Hi! Everyone,

Because no one has touched the problem I posted last week, I guess
my question was not so clear. Now I'd like to describe it in detail:

The offset of an ellipse is the locus of the center of a circle which
rolls on the ellipse. In other words, the distance between the ellipse
and its offset is same everywhere.

This problem comes from the geometric measurement when a probe is used.
The tip of the probe is a ball and the computer just outputs the
positions of the ball's center. Is the offset of an ellipse still
an ellipse? The answer is no! Ironically, DMIS - an American Indutrial
Standard says it is ellipse. So almost all the software which was
implemented on the base of DMIS was wrong. The software was also sold
internationaly. Imagine, how many people have or will suffer from this bug!!!
How many qualified parts with ellipse were/will be discarded? And most
importantly, how many defective parts with ellipse are/will be used?

I was employed as a consultant by a company in Los Angeles last year
to specially solve this problem. I spent two months on analysis of this
problem and six months on programming. Now my solution (nonlinear)
is not ideal because I can only reconstruct an ellipse from its entire
or half offset. It is very difficult to find the original ellipse from
a quarter or a segment of its offset because the method I used is not
analytical. I am now wondering if I didn't touch the base and make things
complicated. Please give me a hint.

I know you may argue this is not a CG problem. You are right, it is not.
However, so many people involved in the problem "sphere from 4 poits".
Why not an ellipse? And why not its offset?

Please post here and let the others share our interests 
(I got several emails from our netters, they said they need the
summary of the answers).