## A rotating circle in perspective

We are looking at a circle of radius $1@ placed
in the plane $z=-2@, projected through perspective
onto the plane $z=-1@. We rotate it around
the axis $z=-2@, $y=0@ to
see what effects are visible.
Notice how the illusion of three dimensioanlity
is created by a small trick. Even with
the thickened disk, but without the cross-bar, the illusion
is missing.

*
Rotate by grabbing the end node, translate by grabbing the middle one.
On the left in each case is the view in
perspective, on the right a side view.
*

There are a number
of things to think about in these pictures.
When the circle is on the axis, at first the
rotation looks like a translation.
If the circle
is off the $z@ axis, there are two locations where you get a circular
image. One is parallel to the perspective plane, of course.
The perspective image *seems* in general
to be an ellipse,
although how to calculate its axis of symmetry
is not obvious.

Bill Casselman

Mathematics Department

U. B. C.