Achsenlinien

Achsenlinien are lines that indicate the orientation of the main axes of an object, a coordinate system, or a reference frame. They serve as reference lines in geometry, drawing, and data analysis, helping to position features, measure distances, or describe rotational properties.

In geometry, axis lines define the coordinate framework: in two dimensions, the x- and y-axes are perpendicular lines intersecting at the origin; in three dimensions, the x-, y-, and z-axes define a right-handed coordinate system. Achsenlinien can also denote lines of symmetry, along which a figure can be reflected onto itself.

In physics and engineering, axis lines include the axes of inertia or principal axes of a rigid body. These lines pass through the center of mass and align with directions about which rotational motion is simplest to describe. They are determined by the inertia tensor or by symmetry elements of the object.

In technical drawing and design, construction lines (Hilfslinien) act as Achsenlinien to achieve correct alignment, proportion, and placement of features. In computer graphics and data analysis, principal axes provide a frame of reference: in principal component analysis (PCA), the data are rotated so that the first principal axis aligns with the direction of greatest variance, and lines along these axes represent the main directions of data spread.

The term is generally used in German to describe lines that serve as reference directions or symmetry guides, rather than as a fixed named object. Alternatives include Achse, Symmetrieachse, and Hauptachse.