proper rotations represented by unit quaternions, with opposite signs identified.

Syntax

rot = rotation(a, b, c, d)
rot = rotation(q)
rot = rotation(cs)

Description

Numeric coefficients and general quaternions are normalised on construction. A point group or reference frame supplies its proper rotational parts. Improper orthogonal transforms cannot be converted to a rotation; use orthogonalTransform to retain parity.

For vector3d data, rot*v rotates each vector. The product rot1*rot2 applies rot2 first, then rot1. Array shapes broadcast, while the trailing four coefficients are internal to each element.

Keywords

keyword	default	description
`dtype`		floating-point type of the stored coefficients

Properties

`a, b, c, d`	unit quaternion coefficients, with opposite signs representing the same rotation
`data`	coefficient array of shape rot.shape + (4,)
`phi1, Phi, phi2`	Bunge Euler angles in radians
`shape`	shape of the rotation array

Members

byAxisAngle	construct right-handed rotations about given axes
byCubochoric	construct rotations from equal-volume cubochoric coordinates
byEuler	rotations defined by Euler angles
byHomochoric	construct rotations from coordinates in the homochoric ball
byMatrix	construct rotations from proper orthogonal matrices
byRodrigues	construct rotations from dimensionless Rodrigues vectors
calcDensity	estimate a smooth density from orientations, directions, angles or real-valued samples
cat	the list of the operands, MATLAB’s [r1, r2]
discrepancy	the discrepancy between two densities and/or weighted point sets on the sphere (S2Fun, vector3d) or on SO(3) (SO3Fun, rotation, orientation), in either order
dot	the inner product up to sign, since q and -q are one rotation
dot_outer	the inner product up to sign, since q and -q are one rotation
double	the coordinates of the images of an embedding in their orthonormal basis, one row per orientation, e.double()
fit	the rotation best mapping the list u onto the list v, by Horn’s quaternion method or Kabsch’s matrix method
id	the identity, 1 + 0i + 0j + 0k (MATLAB’s id and eye)
interp	interp(ori, values, ‘harmonic’ \| ‘bingham’): a function on SO(3) through values at the rotations, by the function spaces above this layer, MATLAB’s rotation/interp
inv	return the rotation that reverses each input rotation
inversion	the inversion, the orthogonalTransform -I
isclose	equal within the angular tolerance tol, MATLAB’s eq
map	the smallest rotation taking u1 to v1, or the one taking u1 to v1 and u2 to v2
matrix	return the numeric rotation matrix of each unit quaternion
mtimes
nan	construct quaternions whose four coefficients are NaN
plotSection	plotSection(odf), plotSection(odf, ‘sigma’), plotSection(ori, oS, sections=9)
rand	uniformly distributed rotations, the Haar measure
rotation	proper rotations represented by unit quaternions, with opposite signs identified
subsref
times
transpose	the transpose of the leading axes
uminus
unique	the disjoint list of quaternions, those equal up to a tolerance in the coefficients taken as one

Used on

CrystalSymmetries, MTEXvsBungeConvention, EBSDKAM, RotationDefinition, RotationImproper, SO3FunConvolution, SO3FunOperations, SO3FunVectorValued

MATLAB’s rotation_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/rotation_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.

The class rotation