[help-3dldf] Re: [metapost] Constructing ellipse from 4 points (fwd)

[Laurence Finston]

---------- Forwarded message ----------
Date: Wed, 02 Nov 2005 11:02:26 -0800
From: Brooks Moses <address@hidden>
To: Laurence Finston <address@hidden>, liste metafont <address@hidden>,
     help-3dldf <address@hidden>, address@hidden
Subject: Re: [metapost] Constructing ellipse from 4 points

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