How can I do the same simulation as this (with euler angles), but using quaternions?

I´m using BNO055 IMU, and I have read all the data (euler angles, quaternions...). This data is send by serial from the micro to Matlab. I have done a short program in order to show the orientation of a cube in 3D, and it rotates depending on the obtained Euler angle values in real time. This is the main program:

%% Initialize the serial port I will work with... Remove previous data and define the COM and baud rate
delete(instrfind({'Port'}, {'COM3'}));
arduino = serial('COM3');
arduino.Baudrate = 9600;
%%puerto_serial = serial('COM3', 'BaudRate', 9600, 'Terminator', 'CR/LF');
fopen(arduino); %%Open serial port
warning('off','MATLAB:serial:fscanf:unsuccesfulRead');

%figure('Name', 'Serial communication: MATLAB + Arduino = CUBE 3D');

while 1
    x = fscanf(arduino, '%f');
    y = fscanf(arduino, '%f');
    z = fscanf(arduino, '%f');
    %quat(1) = fscanf(arduino, '%f'); %w
    %quat(2) = fscanf(arduino, '%f'); %x
    %quat(3) = fscanf(arduino, '%f'); %y
    %quat(4) = fscanf(arduino, '%f'); %z
    plotCube3Angles_2(x, y, z)
    drawnow limitrate
    clf %%Clean image for updating it
end

And this is the function for creating, rotating and ploting the cube with Euler angles.

function plotCube3Angles_2(roll, pitch, yaw)
 
Dim_X = 4; %size of the cube in X
Dim_Y = 3; %size of the cube in Y
Dim_Z = 1; %size in Z axes

vertex_matrix = [0 0 0;
1 0 0;
1 1 0;
0 1 0;
0 0 1;
1 0 1;
1 1 1;
0 1 1];

% vertex_matrix = [0 0 0;
% 4 0 0;
% 4 3 0;
% 0 3 0;
% 0 0 1;
% 4 0 1;
% 4 3 1;
% 0 3 1];
 
faces_matrix = [1 2 6 5
2 3 7 6
3 4 8 7
4 1 5 8
1 2 3 4
5 6 7 8];

CubeCenter_Coord = [Dim_X/2 Dim_Y/2 Dim_Z/2];
%origin = CubeCenter;
origin = [0 0 0]; %offset
CubeParameters = [vertex_matrix(:,1)*Dim_X+origin(1),vertex_matrix(:,2)*Dim_Y+origin(2),vertex_matrix(:,3)*Dim_Z+origin(3)];

axis equal;
cube = patch('Vertices',CubeParameters,'Faces',faces_matrix,'FaceColor', 'blue');
rotate(cube, [1,0,0], roll); %rotate cube, axis direction, angle value
rotate(cube,[0,1,0], pitch);
rotate(cube, [0, 0, 1], -yaw);
view(3); %3D

end

This works fine. Anyway, euler angles have some singularities and it is better to use quaternions for avoiding that issues on the rotating. I have seen there is a function called "rotateframe" that can rotate a frame with the quaternion... but I have not achieved anything. Does anyone know how should I do?

Thanks,

[James Tursa]

Is there a problem with the Euler Angles that are in the data set? Or are you just trying to learn how to use quaternions? Even if the orientation is a singular one with respect to the Euler Angle set you are using, as long as the sender is doing the calculations correctly you should still be able to use them to plot the cube orientation.

[Aitor Burdaspar]

Hello James.

Well, the problem of the Euler angles is that they have some singularities at a concrete orientation. That happens cause you can understand the orientation in 2 different ways with euler angles. For example, in the X axis it jumps from 0 degrees to 360 degrees. In the Y axis, from 180º to -180º...

That´s what I want to avoid with quaternions. Anyway, I have never worked before with quaternions, so I am trying to learn how to use them as you said, yes. Have you got any idea of how to use quats?

Thanks in advance,