xyplane

The XY-plane, or the XY-plane, is the two-dimensional plane in a three-dimensional Cartesian coordinate system defined by z = 0. It consists of all points (x, y, 0) for real x and y, and is perpendicular to the z-axis. It contains the x- and y-axes and passes through the origin.

As a subset of three-dimensional Euclidean space, the XY-plane is a flat, infinite surface with dimension two. Its standard unit normal vector is (0, 0, 1) (or (0, 0, −1) if oriented).

Equations that describe the XY-plane include z = 0; in general, any plane parallel to the XY-plane has the form z = c, for a constant c. The intersection of the XY-plane with other planes or lines yields lines, points, or the entire plane depending on the equation.

In graphs and geometry, the XY-plane serves as the reference plane for plotting functions z = f(x, y) and for projecting three-dimensional data onto two dimensions. The projection onto the XY-plane maps each point (x, y, z) to (x, y, 0).

In computer graphics, CAD, engineering, and mathematics, the XY-plane is one of the three principal coordinate planes, alongside the YZ- and XZ-planes. It is also used as a baseline in 3D modeling and spatial analysis.