What is meant by stereographic projection?

What is meant by stereographic projection?

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. It is conformal, meaning that it preserves angles at which curves meet.

How do you find a 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].

Who invented the stereographic projection?

The stereographic projection was exclusively used for star charts until 1507, when Walther Ludd of St. Dié, Lorraine created the first known instance of a stereographic projection of the Earth’s surface. Its popularity in cartography increased after Rumold Mercator used its equatorial aspect for his 1595 atlas.

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.

What is a Stereonet used for?

Stereonets are a graphical tool representing the hemisphere of a globe, used for presentation, analysis and interpretation of three-dimensional directional data such as planes and lines.

Does stereographic projection preserve angles?

Stereographic projection preserves angles, in the sense that if two curves intersect at an angle A on the sphere, so do their images under stereographic projection.

What is .stereographic used for?

Stereographic is a planar perspective projection, viewed from the point on the globe opposite the point of tangency. It projects points on a spheroid directly to the plane and it is the only azimuthal conformal projection. The projection is most commonly used in polar aspects for topographic maps of polar regions.

How are stereographic projection used in the study of crystals?

The stereographic projection is used to represent the angles between the faces of a crystal and the symmetry relationships between them. Imagine that the crystal is centered within a sphere, the normal to the crystal faces will give a consistent set of points uninfluenced by the relative sizes of the faces.

How is a plane plotted on a Stereonet?

A stereonet should be visualized as the bottom half of a sphere. Planes intersect the sphere as great circles and lines intersect the sphere as points. Its helpful when starting out with stereonets to visualize the plane or line as it cuts through a 3-dimensional bowl (props may be helpful). the north pole of the net.

Why stereographic projection is conformal?

Stereographic projection is conformal, meaning that it preserves angles between curves. Working first in the 0np-plane (see figure 2), we have equal angles α and right angles between the radii and the tangent planes, hence equal angles β, hence equal angles β′, and hence equal lengths b.

What are the parts of a stereographic projection?

There are two parts to any stereographic projection. The projection itself, or , is usually drawn on tracing paper, and represents a bowl-shaped surface embedded in the Earth. The or stereonet is the 3-D equivalent of a protractor. It is used to measure angles on the projection.

What is the sterestereographic net used for?

stereographic net or stereonet is the 3-D equivalent of a protractor. It is used to measure angles on the projection. To measure angles, we need to rotate the net relative to the tracing paper.

How do you make a stereogram with tracing paper?

To construct a stereogram, take a sheet of tracing paper and draw a circle, with the same radius as an available stereonet. This circle is known as the . Mark the centre with a cross, and mark a north arrow on the primitive at the top of the page.

What are great and small circles in stereography?

Great and small circles. The stereographic net assists in the construction of great circles and points. It contains a family of great circles intersecting at the top and bottom points of the net (Fig. 3a). Every fifth cyclographic trace is bolder so that ten degree increments can be easily counted.