Rotate the all center positions in the certain angle

I have 4 data points with x and y coordinates and I want to rotate them at certain angle in counterclockwise or clockwise.

Assume (x1,y1), (x2,y2), (x3,y3) and (x4,y4).

Is there a way to rotate them and find the new positions after rotating?

Thanks

Answer 1

[Anand]

If you have the Image Processing Toolbox, you can use the affine2d object to help you with this. Here's an example of how:

Let's say you're points are (1,1),(100,1),(1,100) and (100,100) and you want to rotate them by 45 degrees.

    %these are the points to rotate
    X = [  1   1;...
         100   1;...
           1 100;...
         100 100];
    %define a transformation matrix for 45 degree rotation
    theta = 45;
    T = [cosd(theta) sind(theta) 0;sind(theta) -cosd(theta) 0;0 0 1];

    %construct an affine2d object using this transformation matrix
    tform = affine2d(T);

    %transform the points in X to new co-ordinates U using the affine2d object
    U = transformPointsForward(tform,X)

    U =

        1.4142         0
       71.4178   70.0036
       71.4178  -70.0036
      141.4214         0

Hope this helps!

[Laura]

Thanks for your answers. I dont think my matlab has affine2d package.

Is there other way around to do it without using affine2d

[Anand]

Yes there is a way to do it without an affine2d object:

%pad X with a column of 1's for z.
X = [X ones(size(X,1),1)];

%transform points in X to new co-ordinates
U = X*T;

%remove the z
U = U(:,1:2)

[Laura]

It makes sense that (1,1) will go to (1.4 , 0) after 45 degree of rotating.

But if you replace (1,1) by (1,0), now the new position is (0.7, 0.7). It does not rotate in the same direction. One is clockwise and other is counterclockwise.

Answer 2

[Matt J]

You can also embed the points into 3D and use

http://www.mathworks.com/matlabcentral/fileexchange/30864-3d-rotation-about-shifted-axis