A ruled surface is a surface that has a parametrization of the form , where is the directrix and the director curve or ruling. Such a surface can be generated by the continuous motion of a straight line in space. Here you can choose to be a constant multiple of one of the functions , , and ( is the constant) and to be a constant multiple of one of the functions , , and ( is the constant). Ruled surfaces occur in architecture.

[3] A. Gray, "Ruled Surfaces," Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed., Boca Raton, FL: CRC Press, 1993 pp. 431–456.