measure angles between geometric objects, or the phase of numeric values.

Syntax

omega = angle(v, w)

Description

For an MTEX object, angle(x, …) calls x.angle(…). Additional positional and keyword arguments are passed to that method unchanged. Its documentation specifies the accepted inputs, units, symmetry handling and optional outputs. Consult the corresponding method for the behaviour of a particular object type.

For numeric arrays without an MTEX method, this calls numpy.angle.

Example

Compare the crystallographic misorientation angle with the angle between the stored rotations. A 90-degree rotation about a cubic fourfold axis is a crystal symmetry operation.

from mtex import crystalFrame, orientation, degree, angle

cs = crystalFrame('m-3m')
a = orientation.byEuler(0, 0, 0, cs)
b = orientation.byEuler(90*degree, 0, 0, cs)
print('With cubic symmetry (degrees):', round(float(angle(a, b)/degree), 6))
print('Stored rotations (degrees):', round(float(angle(a, b, symmetry=False)/degree), 6))

angle returns radians. Dividing by degree converts them to degrees. The default searches symmetry-equivalent orientations, so these two stored rotations describe the same cubic orientation.

With cubic symmetry (degrees): 0.0
Stored rotations (degrees): 90.0

Signature

angle(x, *args, **kwargs)

Methods it calls

fibre	the angle by which ori * h misses r, the least over both orbits, from the chord of the closest pair
grainBoundary	the angle of every segment to a direction, or to the segments of another boundary, in [0, pi/2], the segments having no sense
orientation	the rotational angle up to symmetry, of the orientation or of the misorientation to other
orthogonalTransform	the rotational angle of the rotational part, or the angle between the rotational parts of two
quaternion	the rotational angle in [0, pi], or the angle between two, both from atan2 forms that keep their digits near 0 and pi
S2AxisFieldHarmonic	the angle between the axes of the field and a constant axis, or another field, as a function on the sphere
S2VectorFieldHarmonic	the angle between two fields at every direction, or between the field and a constant vector, a function on the sphere
SO3TangentVector	the angle of the rotation the vector describes, or the angle between two vectors
vector3d	the angle between two vectors

Used on

CrystalDirections, CrystalOperations, CrystalReferenceSystem, LatticeMetric, SymmetryAlignment, DefinitionAsCoordinateTransform, MTEXvsBungeConvention, OrientationDefinition, OrientationEmbeddings, OrientationFundamentalRegion, OrientationGrid, OrientationStandard

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/angle_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.