Quaternions Computation Time too long

Question

Ozan Anli 2022-11-22

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1859288-quaternions-computation-time-too-long

编辑： Jan 2022-11-22

matlab_bsp.mlx

Hello,

we have written a script to illustrate the rotation of objects in space. This is calculated once using rotation matrices and once using quaternions. We have also tracked the computation time and noticed that the computation for the quaternions take longer than for the rotation matrices. According to the theory, the calculation of quaternions should work faster than for rotation matrices. Can you explain why this is not the case here.

Thank you very much in advance.

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Jan 2022-11-22

在 MATLAB Online 中打开

The relevant part of the code:

x = [0;1;0];  % Vector to rotate
theta = 33;   % Angle
n = 999;      % Number of rotations
Rx = rotx(theta);
tic;
for i = 1:n
    y = Rx * x;
    x = y;
end
toc;
Elapsed time is 0.005929 seconds.
y.'
ans = 1×3
         0   -0.8910   -0.4540
% Quaternion
x = [0,1,0];
v = [1,0,0];
v_dach = quaternion(0, v(1), v(2), v(3));
theta = deg2rad(theta);
q = cos(theta/2) + sin(theta/2)*v_dach;
tic;
for i = 1:n
    y = rotatepoint(q,x);
    x = y;
end
toc;
Elapsed time is 0.071161 seconds.
y
y = 1×3
         0   -0.8910   -0.4540

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Answer 1

Jan 2022-11-22

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1859288-quaternions-computation-time-too-long#answer_1108023

编辑：Jan 2022-11-22

在 MATLAB Online 中打开

While the multiplication with the rotation matrix calls an optimzed BLAS library directly, rotatepoint is a function, which calls the functions prepRotate for a normalization and compact after the multiplication. Calling functions have a certain overhead. Look into prepRotate to see, that there are further checks of the inputs and function calls.

The normalization matters, if the vectors have different scalings, e.g. x = [0, 1e180, 0]. Of course considering such exceptions costs runtime. The profiler helps you to examine, where the time is spent:

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"Faster in theory" is not really meaningful, if a function is applied to tiny input data. Maybe the theoretical advantage matters, if your input data has millions of points.