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.