[metapost] Constructing ellipse from 4 points

[Brooks Moses]

At 10:36 AM 11/2/2005, Laurence Finston wrote:
[...]
>It seems to me that it ought to be possible to construct an ellipse
>from the four points v0, v1, h0, and h1.  Does anyone here know how, or
>know where I could look to find out?
>
>Any help would be much appreciated.

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

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.  The first of those links provides 
two ways of doing the first two of those constructions; the last link 
provides the last.

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.

- Brooks