Date  File  Comment by  Comment  Rating 

14 Aug 2014  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  David  Hmmm....
so it seems the optimization for minimum area is to maximize, rather than minimize, log(det(A)). Also, for small d, it may be easier to obtain semi major/minor lengths (a, b) by finding the eigenvalues/vectors of A (eigenvalues are 1/a^2, 1/b^2, etc, rotation matrix columns are the eigenvectors). I'm finding this algorithm gives me det(A) < 0 (a hyperbola) for some point sets. Also, A should be invariant under translation of all the input points (which should just result in a translation of c), but I find it is quite sensitive. 

12 Jun 2014  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  Anton Semechko  sweet, thanks! 

10 Jun 2014  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  Pengju  
28 Aug 2013  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  lan  wonderful！！ 

17 Mar 2013  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  Javier  Hi, thanks for sharing the code it's really good. One question, please could you explain me which it's the differente between this method and least squares? Thank you very much 

11 Jun 2012  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  banjo  thanks. This is good. 

08 Mar 2012  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  Sepehr Farhand  
08 Mar 2012  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  Sepehr Farhand  
15 Nov 2011  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  Glib  
12 Oct 2011  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  Kwame  Can you please show me an example of the function inputs? I keep getting errors about my inputs. 

06 Sep 2011  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  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. 

20 Aug 2011  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  LIAO xj  
18 Feb 2011  Regular Polygons Plots the regular polygon {N/d} with vertices on a circle of radius 'rad'.  laleh  
14 Dec 2010  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  Jimmy  Error appears when I use your function.


17 Aug 2010  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  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 

17 Jul 2010  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  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?


03 Jun 2010  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  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 

05 May 2010  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  Reza Jafari  I would like to thank you the author for the useful code which he developed. It solved many of my problems. The only problem which I faced was due to the singularity of Matrix X in line 76 and singularity of Matrix P * U * P'  (P * u)*(P*u)' in line 96. Do you have any suggestion to avoid singularity for these two matrices? Appreciated. Regards,


26 Jan 2010  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  Rashed  Hi, I have a problem in 3D. Say, I have an 3D array of P(5,5,5) and how can I make this to work? Please suggest. Or, do I need to produce a matrix P containing the coordinates of the region? 

25 Jan 2010  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  Rashed  Thanks a lot. I was looking for something like this. 

18 Jun 2009  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  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 

18 Jun 2009  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  Nima Moshtagh  Here is a paper describing the algorithm and math behind the code: http://www.seas.upenn.edu/~nima/papers/Mim_vol_ellipse.pdf


15 Feb 2009  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  Tony Mei  Terrific!


08 Feb 2009  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  Avinash Uppuluri  Can you also provide a good journal reference for this algorithm. Thanks! 

08 Feb 2009  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  Avinash Uppuluri  Hello Nima Moshtagh, The code posted was very useful. Is there a way to add a weight to the points, giving the importance of each point to be included within the ellipse. (Instead of using the tolerance which excludes points through the periphery). With the idea that points that are of less significance need not be included in the ellipse. Where can I include such a weighing parameter. I can probably do it in the preprocessing stage but is there a way to include it within your code. Thanks! 

18 Oct 2008  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  THank you 

04 Sep 2008  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  Very good program. It has helped me a lot to do with the matlab. Thanks to Nima Moshtagh for submitting the code. 

04 Sep 2008  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  Earlier I was doing only maths! But this has given me the joy of visualization. 

27 May 2008  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  Exactly what I was searching for! Thanks!:) 

28 Apr 2008  Regular Polygons Plots the regular polygon {N/d} with vertices on a circle of radius 'rad'.  
08 Apr 2008  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  works like a charm 

15 Nov 2007  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  Dear Ondrej Danko,


15 Nov 2007  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  "Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space"... I would expect that resulting ellipsoid COVERS all points, I mean no points are outside of the resulting ellipsoid... I had ran a small test if it is so... and surprisingly not all points are necessarily inside. P = rand(3,N);
I am missing something, or it is expected? If expected, any suggestions to modify the algorithm to output ellipsoid strictly covering all points? 

20 Oct 2007  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  I found it quite easy to use and read. 

22 Mar 2007  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  Reply to John Huddleston's comment: Function ellipsoid.m is an standard MATLAB command. It is included in version R13. 

18 Mar 2007  Plot an ellipse in "center form" Draws 2D and 3D ellipses that are given in "center form".  The ellipsoid.m function is missing [X,Y,Z] = ellipsoid(0,0,0,a,b,c,N); 

07 Feb 2007  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  I find that the run time can be radically improved by recognizing that the only points that determine the bounding ellipsoid are on the convex hull, as used by John D'Errico in his minboundsphere. Given points P, the following code finds the reduced set of points lying on the hull. K=convhulln(P.');
for P=randn(3,500)
and finds Q followed by MinVolEllipse(Q, .001) in 0.08 seconds 

16 Sep 2006  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  This is a very good program for doing minimum volume ellipsoids. it has been very helpful and the author has as well. 

29 Aug 2006  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  Excellent stuff! This was exactly what I was looking for and works quite well. Although the math behind it all was a bit beyond me, the author was more than helpful in helping me make the most of what the code has to offer, thanks again Nima! 

15 Jan 2006  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  For tolerance=0.01 in 2D here is how long it takes (approximatly) to find the covering ellipse on a 2.4GHz computer: #point time(sec)


09 Jan 2006  Minimum Volume Enclosing Ellipsoid Computes the minimumvolume covering ellipoid that encloses N points in a Ddimensional space.  This could be useful IF you have small sets of data. I tested this for several problems, in 1, 2 and 5 dimensions. All seemed to work. The only downside is data of even moderate size. The author gives an example with 100 points, solved fairly quickly. But expand that to only 500 points (in 2d) and it takes 140 seconds to run on my computer. 
