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. This is clearer in a diagram (Fig.
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.
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 method?
Stereographic projection is a method used in crystallography and structural geology to depict the angular relationships between crystal faces and geologic structures, respectively. We orient the crystal such that the pole to the (001) face (the c axis) is vertical and points to the North pole of the sphere.
What is stereographic projection in geology?
Stereographic Projection. 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 map a sphere with two stereographic parametrizations?
Although any stereographic projection misses one point on the sphere (the projection point), the entire sphere can be mapped using two projections from distinct projection points. In other words, the sphere can be covered by two stereographic parametrizations (the inverses of the projections) from the plane.
How do you find the stereographic projection of a crystal?
The stereographic projection then appears on the equatorial plane. In the right hand-diagram we see the stereographic projection for faces of an isometric crystal. Note how the ρangle is measured as the distance from the center of the projection to the position where the crystal face plots.
What is the stereographic projection of P onto the plane?
For any point P on M, there is a unique line through N and P, and this line intersects the plane z = 0 in exactly one point P′, known as the stereographic projection of P onto the plane. In Cartesian coordinates (x, y, z) on the sphere and (X, Y) on the plane, the projection and its inverse are given by the formulas