Basisebene

Basisebene is a plane used as a reference in mathematics, geometry, and technical applications. In a three-dimensional Euclidean space it serves as the foundational plane against which coordinates, projections, and constructions are defined. In a standard Cartesian coordinate system the Basisebene is often the xy-plane, consisting of all points with z = 0, but it can be any plane designated as the reference.

Mathematically, a Basisebene can be described by a point p0 on the plane and a normal vector n perpendicular to it. The plane consists of all points p such that (p − p0) · n = 0. The two independent direction vectors spanning the plane define its orientation.

In practice, the Basisebene is used to define sketches, construct cross-sections, and describe the coordinates of points by projection onto the plane. In computer-aided design (CAD) and 3D modeling it serves as the initial sketching plane; in geometry and analytic geometry it aids in coordinate descriptions and transformations. It can be global, tied to a fixed reference frame, or local, attached to a moving object.

Choosing a Basisebene affects calculations of projections, distances, and angles; rotating, translating, or otherwise transforming the Basisebene changes how a scene or model is interpreted, while the underlying space remains unchanged.