In the construction of a surface of revolution, the profile curve performs
a complete rotation about the axis of revolution and is never "scaled".
That is, the shape of the profile curve is never changed in the course
of rotation. The swung surface is an extension to the surface of
revolution. We still need a profile curve that rotates about the axis
of revolution; but, the rotation *does not* have to be 360 degree
and is controlled by a ** trajectory curve**.

Now, the profile curve swings about the axis of revolution, guided by the
trajectory curve. At the same time, the profile curve is also
*scaled* according to the trajectory curve. Without using mathematics
it is difficult to present complete overview here. But, an example could
help understand this process. The following figure contains two curves.
The black one (on the *xz*-plane) is the profile curve, while the
blue curve (on the *xy*-plane) is the trajectory curve.
Click **here** to download a copy of this
file **swung-2.dat**.

The *z*-axis is taken to be the axis of revolution. If the profile
curve swings about the *z*-axis and is scaled by the trajectory
curve in the *xy*-direction, the generated surface looks like the profile
curve in one direction while looks like the trajectory curve in the other
direction. The following
shows the result. It is not difficult to see that the curves that are
approximately horizontal look like the trajectory curve and are scaled
(*i.e.*, if the profile curve has a smaller value at a point, the
"image" of the corresponding trajectory curve becomes smaller).
On the other hand, those vertical curves all have the same shape of the
profile curve. This is the swung surface generated from the given
profile and trajectory curves.

To generate a swung surface, one need to design a profile curve and a
trajectory curve. First, select
**Advanced Features** followed by
**Cross Sectional Design**. This will
bring up the curve system. Please always follow the steps below:

- First, design the profile curve in the
*xz*-plane. You can design this curve in the*xy*-plane and rotate it 90 degree about the*x*, bringing it to the*xz*-plane. - Then, design the trajectory curve in the
*xy*-plane. - After adjusting the positions of these two curves,
in the curve system, use
**Curve**, followed by**Next Curve Segment**to make the profile curve the current curve segment. - Select
**Techniques**, followed by**Generate Swung Surface**. The swung surface defined by these two curves will be shown on the drawing canvas of the surface system.

In the following, the profile curve, which must be designed first, is shown in blank and the trajectory curve is shown in blue.

The following is the generated swung surface. As you can see from the figures, the profile curve provides the "vertical shape" while the trajectory curve gives the "horizontal shape", which is of course semi-circular. Please note that due to scaling, this vase is "fatter" than the one generated by revolution.

As you see from the following figures, the generated swung vase is more squarish than the previous one.

The following shows the resulting swung surface in both rendered patch and wireframe forms.

The following is the resulting swung surface.

The following is the resulting swung surface. The swinging of the circle
generates a tube (*i.e.*, a cylinder). But, due to the scaling, the two
openings at both ends are not perpendicular to the axis of the cylinder.

The following is the resulting swung surface. It is clear that in the horizontal direction the swung surface does have a S shape, while the in the vertical direction preserves the vase-like shape. However, due to scaling, the surface looks a little odd.