how can I rotate the ellipses based on the orientation angle of (x_i,y_i)?

I would like to rotate the ellipses to show the orientation, theta, of the centered data points.

Answer 1

[KSSV]

a=5; % horizontal radius
b=10; % vertical radius
x0=0; % x0,y0 ellipse centre coordinates
y0=0;
t=-pi:0.01:pi;
x=x0+a*cos(t);
y=y0+b*sin(t);
plot(x,y)
hold on
%%Rotate the ellipse by 90 degrees 
th = pi/2 ;

R = [cos(th) -sin(th) ; sin(th) cos(th)] ;
% Rotate all the points 
P = zeros(2,length(x)) ;
for i =1:length(x)
    P(:,i) = R*[x(i) ;y(i)] ;
end
xr = P(1,:) ; yr = P(2,:) ;
plot(xr,yr,'r')

[KSSV]

You have not given any data here...Provided you know the angle of theta by which you want to rotate ellipse....this is the way to rotate. Your question was this only, how to rotate ellipse.

[KSSV]

Thanks is accepting the answer...

[KSSV]

YOu have to run it in a loop....

for i = 1:length(x_i) ;
     P(:,i) = R * [x_i(i) ; y_i(i)];
 end

Answer 2

[Giulio Antufermo]

It didn't really work for me