# Fitting a rotated ellipse to data points [closed]

I have a bunch of x,y scatter data and I am trying to fit an ellipse through them. I understand that this question has been asked before and there are resources for this, e.g.:

Fitting ellipse to 5 given points on the plane

Fitting points to tilted, off-center ellipse

http://forums.wolfram.com/mathgroup/archive/2001/Sep/msg00179.html

However, in my scenario, I need to add in an additional constraint. The ellipse may be rotated, but, it has to rotate about its pivot which is defined by the rightmost/lowest point. I illustrate this problem in the figure below, where the rotation of the 'best-fit' ellipse takes place about its pivot point (circled in red).

In essence, this necessitates that the major semi-axis has to pass through that pivot point.

What would be the best possible way to incorporate this constraint in the ellipse fitting process?

• Could you provide some test data, add a definition of your desired "best fit" (weight functions), and list any Mathematica code you have tried? Otherwise this seems more like a math problem, not a Mathematica issue. – Jens Feb 13 '15 at 4:35
• LinearModelFit used in the second link allows for a Weights option. Simply give the pivot point a very large weight would do the trick, I guess. – Sjoerd C. de Vries Feb 19 '15 at 12:18
• Mmm..., no. That just forces the ellipse to go through that point, not the major axis. – Sjoerd C. de Vries Feb 19 '15 at 12:26