Reproduce pitch from Euler angles using Quaternions in MATLAB-CodePudding

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How can I fix my code so that the quaternion generated pattern is equivalent to the euler's pitch, regardless of my "body" rotation?

Some sample data:

Once the coordinates of the point are available, calculating the pitch could be done by computing the acos of the dot product between the unit vector parallel to OP (O being the global origin) and the unit vector parallel to the z-axis (with components (0,0,1)), in pseudo-code:

% Pseudo code pitch = acos(OP.z/norm(OP))

Here's a plot of the pitch shifted using the first value of the array, which is extremely close to what was obtained by the OP using Euler's angles:

Matlab code

Here's the code I used to generate the plots. As mentioned erlier, I relied on Przemyslaw Baranski's Quaternions. Please, note that my code is a very crude attempt at tackling the problem, with basically no optimization. Uncommenting the lines for the 3D plot slows down the process considerably:

function draw_quats() % point to be rotated P = [ 1, 0, 0 ]; % Import quaternion components q_tab = readtable(strcat("quaternions_data"), 'Delimiter',','); pitch = []; pp = 1; for k = 1:1:numel(q_tab.w) % create a quaternion for rotation Qrot = qGetQuaternionFromComponents(q_tab.x(k), q_tab.y(k), q_tab.z(k), q_tab.w(k)); % rotate point Prot = qRotatePoint( P, Qrot ); Pnorm = sqrt(Prot(1)^2 Prot(2)^2 Prot(3)^2); % % display axes % quiver3( 0,0,0, 1,0,0 ); % hold on; % quiver3( 0,0,0, 0,1,0 ); % quiver3( 0,0,0, 0,0,1 ); % % % display point % plot3( Prot(1), Prot(2), Prot(3), 'b.' ); % % % setup the plot % grid on; % axis equal; % axis([-1 1.0 -1 1.0 -1 1.0]); % xlabel( 'x' ); % ylabel( 'y' ); % zlabel( 'z' ); % % view( 45, 20 ); % drawnow; % Compute pitch pitch(pp) = acos(Prot(3)/Pnorm)*180/pi; pp = pp 1; end figure plot(pitch-pitch(1),'.k'); end

And this is the definition of qGetQuaternionFromComponents:

function Q = qGetQuaternionFromComponents( x, y, z, w ) Q = [w x y z]'; end

In the event you have some of the toolboxes by MATLAB, you can do something like this:

for i = 1:length(attitude) qPoint = quaternion(0,-1,0,0); q = attitude(i); [~,x,y,z] = parts(q * qPoint * conj(q)); Pnorm = sqrt(x^2 y^2 z^2); quats(i) = asind(z/Pnorm); end

References

Euclideanspace.com

Mathworks' FileExchange