[metapost] Constructing ellipse from 4 points

[Laurence Finston]

On Wed, 2 Nov 2005, Brooks Moses wrote:

> A Google search on "ellipse construct 'four points'" finds the following links:
>
>    http://steiner.math.nthu.edu.tw/ne01/whw/Ellipse1/part2.htm
>    http://mathworld.wolfram.com/ConicSection.html
>    http://mathworld.wolfram.com/Ellipse.html

Aha!  I just searched for "ellipse constructions" and found a lot of sites
that didn't look too promising.  Thanks.

>
> The short form is that, to construct an ellipse, you need either five
> points, four points and a tangent line, or four points and knowledge of the
> direction of the major and minor axes.

I can get more points by finding the intersections of the plane with more
of the ellipses on the ellipsoid, and I can get as many of those as I
want.

> Beyond that, I don't know.  My guess is that finding the direction of the
> major and minor axes and using that construction is the way to go.

Thank you for your quick answer.

Laurence