Re: button-hole problem

Hi Peter, and all,

Concerning radial projection in R^3 from a finite point X to a finite plane P
not containing X, you (Sat, 23 Apr 2005) discussed the image of a
circle C in R^3 that is in the plane P' parallel to P and containing X.

> The only situation where the projection is empty, is when the
> projection point is in the same plane as the circle, and the projection
> plane is parallel to this plane.
> ...
> (Actually, in that case the projection is a line interval at infinity.
> So in projective space the projection is again non-empty. And again a
> conic section, now a degenerate ellipse.)

Almost right. 

Let L be the line at infinity of the plane P (or P').
The projection of C always lies in L. But:

 -- the projection of C is a (closed) interval in L only
if the projection center X lies outside the circle C in plane P'.

 -- the projection of C is the whole line L at infinity if the projection
center X lies *inside or on* the circle C in plane P'.

Geometers like to avoid this sort of hair splitting by discussing 
generic cases only.

Whether programmers can afford to do likewise is a good question.

Cheers

Laurent S.