a tangent vector of SO(3), a rotation vector v at a reference rotation or orientation, on the left, exp(v) * oriRef, or on the right, oriRef * exp(v); from vectors or skew matrices

Syntax

SO3TangentVector(v, oriRef)
SO3TangentVector(v, oriRef, 'right')

SO3TangentVector(S, oriRef, side)

From skew matrices of shape (…, 3, 3).

Input

v rotation-vector components as vector3d or numeric arrays, or skew-symmetric matrices
oriRef reference rotation or orientation at which the tangent vectors are based
side ‘left’ for exp(v)oriRef or ‘right’ for oriRefexp(v); default ‘left’

Members

angle the angle of the rotation the vector describes, or the angle between two vectors
cat tangent vectors concatenate on one side
copy a copy of the tangent vectors, components and references
cross the cross product with tangent vectors at the same reference, brought to this side
CS the crystal frame of the reference, None for a rotation
dot the inner product with tangent vectors at the same reference, brought to this side
dot_outer the inner product with tangent vectors at the same reference, brought to this side
eq equal at the same reference within tol in the components (MATLAB’s eq)
exp return the rotations reached by the tangent vectors from their references
frame the frame the components are written in: the specimen frame of the reference on the left, its crystal frame on the right
frameA the frame the orientations map from, the crystal frame
frameB the frame the orientations map to, the specimen or a second crystal frame
left express the tangent vectors on the left of their reference rotations
mean the mean of tangent vectors at one shared reference, weighted when weights are given
mtimes  
plot plot(x, …) draws x as its kind is drawn
plus  
quiver3 arrows in space: tangent vectors in orientation space, a field on the sphere or SO(3), or arrows at positions
quiverSection arrows on a section plot: of a function on the sphere along one of its circles, or at orientations in the sections of orientation space
rdivide  
reshape the tangent vectors in another shape, a reference per element reshaped with them
right express the tangent vectors on the right of their reference rotations
SO3TangentVector a tangent vector of SO(3), a rotation vector v at a reference rotation or orientation, on the left, exp(v) * oriRef, or on the right, oriRef * exp(v)
spinTensor the skew matrix as the tensor of the tensors layer, in the frame of the side
SS the specimen frame of the reference, None for a rotation
subsref  
sum the sum of tangent vectors at one shared reference, over all or along an axis
T the transposed array of tangent vectors, a reference per element transposed with them
times  
toSide the vectors on the side asked for, ‘left’ or ‘right’
unique the disjoint list of tangent vectors at one shared reference

Used on

SingleSlipModel, RotationTangentSpace

MATLAB’s SO3TangentVector_index

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/SO3TangentVector_index_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX 
@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.