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

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

Answer 1

[ha ha]

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);

Answer 2

[Jan]

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);

See also: https://www.mathworks.com/help/matlab/ref/hgtransform.html

[Matt J]

See also Syntax 3 of this FEX file.

[ha ha]

@Jan. I follow you recommend code, & plot the result. The surface is roatated about Z axis, 10degree. It's acceptable. But as you observed, the surface is rotated and also translate. It is NOT only rotate. I prefer that it will be rotated around the center only. Can you check it?

[Matt J]

The AxelRot.m file that I provided a link to will allow you to specify an axis of rotation.

[Bruno Luong]

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);

% Rotate about the center
xyc = [mean(x), mean(y)];
theta = 30/180*pi;
R = [cos(theta) -sin(theta); 
     sin(theta)  cos(theta)];
XY = xyc' + R * ([X(:) Y(:)]-xyc)';
XR = reshape(XY(1,:),size(X));
YR = reshape(XY(2,:),size(Y));

close all
surf(X,Y,z);
hold on
surf(XR,YR,z);

[ha ha]

Thank so much @Bruno Luong

Thank so much @ Matt J

[ha ha]

@ Matt J @Bruno Luong @Jan . Can you help me this topic also? Thanks a lot.

https://www.mathworks.com/matlabcentral/answers/431656-rotate-the-3d-point-data-about-z-axis-and-ox-oy

[Jan]

@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.