Draw angled ellipses around clusters on PCA plot

I would like to draw angled ellipses around clusters in a PCA plot representing the 95% CI for this cluster, similar to what is done by autoplot in R (also, see attached example, or this link https://r-charts.com/correlation/scatter-plot-ellipses-ggplot2/). Any resources for how to do this in matlab, or the math behind how to do this would be much appreciated!

As a note: I did see a post on this forum where people drew ellipses in line with the axes where the height of the ellipse is the 95% CI in X and the width is the 95% CI in Y; this is NOT what I would like, I would like the ellipses at an angle that fits the shape of the clusters, as shown in my examples

Answer 1

[Mathieu NOE]

hello

like this ?

Plot ellipse on scattered 2D data - File Exchange - MATLAB Central (mathworks.com)

see files in attachment

[Reed Trende]

Yes that's perfect, thank you!

Answer 2

[Matt J]

See also elliipticalFit from the FEX downloadable,

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics

It can also be used to plot ellipses as well as fit them, e.g.,

[Center,Axes,Angle]=deal([0 2] , [2 1], 30);    %Ellipse parameters
     
plot( ellipticalFit.groundtruth([],Center,Axes,Angle) );     

Answer 3

[Matt J]

Using polyshapes:

ellipse=rotate( scale(nsidedpoly(1000),[2,1]) ,30);

plot(ellipse)