In 3D computer graphics

3D computer graphics

3D computer graphics are graphics that use a three-dimensional representation of geometric data that is stored in the computer for the purposes of performing calculations and rendering 2D images...

, a lathed object is a 3D model whose vertex geometry is produced by rotating the points of a spline

Spline (mathematics)

In mathematics, a spline is a sufficiently smooth piecewise-polynomial function. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low-degree polynomials, while avoiding Runge's phenomenon for higher...

 or other point set around a fixed axis. The lathing may be partial; the amount of rotation is not necessarily a full 360 degrees. The point set providing the initial source data can be thought of as a cross section through the object along a plane containing its axis of radial symmetry.

The lathe is so named because it produces the same type of object that a real lathe

Lathe

A lathe is a machine tool which rotates the workpiece on its axis to perform various operations such as cutting, sanding, knurling, drilling, or deformation with tools that are applied to the workpiece to create an object which has symmetry about an axis of rotation.Lathes are used in woodturning,...

 would produce: an object that is symmetrical about an axis of rotation. However, unlike objects produced by a real lathe, the object can have an axis of rotation through a hole (e.g. a torus

Torus

In geometry, a torus is a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle...

).

Lathes are very similar to surfaces of revolution. However, lathes are constructed by rotating a curve defined by a set of points instead of a function

Function (mathematics)

In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...

. Note that this means that lathes can be constructed by rotating closed curves or curves that double back on themselves (such as the aforementioned torus), whereas a surface of revolution could not because such curves cannot be described by functions.