Rotation of a 3D vector field around axis

Hi all,

I am trying to rotate a vector field V described by its x,y and z components (Vx,Vy,Vz) and all three having dimensions of a 51x51x51 matrix. I am trying to rotate it around the y-axis of an angle theta. However, when I plot the streamlines of the field it looks very weird (figure 1). Basically, I am trying to tilt the streamlines in red to meet the green ones (figure 2). What I am currently doing is calculating the field over an x-y-z grid, then rotate the three components by use of the rotation matrix and finally plot the streamlines over the original mesh (i.e. I require the xyz coordinates to remain in place whilst the vector direction is rotated by theta.

Thanks in advance for any help provided!

Answer 1

[Gautam]

Hello @AC95,

I was able to rotate the vector field about the y-axis using a rotation matrix

Here's the code uses a rotation matrix to rotate the vector field counter-clockwise by an arbitrary angle “theta”

load wind 
hold on 

% Original streamline plot 
l1 = streamslice(x,y,z,u,v,w,[],[],5, 0.2, "noarrows"); 
axis tight 

theta = pi / 4; % Example: 45 degrees 

% Define the rotation matrix around the y-axis 
Ry = [cos(theta), 0, sin(theta); 
    0, 1, 0; 
    -sin(theta), 0, cos(theta)]; 

Vx_rot = zeros(size(u)); 
Vy_rot = zeros(size(v)); 
Vz_rot = zeros(size(w)); 

for i = 1:size(u, 1) 
    for j = 1:size(u, 2) 
        for k = 1:size(u, 3) 
            % Original vector 
            V = [u(i, j, k); v(i, j, k); w(i, j, k)]; 
            
            % Rotated vector 
            V_rot = Ry * V; 
            
            % Store the rotated components 
            Vx_rot(i, j, k) = V_rot(1); 
            Vy_rot(i, j, k) = V_rot(2); 
            Vz_rot(i, j, k) = V_rot(3); 
        end 
    end 
end 

% Rotated streamline plot 
l2 = streamslice(x,y,z,Vx_rot,Vy_rot,Vz_rot,[],[],5, 0.2,'noarrows'); 
set(l2,'Color','r'); 

hold off 

Below is the output

In this, the red streamlines are rotated by 45 degrees with respect to the blue streamlines.