Express an r-matrix as an r-vector.
Status: vector/matrix support routine.
A rotation matrix describes a rotation through some angle about some arbitrary axis called the Euler axis. The "rotation vector" returned by this routine has the same direction as the Euler axis, and its magnitude is the angle in radians. (The magnitude and direction can be separated by means of the routine PN.)
If R is null, so is the result. If R is not a rotation matrix the result is undefined. R must be proper (i.e. have a positive determinant) and real orthogonal (inverse = transpose).
The reference frame rotates clockwise as seen looking along the rotation vector from the origin.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(3,3) | :: | r | rotation matrix |
|
| real(kind=wp), | intent(out), | dimension(3) | :: | w | rotation vector (Note 1) |
subroutine RM2V ( r, w )
implicit none
real(wp),dimension(3,3),intent(in) :: r !! rotation matrix
real(wp),dimension(3),intent(out) :: w !! rotation vector (Note 1)
real(wp) :: x, y, z, s2, c2, phi, f
x = r(2,3) - r(3,2)
y = r(3,1) - r(1,3)
z = r(1,2) - r(2,1)
s2 = sqrt(x*x + y*y + z*z)
if ( s2 > 0.0_wp ) then
c2 = r(1,1) + r(2,2) + r(3,3) - 1.0_wp
phi = atan2(s2,c2)
f = phi / s2
w(1) = x * f
w(2) = y * f
w(3) = z * f
else
w(1) = 0.0_wp
w(2) = 0.0_wp
w(3) = 0.0_wp
end if
end subroutine RM2V