rotate a 4d object about an axis defined by a 4d input array of rotation angles in matlab

To rotate a 4D object about an axis defined by a 4D input array of rotation angles in MATLAB, you can use the following steps:

1. Convert the 4D input array of rotation angles into a quaternion representing the rotation axis and angle.

main.m
q = angle2quat(alpha,beta,gamma,'XYZW');
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where alpha, beta, and gamma are the rotation angles about the X, Y, and Z axes respectively, and W is the fourth component of the quaternion.

2. Generate a rotation matrix from the quaternion representation using the following code:

main.m
rotationMatrix = quat2rotm(q);
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3. Perform the rotation on your 4D object using matrix multiplication. The size of the object can be anything (Nx4, Mx4xOxP, etc.) as long as the last dimension represents the 4D coordinates. This can be vectorized for efficiency using reshape() and permute() functions.

main.m
% Example: rotating a 4D (N x 4) object called "points" using rotation matrix
rotatedPoints = reshape(permute(rotationMatrix*[reshape(points',4,[],size(points,1))], [2 1 3]), 4, [], size(points,1))';
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This method can be used for multiple rotations by multiplying the rotation matrices together in the desired order.

Note that this implementation assumes that the axis of rotation is the origin of the 4D space. If the axis is located elsewhere, you will need to translate the object so that the axis becomes the origin, rotate it, then translate it back to its original position.