base class for scalar functions on orientation space SO(3)

Description

Represent an orientation distribution or another orientation-dependent property with SO3FunHarmonic coefficients, SO3FunRBF kernel sums, SO3FunCBF fibre sums, SO3FunBingham distributions or SO3FunHandle callables. Evaluate a concrete function at rotations or orientations using f(ori). Its crystal and specimen frames define the symmetry-equivalent orientations at which values agree.

An orientation distribution of mean one uses multiples of a uniform distribution as its units: a value of two means twice the uniform density. General SO3Fun objects can also represent signed or complex functions and are not automatically normalised densities.

This base class provides the common interface; construct one of its representations.

See also

SO3FunHarmonic, SO3FunRBF, SO3FunHandle, calcDensity, unimodalODF

Members

calcAngleDistribution the distribution of the misorientation angle: of a misorientation density, of a list of misorientations, or of the uniform density of two crystal frames
calcAxisDistribution the axis distribution of an SO(3) function, an S2 function of the rotation axes symmetric under the rotations the two frames share
calcComponents the modal orientations of an orientation density, the components: their orientations, their volumes and the mode every seed flowed into
calcError the error between a measurement and a recalculation, or between two SO(3) functions
calcMDF the uncorrelated misorientation distribution function of one or two ODFs
calcMIndex the M-index of an ODF by Skemer et al., computed from the ODF instead of a discrete number of orientations
calcPoleFigure the pole figures an ODF predicts: simulated diffraction intensities, superposed pole figures and any specimen directions
calcTensor the texture average of a single crystal tensor over an ODF, a list of orientations or a map
centerSpecimen an orientation density of an assumed orthotropic texture rotated so that its two fold axes lie on the specimen axes
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
discreteSample a random sample of n orientations drawn from an orientation density, of directions from a density on the sphere, of numbers from a density on an interval, or n random members of a list
dubna the ODF of the Dubna quartz pole figures, MTEX’s example function
entropy the entropy -int f log f of a function on SO(3) or on the sphere
export write a map to the file the extension names
export_VPSC write a map to the file the extension names
fibreVolume the volume of a fibre: the share of an orientation density within a radius of the fibre of the orientations that map the crystal direction h onto the specimen direction r
hist histogram(grains), histogram(grains, prop, bins): the area weighted distribution of a grain property as one histogram per indexed phase, drawn over each other, or with grouped=True side by side (MATLAB’s hist)
load an ODF read from a file, loadODF
max the maximum of a function on SO(3) or the sphere, the value and the position, numLocal local maxima from a grid refined down to the accuracy
min the minimum of a function on SO(3) or the sphere, the value and the position, numLocal local minima
optimalSample the sample of n nodes that reproduces a density best up to the bandwidth, on the sphere or the rotation group
plot3d plot3d(v), plot3d(v, data), plot3d(sF), plot3d(vF), plot3d(oR), plot3d(ori), plot3d(odf)
plot plotSection(odf), plotSection(odf, ‘sigma’), plotSection(ori, oS, sections=9)
plotDiff the difference between measured pole figures and recalculated ones, or two measurements, drawn as pole figures of the error
plotFibre the ODF along the fibre f, as a line over the angle along the fibre
plotIPDF inverse pole figures, one per specimen direction: of an ODF or of a list of orientations
plotPDF pole figures, one per crystal direction: of an ODF, of a list of orientations or of a measured PoleFigure
plotSection plotSection(odf), plotSection(odf, ‘sigma’), plotSection(ori, oS, sections=9)
plotSpektra the Chebyshev coefficients of a kernel, or the harmonic power of a function, per degree
rotate rotate(x, rot) is x.rotate(rot), or rot * x for an object without that method
SO3Fun base class for scalar functions on orientation space SO(3)
sum sum(x) of an MTEX object by its own sum, of an array or with an axis as NumPy sums, of any other iterable as Python sums, so that from mtex import * keeps Python’s sum
times times(A, B) is A.times(B): the product of corresponding coefficients, MATLAB’s A .* B
volume the share of orientations within a radius of a centre: the integral of f over the ball, int_{angle(g, c) < r} f(g) dg, relative to the integral over all orientations

MATLAB’s SO3Fun_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/SO3Fun_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.