Graphics Reference
In-Depth Information
z
z
p
y
y
C
C
x
x
(a)
(b)
Figure 9.33.
Ruled surfaces.
z
Figure 9.34.
Sweeping a rotating line along the z-axis.
new base curve
C
Figure 9.35.
A ruled surface with general base curve.
(
)
=
(
)
puv
,
v
cos
uv
,
sin
ubu
,
,
b
π 0
.
This surface is called a
helicoid
. See Figure 9.34.
Note that, in a sense, there is nothing special about the base curve q(u) of a ruled
surface. We could choose any curve that meets each line in the ruling in precisely one
point as base curve and the resulting ruled surface would be the same. See Figure 9.35.
