Ruled Surface:

Given a parameterized curve c(t) and a sequence of unit vectors z(t) that varies continuously with t, the parametric surface defined by

X(u,v) = c(u) + v z(t)

is called a ruled surface.

Less formally, it is the surface swept out by moving a straight line along the curve c so that it points in the direction z(t) at each time t.

For example, the saddle surfaces z = x y and z = x^2 - y^2 are both ruled surfaces, as is the hyperboloid of one sheet, the helicoid, a cylinder and a cone.

8/12/94 dpvc@geom.umn.edu -- The Geometry Center