How to customize setting the included angle of the XY axis to 120 degrees?

Hi, i am a PHD of chemistry. Considering that I need to build a structural model of the hexagonal crystal system, I need to set the angle between the XY axis to 120 degrees in the 3D drawing, while the Z axis remains perpendicular to the XY plane. What should I do? I would appreciate any advice you can provide!

Answer 1

[Maven Euler]

I understand that you want to set the angle between XY as 120 degree while keeping Z-axis perpendicular to XY plane. This can be achieved by performing coordinate transformation as given bellow:

% Generate a 3D coordinate system 
figure; 
quiver3(0, 0, 0, 1, 0, 0, 'r', 'LineWidth', 2);  % X axis (red) 
hold on; 
quiver3(0, 0, 0, 0, 1, 0, 'g', 'LineWidth', 2);  % Y axis (green) 
quiver3(0, 0, 0, 0, 0, 1, 'b', 'LineWidth', 2);  % Z axis (blue) 
axis equal; 

% Apply rotation transformation 
angle = 120;  % Angle in degrees 
rotationMatrix = [cosd(angle) -sind(angle) 0; sind(angle) cosd(angle) 0; 0 0 1]; 

% Apply the rotation to the coordinate system 
newXAxis = rotationMatrix * [1; 0; 0]; 
newYAxis = rotationMatrix * [0; 1; 0]; 
newZAxis = rotationMatrix * [0; 0; 1]; 

% Plot the rotated coordinate system 
quiver3(0, 0, 0, newXAxis(1), newXAxis(2), newXAxis(3), 'r--', 'LineWidth', 2);  % Rotated X axis (dashed red) 
quiver3(0, 0, 0, newYAxis(1), newYAxis(2), newYAxis(3), 'g--', 'LineWidth', 2);  % Rotated Y axis (dashed green) 
quiver3(0, 0, 0, newZAxis(1), newZAxis(2), newZAxis(3), 'b--', 'LineWidth', 2);  % Z axis (blue) 

The rotated coordinate system is plotted using dashed lines. You can adjust the ‘angle’ variable to set the desired angle between XY axis. You may read further on ‘quiver3’ here: https://in.mathworks.com/help/matlab/ref/quiver3.html