How to roll a 2d plot into a cylinder which then revolves?

Solution of an O.D.E. in a simple 1st order decay problem (that has periodic inputs) has yielded a 2d c vs t plot, with two curves: one for day 1, and the other, for day infinity; namely the cyclic steady state when day n+1 and day n yield the same c vs t curves. The second curve has the same c at te beginning and at the end of a 24 hr cycle, as it should. For engineering purposes, this plot is sufficient. But I want to make it jazzy and roll it up into a cylinder (which I can readily do with a print of the plot on paper), on the screen. The cylinder should revolve slowly about the z axis, thus illustrating the process cycle.

Answer 1

[KSSV]

YOu may procedd something like below:

Radius = 1. ;           % Radius of the cylindrical shell
theta = 360. ;           % Angle of the Cylinder
Height = 2. ;           % Height of the Cylinder
%
NH = 10 ;                % Number of Elements on the Height
NT = 300 ;               % Number of Angular Dicretisation 

% Discretizing the Height and Angle of the cylinder
nH = linspace(0,Height,NH) ;
nT = linspace(0,theta,NT)*pi/180 ;
[H, T] = meshgrid(nH,nT) ;
% Convert grid to cylindrical coordintes
X = Radius*cos(T); 
Y = Radius*sin(T);
Z = H ;

th = linspace(0,2*pi) ;
R = @(th) [1 0 0 ;0 cos(th) -sin(th) ; 0 sin(th) cos(th)] ; % rotation matrix alon x-axes
h = surf(X,Y,Z) ;
axis([-2 2 -2 2 -2 2])
coor = [X(:) Y(:) Z(:)] ;
for i = 1:length(th)
    
    coor1 = coor*R(th(i)) ;
    X1 = reshape(coor1(:,1),NT,NH) ; 
    Y1 = reshape(coor1(:,2),NT,NH) ; 
    Z1 = reshape(coor1(:,3),NT,NH) ; 
    set(h,'XData',X1,'YData',Y1,'ZData',Z1) ;
    drawnow    
    pause(0.1)
end

[Sree]

Thanks. I am making progress with the function warp in the image processing toolbox: