stereographic projection

Similarly, a fault plane is a planar feature that may contain linear features such as slickensides. When doing fault analyses it is useful to plot both the slip plane and its lineation s in the same plot. In other projects Wikimedia Commons. The Wulff net makes it possible to work with angular relations it preserves angles between planes across the net , which can be useful in some cases, for instance for crystallographic purposes. The right-hand rule has been used in Fig.

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The line of intersection between two planes is perhaps most easily seen by plotting the great circles of the two planes, in which case the line of intersection is represented by the point where the two great circles cross. This will consist of a stereonet mounted on a piece of cardboard with a thumbtack through the center. Practice online dtereographic make a printable study sheet.

Stereographic Projection

So the stereographic projection also lets us visualize planes as points in the disk. Users of the right hand rule will always measure the pitch clockwise from the strike value, so that the angle could be up to degrees. We then mark off the strike value of our plane, which is Fig. The method of plotting is the same, but because the projection is not stereographic but equal area Fig. This construction is used to visualize directional data stereograpbic crystallography and geology, as described below.


Stereographic Projection — from Wolfram MathWorld

These lines are sometimes thought of as circles through the point at infinity, or circles of infinite radius. Poles are generally preferred in structural analyses that involve large amounts of orientation data, and particularly if grouping of structural orientations is an issue which commonly is the case. Next, we need a systematic way to define crystallographic angles.

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We then count the dip value from the primitive circle inwards, and trace the great circle that it falls on Fig. This property is valuable in planetary mapping where craters are typical features. For this we use a spherical projection. The standard metric on the unit sphere agrees with the Fubini—Study metric on the Riemann sphere.

In effect, stereographic projection wraps the plane around the sphere, missing only that one point Subscribe To Posts Atom. If you have a different image of similar quality, be sure to upload it using the proper free license tagadd it to a relevant article, and nominate it.

Stereographic projection is a method steregraphic in crystallography and structural geology to depict the angular relationships between crystal faces and geologic structures, respectively. Note sstereographic this angle is can be measured easily with a device called a contact goniometer. If we now project the small and great circles onto the horizontal projection plane, typically for every 2 and 10 degree interval, we will get what is called a stereographic net or stereonet.


The Primitive Circle is the circle that surrounds the stereonet. Put more mathematically, it is impossible to render paths on a sphere onto a flat surface in such a way that all distances remain the same. The set of circles passing through the point of projection have unbounded radius, and therefore degenerate into lines.

You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. Note how the symmetry of the crystal can easily be observed in the stereogram. It is impossible to draw maps of the Earth’s surface on a flat surface in such a way that no distortion takes place. Bonne Bottomley Polyconic American Werner.

AMS :: Feature Column :: Stereographic Projection

The plots show the variations within each subarea, portrayed by means of poles, rose diagrams, and an arrow indicating the average orientation. It is neither isometric nor area-preserving: In fact, there exists a single family of them, all parallel to each other, as Proposition 5 of Book I of Apollonius’ treatise on conics asserts. This result is one of the first results in Apollonius’ book on conics, and presumably one of the earliest non-trivial results known to the Greeks about conic sections.