How to rotate a surface(or a 2D plane) in 3D Cartesian coordinate ?

Question

S 2021-9-3

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1446034-how-to-rotate-a-surface-or-a-2d-plane-in-3d-cartesian-coordinate

评论： darova 2021-9-8

Hi everyone,

I am trying the tilt a 2 dimension plane or surface by some small incremental angle along a particular axis (1. about x - axis and 2. about y-axis) using the rotation matrix formula.

for example,

% the 3D volume has a dimension of -  64 x 64 x 64 
% the plane is placed inside the 3D volume and is defined as a set of points
    y = 24:1:40;                
    x(1, 1:size(y,2)) = 32;
    z(1, 1:size(y,2)) = 20;
    plane = [x; y; z];

So, when I try to rotate this plane about a particular axis using the rotation matrix, R = [cos(theta) -sin(theta) 0; sin(theta) cos(theta) 0; 0 0 1], I am not able to find the new values of the x, y and z point for the considered plane correctly.

I also have confusion about the rotation (pitch, yaw and roll).

Therefore, if someone could please help me understand the concept about the rotation and suggest a correct way to appraoch the problem.

Thank you.