Planarprojektion

Planarprojektion, or planar projection, is a class of map projections in which the surface of a sphere or ellipsoid is projected onto a plane. The projection plane is typically tangent to the sphere at a chosen point or it may cut through the sphere (secant plane). Points on the globe are mapped by projecting along lines through a projection center, which can be the sphere’s center (central projection) or a point on or outside the sphere.

In practice, planar projections are azimuthal: they preserve directions from the projection point to any other point. Different choices of center and plane lead to various named projections. Gnomonic projection uses the sphere’s center projected onto a plane tangent to the sphere; great circles become straight lines, making it useful for navigation but with strong distortion away from the tangent point. Stereographic projection uses the point opposite the tangent plane; it is conformal (angles preserved) and maps circles to circles on the plane. Orthographic projection simulates a view from infinite distance, projecting along parallel lines; it is good for a global perspective of a hemisphere but distorts areas and distances. Lambert azimuthal equal-area projection uses the same tangent-plane setup but preserves area, making it suitable for proportional representation of landmasses around the center.

Distortion in planar projections is unavoidable; each variant emphasizes different properties such as angle, area, or distance. Planarprojektion is commonly used for polar maps, regional mapping, and as a mathematical tool in astronomy and cartography. Its limitations include restricted global validity and significant distortion away from the center point.