How can I rotate a matrix 45 degrees?

I want to rotate this matrix by 45 degrees:

C = [-6 -6 -7 0 7 6 6 -3 -3 0 0 -6; -7 2 1 8 1 2 -7 -7 -2 -2 -7 -7]

C = 2×12

-6 -6 -7 0 7 6 6 -3 -3 0 0 -6 -7 2 1 8 1 2 -7 -7 -2 -2 -7 -7

plot(C(1,:),C(2,:)), xlim([-10 10]), ylim([-10 10])

It plots a simple house shape. I want to take this matrix, or the house rather, and rotate it 45 degrees, and then flip it after the rotation. How would I do that?

Answer 1

[Kevin Holly]

C = [-6 -6 -7 0 7 6 6 -3 -3 0 0 -6; -7 2 1 8 1 2 -7 -7 -2 -2 -7 -7];

p = plot(C(1,:),C(2,:)); xlim([-10 10]); ylim([-10 10]);
rotate(p,[0,0,1],45)

figure
plot(-p.XData,p.YData)
xlim([-10 10])
ylim([-10 10])

[Connor Mondock]

Awesome thanks!

[Connor Mondock]

Actually the second part where it flips doesnt work for me the code where it gets flipped it says "Unable to resolve the name p.XData" any reason why?

[Kevin Holly]

Did you save the plot with the variable name p?

p = plot(C(1,:),C(2,:));

[Connor Mondock]

No I used D instead that was an easy fix thanks

Answer 2

[Jan]

C = [-6 -6 -7 0 7 6 6 -3 -3 0 0 -6; -7 2 1 8 1 2 -7 -7 -2 -2 -7 -7]

C = 2×12

-6 -6 -7 0 7 6 6 -3 -3 0 0 -6 -7 2 1 8 1 2 -7 -7 -2 -2 -7 -7

plot(C(1,:),C(2,:));
xlim([-10 10]);
ylim([-10 10]);
axis equal
hold on;

% Rotate coordinates by 45 deg clockwise:
D = [cosd(45), sind(45); -sind(45), cosd(45)] * C;  % [EDITED, Typo fixed, thanks Alan]
plot(D(1,:), D(2,:), 'r');

Mirroring the y coordinates is a multiplication by [1, 0; 0, -1].

[shubham kumar gupta]

can you tell for higher than 2x12 ? like 3x12?

[Jan]

See this for general rotation matrices in N-D: https://www.mathworks.com/matlabcentral/fileexchange/66446-rotation-matrix

[Alan Keenan]

D = [cosd(45), sind(45); -sind(45), cos(45)] * C;

Why is the last term in the rotation matrix cos rather than cosd?

I have tried this with:

x = -14e-3:1e-3:14e-3;

y = 20e-3:2e-3:34e-3;

when I multyply the x,y combination with the rotation matrix all of the transformed co-ordinates are positive, in your example there is a mix of positive and negative transformed coordinates, why is this?

thanks

[Jan]

@Alan Keenan: "Why is the last term in the rotation matrix cos rather than cosd?" - This is called a typo. Thanks for finding it. The code is fixed now.

You have tried what? Please post your code instead of letting me guess, what "multiply x,y combination" exactly means.

% Maybe:
x = -14e-3:1e-3:14e-3;
y = 20e-3:2e-3:34e-3;
R = [cosd(45), sind(45); -sind(45), cosd(45)];
axes('NextPlot', 'add');  % as: hold('on')
for ix = 1:numel(x)
    for iy = 1:numel(y)
        plot(x(ix), y(iy), 'ro');
        xy2 = R * [x(ix); y(iy)];
        plot(xy2(1), xy2(2), 'bo');
    end
end

Now you ask, why all rotated X and Y coordinates of your example are positive, but with my example data, there are negative values also?

Well, isn't this trivial? A rotation around the origin by 45° moves some points to the 1st quadrant, and some not.

[Alan Keenan]

Thanks for your feedback, I can see now that I need to have my co-ordinates equispaced around the 0,0 origin.

So, instead of x = -14e-3:1e-3:14e-3; y = 20e-3:2e-3:34e-3;

I have used x = -14e-3:1e-3:14e-3; y = -7e-3:2e-3:7e-3;

It gives the following rotation:

I can then add the offset value after the rotation so that I still have the original co-ordinates.