orientation.log

the logarithmic map that translates a orientation into a tangent vector.

Therefore it converts a given orientation, relative to a reference orientation, into its corresponding tangent vector in the tangent space at the reference.

Hence, the log-function computes the relative orientation. This can also be interpreted as misorientation vector between two orientations, which is measured in the tangent space.

The misorientation vector can also be seen as the projection of an orientation onto the tangential space of the orientation space centered at the orientation ori_ref. The inverse mapping from the tangential space onto the orientation space is the exponential map exp.

Syntax

v = log(ori)
v = log(ori,ori_ref,SO3TangentSpace.rightVector)

Input

Output

Example

compute misorientation vector in crystal coordinates

cs = crystalSymmetry('432');
mori = orientation.KurdjumovSachs(cs,cs)
v = log(mori,SO3TangentSpace.rightVector)
round(Miller(v,mori.CS))

mori = misorientation (432 → 432)
 
 (111) || (011)   [101̅] || [111̅]
 
 
v = SO3TangentVector (y↑→x)
 intern symmetries: 432 → 432
 TagentSpace: rightVector
        x        y        z
  0.13283  0.13283 0.723857
 
ans = Miller (432)
  h  k  l
  2  2 11

See also

orientation.logm quaternion.log vector3d.exp Miller.exp