create a rotation matrix for a 4d object given an input of the angle of rotation about a specified axis in matlab

To create a rotation matrix for a 4D object in Matlab, you can use the following steps:

1. First, identify the axis of rotation. Let's say it is the x-axis.
2. Next, create a 4x4 identity matrix using the eye function in Matlab.
3. Use the cos and sin functions to compute the sine and cosine of the angle of rotation in radians. Let's say the angle is 30 degrees.
4. Use these values to populate the appropriate elements in the rotation matrix. For a rotation about the x-axis, the matrix should have the following form:

main.m
[1       0          0         0
 0      cos(theta)  sin(theta)  0
 0     -sin(theta)  cos(theta)  0
 0       0          0         1]
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5. To get the full rotation matrix, you can use the matrix multiplication operation to combine the rotation matrix with the original matrix you want to rotate.

Here's the Matlab code to implement these steps:

main.m
%define the angle of rotation in degrees
theta = 30;
%convert degrees to radians
theta = theta * pi/180;
%create 4x4 identity matrix
R = eye(4);
%populate appropriate elements with sine and cosine values
R(2,2) = cos(theta);
R(2,3) = sin(theta);
R(3,2) = -sin(theta);
R(3,3) = cos(theta);
%perform matrix multiplication to apply the rotation
rotated_matrix = R * original_matrix;
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This will give you the rotated matrix.