Perspective projection ellipse and ellipsoid still ellipse?

Question

I know that in perspective projection the circle turns into an ellipse. but does it convert to ellipse and ellipsoid to ellipse in perspective projection?

Especially in perspective ellipse is still ellipse?. I read here that this is so in orthographic but is it so in perspective projection?

Answer 1

Yes -- it's surprisingly simple:

1. a circle turns into an ellipse under any perspective projection
2. Combined perspective projections are still perspective projections
3. Every ellipse is a circle in some perspective projection

That means that we can turn a projection $P$ into $(PT^{-1})T$ where $T$ is a projection that turns the given ellipse into a circle.

I think there are some degenerate cases where this breaks down.