What is the function to plot a rotating 3-D ellipsoid

I want to make a rotating ellips using mathematical equations on matlab, i must also be able to control rotating speed and direrection

Answer 1

[Amith Kamath]

function [] = visualizeDTrot(C,M,speed,Dir,time)
%%C: the covariance matrix.
%%Dir: direction of the estimate, to be plotted together with the DT ellipsoid.
%%M: the mean vector, usually 0 in case of DT.
%%speed: time to pause between plotting, lowervalue = faster.
%%Dir: 1 or -1 for clockwise, anticlockwise.
%%time: number of iterations for which rotation is needed, higher = longer.

%%example: visualizeDTrot(diag([17 2 2]),[0 0 0],0.4,1,100)

[U,L] = eig(C);

% For N standard deviations spread of data, the radii of the eliipsoid will
% be given by N*SQRT(eigenvalues).

N = 1; % choose your own N
radii = N*sqrt(diag(L));

% generate data for "unrotated" ellipsoid
[xc,yc,zc] = ellipsoid(0,0,0,radii(1),radii(2),radii(3));

% rotate data with orientation matrix U and center M
a = kron(U(:,1),xc); b = kron(U(:,2),yc); c = kron(U(:,3),zc);
data = a+b+c; n = size(data,2);
x = data(1:n,:)+M(1); y = data(n+1:2*n,:)+M(2); z = data(2*n+1:end,:)+M(3);

% now plot the rotated ellipse

if Dir == 1
  i = 1:time;
else 
  i = time:-1:1;
end

for j = i
sc = mesh(x,y,z);
colormap copper
shading interp
zdir = [1 0 0];
axis equal
rotate(sc,zdir,j)
pause(speed)
title('actual ellipsoid represented by data: C and M')
axis equal
xlabel('x axis ---->')
ylabel('y axis ---->')
zlabel('z axis ---->')
alpha(0.5)
end

%%This should do the job!

Credits: http://www.mathworks.com/matlabcentral/newsreader/view_thread/42966