ZKoordinaten

Z coordinates refer to the third component in a three-dimensional Cartesian coordinate system. A point in 3D space is written as (x, y, z), where x and y locate the point on the reference plane (the x–y plane) and z measures its displacement along the axis perpendicular to that plane. The z-axis is perpendicular to the x–y plane, and the positive direction of z depends on the chosen convention. Some systems treat z as increasing toward the viewer, others as increasing away from the viewer or upward in a particular context.

Applications of z coordinates are widespread in fields that involve three-dimensional space. In computer graphics and 3D modeling, z represents depth information used for rendering, depth testing, and perspective projection. In engineering and physics, z is part of the spatial description of objects and phenomena. In geographic information systems, z often denotes elevation or height above a reference surface. The concept is also fundamental in robotics, animation, and scientific visualization, where the position of points and objects is described by (x, y, z).

Mathematically, operations on 3D points manipulate the z coordinate along with x and y. Transformations such as rotation, translation, and scaling are applied via matrices in homogeneous coordinates, and distances between points depend on the x, y, and z differences. Projections from 3D to 2D typically involve a perspective divide that incorporates z, creating the illusion of depth on a flat image.

Notes and conventions: different disciplines and software employ varying handedness and axis directions, so the exact orientation of the z axis can differ. Always check the coordinate convention used in a given context to interpret z correctly.