rotate a 4d object about each axis as defined by a 4 element input array expressed in radians in matlab

To rotate a 4D object in MATLAB, one can use quaternion rotation. A quaternion is a four-element vector [w, x, y, z] that represents a rotation in 3D space. In 4D, a quaternion can represent a rotation about an axis in 4D space.

The following code demonstrates how to rotate a 4D object about each axis as defined by a 4-element input array expressed in radians.

main.m
% Define the 4D object
obj4d = [1 2 3 4];

% Define the rotation angles (in radians)
thetas = [pi/4 pi/6 pi/3 pi/2];

% Convert the angles to quaternions
q1 = angle2quat(thetas(1), 0, 0);
q2 = angle2quat(0, thetas(2), 0);
q3 = angle2quat(0, 0, thetas(3));
q4 = angle2quat(0, 0, 0, thetas(4));

% Combine the quaternions
q = q1 * q2 * q3 * q4;

% Convert the quaternion to a rotation matrix
R = quat2rotm(q);

% Rotate the object
obj4d_rotated = (R * obj4d')';

% Display the results
disp('Original 4D object:');
disp(obj4d);
disp('Rotated 4D object:');
disp(obj4d_rotated);
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In this example, we first define a 4D object as a vector [1 2 3 4]. We then define the rotation angles around each axis (in radians) as thetas = [pi/4 pi/6 pi/3 pi/2].

Next, we convert each angle to a quaternion using the angle2quat function. We then combine these quaternions using multiplication to obtain a single quaternion that represents the composed rotation.

We then convert this quaternion to a rotation matrix using the quat2rotm function. Finally, we apply the rotation matrix to the original object using matrix multiplication to obtain the rotated object.

The results are displayed using the disp function.