On Dec 13, 7:23 pm, Paulo Penteado <pp.pente...@gmail.com> wrote:
> On Dec 14, 1:11 am, MartyL <mlandsf...@yahoo.com> wrote:
>
>> I would like to rotate and arbitrary 3D vector to be aligned with the
>> Z axis. I can translate and scale the vector but I can not find a
>> formula to create the rotation matrix to perform the rotation. It
>> sounds simple but I can't seem to find one.
>> Thanks
>
> Do you mean something like
>
> IDL> t3d,identity(4),matrix=matrix,rotate=[45d0,0d0,0d0]
> IDL> print,matrix
> 1.0000000 0.0000000 0.0000000 0.0000000
> 0.0000000 0.70710678 -0.70710678 0.0000000
> 0.0000000 0.70710678 0.70710678 0.0000000
> 0.0000000 0.0000000 0.0000000 1.0000000
Yes, I am trying to get the transformation matrix for an arbitrary 3D
vector. So the problem is that I need to find the degrees which to
rotate. If I have the vector:
pts = [[5.1,20.4,-12.2],[15.0,55.5,30.4]]
I can translate that to the origin
pts_trans = [[0.0, 0.0, 0.0],[9.9,35.1,42.6]]
and normalize it to a unit vector
pts_norm = [[0.0, 0.0, 0.0],[0.176,0.625,0.759]]
but then I need to determine the rotation angles to rotate it to [0.0,
0.0, 1.0] or the Z axis.
I have found this solution in another news group but it did not
produce the correct results.
--------------------------------
Let V1 = [ x1, y1, z1 ], V2 = [ x2, y2, z2 ]. Assume V1 and V2 are
already normalized.
V3 = normalize(cross(V1, V2)). (the normalization here is
mandatory.)
V4 = cross(V3, V1).
[ V1 ]
M1 = [ V4 ]
[ V3 ]
cos = dot(V2, V1), sin = dot(V2, V4)
[ cos sin 0 ]
M2 = [ -sin cos 0 ]
[ 0 0 1 ]
The sought transformation matrix is just M1^-1 * M2 * M1. This might
well be a standard-text solution.
--------------------------------
I used [0.176,0.625,0.759], from pts_norm, as V1 and [0.0, 0.0, 1.0],
the Z axis, as V2.
My implementation is this:
v1 = [0.176,0.625,0.759D]
v2 = [0.0, 0.0, 1.0D]
v = CROSSP(v1, v2)
v3 = v/NORM(v)
v4 = CROSSP(v3, v1)
m1 = DBLARR(3,3)
m1[*,0] = [v1]
m1[*,1] = [v4]
m1[*,2] = [v3]
rot_cos = TRANSPOSE(v1)#v2
rot_sin = TRANSPOSE(v2)#v4
m2 = DBLARR(3,3)
m2[*,0] = [rot_cos, rot_sin, 0.0]
m2[*,1] = [-rot_sin, rot_cos, 0.0]
m2[*,2] = [0.0, 0.0, 1.0]
m = MATRIX_MULTIPLY(INVERT(m1), m2)
m4 = MATRIX_MULTIPLY(m, m1)
v1_trans = MATRIX_MULTIPLY(v1, m4)
print, v1_trans
IDL output is:
-0.0875152
0.933033
0.341724
which should have been:
0.0
0.0
1.0
I am wondering if I have the order of vectors and matrices wrong in
MATRIX_MULTIPLY.
Any help appreciated.
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