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    Metadata details:
    filename: ODFTutorial.m
    path of file: ./repos/mtex/doc/Tutorials
    
    the code of the file until where you have to start completion: %% ODF Tutorial
%
%% Theory
%
% The orientation distribution function (ODF) is a function on the
% orientation space that associates to each orientation $g$ the volume
% percentage of crystals in a polycrystaline specimen that are in this
% specific orientation, i.e.,
%
% $$\mathrm{odf}(g) = \frac{1}{V} \frac{\mathrm{d}V(g)}{\mathrm{d}g}.$$
%
% In MTEX an entirely random texure will have an ODF constant to one. In
% other word the values of ODFs in MTEX can be interpreted as multiples of
% the random distribution (mrd). 
%
%% Computing an ODF from Individual Orientations
%
% Individual orientations data may be obtained by experimental by EBSD,
% ACOM or 3d X-ray imaging; or from simulations, like VPSC. In t
    
function (ODF) is a function on the
% orientation space that associates to each orientation $g$ the volume
% percentage of crystals in a polycrystaline specimen that are in this
% specific orientation, i.e.,
%
% $$\mathrm{odf}(g) = \frac{1}{V} \frac{\mathrm{d}V(g)}{\mathrm{d}g}.$$
%
% In MTEX an entirely random texure will have an ODF constant to one. In
% other word the values of ODFs in MTEX can be interpreted as multiples of
% the random distribution (mrd). 
%
%% Computing an ODF from Individual Orientations
%
% Individual orientations data may be obtained by experimental by EBSD,
% ACOM or 3d X-ray imaging; or from simulations, like VPSC. In the
% following we consider an EBSD map of an Titanium alloy.

% import the titanium data
mtexdata titanium

% plot an orientation map
plot(ebsd, ebsd.orientations)

%%
% Computing an ODF from individual orientations is done by
% <DensityEstimation.html kernel density estimation> using the command
% <orientation.calcDensity.html |calcDensity|>.

% extract the orientations
ori = ebsd.orientations;

% compute the ODF
odf = calcDensity(ori)

%%
% There many different ways to visualize ODF: <EulerAngleSections.html
% Euler> or <SigmaSections.html sigma sections>, <ODFPlot.html thee
% dimensional plots>, <ODFPoleFigure.html pole figures> and
% <ODFInversePoleFigure.html inverse pole figures>. The most common but not
% recommend