Orientation Density Functions (The Class ODF)

This sections describes the class ODF and gives an overview how to work with orientation density functions in MTEX.

Class Description

ODFs are at the very heart of MTEX. Almost any computation in MTEX can be done by estimating ODFs from various data, analyzing model ODFs, simulating experimental data from ODFs, or calculating any texture characteristics from an ODF. The following mindmap may give you an idea what is possible in MTEX.

Model ODFs

MTEX provides a very simple way to define model ODFs, e.g. unimodal ODFs, fibre ODF, Bingham ODFs or ODFs specified by Fourier coefficients. The central idea is that MTEX allows you to calculate with ODF as with ordinary number. That is you can multiply and ODF with a certain number, you can add, subtract or rotate ODFs. More precise information how to work with model ODFs in MTEX can be found in the section ModelODFs.

Estimating ODFs from EBSD Data or Pole Figure Data

The second natural way how ODFs occurs in MTEX is by estimating them from EBSD or pole figure data. It should be stressed that for MTEX there is no estimated ODFs and difference between model ODFs and estimated ODF. That means any operation that is valid for model ODFs is valid for estimated ODFs as well. More information how to estimate ODFs can be found in the sections ODF estimation from EBSD data and ODF estimation from Pole Figure data.

Analyzing ODFs

MTEX provides a lot of tools to make analyzing and interpreting ODFs as simple as possible. The tools may be split into two groups - texture characteristics and visualization tools.

Have a look at the sections ODF Calculations and ODF plots for more information.

Complete Function list

FourierODFcompute FourierODF from another ODF
bandwidthof the ODF
calcAngleDistributioncompute the angle distribution of an ODF or an MDF
calcAxisDistributioncompute the axis distribution of an ODF or MDF
calcAxisVolumeamount of orientations with a specific misorientation axis
calcComponentsheuristic to find modal orientations
calcErrorcalculate approximation error between two ODFs
calcFouriercompute Fourier coefficients of odf
calcMDFcalculate the uncorrelated misorientation distribution function (MDF) from one or two ODF
calcMIndexMindex of Skemer et al.(2005) based on the difference between
calcModesheuristic to find modal orientations
calcOrientationsdraw random orientations from ODF
calcPDFcomputed the PDF corresponding to an ODF
calcPoleFiguresimulate pole figures from an ODF
calcTensorcompute the average tensor for an ODF
calcpdf_special3compute the pdf for h = (theta,rhoh), r = (theta,rhor)
centerSpecimenrotatates an odf with specimen symmetry into its symmetry axes
charodf > char
concentrationnot yet implemeted
convolute ODF with kernel psi
discreteSampledraw a random sample
displaystandard output
entropycaclulate entropy of ODF
evaluate an odf at orientation g
exportan ODF to an ASCII file
export_VPSCexport an ODF to the VPSC format
export_genericexport an ODF to an ASCII file
export_mtexexport an ODF into the MTEX format
fibreVolumeratio of orientations with a certain orientation
gradient of odf at orientation ori
histcalcualtes a histogram of ODF
isFouriercheck whether odf is given by Fourier coefficients
maxheuristic to find local modal orientations
maxpdfreturns the maximum orientation in a polefigure
meanexpected value of an ODF
minussuperposeing two ODFs
mrdividescaling of the ODF
mtimesscaling of the ODF
neuralgasattempt to distribute measuresites equally according to invers polefigure density (experimental)
normcaclulate texture index of ODF
plots odf
plot3dplots odf
plotDiffdifference plot between two odfs or an odf and a pole figure
plotFibreplot odf along a fibre
plotFourierplots Fourier coefficients of the odf
plotIPDFplot inverse pole figures
plotPDFplot pole figures
plotSectionplot ODF sections
plussuperposeing two ODFs
quantileorientations of an ODF
rdividescaling of the ODF
rotateODF
rotate_outerrotate ODF
slope| grad(r) |
smoothODF
steepestDescentfind maximum with steepest descent
steepestDescentXfind maximum with steepest descent
textureindexcaclulate texture index of ODF
timesscaling of the ODF
uminussuperposeing two ODFs
volumeratio of orientations with a certain orientation