How do you make a stereographic projection?

Spacings of 2° are common. To find the central angle between two points on the sphere based on their stereographic plot, overlay the plot on a Wulff net and rotate the plot about the center until the two points lie on or near a meridian. Then measure the angle between them by counting grid lines along that meridian.

What is stereographic projection in geology?

Stereographic projection is a method used in crystallography and structural geology to depict the angular relationships between crystal faces and geologic structures, respectively. Here we discuss the method used in crystallography, but it is similar to the method used in structural geology.

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].

What is the use of stereographic projection?

Stereographic projection is a technique for displaying the angular properties of a plane faced object on a single drawing or diagram. Directions as well as planes may be shown and any desired angle can be measured directly from the projection using a graphical technique.

Is stereographic projection a Homeomorphism?

Stereographic projection is an important homeomorphism between the plane R 2 \mathbb{R}^2 R2 and the 2 2 2-sphere minus a point.

What are the basic principles of stereoscopic projection?

Principle of stereographic projection A line intersects the sphere in a point. To image features on a sheet of paper, these traces and points are projected from a point at the summit or zenith of the sphere onto the equatorial plane.

What is conformal projection used for?

A conformal projection is a map projection that favors preserving the shape of features on the map but may greatly distort the size of features.

In which projection is projection lines are meet at one point?

A vanishing point is a point on the image plane of a perspective drawing where the two-dimensional perspective projections (or drawings) of mutually parallel lines in three-dimensional space appear to converge.

How does perspective projection work?

Perspective projections are used to produce images which look natural. When we view scenes in everyday life far away items appear small relative to nearer items. A side effect of perspective projection is that parallel lines appear to converge on a vanishing point. This intersection point is the projected point.

What is the basic principle of polar zenithal stereographic projection?

Polar Zenithal Stereographic Projection In this projection, a 2-dimensional plane of projection touches the generating globe at either of the poles. It is a perspective projection, with the source of light lying at the pole diametrically opposite to one at which the projection plane touches the generating globe.

What does stereographic projection preserve?

Stereographic projection preserves circles and angles. That is, the image of a circle on the sphere is a circle in the plane and the angle between two lines on the sphere is the same as the angle between their images in the plane. A projection that preserves angles is called a conformal projection.

How do you make a stereographic projection? Spacings of 2° are common. To find the central angle between two points on the sphere based on their stereographic plot, overlay the plot on a Wulff net and rotate the plot about the center until the two points lie on or near a meridian. Then measure the…