Finding an Ellipse in 3-D Space

Date: 06/14/2005 at 09:48:21
From: Farhat
Subject: three dimensional curve approximation

I want to fit an ellipse to a set of 3D data points.  Can you help?

Date: 06/14/2005 at 12:16:01
From: Doctor George
Subject: Re: three dimensional curve approximation

Hi Farhat,

Thanks for writing to Doctor Math.

This is not a simple problem, and it goes beyond most of what we do
here at Dr. Math.  Here are links to a couple papers that will point
you in the right direction.

This paper covers circle and ellipse fitting in a plane:

  http://www.ulb.ac.be/assoc/bms/Bulletin/sup962/gander.pdf 

This paper covers circle fitting in space.  You can modify the ideas
here for ellipse fitting in space:

  http://nvl.nist.gov/pub/nistpubs/jres/103/6/j36sha.pdf 

Write again if you need more help.

- Doctor George, The Math Forum
  http://mathforum.org/dr.math/