AlbersKegelProjektion

AlbersKegelProjektion refers to the Albers Equal-Area Conic Projection, a two-standard-parallels conic map projection designed to preserve area. It maps the surface of a sphere or ellipsoid to a plane in such a way that equal areas on the globe correspond to equal areas on the map, making it suitable for representing large landmasses at mid-latitudes.

Key properties of the projection include the use of two standard parallels, φ1 and φ2, where the scale is true. Distortion is minimized between these parallels, while shapes and angles become progressively distorted toward the edges. The projection is not conformal, so local shapes are not preserved, but area (size) is preserved.

Mathematically, the projection is defined by a central meridian λ0, a latitude of origin φ0, and the standard parallels φ1 and φ2. Constants are n = (sin φ1 + sin φ2)/2 and C = cos² φ1 + 2 n sin φ1. For a point with latitude φ and longitude λ, the radial distance is ρ = (R/n) sqrt(C − 2 n sin φ), and the map coordinates are x = ρ sin(λ − λ0) and y = ρ0 − ρ cos(λ − λ0), where ρ0 = (R/n) sqrt(C − 2 n sin φ0).

Applications of the Albers projection are common for regional and national maps in mid-latitude countries, where area accuracy is important for display and analysis. It is widely supported in geographic information systems and cartographic libraries and is often chosen for maps of North America, Africa, and similar regions due to its balance between area preservation and distortion control.