Plot an ellipse in "center form"

Draws 2D and 3D ellipses that are given in "center form".

Description

Ellipse_plot(A,c)

This function draws an N-dimensional ellipse (N = 2,3) that is given in "center form":

(x - C)' A (x - C) <= 1

where C is the center of the ellipse, and A is an NxN positive definite symmetric matrix.

A and C could be the outputs of the function: "MinVolEllipse.m", which computes the minimum volume enclosing ellipsoid containing a set of points in an N-dimensional space. For example, you can use this function as follows:

  P = rand(3,100);
  t = 0.001;
  [A , C] = MinVolEllipse(P, t)
  figure
  plot3(P(1,:),P(2,:),P(3,:),'*')
  hold on
  Ellipse_plot(A,C)

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Minimum Volume Enclosing Ellipsoid

• MATLAB release: MATLAB 6.5 (R13)

[John Huddleston]

The ellipsoid.m function is missing

[X,Y,Z] = ellipsoid(0,0,0,a,b,c,N);

[nima moshtagh]

Reply to John Huddleston's comment:

Function ellipsoid.m is an standard MATLAB command. It is included in version R13.

[Blake Richards]

I found it quite easy to use and read.

[david torres]

works like a charm

[Gergely Takacs]

Exactly what I was searching for! Thanks!:)

[Santanu Ghorai]

Earlier I was doing only maths! But this has given me the joy of visualization.

[Tony Mei]

Terrific!
Well, good programs! However, Nima, could you please show me some reference link to the mathematical basis of your algorithm ? Thanks a lot.

[Nima Moshtagh]

Here is a paper describing the "minimum volume enclosing ellipse" algorithm and the math behind the code: http://www.seas.upenn.edu/~nima/papers/Mim_vol_ellipse.pdf

[Bismark Nkansah]

Good work, Nima. I've been trying to follow the link to study the mathematical basis for the algoritm, but without success. Could you please help me?
Is it possible that in determining the minimum volume we can assign weights to the points such that the farther away a point is from the main 'cloud' the smaller its weight?
Thanks a lot.

[Nima Moshtagh]

Here is a link to the (unpublished) paper describing the algorithm and math behind the code:

https://sites.google.com/site/nimamoshtagh/software/MVEE.pdf?attredirects=0

[Jimmy]

Error appears when I use your function.
I found that there is another ellipsoid.m in my external toolbox.
Maybe this ellipsoid.m is called instead of that in Matlab.
So, how to solve this problem?

[LIAO xj]

 

[Ahmed Fasih]

To plot just circles with "r" radius, pass in eye(2)*(r)^-2 as the covariance matrix. A plot function like this shouldn't change the plot more than it needs to: I disabled the "grid" and "axis" commands. It should also return handles to the plot objects it creates: I had to add this as well. But this code gets me 95% there, thanks.

[Kwame]

Can you please show me an example of the function inputs? I keep getting errors about my inputs.