Fitting a 3D circle to a lobsided set of points

Hi all,

Suppose I have a set of 3D points that are roughly in one quadrant of
a circle, and I want to find the plane that they are on, as well as
the center of the circle (and, maybe its radius). Finding the plane
isn't too hard -- simple least-squares fit. Getting the actual circle
is somewhat harder.

I have seen least-squares types of approaches that use SVD, but they
all assume that the center of the circle is at the centroid of the 3D
points. In my case, this is not true.

I have also seen global optimization methods that try to solve similar
problems (like for the center and radius of a sphere). However, I am
worried that such an approach will be quite slow if I do not have some
bounds on how large the circle's radius can be.

So, I'm wondering what other options are out there. Any ideas would be
appreciated.

Thanks.

Dave
.