Does a sphere projected into 2D space always result in an ellipse? My intuition has always been that when any sphere is projected into 2D space that the result will always mathematically be an ellipse (or a circle in degenerate cases).

In the past when I was actively doing my own graphics programming and brought this up with other people they were adamant that I was wrong. If I recall correctly they believed the result could be something vaguely "egg shaped".

Who was correct?



Since there is already one answer submitted, I don't wish to totally change my question but I realize I left out important details due to losing familiarity with the field over the years.

I intended to ask specifically about perspective projection where the projection is a linear application.

The other projections are of course interesting for many uses so I wouldn't want them removed at this point. But it would be great if answers could have perspective projection as their most prominent section.
Assuming a perspective projection and a view point external to the sphere, then the 'boundary' formed by the view point and the circle on the sphere which forms the horizon WRT the view point, will be a cone. 

Doing a perspective projection (onto a plane) is then equivalent to intersecting this cone with the plane which thus produces a conic section. FYI the four, non-degenerate, cases are shown in this image from Wikipedia  

An ellipse/circle is thus a possibility, but not the only one - unbounded parabolas or hyperbolas (and I guess if the plane passes through the eye, even degenerate cases ) are possible.