Rotate a 2D plot around a specific point on the plot?

Hello, I am trying to rotate an object (a plot of a propeller blade cross-section) around a specific point on the plot.

I was given a large list of coordinates to plot. After plotting these many points, the following is plotted:

Now, I need to rotate this blade by a certain number of degrees around a certain point on the plot, for example (0,0), counter-clockwise.

I need to not do this just once, but 205 times (I will use a loop, obviously), and replot each figure on top of eachother, separated by a certain distance in the Z-Plane, so that the plot looks like a wind turbine blade. How can I achieve this?

Answer 1

[Jim Riggs]

% Given data vectors X and Y.  
% Want to rotate the data  through angle "ang" about rotation center Xc, Yc
X = [..];
Y = [..];
ang = ..;
% Specify the coordinates of the center of rotation
Xc = 0.25 ;  % Rotate about the 1/4 chord point
Yc = 0 ;

% The data is roated in a three-step process
% Step 1) Shift the data to the rotation center
Xs = X - Xc;  % shifted data
Ys = Y - Yc;
% Step 2) Rotate the data
Xsr =  Xs*cos(ang) + Ys*sin(ang);    % shifted and rotated data
Ysr = -Xs*sin(ang) + Ys*cos(ang);    %
% Step 3) Un-shift the data (back to the original coordinate system)
Xr = Xsr + Xc;  % Rotated data
Yr = Ysr + Yc;

The above three steps can be combined into a single step:

Xr =  (X-Xc)*cos(ang) + (Y-Yc)*sin(ang) + Xc;
Yr = -(X-Xc)*sin(ang) + (Y-Yc)*cos(ang) + Yc;

Answer 2

[Luna]

I think you can easily use rotate function which already manipulates the data. It is different from view.

rotate

Here for you I have created a simple line and a figure, with a 10 times for loop.

Each time rotated, plots the manipulated data again with holding on, according to origin.

x = 1:10;
y = randi(10,1,10)
figure;
h = plot(x,y);

for i = 1:10    
    rotate(h,[0 0],20); % rotate h line, by [0 0] point, with 20 degrees
    hold on;
    plot(h.XData,h.YData, 'color','b')
end

[Image Analyst]

[Luna]

Yes, it gives something like this, so Ryan can plot his eliptic line (which I don't know its formula) with the same method so hopefully it looks like a turbine blade.