save (e.g. gif) a rotation of a 3D geometry around to an axis

I would like to rotate the 3D geometry of a cube around two known nodes.

How can I modify the code?

% ========  CUBE
xc=1; yc=1; zc=1;    % coordinated of the center
L=10;                 % cube size (length of an edge)
alpha=0.8;           % transparency (max=1=opaque)
X = [0 0 0 0 0 1; 1 0 1 1 1 1; 1 0 1 1 1 1; 0 0 0 0 0 1];
Y = [0 0 0 0 1 0; 0 1 0 0 1 1; 0 1 1 1 1 1; 0 0 1 1 1 0];
Z = [0 0 1 0 0 0; 0 0 1 0 0 0; 1 1 1 0 1 1; 1 1 1 0 1 1];
C='blue';                  % unicolor
X = L*(X-0.5) + xc;
Y = L*(Y-0.5) + yc;
Z = L*(Z-0.5) + zc;
fill3(X,Y,Z,C,'FaceAlpha',alpha);    % draw cube
axis equal

% ========  NODES x ROTATION
axes_2_nodes = [-4,-4,6; -4,-4,-4];

% ========  ROTATION
set(gcf, 'Color', [1 1 1])
set(gca, 'Visible', 'off');
for i=1:5:300
    view(i,33)
    pause(0.15)
end

EDIT

Answer 1

[Kautuk Raj]

I understand that you would like to rotate the 3D geometry of a cube around an axis defined by two known nodes and save this rotation as a GIF.

To rotate the 3D geometry of a cube around two known nodes, you need to apply a rotation transformation to the cube vertices. To save the rotating cube animation as a GIF, you can use MATLAB's built-in functionality to capture frames and write them to a GIF file. Here is the modified version of your code:

% ========  CUBE 
xc=1; yc=1; zc=1;    % coordinates of the center 
L=10;                 % cube size (length of an edge) 
alpha=0.8;           % transparency (max=1=opaque) 
X = [0 0 0 0 0 1; 1 0 1 1 1 1; 1 0 1 1 1 1; 0 0 0 0 0 1]; 
Y = [0 0 0 0 1 0; 0 1 0 0 1 1; 0 1 1 1 1 1; 0 0 1 1 1 0]; 
Z = [0 0 1 0 0 0; 0 0 1 0 0 0; 1 1 1 0 1 1; 1 1 1 0 1 1]; 
C='blue';                  % unicolor 
X = L*(X-0.5) + xc; 
Y = L*(Y-0.5) + yc; 
Z = L*(Z-0.5) + zc; 

% ========  NODES x ROTATION 
axes_2_nodes = [-4,-4,6; -4,-4,-4]; 

% Compute the rotation axis and angle 
p1 = axes_2_nodes(1, :); 
p2 = axes_2_nodes(2, :); 
v = p2 - p1;  % direction vector of the axis 
v = v / norm(v);  % normalize the vector 

theta = pi/180;  % rotation angle in radians (1 degree) 

% Create rotation matrix 
R = @(theta) [ 
    cos(theta) + v(1)^2*(1-cos(theta)), v(1)*v(2)*(1-cos(theta)) - v(3)*sin(theta), v(1)*v(3)*(1-cos(theta)) + v(2)*sin(theta); 
    v(2)*v(1)*(1-cos(theta)) + v(3)*sin(theta), cos(theta) + v(2)^2*(1-cos(theta)), v(2)*v(3)*(1-cos(theta)) - v(1)*sin(theta); 
    v(3)*v(1)*(1-cos(theta)) - v(2)*sin(theta), v(3)*v(2)*(1-cos(theta)) + v(1)*sin(theta), cos(theta) + v(3)^2*(1-cos(theta)) 
    ]; 

% Initialize GIF settings 
filename = 'rotating_cube.gif'; 
delay_time = 0.15; 
frame_count = 0; 

% Apply rotation 
set(gcf, 'Color', [1 1 1]) 
set(gca, 'Visible', 'off'); 
hold on; 

for i=1:5:300 
% Rotate each vertex of the cube 
for j = 1:numel(X) 
    point = [X(j) - p1(1); Y(j) - p1(2); Z(j) - p1(3)]; 
    rotated_point = R(theta * i) * point; 
    X(j) = rotated_point(1) + p1(1); 
    Y(j) = rotated_point(2) + p1(2); 
    Z(j) = rotated_point(3) + p1(3); 
end 

% Redraw the cube 
fill3(X,Y,Z,C,'FaceAlpha',alpha); 
axis equal 
view(i,33) 
drawnow; 

% Capture the frame 
frame = getframe(gcf); 
im = frame2im(frame); 
[imind, cm] = rgb2ind(im, 256); 

% Write to the GIF file 
    if frame_count == 0 
        imwrite(imind, cm, filename, 'gif', 'Loopcount', inf, 'DelayTime', delay_time); 
    else 
        imwrite(imind, cm, filename, 'gif', 'WriteMode', 'append', 'DelayTime', delay_time); 
    end 
     
    frame_count = frame_count + 1; 
    cla;  % Clear current axes 
end 
 
hold off;

This code rotates the cube around the specified axis defined by the two nodes. The rotation is incremented in each step of the loop to create an animation effect. Adjust the theta value and the loop parameters as needed to achieve the desired rotation speed and smoothness. Further, the code captures each frame of the rotating cube and writes it to a GIF file named rotating_cube.gif. The delay_time variable controls the time delay between frames in the GIF.

I trust this response will guide you towards resolving your query.

[Alberto Acri]

Thank you for your reply! The code looks great!

How can I adjust the rotation speed and impose it smoothly throughout the rotation? (as in the code I showed at the beginning: the rotation is not around two nodes but is kept smooth during the rotation)

For example I modified your code here:

theta_deg = 0.1;
theta = deg2rad(theta_deg);  %pi/180;  % rotation angle in radians (1 degree) 

and the cube rotates initially slowly and then faster and faster. How can I avoid this?

EDIT: I need the rotation around the red axis.