circle containing the two poles count in degree streonet half of the angle found in D above. Horizontal lines intersect the southern hemisphere in two antipodal points along the equator, either of which can be projected to the disk; it is understood that antipodal points on the boundary of the disk represent a single line.
Stereographic projection for structural analysis
A comprehensive introduction to differential geometry, Volume IV. The stereonets is a type of standardized mapping system that allows us to represent various angles in 3D space on a 1D paper. Stereographic projection is also applied to the visualization of polytopes.
The area element is given in XY coordinates by. As before, the stereographic stereonnet is conformal and invertible outside of a eqyal set.
On the disk, the latter has nearly four times the area of the former.