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Plot an ellipse in "center form"

version (2.09 KB) by Nima Moshtagh
Draws 2D and 3D ellipses that are given in "center form".


Updated 16 Nov 2007

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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)
hold on

Cite As

Nima Moshtagh (2021). Plot an ellipse in "center form" (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (19)

Dimitrios Bousias

Uri Cohen


If i multiply A with (1-epsilon) then the ellipse gets bigger which is not logical since i lower the eigen values by multiplying A with a number lower than one and if i multiply A with a number bigger than 1 then the ellipse gets smaller.

Is there a bug?
If not, can you please explain?



Sepehr Farhand


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

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.



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?

Nima Moshtagh

Here is a link to the (unpublished) paper describing the algorithm and math behind the code:

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 paper describing the "minimum volume enclosing ellipse" algorithm and the math behind the code:

Tony Mei

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

Santanu Ghorai

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

Gergely Takacs

Exactly what I was searching for! Thanks!:)

david torres

works like a charm

Blake Richards

I found it quite easy to use and read.

nima moshtagh

Reply to John Huddleston's comment:

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

John Huddleston

The ellipsoid.m function is missing

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

MATLAB Release Compatibility
Created with R13
Compatible with any release
Platform Compatibility
Windows macOS Linux

Inspired by: Minimum Volume Enclosing Ellipsoid

Inspired: fakenmc/amvidc, Ellipsoid Method

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