[help-3dldf] Re: [metafont] Re: button-hole problem

[Peter Vanroose]

> On the image plane it is a conic section, ie an ellipse, a
> parabola, or hyperbola.
...
> After I posted my question, I was somewhat mortified when I
> remembered something about circles in perspective always being
> ellipses.

No, circles can indeed project as a parabola or a hyperbola.
Take the following example:

- project onto a horizontal plane.
- place a circle vertically with its lowest L point on that plane.
- take as projection "eye" point P any point which is at the same
height above the plane as the highest point H of the circle.

In this case the projection is a parabola, with its top in L and its
axis parallel to the line PH.

If you want a hyperbola, move the eye point P a bit down (towards the
projection plane). If you want an ellipse, move P upward.


--      Peter.