Make Your Own Ruled Surface

a

b

f

Cos[x]

g

Sin[x]

h

0

i

Sin[x]

j

Cos[x]

k

1

A ruled surface is a surface that has a parametrization of the form

x(u,v)=α(u)+vγ(u)

, where

α

is the directrix and

γ

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

α

to be a constant multiple of one of the functions

f

,

g

, and

h

(

a

is the constant) and

γ

to be a constant multiple of one of the functions

i

,

j

, and

k

(

b

is the constant). Ruled surfaces occur in architecture.