# rotation meshgrid surface with the predefined angel(using rotation matrix)

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ha ha on 23 Nov 2018
Commented: Jan on 24 Nov 2018
Let's say:
x=1:0.2:1.8= [1 1.2 1.4 1.6 1.8];
y=2:0.2:3 = [2 2.2 2.4 2.6 2.8 3];
z=[2 5 2 2 2; 2.1 2.1 2.1 2.1 2.1; 2 2 2 2 2; 3 3 3 3 3; 1 1 1 1 1; 2.5 2.5 2.5 2.5 2.5]; %matrix 6-by-5
[X,Y] = meshgrid(x,y);
surf(X,Y,Z);% the plot show below
The question is: How can I rotate the plot data with the angel=10 (degree), counterclockwise about Z axis, & How can I plot the new meshgrid surface (using the new rotate data) as the below figure?
angel=10;
R=[cosd(angel) -sind(angel) 0;sind(angel) cosd(angel) 0;0 0 1];%the rotation matrix R
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### Accepted Answer

ha ha on 23 Nov 2018
Edited: ha ha on 23 Nov 2018
clear;clc;x = 1:0.2:1.8;
y = 2:0.2:3;
z=[ 2 5 2 2 2;2.1 2.1 2.1 2.1 2.1;2 2 2 2 2;3 3 3 3 3;1 1 1 1 1;2.5 2.5 2.5 2.5 2.5];
[X,Y] = meshgrid(x,y);
xyc = [mean(x), mean(y)];% Rotate about the center
angel = 30;
R = [cosd(angel), -sind(angel); sind(angel), cosd(angel)];
XY = xyc' + R * ([X(:) Y(:)]-xyc)';
XR = reshape(XY(1,:),size(X));
YR = reshape(XY(2,:),size(Y));
surf(X,Y,z);
hold on;surf(XR,YR,z);
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### More Answers (1)

Jan on 23 Nov 2018
Edited: Jan on 23 Nov 2018
A 2D rotation is sufficient, if you want to rotate the X and Y coordinates only.
x = 1:0.2:1.8; % [1 1.2 1.4 1.6 1.8];
y = 2:0.2:3; % [2 2.2 2.4 2.6 2.8 3];
Z = [2 , 5, 2, 2, 2; 2.1, 2.1, 2.1, 2.1, 2.1; 2, 2, 2, 2, 2; ...
3, 3, 3 3 3; 1 1 1 1 1; 2.5 2.5 2.5 2.5 2.5]; %matrix 6-by-5
[X, Y] = meshgrid(x,y);
subplot(1,2,1)
surf(X,Y,Z);
angel = 10;
R = [cosd(angel), -sind(angel); sind(angel), cosd(angel)];
XY = R * [X(:).'; Y(:).'];
XX = reshape(XY(1, :), size(X));
YY = reshape(XY(2, :), size(Y);
subplot(1,2,2)
surf(XX, YY, Z);
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Jan on 24 Nov 2018
@haha: Please do not advertise another thread. Imagine the pollution of the forum, if all users would do this. Thanks.
"But as you observed, the surface is rotated and also translate. It is NOT only rotate." - My suggested code was a pure rotation around the origin of the corrdinate system. The modification by removing the mean of the points at first and add them after a rotation includes a translation in addition.

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