zkoordinaatti

Zkoordinaatti, or the z-coordinate, is the third coordinate in a three-dimensional Cartesian coordinate system. It describes a point’s position along the axis usually labeled z, which is perpendicular to the x- and y-axes.

A point in 3D space is given by (x, y, z). The z-value denotes height or depth depending on the axis orientation. In the standard right-handed Cartesian system, x cross y equals z, which fixes the sense of rotation and orientation of the axes.

The z-coordinate plays a central role in many mathematical and applied contexts. It is used to specify elevation on maps, depth in computer graphics, and the third dimension in physical space. Distances between points follow the formula sqrt((Δx)^2 + (Δy)^2 + (Δz)^2).

Functions of two variables often define surfaces as z = f(x, y). In other coordinate systems, z also serves as the axis in cylindrical and spherical coordinates, where the radial components are complemented by a vertical or axial component.

Examples: The point (3, −2, 5) has z = 5, placing it five units above the reference plane in the conventional orientation. In 3D modeling and rendering, the z-coordinate controls vertical placement of vertices and the depth of objects.

The term z-coordinate derives from the common practice of labeling spatial axes with x, y and z, with z chosen as the final axis in Western mathematical notation.