Stereographic Projection

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Introduction

Stereographic projection is a method of projecting points on the surface of the earth or sphere from a certain point (usually a pole) of the sphere onto a plane. This projection method distributes points on the sphere and projects them from a certain point to the projection plane opposite it, and finally presents them in the form of a circular map. This method was invented by ancient Greek mathematicians and is widely used in many fields such as astronomy, crystallography and map making.

Projection Basic

Commonly used data formats in stereographic projection include:

**WKT (Well-Known Text): **A text format used to describe the projection parameters of geographic spatial information, compatible with most GIS software.
GeoTIFF: A raster data format with embedded projection information, commonly used for topographic or meteorological data.
Shapefile (.shp): Used to store polygon, line and point data, and the accompanying .prj file saves the projection parameters.
PROJ.4 / EPSG code: Used to concisely represent projection parameters (for example: +proj=stere), which is easy to use in software.

Pros

Accurate angle: It is an orthographic projection, which can accurately maintain the angle relationship on the map and is suitable for navigation and astronomical observation.
Circularity preservation: The circle on the sphere remains a circle after projection, which is easy to understand intuitively.
Polar region advantage: It can represent the Arctic and Antarctic regions with high accuracy, which is very useful in polar research and meteorological analysis.
Strong symmetry: With the projection center as the symmetry axis, the visual effect is beautiful and is often used for illustration and scientific visualization.

Cons

Area distortion: Although the angle is accurate, the area cannot be preserved. The farther away from the center point, the more obvious the area enlargement.
Distance inaccuracy: The distance between any two points cannot be accurately measured after projection.
Limited scope of use: Suitable for local polar regions, not suitable for global maps.
Uneven readability: The farther away from the center, the greater the deformation and the lower the visual recognition.

Application Scenario

Stereographic projection is widely used in polar-centric map making, constellation mapping in astronomy, and visualization of air routes. In particular, because most earth observation satellites use polar orbits, the use of pole-centered stereographic projection is extremely effective in meteorological satellite data processing and ice sheet monitoring. In addition, it is also used in crystal structure visualization, directional data analysis, earthquake epicenter distribution analysis, etc., not only limited to geography, but also covers many fields such as physics and earth science.

Example

A stereographic projection map that projects the Earth onto a flat surface with the North Pole as the point of intersection.

A three-dimensional illustration of the projection of the sphere from the North Pole onto a plane beneath the sphere.

Mercator Projection

Transverse Mercator Projection

Wagner Projection

Longitude / Latitude Projection