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What do you mean 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.

What is the purpose 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.

Who developed 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 the source of light in stereo graphic projection?

At the opposite end where the tangent plane touches the reference globe is the light source for the stereographic projection. This map projection is commonly used for polar aspects and navigation maps because of how it preserves shapes (conformal).

What is Polar zenithal stereographic projection?

Polar Zenithal Stereographic Projection 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 are the types of projection?

There are two main types of projection:

  • A. Parallel and Orthographic.
  • Station-point and Perspective.
  • Parallel and Convergent.
  • Perspective and Parallel.

What is the meaning of stereographic?

: of, relating to, or being a delineation of the form of a solid body (such as the earth) on a plane stereographic projection.

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.

How many types of zenithal projections are there?

This group of map projections can be classified into three types: Gnomonic projection, Stereographic projection and Orthographic projection.

What is the definition of a stereographic projection?

The stereographic projection, in geometry, 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. Where it is defined, the mapping is smooth and bijective. It is conformal, meaning that it preserves angles.

Can a stereographic projection miss one point on the sphere?

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.

When do parallel lines intersect in stereographic projection?

All lines in the plane, when transformed to circles on the sphere by the inverse of stereographic projection, meet at the projection point. Parallel lines, which do not intersect in the plane, are transformed to circles tangent at projection point.

How is stereographic projection used in a Schlegel diagram?

Stereographic projection is also applied to the visualization of polytopes. In a Schlegel diagram, an n-dimensional polytope in R n+1 is projected onto an n-dimensional sphere, which is then stereographically projected onto R n. The reduction from R n+1 to R n can make the polytope easier to visualize and understand.