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
FourierODF | compute FourierODF from another ODF |
bandwidth | of the ODF |
calcAngleDistribution | compute the angle distribution of an ODF or an MDF |
calcAxisDistribution | compute the axis distribution of an ODF or MDF |
calcAxisVolume | amount of orientations with a specific misorientation axis |
calcComponents | heuristic to find modal orientations |
calcError | calculate approximation error between two ODFs |
calcFourier | compute Fourier coefficients of odf |
calcMDF | calculate the uncorrelated misorientation distribution function (MDF) from one or two ODF |
calcMIndex | Mindex of Skemer et al.(2005) based on the difference between |
calcModes | heuristic to find modal orientations |
calcOrientations | draw random orientations from ODF |
calcPDF | calculate pdf |
calcPoleFigure | simulate pole figures from an ODF |
calcTensor | compute the average tensor for an ODF |
calcpdf_special3 | compute the pdf for h = (theta,rhoh), r = (theta,rhor) |
centerSpecimen | rotatates an odf with specimen symmetry into its symmetry axes |
char | odf > char |
concentration | not yet implemeted |
conv | olute ODF with kernel psi |
discreteSample | draw a random sample |
display | standard output |
entropy | caclulate entropy of ODF |
eval | uate an odf at orientation g |
export | an ODF to an ASCII file |
export_VPSC | export an ODF to the VPSC format |
export_generic | export an ODF to an ASCII file |
export_mtex | export an ODF into the MTEX format |
fibreVolume | ratio of orientations with a certain orientation |
grad | ient of odf at orientation ori |
hist | calcualtes a histogram of ODF |
isFourier | check whether odf is given by Fourier coefficients |
max | heuristic to find local modal orientations |
maxpdf | returns the maximum orientation in a polefigure |
mean | expected value of an ODF |
minus | superposeing two ODFs |
mrdivide | scaling of the ODF |
mtimes | scaling of the ODF |
neuralgas | attempt to distribute measuresites equally according to invers polefigure density (experimental) |
norm | caclulate texture index of ODF |
plot | s odf |
plot3d | plots odf |
plotDiff | difference plot between two odfs or an odf and a pole figure |
plotFibre | plot odf along a fibre |
plotFourier | plots Fourier coefficients of the odf |
plotIPDF | plot inverse pole figures |
plotPDF | plot pole figures |
plotSection | plot ODF sections |
plus | superposeing two ODFs |
quantile | orientations of an ODF |
rdivide | scaling of the ODF |
rotate | ODF |
slope | | grad(r) | |
smooth | ODF |
steepestDescent | find maximum with steepest descent |
steepestDescentX | find maximum with steepest descent |
textureindex | caclulate texture index of ODF |
times | scaling of the ODF |
uminus | superposeing two ODFs |
volume | ratio of orientations with a certain orientation |
MTEX 4.5.2 |