Generates the roto-translation matrix for the rotation around an arbitrary line in 3D. The line need not pass through the origin. Optionally, also, applies this transformation to a list of 3D coordinates.
u, x0: 3D vectors specifying the line in parametric form x(t)=x0+t*u
Default for x0 is [0,0,0] corresponding to pure rotation (no shift).
If x0= is passed as input, this is also equivalent to passing x0=[0,0,0].
deg: The counter-clockwise rotation about the line in degrees. Counter-clockwise is defined using the
right hand rule in reference to the direction of u.
M: A 4x4 affine transformation matrix representing
the roto-translation. Namely, M will have the form
M=[R,t;0 0 0 1]
where R is a 3x3 rotation and t is a 3x1 translation vector.
Same as Syntax 1 except that R and t are returned as separate arguments.
This syntax requires 4 input arguments be specified,
[XYZnew, R, t] = AxelRot(XYZold, deg, u, x0)
where the columns of the 3xN matrix XYZold specify a set of N point coordinates in 3D space. The output XYZnew is the transformation of the columns of XYZold, i.e., the original coordinates rotated appropriately about the axis. All other input/output arguments have the same meanings as before.