waxis

Waxis, sometimes written w-axis, is not a single formal object but a term used in several fields to denote the axis associated with the variable w. Its meaning depends on the discipline and the convention used.

In mathematics and geometry, w is often the fourth coordinate in a system of homogeneous coordinates (x, y, z, w). The w-axis refers to the direction in which w varies while x, y, and z are held fixed. In projective space, points are represented by equivalence classes of (x, y, z, w) not all zero, with scaling by a nonzero factor. The w-coordinate plays the role of a scaling factor when converting to Euclidean coordinates; as a result the explicit w-axis is less visible in the affine view.

In computer graphics and related geometry, w appears as the homogeneous coordinate used to enable perspective projection. After applying a transform, coordinates are typically normalized by w (dividing by w) to obtain standard 3D points, so the visible images do not display a separate w-axis, even though w governs depth scaling.

In physics and signal processing, w is commonly used to denote angular frequency (often written ω). On plots of a system’s response versus frequency, the axis labeled w or ω is the frequency axis.

In data visualization and programming, w may simply denote a variable chosen by the author, and a graph’s axis labeled w would be its corresponding dimension.

See also: homogeneous coordinates; angular frequency; coordinate systems.