diff --git a/latex/geometry/.gitignore b/latex/geometry/.gitignore
new file mode 100644
index 0000000..79f29c6
--- /dev/null
+++ b/latex/geometry/.gitignore
@@ -0,0 +1,9 @@
+*.aux
+*.log
+*.nav
+*.out
+/CrystalGeometry.pdf
+*.snm
+*.synctex.gz
+*.toc
+*.vrb
diff --git a/latex/geometry/CrystalGeometry.tex b/latex/geometry/CrystalGeometry.tex
new file mode 100644
index 0000000..8241f4a
--- /dev/null
+++ b/latex/geometry/CrystalGeometry.tex
@@ -0,0 +1,2636 @@
+% presentation
+\documentclass[compress]{beamer}
+
+% handout
+%\documentclass[handout]{beamer}
+
+\usepackage{../mtex,fancyvrb,booktabs}
+\usepackage{tikz}
+%\usepackage{subfigure}
+\usepackage[labelformat=empty]{subcaption}
+\captionsetup{compatibility=false}
+
+\author{R. Hielscher}
+
+\title{Crystal Geometry}
+%\subtitle{Chemnitz {\bf{\color{red}M}TEX} Workshop 2015}
+
+\institute{Faculty of Mathematics,\\
+	Chemnitz University of Technology, Germany}
+
+\date{{\bf{\color{red}M}TEX} Workshop 2015}
+
+
+\newcommand{\crystal}[5]{%
+  \draw[->, >=latex, #5] (#1) --+ (#2);%
+  \draw[->, >=latex, #5] (#1) --+ (#3);%
+  \draw[->, >=latex, #5] (#1) --+ (#4);%
+}
+
+\newcommand{\fillcrystal}[5]{%
+  \filldraw[fill=red!25,draw=red!35,opacity=0.5]
+%  (0,0) + (1,0) -- (0,0) --++ (0,1) --+ (1,0);
+  (#1) +(#2) -- (#1) --++ (#3) -- +(#2) ;%
+  \filldraw[fill=red!45,draw=red!35,opacity=0.5]
+  (#1) +(#3) -- (#1) --++ (#4) -- +(#3) ;%
+  \filldraw[fill=red!65,draw=red!35,opacity=0.5]
+  (#1) +(#4) -- (#1) --++ (#2) -- +(#4) ;%
+  \draw[->, >=latex, #5] (#1) --+ (#2);%
+  \draw[->, >=latex, #5] (#1) --+ (#3);%
+  \draw[->, >=latex, #5] (#1) --+ (#4);%
+}
+
+\newcommand{\filldirection}[5]{%
+  \filldraw[fill=red!25,draw=red!35,opacity=0.5]
+%  (0,0) + (1,0) -- (0,0) --++ (0,1) --+ (1,0);
+  (#1) +(#2) -- (#1) --++ (#3) -- +(#2) ;%
+  \filldraw[fill=red!45,draw=red!35,opacity=0.5]
+  (#1) +(#3) -- (#1) --++ (#4) -- +(#3) ;%
+  \filldraw[fill=red!65,draw=red!35,opacity=0.5]
+  (#1) +(#4) -- (#1) --++ (#2) -- +(#4) ;%
+  \draw[->, >=latex, #5] (#1) --+ (#2);%
+  \draw[->, >=latex, #5] (#1) --+ (#3);%
+  \draw[->, >=latex,color=red, very thick] (#1) --+ (#4);%
+}
+
+
+\begin{document}
+
+\begin{frame}
+  \maketitle{}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Table of Content}
+
+\tableofcontents{}
+
+\end{frame}
+
+
+\section{Vectors}
+
+\subsection*{Vector3d}
+
+\begin{frame}[fragile]
+  \frametitle{Three dimensional vectors - The \MTEX Class \texttt{\bf vector3d}}
+
+  \begin{overlayarea}{\textwidth}{8cm}
+  Three dimensional vectors are given by there coordinates with respect to a
+  orthogonal coordinate system $\vec X, \vec Y, \vec Z$
+  \begin{equation*}
+    \vec r = x \cdot \vec X + y \cdot \vec Y + z \cdot \vec Z
+  \end{equation*}
+
+  \pause
+
+  For general vectors, \MTEX does not care about the coordinate system, but
+  works only with the coordinates.
+
+  \begin{columns}
+    \begin{column}{8cm}
+
+      \begin{lstlisting}[style=input]
+r = vector3d(1,2,3)
+  \end{lstlisting}
+      \begin{onlyenv}<2>
+        \vspace{-0.3cm}
+\begin{lstlisting}[style=output]
+r = /+vector3d+/ (show methods, plot)
+  size: 1 x 1
+  x y z
+  1 2 3
+\end{lstlisting}
+      \end{onlyenv}
+
+
+      \pause
+      \medskip
+
+      The alignment of the coordinate system is only important when plotting
+      data
+      \begin{onlyenv}<3|handout>
+\begin{lstlisting}[style=input]
+plotx2north, plotzOutOfPlane
+plot(r)
+\end{lstlisting}
+      \end{onlyenv}
+      \begin{onlyenv}<4>
+\begin{lstlisting}[style=input]
+plotx2east, plotzOutOfPlane
+plot(r)
+\end{lstlisting}
+      \end{onlyenv}
+
+    \end{column}
+    \begin{column}{3.5cm}
+      \only<3|handout>{\includegraphics[width=3.5cm]{pic/vectorNorth}}
+      \only<4>{\includegraphics[width=3.5cm]{pic/vectorEast}}
+    \end{column}
+  \end{columns}
+
+  \pause
+  \medskip
+
+  Only for directions relative to the crystal coordinate system the reference
+  frame is considered.
+
+\end{overlayarea}
+\end{frame}
+
+\subsection*{Definition}
+
+\begin{frame}[fragile,fragile,fragile]
+  \frametitle{Defining vectors}
+
+  \begin{overlayarea}{\textwidth}{8cm}
+
+    polar coordinates $\vec r = (\sin \theta \cos \rho,\sin \theta \sin \rho,\cos \theta)^{t}$
+
+\begin{lstlisting}[style=input]
+r = vector3d('theta',theta,'rho',rho)
+\end{lstlisting}
+
+  \pause \medskip
+
+  predefined vectors
+\begin{lstlisting}[style=input]
+r = xvector, r = yvector, r = zvector
+\end{lstlisting}
+
+  \pause \medskip
+
+  combine vectors
+\begin{lstlisting}[style=input]
+r = [xvector, yvector, vector3d(1,1,1)];
+\end{lstlisting}
+
+\begin{onlyenv}<3>
+  \vspace{-.3cm}
+\begin{lstlisting}[style=output]
+r = /+vector3d+/ (show methods, plot)
+  size: 1 x 3
+  x y z
+  1 0 0
+  0 1 0
+  1 1 1
+\end{lstlisting}
+\end{onlyenv}
+
+  \pause \medskip
+
+  importing vectors
+\begin{lstlisting}[style=input]
+r = loadVector3d('file','ColumnNames',{'x','y','z'})
+\end{lstlisting}
+\begin{onlyenv}<4>
+  \vspace{-.3cm}
+\begin{lstlisting}[style=output]
+r = /+vector3d+/ (show methods, plot)
+  size: 200 x 1
+\end{lstlisting}
+\end{onlyenv}
+
+\end{overlayarea}
+\end{frame}
+
+\subsection*{Calculations}
+
+\begin{frame}[fragile]
+  \frametitle{Vector Calculations}
+
+  simple algebra
+\begin{lstlisting}[style=input]
+r = 2*xvector - yvector;
+\end{lstlisting}
+
+  \pause \medskip
+
+
+  basic operations
+\begin{lstlisting}[style=input]
+dot(v1,v2)   % dot product
+cross(v1,v2) % cross product
+angle(v1,v2) % angle between two vectors
+\end{lstlisting}
+
+  \pause \medskip
+
+  extract properties
+\begin{lstlisting}[style=input]
+r.theta      % polar angle in radiant
+r.rho        % azimuth angle in radiant
+r.x, r.y, r.z
+\end{lstlisting}
+
+\end{frame}
+
+
+\subsection*{Indexing}
+
+\begin{frame}[fragile]
+  \frametitle{Indexing of Vectors}
+
+  \begin{overlayarea}{\textwidth}{8cm}
+
+    consider a list of vectors
+    \begin{lstlisting}[style=input]
+r = vector3d([0 0 1 1],[1 0 1 1],[1 1 1 0]);
+    \end{lstlisting}
+
+    \begin{onlyenv}<1>
+      \vspace{-.3cm}
+      \begin{lstlisting}[style=output]
+r = /+vector3d+/ (show methods, plot)
+  size: 1 x 4
+  x y z
+  0 1 1
+  0 0 1
+  1 1 1
+  1 1 0
+      \end{lstlisting}
+    \end{onlyenv}
+
+    \pause \medskip
+
+    single out the second vector
+    \begin{lstlisting}[style=input]
+r(2)
+    \end{lstlisting}
+
+    \begin{onlyenv}<2>
+      \vspace{-0.3cm}
+      \begin{lstlisting}[style=output]
+r = /+vector3d+/ (show methods, plot)
+  size: 1 x 1
+  x y z
+  0 0 1
+      \end{lstlisting}
+    \end{onlyenv}
+
+    \pause \medskip
+
+    single out the second and the fourth vector
+    \begin{lstlisting}[style=input]
+r([2 4])
+    \end{lstlisting}
+    \begin{onlyenv}<3>
+      \vspace{-0.3cm}
+      \begin{lstlisting}[style=output]
+r = /+vector3d+/ (show methods, plot)
+  size: 1 x 2
+  x y z
+  0 0 1
+  1 1 0
+      \end{lstlisting}
+    \end{onlyenv}
+
+  \pause \medskip
+
+single out vectors by a logical condition
+    \begin{lstlisting}[style=input]
+r(r.x>0)
+    \end{lstlisting}
+        \begin{onlyenv}<4>
+          \vspace{-0.3cm}
+      \begin{lstlisting}[style=output]
+r = /+vector3d+/ (show methods, plot)
+  size: 1 x 2
+  x y z
+  1 1 1
+  1 1 0
+     \end{lstlisting}
+    \end{onlyenv}
+
+    \pause \medskip
+
+    \alert{The above techniques applies also to lists of
+    orientations, EBSD data, grains, boundary segments, etc.}
+  \end{overlayarea}
+\end{frame}
+
+
+\subsection*{Changing Vectors}
+
+\begin{frame}[fragile]
+  \frametitle{Changing Vectors}
+
+  \begin{overlayarea}{\textwidth}{8cm}
+
+    consider again the list of vectors
+    \begin{lstlisting}[style=input]
+r = vector3d([0 0 1 1],[1 0 1 1],[1 1 1 0]);
+    \end{lstlisting}
+
+    \begin{onlyenv}<1>
+      \vspace{-0.3cm}
+      \begin{lstlisting}[style=output]
+r = /+vector3d+/ (show methods, plot)
+  size: 1 x 4
+  x y z
+  0 1 1
+  0 0 1
+  1 1 1
+  1 1 0
+      \end{lstlisting}
+    \end{onlyenv}
+
+    \pause \medskip
+
+    replace the second vector by another vector
+    \begin{lstlisting}[style=input]
+r(2) = yvector
+    \end{lstlisting}
+
+    \begin{onlyenv}<2>
+      \vspace{-0.3cm}
+      \begin{lstlisting}[style=output]
+r = /+vector3d+/ (show methods, plot)
+  size: 1 x 4
+  x y z
+  0 1 1
+  0 1 0
+  1 1 1
+  1 1 0
+      \end{lstlisting}
+    \end{onlyenv}
+
+    \pause \medskip
+
+    remove the second vector completely
+    \begin{lstlisting}[style=input]
+r(2) = []
+    \end{lstlisting}
+    \begin{onlyenv}<3>
+      \vspace{-0.3cm}
+      \begin{lstlisting}[style=output]
+r = /+vector3d+/ (show methods, plot)
+  size: 1 x 3
+  0 1 1
+  1 1 1
+  1 1 0
+      \end{lstlisting}
+    \end{onlyenv}
+
+  \pause \medskip
+
+  change the x coordinate of all vectors
+    \begin{lstlisting}[style=input]
+r.x = 0
+    \end{lstlisting}
+        \begin{onlyenv}<4>
+          \vspace{-0.3cm}
+      \begin{lstlisting}[style=output]
+r = /+vector3d+/ (show methods, plot)
+  size: 1 x 3
+  0 1 1
+  0 1 1
+  0 1 0
+     \end{lstlisting}
+    \end{onlyenv}
+
+    \pause \medskip
+
+    \alert{The above techniques applies also to pole figure data,
+    orientations, EBSD data, grains, etc.}
+  \end{overlayarea}
+
+
+\end{frame}
+
+
+\subsection*{Plotting}
+\label{sec:plotting}
+
+\begin{frame}[fragile]
+  \frametitle{Plotting Vectors}
+
+  \begin{columns}
+    \begin{column}{8.5cm}
+      \begin{overlayarea}{\textwidth}{8cm}
+
+      spherical projections: \texttt{earea, edist, eangle}
+      hemisphere: \texttt{upper, lower}
+
+      \begin{onlyenv}<1>
+        \begin{lstlisting}[style=input]
+plot(r,'projection','eangle','upper')
+\end{lstlisting}
+      \end{onlyenv}
+
+      \pause
+
+      \begin{onlyenv}<2->
+        \begin{lstlisting}[style=input]
+plot(r,'projection','earea','upper')
+\end{lstlisting}
+      \end{onlyenv}
+
+\pause \medskip
+
+combined plots
+
+\begin{lstlisting}[style=input]
+plot(vector3d(1,1,1),'upper');
+hold all
+plot(vector3d(1,2,3),'label','B');
+plot(vector3d(-1,2,1),'label','A');
+hold off
+\end{lstlisting}
+
+      \pause \medskip
+
+      data plots
+
+      \begin{lstlisting}[style=input]
+r = randv(100)  % 100 random points
+plot(r,1:100)   % colored by number
+quiver(r,orth(r)) % a vector field
+      \end{lstlisting}
+
+    \end{overlayarea}
+  \end{column}
+
+  \begin{column}{3.5cm}
+
+    \begin{overlayarea}{\textwidth}{8cm}
+      \includegraphics<1-2>[width=3.5cm]{pic/vectoreangle}
+
+      \includegraphics<2>[width=3.5cm]{pic/vectorearea}
+
+      \includegraphics<3>[width=3.5cm]{pic/vectorCombined}
+
+      \includegraphics<4>[width=3.5cm]{pic/vectorColor}
+
+      \includegraphics<4>[width=3.5cm]{pic/quiver}
+    \end{overlayarea}
+  \end{column}
+  \end{columns}
+
+\end{frame}
+
+\subsection*{Annotations}
+
+\begin{frame}[fragile]
+  \frametitle{Customize Plots}
+
+\begin{columns}
+  \begin{column}{8.5cm}
+
+\begin{overprint}
+  \onslide<1|handout:0>%
+  General Syntax%
+\begin{lstlisting}[style=input]
+plot(vector3d,<options>)
+\end{lstlisting}
+  \onslide<2|handout:1>%
+  General Syntax
+\begin{lstlisting}[style=input]
+annotate(orientation,<options>)
+\end{lstlisting}
+\end{overprint}
+
+Options
+\begin{lstlisting}[style=input]
+Marker            % marker shape
+MarkerSize        % marker size
+MarkerFaceColor   % face color
+MarkerEdgeColor   % edge color
+label             % a label text
+color, background % text colors
+\end{lstlisting}
+
+\begin{overprint}
+  \onslide<1|handout:0>%
+  Example
+\begin{lstlisting}[style=input]
+plot([xvector,yvector,zvector],
+ 'Backgroundcolor','w','Marker','s',
+ 'MarkerEdgeColor','w','labeled',
+ 'MarkerFaceColor','k')
+\end{lstlisting}
+
+  \onslide<2|handout:1>
+Example
+\begin{lstlisting}[style=input]
+plot(q0,'label','A',...
+ 'Backgroundcolor','w','Marker','s',
+ 'MarkerEdgeColor','w',...
+ 'MarkerFaceColor','r')
+\end{lstlisting}
+
+\end{overprint}
+
+\end{column}
+
+\begin{column}{3.5cm}
+    \onslide<1->
+    \only<1|handout:0>{%
+    \includegraphics[width=3.5cm]{pic/annotationv}%
+    }%
+    \only<2>{%
+    \includegraphics[width=3.3cm]{pic/annotationq}%
+    }%
+\end{column}
+
+\end{columns}
+
+\end{frame}
+
+\subsection*{Axes}
+
+\begin{frame}[fragile]
+  \frametitle{Axes}
+
+  \begin{columns}
+    \begin{column}{8.5cm}
+      \begin{overlayarea}{8.5cm}{8cm}
+        Axes are three dimensional vectors where we do not care about length and
+        direction, e.g. plane normals.
+
+\begin{lstlisting}[style=input]
+r = vector3d(1,1,1,'antipodal')
+\end{lstlisting}
+
+\medskip
+\pause
+
+Then \textbf{\texttt{r}} and \textbf{\texttt{-r}} represent the same axis
+\begin{lstlisting}[style=input]
+eq(r, -r)
+\end{lstlisting}
+\begin{onlyenv}<2>
+  \vspace{-0.3cm}
+\begin{lstlisting}[style=output]
+  1
+\end{lstlisting}
+\end{onlyenv}
+
+\medskip
+\pause
+
+The angle to an axis is always less then $90^{\degree}$
+\begin{lstlisting}[style=input]
+angle(r,-xvector) / degree
+\end{lstlisting}
+\begin{onlyenv}<3>
+  \vspace{-0.3cm}
+\begin{lstlisting}[style=output]
+  54.7
+\end{lstlisting}
+\end{onlyenv}
+
+\medskip
+\pause
+
+The option \textbf{antipodal} in a contour plot
+\begin{onlyenv}<4>
+\begin{lstlisting}[style=input]
+r = randv(1000)
+plot(r,'contourf')
+\end{lstlisting}
+\end{onlyenv}
+\begin{onlyenv}<5>
+\begin{lstlisting}[style=input]
+r = randv(1000)
+plot(r,'contourf','antipodal')
+\end{lstlisting}
+\end{onlyenv}
+\end{overlayarea}
+\end{column}
+  \begin{column}{3.5cm}
+    \only<1-3>{\includegraphics[width=3.5cm]{pic/vectorAntipodal}}
+    \only<4>{\includegraphics[width=3.5cm]{pic/vectorContour}}
+    \only<5>{\includegraphics[width=3.5cm]{pic/vectorContourAntipodal}}
+  \end{column}
+\end{columns}
+
+
+\end{frame}
+
+\section{Rotations}
+
+\subsection*{Basics}
+
+\begin{frame}[fragile]
+  \frametitle{Rotations}
+
+  A rotation is a transformation that maps a right handed coordinate system
+  $(\vec X_{1}, \vec Y_{1}, \vec Z_{1})$ onto another right handed coordinate
+  system $(\vec X_{2}, \vec Y_{2}, \vec Z_{2})$. It is given by the rotation
+  matrix
+
+  % \begin{equation*}
+  %   \bf R = \left(
+  %     \begin{matrix}
+  %       \vec X_{1} \cdot \vec X_{2} & \vec Y_{1} \cdot \vec X_{2}& \vec Z_{1} \cdot \vec X_{2} \\
+  %       \vec X_{1} \cdot \vec Y_{2} & \vec Y_{1} \cdot \vec Y_{2}& \vec Z_{1} \cdot \vec Y_{2} \\
+  %       \vec X_{1} \cdot \vec Z_{2} & \vec Y_{1} \cdot \vec Z_{2}& \vec Z_{1} \cdot \vec Z_{2}
+  %     \end{matrix}
+  %   \right).
+  % \end{equation*}
+  \begin{equation*}
+    \mathbf R = (\vec X_{2}, \vec Y_{2}, \vec Z_{2}) \cdot (\vec X_{1}, \vec Y_{1}, \vec Z_{1})^{t}
+  \end{equation*}
+
+  \medskip
+
+  We have $\mathbf R \vec X_{1} = \vec X_{2}$, $\mathbf R \vec Y_{1} = \vec
+  Y_{2}$ and $\mathbf R \vec Z_{1} = \vec Z_{2}$.
+
+  \medskip
+  \pause
+
+  On the other hand, $\bf R$ transforms coordinates with respect to $(\vec
+  X_{2}, \vec Y_{2}, \vec Z_{2})$ into coordinates with respect to $(\vec
+  X_{1}, \vec Y_{1}, \vec Z_{1})$. I.e. for
+
+  \begin{equation*}
+    \vec r
+    = x_{1} \vec X_{1} + y_{1} \vec Y_{1} + z_{1} \vec Z_{1}
+    = x_{2} \vec X_{2} + y_{2} \vec Y_{2} + z_{2} \vec Z_{2}
+  \end{equation*}
+
+  we have
+
+  \begin{equation*}
+    \mathbf R
+    \left(
+      \begin{matrix}
+        x_{2}\\
+        y_{2}\\
+        z_{2}
+      \end{matrix}\right)
+    = \left(
+      \begin{matrix}
+        x_{1}\\
+        y_{1}\\
+        z_{1}
+      \end{matrix}\right)
+  \end{equation*}
+
+\end{frame}
+
+\subsection*{Euler Angles}
+\label{sec:euler-angles}
+
+\begin{frame}[fragile]
+  \frametitle{Euler Angles}
+  \begin{overlayarea}{\textwidth}{8cm}
+
+  Most commonly, rotations are given by Bunge Euler angles.
+
+  \begin{lstlisting}[style=input]
+R = rotation('Euler',10*degree,20*degree,30*degree)
+  \end{lstlisting}
+  \begin{onlyenv}<1>
+    \vspace{-0.3cm}
+  \begin{lstlisting}[style=output]
+R = /+rotation+/ (show methods, plot)
+  size: 1 x 1
+
+  Bunge Euler angles in degree
+  phi1  Phi phi2 Inv.
+    10   20   30    0
+  \end{lstlisting}
+  \end{onlyenv}
+
+  \pause
+  \medskip
+
+  \begin{lstlisting}[style=input]
+R = rotation('Euler',...
+    10*degree,20*degree,30*degree,'Roe')
+  \end{lstlisting}
+  \begin{onlyenv}<2>
+    \vspace{-0.3cm}
+  \begin{lstlisting}[style=output]
+R = /+rotation+/ (show methods, plot)
+  size: 1 x 1
+
+  Bunge Euler angles in degree
+  phi1  Phi phi2 Inv.
+   100   20  300    0
+  \end{lstlisting}
+\end{onlyenv}
+
+\pause
+\medskip
+
+Supported conventions are \texttt{Bunge}, \texttt{Matthies}, \texttt{Roe},
+\texttt{Kocks}, \texttt{Canova}.
+  \begin{lstlisting}[style=input]
+setMTEXpref('EulerAngleConvention','Roe')
+  \end{lstlisting}
+
+  \begin{onlyenv}<3>
+    \vspace{-0.3cm}
+  \begin{lstlisting}[style=output]
+R = /+rotation+/ (show methods, plot)
+  size: 1 x 1
+
+  Roe Euler angles in degree
+  Psi Theta   Phi Inv.
+   10    20    30    0
+ \end{lstlisting}
+\end{onlyenv}
+\end{overlayarea}
+\end{frame}
+
+\subsection*{Axis Angle Representation}
+\label{sec:axis-angle-repr}
+
+\begin{frame}[fragile]
+  \frametitle{Other Ways to Define a Rotation}
+
+  A rotation is uniquely defined by its rotation axis and its rotation angle
+
+  \begin{lstlisting}[style=input]
+R = rotation('axis',xvector,'angle',45*degree)
+  \end{lstlisting}
+
+  \pause
+  \medskip
+
+  Conversely, one can compute axis / angle from a rotation
+
+  \begin{lstlisting}[style=input]
+R.axis, R.angle
+  \end{lstlisting}
+
+  \pause
+  \medskip
+
+Given four vectors $\vec u_{1}, \vec u_{2}, \vec v_{1}, \vec v_{2}$ there is a
+unique rotation $\mathbf R$ such that  $\mathbf R \vec u_{1} = \vec v_{1}$ and
+$\mathbf R \vec u_{2} = \vec v_{2}$
+
+\begin{lstlisting}[style=input]
+R = rotation('map',u1,v1,u2,v2)
+\end{lstlisting}
+
+  \pause
+  \medskip
+
+Of course one can also define a rotation by its $3 \times 3$ matrix
+
+  \begin{lstlisting}[style=input]
+R = rotation('matrix',A)
+  \end{lstlisting}
+
+or by quaternions
+
+  \begin{lstlisting}[style=input]
+R = rotation('quaternion',a,b,c,d)
+  \end{lstlisting}
+
+\end{frame}
+
+\subsection*{Basic Calculations}
+\label{sec:euler-angles}
+
+\begin{frame}[fragile]
+  \frametitle{Basic Calculations}
+
+    rotate a vector
+    \begin{lstlisting}[style=input]
+R = rotation('axis',xvector,'angle',-45*degree);
+R * vector3d(0,1,1)
+    \end{lstlisting}
+
+
+  \begin{columns}
+    \begin{column}{8cm}
+  \begin{overlayarea}{8cm}{8cm}
+\begin{onlyenv}<1>
+  \vspace{-0.3cm}
+\begin{lstlisting}[style=output]
+ans = /+vector3d+/ (show methods, plot)
+  size: 1 x 1
+  x       y       z
+  0 1.41421       0
+  \end{lstlisting}
+\end{onlyenv}
+
+\pause
+ \medskip
+
+ the inverse rotation
+ \begin{lstlisting}[style=input]
+ inv(R)
+ \end{lstlisting}
+ \begin{onlyenv}<2>
+   \vspace{-0.3cm}
+  \begin{lstlisting}[style=output]
+ans = /+rotation+/ (show methods, plot)
+  size: 1 x 1
+
+  Bunge Euler angles in degree
+  phi1  Phi phi2 Inv.
+     0   45    0    0
+  \end{lstlisting}
+ \end{onlyenv}
+
+ \pause
+ \medskip
+
+ combine rotations
+ \begin{lstlisting}[style=input]
+R * inv(R)
+\end{lstlisting}
+
+\begin{onlyenv}<3>
+  \vspace{-0.3cm}
+  \begin{lstlisting}[style=output]
+ans = /+rotation+/ (show methods, plot)
+  size: 1 x 1
+
+  Bunge Euler angles in degree
+  phi1  Phi phi2 Inv.
+     0    0    0    0
+  \end{lstlisting}
+\end{onlyenv}
+
+\pause
+\medskip
+
+plotting
+\begin{lstlisting}[style=input]
+R = randq(100)
+scatter(R) % Rodriguez space
+\end{lstlisting}
+
+\end{overlayarea}
+\end{column}
+
+\begin{column}{3.7cm}
+  \includegraphics[width=3.7cm]{pic/rotationScatter}
+\end{column}
+
+\end{columns}
+
+\end{frame}
+
+\subsection*{Improper Rotations}
+
+\begin{frame}[fragile]
+  \frametitle{Improper Rotations}
+
+  \begin{overlayarea}{\textwidth}{7cm}
+
+    An improper rotation is a rotation followed by an inversion
+    \begin{lstlisting}[style=input]
+I = -rotation('Euler',10*degree,20*degree,30*degree)
+    \end{lstlisting}
+    \begin{onlyenv}<1>
+      \vspace{-0.3cm}
+      \begin{lstlisting}[style=output]
+I = /+rotation+/ (show methods, plot)
+  size: 1 x 1
+
+  Bunge Euler angles in degree
+  phi1  Phi phi2 Inv.
+    10   20   30    1
+  \end{lstlisting}
+  \end{onlyenv}
+
+  \pause
+  \bigskip
+
+  reflections
+  \begin{lstlisting}[style=input]
+R = reflection(xvector+yvector)
+  \end{lstlisting}
+  \begin{onlyenv}<2>
+    \vspace{-0.3cm}
+  \begin{lstlisting}[style=output]
+R = /+rotation+/ (show methods, plot)
+  size: 1 x 1
+
+  Bunge Euler angles in degree
+  phi1  Phi phi2 Inv.
+    45  180  315    1
+  \end{lstlisting}
+  \end{onlyenv}
+
+  \pause
+  \bigskip
+
+  angles between proper and improper rotations
+  \begin{lstlisting}[style=input]
+angle(I,[R,-R])
+  \end{lstlisting}
+  \begin{onlyenv}<3>
+    \vspace{-0.3cm}
+    \begin{lstlisting}[style=output]
+  168.5677  180.0000
+  \end{lstlisting}
+  \end{onlyenv}
+
+  \pause
+  \bigskip
+
+  check for improper rotations
+\begin{lstlisting}[style=input]
+I.isImproper
+  \end{lstlisting}
+  \begin{onlyenv}<4>
+    \vspace{-0.3cm}
+    \begin{lstlisting}[style=output]
+  1
+  \end{lstlisting}
+  \end{onlyenv}
+
+\end{overlayarea}
+\end{frame}
+
+\section{Crystal Symmetries}
+\label{sec:symmetries}
+
+\subsection*{Crystal Symmetries}
+\label{sec:crystal-symmetries}
+
+\begin{frame}[fragile,fragile]
+  \frametitle{Crystal Symmetry}
+
+  \begin{columns}
+  \begin{column}{8cm}
+
+    \begin{overlayarea}{8cm}{8cm}
+      The \alert{point group} $\mathbf C$ of a crystal are all rotations
+      $\mathbf R$ that keep the crystal lattice invariant.
+
+\begin{lstlisting}[style=input]
+CS = crystalSymmetry('m-3m')
+\end{lstlisting}
+    \begin{onlyenv}<1>
+\vspace{-.3cm}\begin{lstlisting}[style=output]
+CS = /+crystalSymmetry+/ (show methods, plot)
+
+  symmetry: m-3m
+  a, b, c : 1, 1, 1
+\end{lstlisting}
+    \end{onlyenv}
+
+    \pause \medskip
+
+    extract the rotations of a point group
+\begin{lstlisting}[style=input]
+ rotation(crystalSymmetry('222'))
+\end{lstlisting}
+    \begin{onlyenv}<2>
+\vspace{-.3cm}\begin{lstlisting}[style=output]
+ans = /+rotation+/ (show methods, plot)
+  size: 4 x 1
+
+  Bunge Euler angles in degree
+  phi1  Phi phi2 Inv.
+     0    0    0    0
+   180    0    0    0
+    45  180   45    0
+    45  180  225    0
+\end{lstlisting}
+    \end{onlyenv}
+
+    \pause \medskip
+
+    import data from crystal information files
+\begin{lstlisting}[style=input]
+CS = loadCIF('Quarz.cif')
+\end{lstlisting}
+    \begin{onlyenv}<3>
+\vspace{-.3cm}\begin{lstlisting}[style=output]
+CS = /+crystalSymmetry+/ (show methods, plot)
+
+  mineral           : Quartz
+  symmetry          : P 32 2 1 (321)
+  a, b, c           : 4.9, 4.9, 5.4
+  alpha, beta, gamma: 90°, 90°, 120°
+  reference frame   : X||a*, Y||b, Z||c*
+\end{lstlisting}
+\end{onlyenv}
+
+    \pause
+    \vspace{-.3cm}
+
+\begin{lstlisting}[style=input]
+CS = loadPHL('minerals.phl')
+\end{lstlisting}
+    \begin{onlyenv}<4>
+\vspace{-.3cm}\begin{lstlisting}[style=output]
+CS{1} = /+crystalSymmetry+/ (show methods, plot)
+
+  mineral : Magnetite
+  density : 5.054
+  symmetry: m-3m
+  a, b, c : 8.4, 8.4, 8.4
+\end{lstlisting}
+\end{onlyenv}
+
+\pause
+\medskip
+
+    switch to Laue / purely rotational group
+\begin{lstlisting}[style=input]
+CS.Laue
+CS.properGroup
+\end{lstlisting}
+
+  \end{overlayarea}
+\end{column}
+  \begin{column}{3.7cm}
+    \includegraphics<1->[width=3.7cm]{pic/m-3m}
+
+    \medskip
+
+    \includegraphics<3->[width=3.7cm]{pic/quartz}
+
+    %\includegraphics<1-2>[width=3.7cm]{pic/m-3mHKL}
+    %\includegraphics<3>[width=3.7cm]{pic/quartzHKL}
+  \end{column}
+\end{columns}
+\end{frame}
+
+\subsection*{Laue and Proper Symmetry Groups}
+\begin{frame}[fragile]
+
+  \begin{figure}[H]
+    \centering
+    \begin{subfigure}{0.3\textwidth}
+      \includegraphics[width=\textwidth]{pic/432}
+      \subcaption{$432$}
+    \end{subfigure}
+    \begin{subfigure}{0.3\textwidth}
+      \includegraphics[width=\textwidth]{pic/43m}
+      \subcaption{$\bar 43m$}
+    \end{subfigure}
+    \begin{subfigure}{0.3\textwidth}
+      \includegraphics[width=\textwidth]{pic/m-3m}
+      \subcaption{$m\bar 3 m$}
+    \end{subfigure}
+
+    \begin{subfigure}{0.3\textwidth}
+      \centering
+      \includegraphics[width=0.95\textwidth]{pic/2mm}
+      \caption{$2mm$}
+    \end{subfigure}
+    \begin{subfigure}{0.3\textwidth}
+      \centering
+      \includegraphics[width=0.95\textwidth]{pic/m2m}
+      \caption{$m2m$}
+    \end{subfigure}
+    \begin{subfigure}{0.3\textwidth}
+      \centering
+      \includegraphics[width=0.95\textwidth]{pic/mm2}
+      \caption{$mm2$}
+    \end{subfigure}
+  \end{figure}
+
+\end{frame}
+
+\subsection*{trigonal}
+
+\begin{frame}
+
+  \begin{figure}[H]
+    \centering
+    \begin{subfigure}{0.3\textwidth}
+      \includegraphics[width=\textwidth]{pic/sym321}
+      \subcaption{$321$}
+    \end{subfigure}
+    \begin{subfigure}{0.3\textwidth}
+      \includegraphics[width=\textwidth]{pic/sym3m1}
+      \subcaption{$3m1$}
+    \end{subfigure}
+    \begin{subfigure}{0.3\textwidth}
+      \includegraphics[width=\textwidth]{pic/sym-3m1}
+      \caption{$\bar 3m1$}
+    \end{subfigure}
+    \begin{subfigure}{0.3\textwidth}
+      \includegraphics[width=\textwidth]{pic/sym312}
+      \caption{$312$}
+    \end{subfigure}
+    \begin{subfigure}{0.3\textwidth}
+      \includegraphics[width=\textwidth]{pic/sym31m}
+      \caption{$31m$}
+    \end{subfigure}
+    \begin{subfigure}{0.3\textwidth}
+      \includegraphics[width=\textwidth]{pic/sym-31m}
+      \caption{$\bar 31m$}
+    \end{subfigure}
+  \end{figure}
+
+\end{frame}
+
+
+\subsection*{Crystal Symmetries}
+\label{sec:crystal-symmetries}
+
+\begin{frame}[fragile]
+  \frametitle{Unit Cell, Reciprocal and Orthogonal Coordinate System}
+
+  \begin{overlayarea}{\textwidth}{8cm}
+    The unit cell of a crystal is specified by the length of its three edges
+    $\vec a, \vec b, \vec c$ and by angles $\alpha, \beta, \gamma$ they enclose.
+
+  \begin{lstlisting}[style=input]
+C = crystalSymmetry('1',[a b c],[alpha beta gamma])
+  \end{lstlisting}
+
+  \begin{columns}
+    \begin{column}{7.5cm}
+
+      \begin{uncoverenv}<2->
+        The axes of the reciprocal lattice are defined
+        orthogonal to $\vec a, \vec b, \vec c$, i.e.
+\vspace{-0.2cm}
+\begin{equation*}
+  \vec a^{*} = \frac{\vec b \times \vec c}{V}, \;
+  \vec b^{*} = \frac{\vec c \times \vec a}{V}, \;
+  \vec c^{*} = \frac{\vec a \times \vec b}{V}
+\end{equation*}
+
+\vspace{-0.4cm}
+
+with  $V = \vec a \cdot (\vec b \times \vec c)$  volume of the unit cell
+      \end{uncoverenv}
+
+      \medskip
+
+      \begin{uncoverenv}<3->
+        We will need also an orthogonal coordinate system $(\vec x, \vec y,
+        \vec z)$ fixed to the crystal.
+      \end{uncoverenv}
+
+      \medskip
+
+      \begin{uncoverenv}<4->
+        \alert{There are different conventions.}
+      \end{uncoverenv}
+
+  \end{column}
+
+    \begin{column}{4.5cm}
+      \begin{tikzpicture}[x  = {(-0.5cm,-0.5cm)},
+        y  = {(0.9659cm,-0.25882cm)},
+        z  = {(0cm,1cm)},
+        scale = 2]
+
+\draw[draw=green, dashed] (0,0,0) -- (1.2,0,0) -- (1,1,0) -- (-0.2,1,0) --
+(0,1.2,1) -- (0.2,0.2,1) --  (1.4,0.2,1) -- (1.2,0,0);
+
+\draw[draw=green, dashed] (0,1.2,1) -- (1.2,1.2,1) -- (1,1,0);
+\draw[draw=green, dashed] (1.2,1.2,1) -- (1.4,0.2,1);
+
+
+\draw[draw=green,very thick] (0,0,0) -- (1.2,0,0) node [anchor=north,color=green!70!black] {$\vec a$};
+\draw[draw=green,very thick] (0,0,0) -- (-0.2,1,0) node [anchor=west,color=green!70!black] {$\vec b$};
+\draw[draw=green,very thick] (0,0,0) -- (0.2,0.2,1) node[anchor=south,color=green!70!black] {$\vec c$};
+
+\only<1>{
+\draw[draw=green] (0.3,0,0) arc (250:329:0.3cm);% node {$\alpha$};
+\draw[draw=green] (-0.03,0.2,0) arc (0:68:0.3cm);% node {$\alpha$};
+\draw[draw=green] (0.3,0,0) arc (200:112:0.3cm);% node {$\alpha$};
+\node at (0.15,0.01,0.1)[color=green!70!black]{$\beta$};
+\node at (0.01,0.15,0.1)[color=green!70!black]{$\alpha$};
+\node at (0.15,0.1,0)[color=green!70!black]{$\gamma$};
+}
+
+
+\only<2->{
+\draw[->,draw=red,very thick] (0,0,0) -- (0,0,1.2) node [anchor=west,color=red!70!black] {$\vec c^{*}$};
+\draw[->,draw=red,very thick] (0,0,0) -- (1,0.2,-0.24) node [anchor=west,color=red!70!black] {$\vec a^{*}$};
+\draw[->,draw=red,very thick] (0,0,0) -- (0,1.2,-0.24) node [anchor=north,color=red!70!black] {$\vec b^{*}$};
+}
+
+\only<3|handout>{
+\draw[->,draw=black,ultra thick] (0,0,0) -- (1,0,0) node
+[anchor=north,color=black] {$\vec{\mathbf x}$};
+\draw[->,draw=black,ultra thick] (0,0,0) -- (0,1,0) node
+[anchor=north,color=black] {$\vec{\mathbf y}$};
+\draw[->,draw=black,ultra thick] (0,0,0) -- (0,0,1) node
+[anchor=east,color=black] {$\vec{\mathbf z}$};
+}
+
+\only<4>{
+\draw[->,draw=black,ultra thick] (0,0,0) -- (1,0.2,0) node
+[anchor=north,color=black] {$\vec{\mathbf x}$};
+\draw[->,draw=black,ultra thick] (0,0,0) -- (-0.2,1,0) node
+[anchor=north,color=black] {$\vec{\mathbf y}$};
+\draw[->,draw=black,ultra thick] (0,0,0) -- (0,0,1) node
+[anchor=east,color=black] {$\vec{\mathbf z}$};
+}
+
+\end{tikzpicture}
+
+\end{column}
+\end{columns}
+
+\begin{onlyenv}<3|handout>
+  \begin{lstlisting}[style=input]
+CS = crystalSymmetry('321',[a b c],'X||a','Z||c*')
+  \end{lstlisting}
+\end{onlyenv}
+
+\begin{onlyenv}<4->
+  \begin{lstlisting}[style=input]
+CS = crystalSymmetry('321',[a b c],'X||b','Z||c*')
+\end{lstlisting}
+The alignment of $\vec x$, $\vec y$, $\vec z$ is important as the Euler angles
+refer to them.
+\end{onlyenv}
+
+\end{overlayarea}
+
+\end{frame}
+
+\section{Miller Indices}
+\label{sec:miller-indices}
+
+\subsection*{definition}
+\label{sec:definition}
+
+\begin{frame}[fragile]
+  \frametitle{Miller Indices - Crystal Fixed Directions}
+
+  A direction with respect to the crystal coordinate system  $\mathbf C$
+
+  \begin{columns}
+    \begin{column}{7cm}
+
+      \begin{overlayarea}{8cm}{8cm}
+
+        \begin{equation*}
+          \vec m = u \cdot \vec a+ v \cdot \vec b + w \cdot \vec c.
+        \end{equation*}
+
+    \begin{onlyenv}<2->
+\begin{lstlisting}[style=input]
+CS = crystalSymmetry('mmm',[1 2 3])
+m = Miller(1,1,1,CS,'uvw')
+\end{lstlisting}
+\end{onlyenv}
+\begin{onlyenv}<2>
+\vspace{-.3cm}\begin{lstlisting}[style=output]
+m = /+Miller+/ (show methods, plot)
+  size: 1 x 1
+  symmetry: mmm
+  u 1
+  v 1
+  w 1
+\end{lstlisting}
+\end{onlyenv}
+
+    \begin{onlyenv}<3->
+A direction in reciprocal coordinates
+\begin{equation*}
+  \vec r = h \cdot \vec a^{*}+ k \cdot \vec b^{*} + \ell \cdot \vec c^{*}.
+\end{equation*}
+\begin{lstlisting}[style=input]
+m = Miller(1,1,1,CS,'hkl')
+\end{lstlisting}
+\end{onlyenv}
+\begin{onlyenv}<3>
+  \vspace{-.3cm}
+  \begin{lstlisting}[style=output]
+m = /+Miller+/ (show methods, plot)
+  size: 1 x 1
+  symmetry: mmm
+  h 1
+  k 1
+  l 1
+\end{lstlisting}
+\end{onlyenv}
+
+\medskip
+
+\begin{onlyenv}<4->
+  A direction in the orthogonal coordinate system
+  \begin{lstlisting}[style=input]
+m = Miller(xvector,CS)
+\end{lstlisting}
+\end{onlyenv}
+\end{overlayarea}
+\end{column}
+    \begin{column}{4cm}
+
+      \begin{overlayarea}{4cm}{7cm}
+
+      \begin{center}
+        \includegraphics<2>[width=4cm]{pic/MillerUVW}
+%        \includegraphics<3>[width=4cm]{pic/MillerHKL}
+        \includegraphics<3->[width=4cm]{pic/MillerPlane}
+      \end{center}
+      \vspace{-0.2cm}
+        \begin{onlyenv}<2-|handout>
+          \begin{lstlisting}[style=input]
+plot(m,'labeled')
+          \end{lstlisting}%
+        \end{onlyenv}%
+        \vspace{-0.25cm}
+        \begin{onlyenv}<3->%
+          \begin{lstlisting}[style=input]
+hold all
+plot(m,'labeled')
+          \end{lstlisting}%
+        \end{onlyenv}%
+        \vspace{-0.25cm}
+        \begin{onlyenv}<3->%
+          \begin{lstlisting}[style=input]
+plot(m,'plane')
+          \end{lstlisting}
+        \end{onlyenv}
+          \end{overlayarea}
+      \end{column}
+    \end{columns}
+
+\end{frame}
+
+\subsection*{The trigonal case}
+
+\begin{frame}[fragile]
+  \frametitle{Trigonal and Hexagonal Symmetries}
+
+  \vspace{-.3cm}
+
+  \begin{center}
+    \includegraphics[width=4cm]{pic/hkl}
+    \includegraphics[width=4cm]{pic/uvtw}
+    \includegraphics[width=4cm]{pic/uvw}
+  \end{center}
+
+  \vspace{-.5cm}
+
+  define lists of crystal directions
+  \vspace{-.2cm}
+  \begin{lstlisting}[style=input]
+m = Miller({1 0 -1 0},{1 1 -2 1},CS,'hkil')
+m = Miller({1 0 -1 0},{1 1 -2 2},CS,'UVTW')
+m = Miller({1 0 0},{1 0 1},CS,'uvw')
+  \end{lstlisting}%
+
+  \medskip
+
+  Plot all symmetrically equivalent directions
+    \vspace{-.2cm}
+  \begin{lstlisting}[style=input]
+plot(m,'symmetrised','labeled')
+  \end{lstlisting}
+
+
+
+\end{frame}
+
+\subsection*{Calculations}
+
+\begin{frame}[fragile]
+  \frametitle{Calculating with Crystal Directions}
+
+   \begin{columns}
+     \begin{column}{8.6cm}
+         \begin{overlayarea}{\textwidth}{8cm}
+           Find all symmetrically equivalent directions
+           \begin{lstlisting}[style=input]
+CS = loadCIF('quartz')
+m = Miller(1,1,-2,1,CS,'hkil')
+symmetrise(m)
+           \end{lstlisting}
+
+           \begin{onlyenv}<1>
+             \vspace{-.3cm}
+            \begin{lstlisting}[style=output]
+ans = /+Miller+/ (show methods, plot)
+  size: 6 x 1
+  mineral: Quartz (P 32 2 1, X||a*, Y||b, Z||c*)
+  h  1 -2  1  1 -2  1
+  k  1  1 -2 -2  1  1
+  i -2  1  1  1  1 -2
+  l  1  1  1 -1 -1 -1
+       \end{lstlisting}
+     \end{onlyenv}
+
+        \pause
+        \medskip
+
+        Change from reciprocal coordinate system to $\vec a$, $\vec b$, $\vec c$
+  \begin{lstlisting}[style=input]
+m.dispStyle = 'UVTW'
+  \end{lstlisting}
+           \begin{onlyenv}<2>
+             \vspace{-.3cm}
+             \begin{lstlisting}[style=output]
+m = /+Miller+/ (show methods, plot)
+  size: 6 x 1
+  mineral: Quartz (P 32 2 1, X||a*, Y||b, Z||c*)
+  U  0.0828
+  V  0.0828
+  T -0.1655
+  W  0.1027
+       \end{lstlisting}
+     \end{onlyenv}
+
+        \pause
+        \vspace{-.3cm}
+
+  \begin{lstlisting}[style=input]
+round(m)
+  \end{lstlisting}
+           \begin{onlyenv}<3>
+             \vspace{-.3cm}
+             \begin{lstlisting}[style=output]
+ans = /+Miller+/ (show methods, plot)
+  size: 6 x 1
+  mineral: Quartz (P 32 2 1, X||a*, Y||b, Z||c*)
+  U  4
+  V  4
+  T -8
+  W  5
+       \end{lstlisting}
+     \end{onlyenv}
+
+        \pause
+        \medskip
+
+        Access the coordinates and properties
+  \begin{lstlisting}[style=input]
+m.U, m.hkl, m.uvw, m.UVTW
+m.dspacing % d-spacing of planes
+  \end{lstlisting}
+
+        \pause
+        \medskip
+
+angle modulo symmetry
+        \begin{lstlisting}[style=input]
+angle(m1,m2) / degree
+\end{lstlisting}
+
+
+ \end{overlayarea}
+
+     \end{column}
+     \begin{column}{3.5cm}
+       \includegraphics<1->[width=3.5cm]{pic/MillerSymmetrised}%\\
+%       \includegraphics<1->[width=4cm]{pic/Symmetry}
+     \end{column}
+   \end{columns}
+\end{frame}
+
+\section{Orientations}
+\label{sec:orientations}
+
+\subsection*{Definition}
+
+\begin{frame}
+  \frametitle{Crystal Orientations}
+
+  \begin{columns}
+
+    \begin{column}{6.3cm}
+
+      \begin{overlayarea}{6.4cm}{8cm}
+        Let a vector $\vec v$ be given by specimen coordinates
+        $(r_{1},r_{2},r_{3})^{t}$ \underline{and} crystal coordinates
+        $(h_{1},h_{2},h_{3})^{t}$, i.e.,
+        \begin{equation*}
+          \vec v = r_{1} \vec X + r_{2} \vec Y + r_{3} \vec Y
+                 = h_{1} \vec x + h_{2} \vec y + h_{3} \vec z.
+        \end{equation*}
+
+        \pause
+
+        The coordinate transform $\mathbf O$ with
+      \begin{equation*}
+        \left(r_{1},r_{2},r_{3}\right)^{t}
+        =
+         \mathbf O
+         \left(
+          h_{1},h_{2},h_{3} \right)^{t}
+      \end{equation*}
+      is called \alert{crystal orientation}.
+
+      \pause
+      \medskip
+
+      The orientation $\mathbf O$ maps the specimen coordinate system $\vec X,
+      \vec Y, \vec Z$ onto the crystal coordinate systems $\vec x, \vec y,
+      \vec z$.
+
+      \pause
+      \medskip
+
+      The orientation $\mathbf O$ is well defined only up the crystal
+      symmetry.
+
+    \end{overlayarea}
+  \end{column}
+
+    \begin{column}{5cm}
+
+      \onslide<1->
+      \begin{tikzpicture}[scale=0.5]
+
+        \draw[->, >=latex, color=green!80, thick] (0,0) -- (0,12) node[left] {$\vec Z$};
+        \draw[->, >=latex, color=green!80, thick] (0,0) -- (6,0) node[right] {$\vec Y$};
+        \draw[->, >=latex, color=green!80, thick] (0,0) -- (-2,-2) node[left] {$\vec X$};
+%        \draw (6,11) node[color=green]{$K_S$};
+
+        \foreach \xpos/\ypos/\xx/\xy/\yx/\yy/\zx/\zy
+        in {
+0.20/1.63/-0.20/0.13/1.09/0.10/-0.31/-2.21,
+3.11/7.11/0.80/0.87/-0.20/0.55/1.50/-0.90,
+3.70/4.70/-0.03/0.87/0.36/-0.55/-2.12/-0.90,
+-1.91/1.15/-0.81/-0.59/0.59/-0.81/-1.00/-1.00,
+2.90/9.73/-0.06/0.62/-1.11/-0.17/-0.22/-1.83,
+%-0.67/6.44/-0.86/0.34/0.59/1.05/0.81/-0.37,
+%1.13/9.19/-0.79/-0.78/0.37/-0.79/-1.40/0.21,
+%2.28/0.74/0.44/1.02/-0.70/0.43/1.50/0.28,
+%0.70/0.07/-0.06/1.08/-0.83/-0.25/1.50/0.28,
+3.81/2.27/1.04/0.35/-0.40/0.54/-0.22/-1.83,
+%-1.71/7.06/-0.16/0.06/0.61/1.04/1.85/-0.81,
+%3.37/1.43/-0.61/-0.60/0.93/-0.23/-0.22/-1.83,
+%-0.49/9.19/0.24/0.73/0.27/0.84/-2.12/0.28,
+-1.21/9.29/1.07/-0.04/0.29/0.64/-0.22/-1.83,
+%2.21/8.17/1.01/0.53/0.27/0.34/0.81/-1.85,
+-0.74/3.46/-0.93/-0.71/0.05/0.48/-1.23/1.43,
+-1.51/8.21/-0.68/-0.33/-0.53/-0.87/-1.43/1.23,
+%1.37/1.83/1.07/0.51/-0.29/0.99/-0.22/0.21,
+0.25/6.41/0.24/1.01/0.90/-0.27/-1.23/-0.81,
+0.23/-1.12/-0.77/-0.57/0.31/-0.95/1.50/0.28
+        }
+        \fillcrystal{\xpos,\ypos}{\xx,\xy}{\yx,\yy}{\zx,\zy}{color=red};
+
+      \end{tikzpicture}
+    \end{column}
+\end{columns}
+\end{frame}
+
+\subsection*{Defining Orientations}
+\label{sec:defin-orient}
+
+\begin{frame}[fragile]
+  \frametitle{Defining Orientations}
+
+    \begin{overlayarea}{\textwidth}{8cm}
+      define an orientation by Euler angles
+  \begin{lstlisting}[style=input]
+CS = crystalSymmetry('321')
+SS = specimenSymmetry('1')
+O  = orientation('Euler',10*degree,5*degree,0,CS,SS)
+  \end{lstlisting}
+  \begin{onlyenv}<1>
+    \vspace{-.3cm}
+  \begin{lstlisting}[style=output]
+O = /+orientation+/ (show methods, plot)
+  size: 1 x 1
+  crystal symmetry: 321, X||a*, Y||b, Z||c*
+  sample symmetry : 1
+
+  Bunge Euler angles in degree
+  Psi Theta   Phi Inv.
+   10     5     0    0
+  \end{lstlisting}
+  \end{onlyenv}
+
+  \pause
+  import orientations
+  \begin{lstlisting}[style=input]
+O  = loadOrientation('filename',CS,SS,...
+'ColumnNames',{'phi1','Phi','phi2'})
+  \end{lstlisting}
+  \begin{onlyenv}<2>
+    \vspace{-.3cm}
+  \begin{lstlisting}[style=output]
+O = /+orientation+/ (show methods, plot)
+  size: 1000 x 1
+  crystal symmetry: 321, X||a*, Y||b, Z||c*
+  sample symmetry : 1
+  \end{lstlisting}
+  \end{onlyenv}
+
+\pause
+
+define orientations by Miller indices
+   \begin{lstlisting}[style=input]
+O  = orientation('Miller',[h k l],[u,v,w],CS,SS)
+  \end{lstlisting}
+
+\pause
+
+standard orientations: \texttt{Cube, CubeND22, CubeND45, CubeRD, Goss,
+invGoss, Copper, Copper2, SR, SR2, SR3, SR4, Brass, Brass2, PLage, PLage2,
+QLage, QLage2, QLage3, QLage4}
+
+\begin{lstlisting}[style=input]
+O  = brassOrientation(CS,SS)
+\end{lstlisting}
+\end{overlayarea}
+\end{frame}
+
+\subsection*{Calculating with Orientations}
+\label{sec:calc-with-orient}
+
+\begin{frame}[fragile,fragile,fragile,fragile]
+  \frametitle{Calculating with Orientations}
+
+
+  \begin{overlayarea}{\textwidth}{8cm}
+  find all symmetrically equivalent orientations
+\begin{lstlisting}[style=input]
+symmetrise(O)
+\end{lstlisting}
+  \begin{onlyenv}<1>
+    \vspace{-.3cm}
+    \begin{lstlisting}[style=output]
+ans = /+orientation+/ (show methods, plot)
+  size: 6 x 1
+  crystal symmetry: 321, X||a*, Y||b, Z||c*
+  sample symmetry : 1
+
+  Roe Euler angles in degree
+  Psi Theta   Phi Inv.
+   10     5     0    0
+   10     5   120    0
+   10     5   240    0
+  190   175    60    0
+  190   175   180    0
+  190   175   300    0
+\end{lstlisting}
+  \end{onlyenv}
+
+  \pause
+  \medskip
+
+  convert crystal into specimen coordinates
+\begin{lstlisting}[style=input]
+h = Miller(1,0,-1,0,CS);
+r = O * h
+\end{lstlisting}
+  \begin{onlyenv}<2>
+    \vspace{-.3cm}
+    \begin{lstlisting}[style=output]
+r = /+vector3d+/ (show methods, plot)
+  size: 1 x 1
+         x        y        z
+  0.984808 0.173648        0
+\end{lstlisting}
+  \end{onlyenv}
+
+  \pause
+  \medskip
+
+  convert specimen into crystal coordinates
+\begin{lstlisting}[style=input]
+inv(O) * r
+\end{lstlisting}
+  \begin{onlyenv}<3>
+    \vspace{-.3cm}
+    \begin{lstlisting}[style=output]
+ans = /+Miller+/ (show methods, plot)
+  size: 1 x 1
+  symmetry: 321, X||a*, Y||b, Z||c*
+  h  1
+  k  0
+  i -1
+  l  0
+\end{lstlisting}
+  \end{onlyenv}
+
+  \pause
+  \medskip
+
+  change specimen coordinates
+  \begin{lstlisting}[style=input]
+R  = rotation('axis',zvector,'angle',90*degree)
+O2 = R * O1
+\end{lstlisting}
+\end{overlayarea}
+
+\end{frame}
+
+
+\subsection*{Pole Figures}
+
+\begin{frame}[fragile]
+  \frametitle{Pole Figures and Inverse Pole Figures}
+
+  \begin{columns}
+    \begin{column}{8.5cm}
+      Lattice planes in specimen coordinates
+      \begin{lstlisting}[style=input]
+h = Miller({1 0 0},{0 1 0},ori.CS)
+plot(symmetrise(ori) * h(1))
+plot(ori * symmetrise(h(1)))
+      \end{lstlisting}
+
+      \pause
+      \medskip
+
+      \begin{lstlisting}[style=input]
+plotPDF(ori,h)
+      \end{lstlisting}
+      \pause
+      \vspace{-0.3cm}
+      \begin{lstlisting}[style=input]
+plotPDF(ori,h,'contourf')
+      \end{lstlisting}
+
+      \pause
+      \medskip
+
+      specimen directions in crystal coordinates
+      \begin{lstlisting}[style=input]
+plot(symmetrise(inv(ori)) * xvector)
+plot(symmetrise(inv(ori) * xvector))
+      \end{lstlisting}
+      \pause
+      \vspace{-0.3cm}
+      \begin{lstlisting}[style=input]
+v = [xvector,yvector]
+plotIPDF(ori,v)
+      \end{lstlisting}
+      \pause
+      \vspace{-0.3cm}
+      \begin{lstlisting}[style=input]
+plotIPDF(ori,v,'contourf')
+      \end{lstlisting}
+
+
+    \end{column}
+    \begin{column}{3.5cm}
+
+      \begin{onlyenv}<1>
+        \includegraphics[width=\textwidth]{pic/pfSimple}
+      \end{onlyenv}
+
+      \begin{onlyenv}<2>
+        \includegraphics[width=0.95\textwidth]{pic/pfSimple100}
+
+        \medskip
+
+        \includegraphics[width=0.95\textwidth]{pic/pfSimple010}
+      \end{onlyenv}
+
+      \begin{onlyenv}<3>
+        \includegraphics[width=0.95\textwidth]{pic/pfSimple100Smooth}
+
+        \medskip
+
+        \includegraphics[width=0.95\textwidth]{pic/pfSimple010Smooth}
+      \end{onlyenv}
+
+      \begin{onlyenv}<4>
+        \includegraphics[width=\textwidth]{pic/ipfSimple}
+      \end{onlyenv}
+
+      \begin{onlyenv}<5>
+        \includegraphics[width=0.95\textwidth]{pic/ipfSimple100}
+
+        \medskip
+
+        \includegraphics[width=0.95\textwidth]{pic/ipfSimple010}
+      \end{onlyenv}
+
+      \begin{onlyenv}<6>
+        \includegraphics[width=0.95\textwidth]{pic/ipfSimple100Smooth}
+
+        \medskip
+
+        \includegraphics[width=0.95\textwidth]{pic/ipfSimple010Smooth}
+      \end{onlyenv}
+    \end{column}
+  \end{columns}
+
+\end{frame}
+
+\subsection*{ODF Plots}
+
+\begin{frame}[fragile]
+  \frametitle{Plotting in Orientation Space}
+
+  \begin{onlyenv}<1>
+    \begin{lstlisting}[style=input]
+plotSection(ori,'phi2',(0:30:150)*degree)
+    \end{lstlisting}
+
+    \includegraphics[width=\textwidth]{pic/odfOri}
+  \end{onlyenv}
+
+  \begin{onlyenv}<2>
+    \begin{lstlisting}[style=input]
+plotSection(ori,'phi2',(0:30:150)*degree,'contourf',...
+        'halfwidth',10*degree)
+    \end{lstlisting}
+
+    \includegraphics[width=0.95\textwidth]{pic/odfOriSmooth}
+  \end{onlyenv}
+
+    \begin{onlyenv}<3>
+    \begin{lstlisting}[style=input]
+plotSection(ori,'sigma',(0:30:150)*degree,'contourf')
+    \end{lstlisting}
+    \vspace{-0.3cm}
+    \begin{center}
+      \includegraphics[width=0.9\textwidth]{pic/odfOriSmoothSigma}
+    \end{center}
+
+  \end{onlyenv}
+
+\end{frame}
+
+\subsection*{Operations on Orientations}
+
+\begin{frame}[fragile]
+  \frametitle{Operations on Orientations}
+
+%   the misorientation angle and axis
+%   \begin{lstlisting}[style=input]
+% angle(ori1,ori2) / degree
+% axis(ori1,ori2)
+%   \end{lstlisting}
+
+%   \begin{onlyenv}<1>
+%     \begin{lstlisting}[style=output]
+% ans = /+Miller+/ (show methods, plot)
+%   size: 1 x 1
+%   mineral: Forsterite (mmm)
+%   h 2.729
+%   k 7.6909
+%   l 1.9193
+%     \end{lstlisting}
+%   \end{onlyenv}
+
+%   \pause
+%   \medskip
+
+mean orientation
+  \begin{lstlisting}[style=input]
+mean(ori)
+  \end{lstlisting}
+
+  \begin{onlyenv}<2>
+    \begin{lstlisting}[style=output]
+ans = /+orientation+/ (show methods, plot)
+  size: 1 x 1
+  crystal symmetry : Forsterite (mmm)
+  specimen symmetry: 1
+
+  Bunge Euler angles in degree
+     phi1     Phi    phi2    Inv.
+  342.532 68.3179 284.955       0
+    \end{lstlisting}
+  \end{onlyenv}
+
+\pause
+\medskip
+
+  mean orientation spread
+  \begin{lstlisting}[style=input]
+mean(angle(ori,mean(ori)))./degree
+  \end{lstlisting}
+
+  \begin{onlyenv}<3>
+    \begin{lstlisting}[style=output]
+ans =
+
+   47.2287
+\end{lstlisting}
+  \end{onlyenv}
+
+\pause
+\medskip
+
+volume portions
+\begin{lstlisting}[style=input]
+volume(ori,mean(ori),10*degree)
+fibreVolume(ori,Miller(1,0,0,ori.CS),xvector)
+\end{lstlisting}
+
+\pause
+\medskip
+
+export to ASCII file
+\begin{lstlisting}[style=input]
+export(ori,'file.txt','bunge','degree')
+\end{lstlisting}
+
+\end{frame}
+
+
+
+
+\section{Misorientations}
+
+
+\subsection*{Coordinate Transforms}
+\label{sec:orientations}
+
+
+\begin{frame}[fragile]
+  \frametitle{Coordinate Transforms}
+
+  \begin{overlayarea}{\textwidth}{8cm}
+  Remember, an orientation converts crystal into specimen
+  coordinates
+  \vspace{-.2cm}
+  \begin{lstlisting}[style=input]
+O1 = orientation('Euler',0,0,0,CS_Mag)
+r = O1 * Miller(1,1,1,CS_Mag)
+\end{lstlisting}
+  \begin{onlyenv}<1>
+\vspace{-.3cm}\begin{lstlisting}[style=output]
+r = /+vector3d+/ (show methods, plot)
+ size: 1 x 1
+         x        y        z
+  0.119107 0.119107 0.119107
+\end{lstlisting}
+  \end{onlyenv}
+
+  \pause
+  \medskip
+
+  The inverse of an orientation converts specimen into crystal coordinates
+  \vspace{-.2cm}
+  \begin{lstlisting}[style=input]
+O2 = orientation('Euler',...
+       135*degree,55*degree,60*degree,CS_Hem)
+inv(O2) * r
+\end{lstlisting}
+  \begin{onlyenv}<2>
+    \vspace{-.3cm}
+    \begin{lstlisting}[style=output]
+ans = /+Miller+/ (show methods, plot)
+ size: 1 x 1
+ mineral: Hematite (-3m1, X||a*, Y||b, Z||c)
+  h 0
+  k 0
+  i 0
+  l 1
+
+\end{lstlisting}
+  \end{onlyenv}
+
+  \pause
+  \medskip
+
+  Hence, $\text{\bf inv}(\mathbf{O2}) \cdot \mathbf{O1}$ converts crystal  into
+  crystal coordinates
+    \vspace{-.2cm}
+  \begin{lstlisting}[style=input]
+O2 = inv(O2) * O1 * Miller(1,1,1,0,CS_Mag)
+  \end{lstlisting}
+  \begin{onlyenv}<3>
+    \vspace{-.3cm}
+    \begin{lstlisting}[style=output]
+ans = /+Miller+/ (show methods, plot)
+ size: 1 x 1
+ mineral: Hematite (-3m1, X||a*, Y||b, Z||c)
+  h 0
+  k 0
+  i 0
+  l 1
+
+\end{lstlisting}
+  \end{onlyenv}
+
+\end{overlayarea}
+
+\end{frame}
+
+
+
+\subsection*{Misorientations}
+\label{sec:orientations2}
+
+\begin{frame}[fragile]
+  \frametitle{Misorientations}
+
+  \begin{overlayarea}{\textwidth}{8cm}
+
+  A \alert{misorientation} {\bf MO} transforms coordinates with respect to
+  crystal A into coordinates with respect to crystal B.
+\vspace{-0.1cm}
+\begin{lstlisting}[style=input]
+MO = inv(O1) * O2
+\end{lstlisting}
+
+\begin{onlyenv}<1>
+  \vspace{-.3cm}
+  \begin{lstlisting}[style=output]
+MO = /+misorientation+/ (show methods, plot)
+  size: 1 x 1
+  crystal symmetry : Magnetite (m-3m)
+  crystal symmetry : Hematite (-3m1, X||a*, Y||b, Z||c)
+
+  Bunge Euler angles in degree
+  phi1  Phi phi2 Inv.
+   120   55   45    0
+\end{lstlisting}
+\end{onlyenv}
+
+  \pause
+  \medskip
+
+As \textbf{O1} and \textbf{O2} are suspect to crystal symmetry, there are  many
+symmetrically equivalent misorientations to \textbf{oM}.
+
+\vspace{-0.1cm}
+\begin{lstlisting}[style=input]
+oM.symmetrise
+\end{lstlisting}
+
+\begin{onlyenv}<2>
+  \vspace{-.3cm}
+  \begin{lstlisting}[style=output]
+MO = /+misorientation+/ (show methods, plot)
+  size: 576 x 1
+  crystal symmetry : Magnetite (m-3m)
+  crystal symmetry : Hematite (-3m1, X||a*, Y||b, Z||c)
+\end{lstlisting}
+\end{onlyenv}
+
+  \pause
+
+\vspace{-0.3cm}
+\begin{lstlisting}[style=input]
+plotPDF(MO,Miller({0 0 0 1},{1 1 -2 1},CS_Hem))
+plotIPDF(MO,Miller({0 0 1},{1 1 1},CS_Mag))
+\end{lstlisting}
+
+\vspace{-0.5cm}
+
+\begin{onlyenv}<3>
+  \begin{center}
+    \includegraphics[height=3cm]{pic/HemPDF111.pdf}
+    \quad
+    \includegraphics[height=3cm]{pic/MagPDF110.pdf}
+  \end{center}
+\end{onlyenv}
+
+\end{overlayarea}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Misorientation angel and axis}
+
+  \begin{overlayarea}{\textwidth}{8cm}
+
+    the smallest rotational angle of all symmetrically equivalent
+    misorientations to \textbf{MO} is called \structure{misorientation angle}
+    \begin{lstlisting}[style=input]
+angle(O1,O2) / degree
+angle(MO) /degree
+    \end{lstlisting}
+
+  \pause
+  \medskip
+
+  the misorientation realizing this minimum angle is computed by
+  \vspace{-0.2cm}
+    \begin{lstlisting}[style=input]
+MO.project2FundamentalRegion
+    \end{lstlisting}
+\begin{onlyenv}<2>
+  \vspace{-.3cm}
+  \begin{lstlisting}[style=output]
+MO = /+misorientation+/ (show methods, plot)
+  size: 1 x 1
+  crystal symmetry : Magnetite (m-3m)
+  crystal symmetry : Hematite (-3m1, X||a*, Y||b, Z||c)
+
+  Bunge Euler angles in degree
+     phi1     Phi    phi2    Inv.
+  60.1624 54.6037 314.719       0
+\end{lstlisting}
+\end{onlyenv}
+
+\pause
+\medskip
+
+  its rotational axis is called the \structure{misorientation axis} of
+  \textbf{MO}
+  \vspace{-0.2cm}
+\begin{lstlisting}[style=input]
+axis(MO)
+\end{lstlisting}
+\vspace{-.3cm}
+
+  \begin{onlyenv}<3>
+\begin{lstlisting}[style=output]
+ans = /+Miller+/ (show methods, plot)
+ size: 1 x 1
+ mineral: Hematite (-3m1, X||a*, Y||b, Z||c)
+  h  0.6191
+  k  3.8882
+  i -4.5073
+  l  3.3513
+\end{lstlisting}
+\end{onlyenv}
+
+  \pause
+\begin{lstlisting}[style=input]
+axis(inv(MO))
+\end{lstlisting}
+\vspace{-.3cm}
+    \begin{onlyenv}<4>
+\begin{lstlisting}[style=output]
+ans = /+Miller+/ (show methods, plot)
+ size: 1 x 1
+ mineral: Magnetite (m-3m)
+  h  4.9324
+  k -6.4797
+  l  2.0431
+\end{lstlisting}
+\end{onlyenv}
+
+\pause
+
+\begin{lstlisting}[style=input]
+axis(O1,O2)
+\end{lstlisting}
+
+  \begin{onlyenv}<5>
+\vspace{-.3cm}
+\begin{lstlisting}[style=output]
+ans = /+vector3d+/ (show methods, plot)
+ size: 1 x 1
+          x         y         z
+  0.0495585  0.992437 -0.112305
+\end{lstlisting}
+\end{onlyenv}
+
+  \end{overlayarea}
+
+\end{frame}
+
+
+\subsection*{Statistics}
+
+\begin{frame}[fragile]
+  \frametitle{Misorientation Statistics}
+
+  \begin{columns}
+    \begin{column}{8cm}
+      \begin{lstlisting}[style=input]
+plotAngleDistribution(MO)
+hold on
+plotAngleDistribution(MO.CS)
+hold off
+      \end{lstlisting}
+
+      \includegraphics[width=\textwidth]{pic/angleDistri}
+
+      \pause
+
+  \begin{lstlisting}[style=input]
+plotAxisDistribution(MO)
+  \end{lstlisting}
+
+  \pause
+\vspace{-0.3cm}
+  \begin{lstlisting}[style=input]
+plotAxisDistribution(MO,'contourf')
+  \end{lstlisting}
+\end{column}
+\begin{column}{4cm}
+  \begin{overlayarea}{\textwidth}{8cm}
+    \begin{onlyenv}<2->
+      \includegraphics[width = \textwidth]{pic/axisDistri}
+    \end{onlyenv}
+
+    \medskip
+
+    \begin{onlyenv}<3>
+      \includegraphics[width = \textwidth]{pic/axisDistriSmooth}
+    \end{onlyenv}
+  \end{overlayarea}
+
+\end{column}
+
+\end{columns}
+
+\end{frame}
+
+
+\subsection*{Phase Transitions}
+
+
+\begin{frame}[fragile]
+  \frametitle{Phase Transitions}
+
+  \begin{overlayarea}{\textwidth}{8cm}
+    We want to model the phase transition from magnetite to hematite given by
+    the orientation relationship $\{111\}_{\text{m}} || \{0001\}_{\text{h}}$
+    and $\{\overline{1}01\}_{\text{m}} || \{00\overline{1}0\}_{\text{h}}$
+    \begin{lstlisting}[style=input]
+CS_Mag = loadCIF('Magnetite')
+CS_Hem = loadCIF('Hematite')
+   \end{lstlisting}
+   \begin{onlyenv}<1>
+     \vspace{-0.3cm}
+     \begin{lstlisting}[style=output]
+cs_Magnetite = /+crystalSymmetry+/ (show methods, plot)
+  mineral : Magnetite
+  symmetry: m-3m
+  a, b, c : 8.4, 8.4, 8.4
+
+cs_Hematite = /+crystalSymmetry+/ (show methods, plot)
+  mineral : Hematite
+  symmetry : -3m1
+  a, b, c : 5, 5, 14
+  reference frame: X||a*, Y||b, Z||c
+    \end{lstlisting}
+  \end{onlyenv}
+
+  \pause
+  \medskip
+
+  \begin{lstlisting}[style=input]
+Mag2Hem = orientation('map',...
+  Miller(1,1,1,CS_Mag),Miller(0,0,0,1,CS_Hem),...
+  Miller(-1,0,1,CS_Mag),Miller(1,0,-1,0,CS_Hem),...
+  CS_Mag,CS_Hem)
+  \end{lstlisting}
+  \begin{onlyenv}<2>
+    \vspace{-0.3cm}
+    \begin{lstlisting}[style=output]
+Mag2Hem = /+misorientation+/ (show methods, plot)
+  size: 1 x 1
+  crystal symmetry : Magnetite (m-3m)
+  crystal symmetry : Hematite (-3m1, X||a*, Y||b, Z||c)
+
+  Bunge Euler angles in degree
+  phi1 Phi phi2 Inv.
+  120 54.7356 45 0
+    \end{lstlisting}
+  \end{onlyenv}
+\end{overlayarea}
+\end{frame}
+
+
+\subsection*{Phase Transition II}
+
+\begin{frame}[fragile]
+  \frametitle{Phase Transition}
+
+  \begin{overlayarea}{\textwidth}{8cm}
+  For measured hematite orientation
+  \begin{lstlisting}[style=input]
+ori_Hem = orientation('Euler',0,0,0,CS_Hem)
+  \end{lstlisting}
+  \begin{onlyenv}<1>
+    \vspace{-0.3cm}
+    \begin{lstlisting}[style=output]
+ori_Hem = /+orientation+/ (show methods, plot)
+  size: 1 x 1
+  crystal symmetry : Hematite (-3m1, X||a*, Y||b, Z||c)
+  specimen symmetry: 1
+
+  Bunge Euler angles in degree
+  phi1  Phi phi2 Inv.
+     0    0    0    0
+    \end{lstlisting}
+  \end{onlyenv}
+  we can compute the initial magnetite orientation by
+  \begin{lstlisting}[style=input]
+ori_Mag = ori_Hem * Mag2Hem
+  \end{lstlisting}
+
+\pause
+
+  \begin{onlyenv}<2>
+    \vspace{-0.3cm}
+    \begin{lstlisting}[style=output]
+ori_Mag = /+orientation+/ (show methods, plot)
+  size: 1 x 1 crystal
+  symmetry : Magnetite (m-3m)
+  specimen symmetry: 1
+
+  Bunge Euler angles in degree
+  phi1 Phi phi2 Inv.
+  120 54.7356 45 0
+    \end{lstlisting}
+  \end{onlyenv}
+
+  \pause
+  \medskip
+
+  We should care about symmetric equivalence
+  \begin{lstlisting}[style=input]
+ori_Mag = ori_Hem * symmetrise(Mag2Hem)
+  \end{lstlisting}
+  \begin{onlyenv}<3->
+    \vspace{-0.3cm}
+    \begin{lstlisting}[style=output]
+ori_Mag = /+orientation+/ (show methods, plot)
+  size: 1 x 96
+  crystal symmetry : Magnetite (m-3m)
+  specimen symmetry: 1
+    \end{lstlisting}
+  \end{onlyenv}
+
+\pause
+
+\alert{MTEX keeps track about the symmetries throughout all computations and
+  warns in case of mismatch.}
+\end{overlayarea}
+\end{frame}
+
+
+\subsection*{phase transistion III}
+
+\begin{frame}[fragile]
+  \frametitle{Relationship Between Lattice Planes}
+
+  \begin{overlayarea}{\textwidth}{8cm}
+
+  Compute the minimal angle between two lattice planes of two
+  different grains having different orientation and different phase.
+ \begin{lstlisting}[style=input]
+m_Mag = Miller(1,0,0,cs_Magnetite);
+m_Hem = Miller(1,1,-2,0,cs_Hematite);
+ \end{lstlisting}
+  \begin{onlyenv}<1>
+    \vspace{-.3cm}
+    \begin{lstlisting}[style=output]
+m_Mag = /+Miller+/ (show methods, plot)
+ size: 1 x 1
+ mineral: Magnetite (432)
+  h 1
+  k 0
+  l 0
+
+m_Hem = Miller (show methods, plot)
+ size: 1 x 1
+ mineral: Hematite (321, X||a*, Y||b, Z||c)
+  h  1
+  k  1
+  i -2
+  l  0
+\end{lstlisting}
+  \end{onlyenv}
+
+  \pause
+  \medskip
+
+  The orientation relation should be given by
+  \begin{lstlisting}[style=input]
+Mag2Hem = orientation('map',...
+  Miller(1,1,1,CS_Mag),Miller(0,0,0,1,CS_Hem),...
+  Miller(-1,0,1,CS_Mag),Miller(1,0,-1,0,CS_Hem),...
+  CS_Mag,CS_Hem)
+  \end{lstlisting}
+  \begin{onlyenv}<2>
+    \vspace{-0.3cm}
+    \begin{lstlisting}[style=output]
+Mag2Hem = /+misorientation+/ (show methods, plot)
+  size: 1 x 1
+  crystal symmetry : Magnetite (m-3m)
+  crystal symmetry : Hematite (-3m1, X||a*, Y||b, Z||c)
+
+  Bunge Euler angles in degree
+  phi1 Phi phi2 Inv.
+  120 54.7356 45 0
+    \end{lstlisting}
+  \end{onlyenv}
+
+  \pause
+  \medskip
+
+  The minimum angle
+  \begin{lstlisting}[style=input]
+min(angle(Mag2Hem * m_Mag.symmetrise,m_Hem ))/degree
+ \end{lstlisting}
+  \begin{onlyenv}<3>
+    \vspace{-.3cm}
+    \begin{lstlisting}[style=output]
+  35.2644
+    \end{lstlisting}
+  \end{onlyenv}
+
+\end{overlayarea}
+
+\end{frame}
+
+% \section{Exercises}
+
+% \subsection*{Exercises2}
+
+% \begin{frame}
+
+%   \begin{Exercise}
+%     Consider trigonal crystal symmetry.
+
+%   \begin{enumerate}[a)]
+%     \item Find all crystallographic directions symmetrically equivalent to $h
+%       = (1, 0, \bar 1, 0)$ (Miller indices)!
+%     \item Find crystallographic directions such that the number of their
+%       crystallographic equivalent directions on the upper hemisphere (without
+%       equator) is 1, 3, and 6, when including antipodal symmetry!
+%     \item Consider the orientation given by the Euler angles $(30\degree,
+%       90\degree, 90\degree)$ in Bunge convention. Give the Euler angles of
+%       all symmetrically equivalent orientations!
+%     \item Which positions in the (0,0,0,1) - pole figure corresponds to the
+%       above orientation. Which crystal direction is rotated by this
+%       orientation to the specimen direction (0,0,1)?
+%     \item Construct an orientation that rotates the crystallographic
+%       directions $(0,0,0,1)$ and $(2,\bar 1,\bar 1,0)$ onto the specimen
+%       directions $(1,0,0)$ and $(0,1,0)$, respectively. Describe the rotation
+%       by axis and angle.
+%     \end{enumerate}
+
+%   \end{Exercise}
+
+% \end{frame}
+
+\end{document}
+
+
+% \begin{frame}[fragile]
+% \begin{lstlisting}[mathescape=true]
+% rot = rotation('Euler',$\phi_1$,$\Phi$,$\phi_2$,'ZXZ')
+% rot = rotation('Euler',$\alpha$,$\beta$,$\gamma$,'ABG')
+% rot = rotation('axis',v,'angle',omega)
+% rot = rotation('map',$u_1$, $v_1$, $u_2$, $v_2$) % $\mathbf{gu}_1=\mathbf{v}_1,\mathbf{gu}_2=\mathbf{v}_2$
+% \end{lstlisting}
+
+% \begin{columns}
+%   \begin{column}{8.5cm}
+
+%     Calculations:
+
+% \begin{lstlisting}
+% v = rot * u    % apply rot to u
+% rot = rot1 * rot2
+% \end{lstlisting}
+
+%     Basic Functions:
+
+% \begin{lstlisting}[mathescape=true]
+% angle(rot), axis(rot)
+% angle(rot1,rot2), inv(rot)
+% [$\phi_1$,$\Phi$,$\phi_2$] = Euler(rot)
+% [$\alpha$,$\beta$,$\gamma$] = Euler(rot,'ABG')
+% \end{lstlisting}
+
+%   \end{column}
+
+%   \begin{column}{3cm}
+%     \includegraphics[width=3cm]{pic/quaternion}
+%   \end{column}
+
+% \end{columns}
+% \end{frame}
+
+
+% \subsection*{Symmetry}
+% \begin{frame}[fragile]
+%   \frametitle{Crystal Symmetries - The \MTEX Class \texttt{\bf symmetry}}
+
+%   Definition:
+
+% \begin{lstlisting}
+% S = symmetry('triclinic',[a,b,c],[alpha,beta,gamma])
+% S = symmetry('-3m',[a,b,c],/+'X||a*'+/);
+% S = symmetry('-3m',[a,b,c],'X||a','Z||c*');
+% S = symmetry('O');
+% \end{lstlisting}
+
+% \medskip
+
+% \begin{columns}
+%   \begin{column}{8.5cm}
+
+% Load Symmetry from CIF file:
+
+% \begin{lstlisting}
+% symmetry('quartz.cif')
+% \end{lstlisting}
+
+% \medskip
+
+%     Basic Functions:
+
+% \begin{lstlisting}
+% symmetrise(v,S)
+% symmetrise(rot,CS,SS)
+% rotation(S)
+% project2FundamentalRegion(v,CS)
+% project2FundamentalRegion(rot,CS,SS)
+% \end{lstlisting}
+%   \end{column}
+
+%   \begin{column}{3cm}
+%     \includegraphics[width=3cm]{pic/sym}
+%   \end{column}
+
+% \end{columns}
+
+% \end{frame}
+
+% \subsection*{Miller}
+
+% \begin{frame}[fragile]
+%   \frametitle{Crystal Directions - The \MTEX Class \texttt{\bf Miller}}
+
+%   Definition:
+
+% \begin{lstlisting}
+% m = Miller(u,v,w,CS,'uvw');
+% m = Miller(h,k,i,l,CS,'hkl');
+% m = [Miller(1,1,-2,3,CS),Miller(0,1,-1,0,CS)]
+% \end{lstlisting}
+
+% \medskip
+
+% \begin{columns}
+%   \begin{column}{8.5cm}
+
+%     Calculations:
+
+% \begin{lstlisting}
+% h1 + h2
+% rot * h     % apply rot on h
+% \end{lstlisting}
+
+%     \medskip
+
+%     Basic Functions:
+
+%     \begin{onlyenv}<1>
+% \begin{lstlisting}
+% eq(h1,h2), angle(h1,h2)
+% symmetrise(h)  %get all equivalent
+% plot([h1,h2],'all')
+% \end{lstlisting}
+%     \end{onlyenv}
+
+% 	\end{column}
+
+%   \begin{column}{3cm}
+%     \includegraphics[width=3cm]{pic/miller}
+%   \end{column}
+% \end{columns}
+
+
+% 	\begin{onlyenv}<2>
+
+% 		\lstset{stringstyle=\color{red},emph={antipodal},emphstyle=\em\color{red}}
+
+% \begin{lstlisting}
+% get(h,'hkl')
+% eq(h1,h2,`antipodal`), angle(h1,h2,`antipodal`)
+% symmetrise(h,`antipodal`)
+% plot([h1,h2],'all',`antipodal`)
+% \end{lstlisting}
+
+
+%     \end{onlyenv}
+
+
+% \end{frame}
+
+
+
+% \begin{frame}[fragile]
+%   \frametitle{Orientations - The \MTEX Class \texttt{\bf orientation}}
+
+% Definition:
+
+% \begin{lstlisting}[mathescape=true]
+% ori = orientation(rot,CS,SS)
+% ori = orientation('Euler',$\phi_1$,$\Phi$,$\phi_2$,CS,SS)
+% ori = orientation('Euler',$\alpha$,$\beta$,$\gamma$,'ABG',CS,SS)
+% ori = orientation('Miller',[h k l],[u v w],CS,SS)
+% ori = orientation('brass',CS,SS)
+% \end{lstlisting}
+
+% \begin{columns}
+%   \begin{column}{8.5cm}
+
+%     Calculations:
+
+% \begin{lstlisting}
+% r = ori * h, h = ori \ r
+% ori = rot * ori
+% \end{lstlisting}
+
+%     Basic Functions:
+
+% \begin{lstlisting}[mathescape=true]
+% eq(ori1,ori2), angle(ori1,ori2)
+% symmetrise(ori), angle(ori)
+% project2FundamentalRegion(ori,ref_ori)
+% [$\phi_1$,$\Phi$,$\phi_2$]  = Euler(ori)
+% \end{lstlisting}
+
+%   \end{column}
+
+%   \begin{column}{3cm}
+%     \includegraphics[width=3cm]{pic/quaternion}
+%   \end{column}
+
+% \end{columns}
+% \end{frame}
+
+2732626
diff --git a/latex/geometry/pic/.gitignore b/latex/geometry/pic/.gitignore
new file mode 100644
index 0000000..2b9d38f
--- /dev/null
+++ b/latex/geometry/pic/.gitignore
@@ -0,0 +1 @@
+*.directory
diff --git a/latex/geometry/pic/2mm.pdf b/latex/geometry/pic/2mm.pdf
new file mode 100644
index 0000000..7f319b0
Binary files /dev/null and b/latex/geometry/pic/2mm.pdf differ
diff --git a/latex/geometry/pic/432.pdf b/latex/geometry/pic/432.pdf
new file mode 100644
index 0000000..d737498
Binary files /dev/null and b/latex/geometry/pic/432.pdf differ
diff --git a/latex/geometry/pic/43m.pdf b/latex/geometry/pic/43m.pdf
new file mode 100644
index 0000000..db345dd
Binary files /dev/null and b/latex/geometry/pic/43m.pdf differ
diff --git a/latex/geometry/pic/HemPDF111.pdf b/latex/geometry/pic/HemPDF111.pdf
new file mode 100644
index 0000000..8164306
Binary files /dev/null and b/latex/geometry/pic/HemPDF111.pdf differ
diff --git a/latex/geometry/pic/MagPDF110.pdf b/latex/geometry/pic/MagPDF110.pdf
new file mode 100644
index 0000000..e5677ae
Binary files /dev/null and b/latex/geometry/pic/MagPDF110.pdf differ
diff --git a/latex/geometry/pic/MillerPlane.pdf b/latex/geometry/pic/MillerPlane.pdf
new file mode 100644
index 0000000..68bed2f
Binary files /dev/null and b/latex/geometry/pic/MillerPlane.pdf differ
diff --git a/latex/geometry/pic/MillerSymmetrised.pdf b/latex/geometry/pic/MillerSymmetrised.pdf
new file mode 100644
index 0000000..183477c
Binary files /dev/null and b/latex/geometry/pic/MillerSymmetrised.pdf differ
diff --git a/latex/geometry/pic/MillerUVW.pdf b/latex/geometry/pic/MillerUVW.pdf
new file mode 100644
index 0000000..b42bfb5
Binary files /dev/null and b/latex/geometry/pic/MillerUVW.pdf differ
diff --git a/latex/geometry/pic/angleDistri.pdf b/latex/geometry/pic/angleDistri.pdf
new file mode 100644
index 0000000..bc68f3e
Binary files /dev/null and b/latex/geometry/pic/angleDistri.pdf differ
diff --git a/latex/geometry/pic/annotationq.pdf b/latex/geometry/pic/annotationq.pdf
new file mode 100644
index 0000000..27e87fd
Binary files /dev/null and b/latex/geometry/pic/annotationq.pdf differ
diff --git a/latex/geometry/pic/annotationv.pdf b/latex/geometry/pic/annotationv.pdf
new file mode 100644
index 0000000..f2fc82d
Binary files /dev/null and b/latex/geometry/pic/annotationv.pdf differ
diff --git a/latex/geometry/pic/axisDistri.pdf b/latex/geometry/pic/axisDistri.pdf
new file mode 100644
index 0000000..76de75b
Binary files /dev/null and b/latex/geometry/pic/axisDistri.pdf differ
diff --git a/latex/geometry/pic/axisDistriSmooth.pdf b/latex/geometry/pic/axisDistriSmooth.pdf
new file mode 100644
index 0000000..c354b98
Binary files /dev/null and b/latex/geometry/pic/axisDistriSmooth.pdf differ
diff --git a/latex/geometry/pic/hkl.pdf b/latex/geometry/pic/hkl.pdf
new file mode 100644
index 0000000..cf8200a
Binary files /dev/null and b/latex/geometry/pic/hkl.pdf differ
diff --git a/latex/geometry/pic/ipfSimple.pdf b/latex/geometry/pic/ipfSimple.pdf
new file mode 100644
index 0000000..ff48273
Binary files /dev/null and b/latex/geometry/pic/ipfSimple.pdf differ
diff --git a/latex/geometry/pic/ipfSimple010.pdf b/latex/geometry/pic/ipfSimple010.pdf
new file mode 100644
index 0000000..cfde83b
Binary files /dev/null and b/latex/geometry/pic/ipfSimple010.pdf differ
diff --git a/latex/geometry/pic/ipfSimple010Smooth.pdf b/latex/geometry/pic/ipfSimple010Smooth.pdf
new file mode 100644
index 0000000..a8de69d
Binary files /dev/null and b/latex/geometry/pic/ipfSimple010Smooth.pdf differ
diff --git a/latex/geometry/pic/ipfSimple100.pdf b/latex/geometry/pic/ipfSimple100.pdf
new file mode 100644
index 0000000..455a71f
Binary files /dev/null and b/latex/geometry/pic/ipfSimple100.pdf differ
diff --git a/latex/geometry/pic/ipfSimple100Smooth.pdf b/latex/geometry/pic/ipfSimple100Smooth.pdf
new file mode 100644
index 0000000..bce5894
Binary files /dev/null and b/latex/geometry/pic/ipfSimple100Smooth.pdf differ
diff --git a/latex/geometry/pic/m-3m.pdf b/latex/geometry/pic/m-3m.pdf
new file mode 100644
index 0000000..b4380f4
Binary files /dev/null and b/latex/geometry/pic/m-3m.pdf differ
diff --git a/latex/geometry/pic/m2m.pdf b/latex/geometry/pic/m2m.pdf
new file mode 100644
index 0000000..5a411f7
Binary files /dev/null and b/latex/geometry/pic/m2m.pdf differ
diff --git a/latex/geometry/pic/mm2.pdf b/latex/geometry/pic/mm2.pdf
new file mode 100644
index 0000000..f1d3d57
Binary files /dev/null and b/latex/geometry/pic/mm2.pdf differ
diff --git a/latex/geometry/pic/odfOri.pdf b/latex/geometry/pic/odfOri.pdf
new file mode 100644
index 0000000..8675c70
Binary files /dev/null and b/latex/geometry/pic/odfOri.pdf differ
diff --git a/latex/geometry/pic/odfOriSmooth.pdf b/latex/geometry/pic/odfOriSmooth.pdf
new file mode 100644
index 0000000..c73b112
Binary files /dev/null and b/latex/geometry/pic/odfOriSmooth.pdf differ
diff --git a/latex/geometry/pic/odfOriSmoothSigma.pdf b/latex/geometry/pic/odfOriSmoothSigma.pdf
new file mode 100644
index 0000000..ad3ad41
Binary files /dev/null and b/latex/geometry/pic/odfOriSmoothSigma.pdf differ
diff --git a/latex/geometry/pic/pfSimple.pdf b/latex/geometry/pic/pfSimple.pdf
new file mode 100644
index 0000000..d95841e
Binary files /dev/null and b/latex/geometry/pic/pfSimple.pdf differ
diff --git a/latex/geometry/pic/pfSimple010.pdf b/latex/geometry/pic/pfSimple010.pdf
new file mode 100644
index 0000000..b099bce
Binary files /dev/null and b/latex/geometry/pic/pfSimple010.pdf differ
diff --git a/latex/geometry/pic/pfSimple010Smooth.pdf b/latex/geometry/pic/pfSimple010Smooth.pdf
new file mode 100644
index 0000000..f430482
Binary files /dev/null and b/latex/geometry/pic/pfSimple010Smooth.pdf differ
diff --git a/latex/geometry/pic/pfSimple100.pdf b/latex/geometry/pic/pfSimple100.pdf
new file mode 100644
index 0000000..191ec4f
Binary files /dev/null and b/latex/geometry/pic/pfSimple100.pdf differ
diff --git a/latex/geometry/pic/pfSimple100Smooth.pdf b/latex/geometry/pic/pfSimple100Smooth.pdf
new file mode 100644
index 0000000..48e6100
Binary files /dev/null and b/latex/geometry/pic/pfSimple100Smooth.pdf differ
diff --git a/latex/geometry/pic/quartz.pdf b/latex/geometry/pic/quartz.pdf
new file mode 100644
index 0000000..0b336a2
Binary files /dev/null and b/latex/geometry/pic/quartz.pdf differ
diff --git a/latex/geometry/pic/quiver.pdf b/latex/geometry/pic/quiver.pdf
new file mode 100644
index 0000000..705d4ed
Binary files /dev/null and b/latex/geometry/pic/quiver.pdf differ
diff --git a/latex/geometry/pic/rotationScatter.pdf b/latex/geometry/pic/rotationScatter.pdf
new file mode 100644
index 0000000..895abee
Binary files /dev/null and b/latex/geometry/pic/rotationScatter.pdf differ
diff --git a/latex/geometry/pic/sym-31m.pdf b/latex/geometry/pic/sym-31m.pdf
new file mode 100644
index 0000000..3bc8e2e
Binary files /dev/null and b/latex/geometry/pic/sym-31m.pdf differ
diff --git a/latex/geometry/pic/sym-3m1.pdf b/latex/geometry/pic/sym-3m1.pdf
new file mode 100644
index 0000000..fdfeafb
Binary files /dev/null and b/latex/geometry/pic/sym-3m1.pdf differ
diff --git a/latex/geometry/pic/sym312.pdf b/latex/geometry/pic/sym312.pdf
new file mode 100644
index 0000000..56b4441
Binary files /dev/null and b/latex/geometry/pic/sym312.pdf differ
diff --git a/latex/geometry/pic/sym31m.pdf b/latex/geometry/pic/sym31m.pdf
new file mode 100644
index 0000000..9d9d979
Binary files /dev/null and b/latex/geometry/pic/sym31m.pdf differ
diff --git a/latex/geometry/pic/sym321.pdf b/latex/geometry/pic/sym321.pdf
new file mode 100644
index 0000000..2abd0a6
Binary files /dev/null and b/latex/geometry/pic/sym321.pdf differ
diff --git a/latex/geometry/pic/sym3m1.pdf b/latex/geometry/pic/sym3m1.pdf
new file mode 100644
index 0000000..dc478cb
Binary files /dev/null and b/latex/geometry/pic/sym3m1.pdf differ
diff --git a/latex/geometry/pic/uvtw.pdf b/latex/geometry/pic/uvtw.pdf
new file mode 100644
index 0000000..c23364d
Binary files /dev/null and b/latex/geometry/pic/uvtw.pdf differ
diff --git a/latex/geometry/pic/uvw.pdf b/latex/geometry/pic/uvw.pdf
new file mode 100644
index 0000000..d622bbf
Binary files /dev/null and b/latex/geometry/pic/uvw.pdf differ
diff --git a/latex/geometry/pic/vectorAntipodal.pdf b/latex/geometry/pic/vectorAntipodal.pdf
new file mode 100644
index 0000000..b6ec39c
Binary files /dev/null and b/latex/geometry/pic/vectorAntipodal.pdf differ
diff --git a/latex/geometry/pic/vectorColor.pdf b/latex/geometry/pic/vectorColor.pdf
new file mode 100644
index 0000000..975e303
Binary files /dev/null and b/latex/geometry/pic/vectorColor.pdf differ
diff --git a/latex/geometry/pic/vectorCombined.pdf b/latex/geometry/pic/vectorCombined.pdf
new file mode 100644
index 0000000..97f44b8
Binary files /dev/null and b/latex/geometry/pic/vectorCombined.pdf differ
diff --git a/latex/geometry/pic/vectorContour.pdf b/latex/geometry/pic/vectorContour.pdf
new file mode 100644
index 0000000..7390726
Binary files /dev/null and b/latex/geometry/pic/vectorContour.pdf differ
diff --git a/latex/geometry/pic/vectorContourAntipodal.pdf b/latex/geometry/pic/vectorContourAntipodal.pdf
new file mode 100644
index 0000000..7518d0b
Binary files /dev/null and b/latex/geometry/pic/vectorContourAntipodal.pdf differ
diff --git a/latex/geometry/pic/vectorEast.pdf b/latex/geometry/pic/vectorEast.pdf
new file mode 100644
index 0000000..5ae7655
Binary files /dev/null and b/latex/geometry/pic/vectorEast.pdf differ
diff --git a/latex/geometry/pic/vectorNorth.pdf b/latex/geometry/pic/vectorNorth.pdf
new file mode 100644
index 0000000..01b8829
Binary files /dev/null and b/latex/geometry/pic/vectorNorth.pdf differ
diff --git a/latex/geometry/pic/vectoreangle.pdf b/latex/geometry/pic/vectoreangle.pdf
new file mode 100644
index 0000000..f7714a1
Binary files /dev/null and b/latex/geometry/pic/vectoreangle.pdf differ
diff --git a/latex/geometry/pic/vectorearea.pdf b/latex/geometry/pic/vectorearea.pdf
new file mode 100644
index 0000000..8eebc6e
Binary files /dev/null and b/latex/geometry/pic/vectorearea.pdf differ
diff --git a/latex/geometry/work.m b/latex/geometry/work.m
new file mode 100644
index 0000000..b3c2240
--- /dev/null
+++ b/latex/geometry/work.m
@@ -0,0 +1,495 @@
+%%
+
+r = vector3d(1,2,3);
+
+
+plotx2east
+plot(r,'upper','grid','on')
+annotate([xvector,yvector,zvector],'label',{'X','Y','Z'},...
+  'backgroundColor','w')
+set(gcf,'position',[200,200,200,200])
+saveFigure('pic/vectorEast.pdf')
+
+plotx2north
+plot(r,'upper','grid','on')
+annotate([xvector,yvector,zvector],'label',{'X','Y','Z'},...
+  'backgroundColor','w')
+set(gcf,'position',[200,200,200,200])
+saveFigure('pic/vectorNorth.pdf')
+
+%%
+
+plotx2east
+plot(r,'upper','grid','on','projection','earea')
+annotate([xvector,yvector,zvector],'label',{'X','Y','Z'},...
+  'backgroundColor','w')
+set(gcf,'position',[200,200,200,200])
+saveFigure('pic/vectorearea.pdf')
+
+%%
+
+plotx2east
+plot(r,'upper','grid','on','projection','eangle')
+annotate([xvector,yvector,zvector],'label',{'X','Y','Z'},...
+  'backgroundColor','w')
+set(gcf,'position',[200,200,200,200])
+saveFigure('pic/vectoreangle.pdf')
+
+%%
+close all
+plot(vector3d(1,1,1),'upper','grid','on');
+hold all
+plot(vector3d(1,2,3),'label','B');
+plot(vector3d(-1,2,1),'label','A');
+hold off
+set(gcf,'position',[200,200,200,200])
+
+saveFigure('pic/vectorCombined.pdf')
+
+%%
+r = randv(100)  % 100 random points
+scatter(r,1:100,'upper','grid','on')   % colored by their number
+colormap jet
+set(gcf,'position',[200,200,200,200])
+saveFigure('pic/vectorColor.pdf')
+
+%%
+
+quiver(r,orth(r),'upper','arrowSize',0.08)
+set(gcf,'position',[200,200,200,200])
+%saveFigure('pic/quiver.pdf')
+
+d = orth(r); d.antipodal = true;
+quiver(r,d,'upper','arrowSize',0.08)
+
+%%
+
+mtexdata dubna
+
+plot(pf({1:2}))
+mtexColorMap Jet
+annotate([xvector,yvector,zvector],'label',{'X','Y','Z'},...
+  'backgroundColor','w')
+set(gcf,'position',[200,200,200,450])
+
+saveFigure('pic/annotationv.pdf')
+
+%%
+
+odf = calcODF(pf,'zero_range')
+q0 = odf.calcModes
+
+plotPDF(odf,pf.allH(1:2))
+mtexColorMap white2black
+
+annotate(q0,'label','A','Marker','s','MarkerEdgeColor','w',...
+  'backgroundColor','w','MarkerFaceColor','r')
+set(gcf,'position',[200,200,200,450])
+
+ saveFigure('pic/annotationq.pdf')
+%TODO
+
+%%
+
+r = vector3d(1,1,1,'antipodal')
+
+plot(r,'grid','on','labeled')
+annotate([xvector,yvector,zvector],'label',{'X','Y','Z'},...
+  'backgroundColor','w')
+set(gcf,'position',[200,200,200,390])
+saveFigure('pic/vectorAntipodal.pdf')
+
+%%
+
+r = randv(1000);
+plot(r,'contourf')
+set(gcf,'position',[200,200,200,390])
+saveFigure('pic/vectorContour.pdf')
+%%
+
+r = randv(1000);
+plot(r,'contourf','antipodal','complete')
+set(gcf,'position',[200,200,200,390])
+saveFigure('pic/vectorContourAntipodal.pdf')
+
+%%
+
+R = randq(100)
+
+scatter(R)
+set(gcf,'position',[200,200,200,390])
+saveFigure('pic/rotationScatter.pdf')
+
+%%
+
+cs = crystalSymmetry('m-3m')
+
+plot(cs,'upper')
+set(gcf,'position',[200,200,300,300])
+saveFigure('pic/m-3m.pdf')
+
+plotHKL(cs,'upper')
+set(gcf,'position',[200,200,200,210])
+saveFigure('pic/m-3mHKL.pdf')
+
+cs = crystalSymmetry('m-3m')
+
+%%
+
+cs = loadCIF('quartz')
+
+plot(cs,'upper')
+set(gcf,'position',[200,200,300,300])
+saveFigure('pic/quartz.pdf')
+
+plotHKL(cs,'upper')
+set(gcf,'position',[200,200,300,310])
+saveFigure('pic/quartzHKL.pdf')
+
+%%
+
+C = loadPHL('/home/hielscher/mtex/master/data/cif/crystal.phl')
+
+
+%% 
+
+plot(crystalSymmetry('432'),'upper')
+set(gcf,'position',[200,200,300,300])
+saveFigure('pic/432.pdf')
+
+plot(crystalSymmetry('-43m'),'upper')
+set(gcf,'position',[200,200,300,300])
+saveFigure('pic/43m.pdf')
+
+%%
+
+cs = crystalSymmetry('mm2');
+a = Miller(1,0,0,cs,'uvw');
+plot(cs,'upper')
+hold on
+plot(a,'MarkerFaceColor','red')
+hold off
+%set(gcf,'position',[200,200,300,300])
+saveFigure('pic/mm2.pdf','crop')
+
+cs = crystalSymmetry('m2m');
+a = Miller(1,0,0,cs,'uvw');
+plot(cs,'upper')
+hold on
+plot(a,'MarkerFaceColor','red')
+hold off
+%set(gcf,'position',[200,200,300,300])
+saveFigure('pic/m2m.pdf','crop')
+
+cs = crystalSymmetry('2mm');
+a = Miller(1,0,0,cs,'uvw');
+plot(cs,'upper')
+hold on
+plot(a,'MarkerFaceColor','red')
+hold off
+%set(gcf,'position',[200,200,300,300])
+saveFigure('pic/2mm.pdf','crop')
+
+%%
+
+names = {'321','3m1','-3m1','312','31m','-31m'};
+
+for i = 1:length(names)
+  cs = crystalSymmetry(names{i});
+  a = Miller(1,0,0,cs,'uvw');
+  plot(cs,'upper')
+  hold on
+  plot(a,'MarkerFaceColor','red')
+  set(gcf,'position',[200,200,300,300])
+  saveFigure(['pic/sym' names{i} '.pdf'],'crop')
+  hold off
+end
+
+%%
+
+setMTEXpref('FontSize',15)
+
+cs = crystalSymmetry('-3m1')
+
+plot(cs,'upper')
+
+h = [Miller(1,0,0,cs),Miller(1,1,1,cs)];
+hold on
+plot(h(1),'symmetrised','labeled','MarkerFaceColor','r','backgroundcolor','w')
+plot(h(2),'symmetrised','labeled','MarkerFaceColor','b','backgroundcolor','w')
+set(gcf,'position',[200,200,300,300])
+hold off
+%saveFigure('pic/hkl.pdf','crop')
+
+%%
+
+plot(cs,'upper')
+
+h = [Miller(1,0,0,cs,'uvw'),Miller(1,1,1,cs,'uvw')];
+hold on
+plot(h(1),'symmetrised','labeled','MarkerFaceColor','r','backgroundcolor','w')
+plot(h(2),'symmetrised','labeled','MarkerFaceColor','b','backgroundcolor','w')
+set(gcf,'position',[200,200,300,300])
+hold off
+%saveFigure('pic/uvw.pdf','crop')
+
+%%
+
+plot(cs,'upper')
+
+h = [Miller(1,0,-1,0,cs,'uvtw'),Miller(1,1,-2,2,cs,'uvtw')];
+hold on
+plot(h(1),'symmetrised','labeled','MarkerFaceColor','r','backgroundcolor','w')
+plot(h(2),'symmetrised','labeled','MarkerFaceColor','b','backgroundcolor','w')
+set(gcf,'position',[200,200,300,300])
+hold off
+%saveFigure('pic/uvtw.pdf','crop')
+
+
+
+
+%%
+setMTEXpref('textInterpreter','LaTeX')
+plotx2north
+m = Miller(1,1,-2,1,cs)
+plot(m,'symmetrised','labeled','grid','on','backgroundColor','w')
+set(gcf,'position',[200,200,220,430])
+saveFigure('pic/MillerSymmetrised.pdf')
+
+%%
+
+cs = crystalSymmetry('mmm',[1 2 3])
+m = Miller(1,1,1,cs,'uvw')
+plot(m,'labeled','upper','grid','on')
+set(gcf,'position',[200,200,200,200])
+saveFigure('pic/MillerUVW.pdf')
+
+%%
+hold all
+m = Miller(1,1,1,cs,'hkl')
+plot(m,'labeled','upper','grid','on')
+set(gcf,'position',[200,200,200,200])
+hold off
+saveFigure('pic/MillerUVW.pdf')
+
+%%
+hold on
+plot(m,'plane','linecolor','r','linewidth',1.5)
+hold off
+set(gcf,'position',[200,200,200,200])
+saveFigure('pic/MillerPlane.pdf')
+
+%%
+
+CS = loadCIF('quartz');
+m = Miller(1,1,-2,1,CS)
+m.dispStyle = 'UVTW'
+
+round(m)
+
+%%
+
+mtexdata fo
+ori = ebsd('Fo').orientations
+ori= ori(discretesample(ones(1,length(ori)),200))
+
+
+
+%%
+
+figure(1)
+plot(ori*Miller(1,0,0,ori.CS),'lower')
+set(gcf,'position',[200,200,200,200])
+saveFigure('pic/pfSimple.pdf','crop')
+
+%%
+figure(2)
+plot(ori*symmetrise(Miller(1,0,0,ori.CS)),'lower')
+
+%%
+
+plotPDF(ori,Miller(1,0,0,ori.CS),'upper')
+set(gcf,'position',[200,200,300,320])
+saveFigure('pic/pfSimple100.pdf','crop')
+
+plotPDF(ori,Miller(0,1,0,ori.CS),'upper')
+set(gcf,'position',[200,200,300,320])
+saveFigure('pic/pfSimple010.pdf','crop')
+
+%%
+
+plotPDF(ori,Miller(1,0,0,ori.CS),'upper','contourf')
+set(gcf,'position',[200,200,300,320])
+saveFigure('pic/pfSimple100Smooth.pdf','crop')
+
+plotPDF(ori,Miller(0,1,0,ori.CS),'upper','contourf')
+set(gcf,'position',[200,200,300,320])
+saveFigure('pic/pfSimple010Smooth.pdf','crop')
+
+
+
+%%
+
+plot(symmetrise(inv(ori))*xvector,'upper')
+set(gcf,'position',[200,200,200,200])
+saveFigure('pic/ipfSimple.pdf','crop')
+
+%%
+
+plotIPDF(ori,xvector)
+set(gcf,'position',[200,200,300,320])
+saveFigure('pic/ipfSimple100.pdf','crop')
+
+plotIPDF(ori,yvector)
+set(gcf,'position',[200,200,300,320])
+saveFigure('pic/ipfSimple010.pdf','crop')
+
+%%
+
+plotIPDF(ori,xvector,'contourf')
+set(gcf,'position',[200,200,300,320])
+saveFigure('pic/ipfSimple100Smooth.pdf','crop')
+
+plotIPDF(ori,yvector,'contourf')
+set(gcf,'position',[200,200,300,320])
+saveFigure('pic/ipfSimple010Smooth.pdf','crop')
+
+%%
+
+setMTEXpref('FontSize',13)
+
+plotSection(ebsd('Fo').orientations,'phi2',(0:5)*30*degree,'MarkerSize',15)
+drawNow(gcm,'figSize','tiny')
+%saveFigure('pic/odfOri.pdf','crop')
+
+%%
+
+plotSection(ebsd('Fo').orientations,'phi2',(0:5)*30*degree,'contourf','halfwidth',10*degree)
+drawNow(gcm,'figSize','tiny')
+%saveFigure('pic/odfOriSmooth.pdf','crop')
+
+%%
+
+oS = omegaSections(ori.CS,ori.SS);
+oS.omega = (0:5)*30*degree;
+oS.referenceField = @(r) pfSections.sigmaField(r)
+plotSection(ebsd('Fo').orientations,oS,'contourf','halfwidth',10*degree)
+%saveFigure('pic/odfOriSmoothSigma.pdf','crop')
+
+%%
+
+ori = ebsd('Fo').orientations
+mean(ori)
+
+%%
+
+mean(angle(mean(ori),ori))./degree
+
+sqrt(mean(angle(mean(ori),ori).^2))./degree
+
+
+%%
+
+CS_Mag = loadCIF('Magnetite')
+CS_Hem = loadCIF('Hematite')
+Mag2Hem = orientation('map', ...
+  Miller(1,1,1,CS_Mag), Miller(0,0,0,1, CS_Hem) , ...
+  Miller(-1,0,1, CS_Mag), Miller(1,0,-1,0,CS_Hem), ...
+  CS_Mag, CS_Hem);
+
+
+O1 = orientation('Euler',0,0,0,CS_Mag);
+O2 = O1 * inv(Mag2Hem)
+
+
+%%
+
+r = O1 * Miller(1,1,1,CS_Mag)
+
+%%
+
+O2 = orientation('Euler',135*degree,55*degree,60*degree,CS_Hem)
+
+round(inv(O2) * r)
+
+%%
+
+MO = inv(O2) * O1
+
+%%
+
+
+plotIPDF(MO,Miller({0,0,1},{1,1,1},CS_Hem),'complete','upper')
+
+%saveFigure('pic/HemPDF111.pdf','crop')
+
+%%
+
+plotPDF(MO,Miller({1,0,0},{1,1,1},CS_Mag),'complete','upper')
+%saveFigure('pic/MagPDF110.pdf','crop')
+
+%%
+
+mtexdata fo
+
+grains = calcGrains(ebsd)
+
+mori = grains.boundary('Fo','Fo').misorientation
+
+%%
+
+axis(MO)
+
+
+
+%%
+
+plotAngleDistribution(mori)
+
+hold on
+plotAngleDistribution(mori.CS)
+hold off
+
+%saveFigure('pic/angleDistri.pdf','crop')
+
+%%
+
+plotAxisDistribution(mori)
+%saveFigure('pic/axisDistri.pdf','crop')
+
+%%
+
+plotAxisDistribution(mori,'contourf')
+mtexColorbar
+%saveFigure('pic/axisDistriSmooth.pdf','crop')
+
+
+%%
+
+Mag2Hem = orientation('map',...
+  Miller(1,1,1,CS_Mag),Miller(0,0,0,1,CS_Hem),...
+  Miller(-1,0,1,CS_Mag),Miller(1,0,-1,0,CS_Hem),...
+  CS_Mag,CS_Hem)
+
+ori_Hem = orientation('Euler',0,0,0,CS_Hem);
+ori_Mag = ori_Hem * symmetrise(Mag2Hem)
+
+
+%%
+
+O1 = orientation('Euler',90*degree,45*degree,0,CS_Mag)
+O2 = orientation('Euler',180*degree,35*degree,0,CS_Hem)
+
+O1 * inv(O1) * O2
+
+%%
+
+
+
+%%
+
+O1 * Miller(1,1,1,CS_Mag)
+
+%%
+
+O2 = 
\ No newline at end of file
diff --git a/latex/mtex.sty b/latex/mtex.sty
new file mode 100644
index 0000000..f6d59b4
--- /dev/null
+++ b/latex/mtex.sty
@@ -0,0 +1,124 @@
+
+\mode<beamer>{
+  \usetheme{Frankfurt}
+  \mode<presentation>
+}
+
+\mode<handout>{
+  \usepackage{pgfpages}
+  \pgfpagesuselayout{2 on 1}[a4paper]
+}
+\usepackage{fancyvrb}
+
+% layout settings
+\setbeamertemplate{blocks}[rounded][shadow=false]
+\setbeamertemplate{navigation symbols}{}
+\setbeamersize{text margin left = 4mm}
+\setbeamersize{text margin right = 4mm}
+
+% other packages
+%\usetheme[Boadilla]{}
+\usepackage{calc}
+\usepackage{stmaryrd}
+%
+
+\usepackage{booktabs}
+%\useinnertheme{rounded}
+\usecolortheme{dolphin}
+\usecolortheme{rose}
+%\setbeamercolor{title}{fg=black,bg=white!80!black}
+\setbeamercolor{title}{fg=black,bg=white!80!blue}
+\usefonttheme[onlysmall]{structurebold}
+%\setbeamercovered{invisible}
+\setbeamercovered{transparent}
+
+
+\usepackage{colortbl}
+
+\usepackage[final]{listings}
+
+\definecolor{lightgray}{gray}{0.9}
+\definecolor{lightergray}{gray}{0.92}
+\definecolor{mygreen}{rgb}{0.1,0.9,0.3}
+\definecolor{commentgreen}{rgb}{0.3,1,0.5}
+
+\definecolor{lightgray}{gray}{0.9} \lstset{backgroundcolor=\color{lightgray}}
+\lstdefinelanguage{rock}{morekeywords=
+{mean,std,hist,save,load,rotate,min,max,get,tensor,loadTensor,
+scale,union,delete,degree,kernel,gethw,getparameter,bandwidth,
+symmetry,Miller,Miller2quat,uniformODF,unimodalODF,fibreODF,xvector,yvector,zvector,
+loadPoleFigure,PoleFigure,plot,plotpdf,plotipdf,calcODF,calcKernel,calcTensor,calcMDF,calcMisorientation,
+vector3d,cross,norm, dot,sum,savefigure,plotDiff,calcerror,
+quaternion,idquaternion,dist,Laue,length,angle,angle_outer,add,subGrid,refine,GridLength,getResolution,getRho,
+polar,S2Grid,santafee,mix2,modalorientation,fourier,textureindex,entropy,volume,
+surface, fibrevolume,uiimport,scatter,cif2symmetry,remove_outlier,
+simulatePoleFigure,SimulateEBSD,grainfun,hold,getFundamentalRegion,symvec,
+FourierODF,find_outlier,bar,copyproperty,plotspatial,hasholes,principalcomponents,
+hullprincipalcomponents,loadEBSD,calcGrains,plotboundaries,plotodf,plotspatial,area,
+aspectratio,grain,grainfun,grainsize,get,plotgrains,plotellipse,plotsubfractions,plotboundary,
+hasholes,hassubfraction,hullarea,hullcentroid,hullperimeter,centroid,borderlength,
+deltaarea,equivalentperimeter,perimeter,joincount,link,misorientation,neighbours,
+paris,shapefactor,toebsd,rotation,axis,Euler,symmetrise,orientation,eq,inverse,BinghamODF,set,
+project2FundamentalRegion,annotate,plotAngleDistribution,plotAxisDistribution,volumeCompressibility,
+YoungsModulus, shearModulus, linearCompressibility, ChristoffelTensor,
+velocity,
+PoissonRatio,plotx2north,plotx2east,plotzOutOfPlane,setMTEXpref,import,loadOrientation,loadVector3d,brassOrientation,double,EinsteinSum,directionalMagnitude,inv,sqrt,SchmidTensor,find,isnull,calcShearStress,contourf,colorbar,
+crystalSymmetry,specimenSymmetry,loadCIF,loadPHL,orth,randv,isImproper,dspacing,round,properGroup,export,
+mtexColorMap,KAM,fliplr,flipud},
+sensitive=false, morestring=[b][\emph]', moredelim=[is][\alert]{/+}{+/},
+moredelim=[is][\color{blue}\underbar]{/+}{+/},
+morecomment=[s][\emph]{<options}{>}, morecomment=[l]{\%},
+commentstyle=\color{darkgray}\itshape }
+
+\lstset{language=rock}
+\lstset{emph={symmetries,concentration},emphstyle={\bf \color{white!25!black}}}
+
+ \lstdefinestyle{input}{
+ 	frame=leftline,
+ 	framerule=2pt,
+ 	rulecolor=\color{mygreen},
+ 	backgroundcolor=\color{lightgray},
+ 	basicstyle=\color{black}}
+
+ \lstdefinestyle{output}{
+ 	frame=leftline,
+ 	framerule=2pt,
+ 	rulecolor=\color{gray},
+ 	backgroundcolor=\color{lightergray},
+ 	basicstyle=\scriptsize\ttfamily\color{darkgray},
+ 	% emph={ODF,Miller,PoleFigure,Symmetry,Vector3d,rotation,orientation,vector3d,misorientation,tensor,EBSD},
+        % emphstyle={\color{blue}\underbar}
+        }
+
+
+%  \lstdefinestyle{input}{
+%  	frame=leftline,
+%  	framerule=2pt,
+%  	rulecolor=\color{mygreen},
+%  	backgroundcolor=\color{lightgray},
+%  	basicstyle=\smaller\color{black}}
+
+%  \lstdefinestyle{output}{
+%  	frame=leftline,
+%  	framerule=2pt,
+%  	rulecolor=\color{gray},
+%  	backgroundcolor=\color{lightergray},
+%  	basicstyle=\scriptsize\ttfamily\color{darkgray}
+%  	}
+% %emph={ODF,Miller,PoleFigure,Symmetry,Vector3d,rotation,orientation,vector3d,misori%entation,tensor},
+% %        emphstyle={\color{blue}\underbar}
+
+\newtheorem{Remark}{Remark}
+\newtheorem{Proposition}{Proposition}
+\renewcommand{\O}{\mathcal O}
+\newcommand{\PGroup}{S_\text{Point}}
+\newcommand{\Y}{\mathcal Y}
+\renewcommand{\angle}{\measuredangle}
+\newcommand{\mtex}{{\large \bf{\color{red}M}TEX\,}}%
+\newcommand{\MTEX}{{\bf {\color{red}M}TEX\,}}%
+\newcommand{\degree}{\ensuremath{^\circ}}   % Gradzeichen
+%\newcommand{\degree}{^\circ}
+\newcounter{exercisescounter}
+\newenvironment{Exercise}{\refstepcounter{exercisescounter}%
+  \begin{block}{Exercise \arabic{exercisescounter}}}
+  {\end{block}}
diff --git a/scripts/ExercisesWithSolutions.m b/scripts/ExercisesWithSolutions.m
new file mode 100644
index 0000000..57d752d
--- /dev/null
+++ b/scripts/ExercisesWithSolutions.m
@@ -0,0 +1,313 @@
+%%             MTEX Workshop Belo Horizonte 2015
+%
+%%                      Exercises
+%
+%                Ralf Hielscher (1) and David Mainprice (2)
+%
+%  (1) TU Chemnitz, Germany
+%  (2) Universite Montpellier, France
+%
+% The following script guides you through the analysis of an Forsterite
+% sample. The original script by David Mainprice was about 800 lines. I
+% removed all the code and encourage you to rewrite it. You may find some
+% hints on the way.
+%
+% important shortcuts:
+% Strg + Return         - run the current section
+% Shift + Strg + Return - run the current section and go to the next one
+% F9                    - evaluate the selected command
+%
+
+
+%% Import the Data
+% This is already complete ...
+
+% crystal symmetry
+CS = {... 
+  'notIndexed',...
+  crystalSymmetry('mmm', [4.756 10.207 5.98], 'mineral', 'Forsterite', 'color', 'light blue'),...
+  crystalSymmetry('mmm', [18.2406 8.8302 5.1852], 'mineral', 'Enstatite', 'color', 'light green'),...
+  crystalSymmetry('12/m1', [9.746 8.99 5.251], [90,105.63,90]*degree, 'X||a*', 'Y||b', 'Z||c', 'mineral', 'Diopside', 'color', 'light red')};
+
+% create an EBSD variable containing the data
+ebsd = loadEBSD('pm-17_1.crc',CS,'convertSpatial2EulerReferenceFrame')
+
+% defines axis alignment
+plotx2east
+
+%% Exercise 1 - phase map
+%
+% Visualize the phase map and compute area fractions of the different
+% phases
+% a) including not indexed pixels
+% b) ignoring not indexed pixels
+%
+% useful commands: ebsd('indexed'), ebsd('notIndexed'), length
+
+
+%% Exercise 2 - Forsterite texture
+%
+% Determine the texure index J (Bunge, 1982) and the Uncorrelated
+% Misorientation Angle = M-index (Skemer et al., 2005) of the Forsterite
+% phase. Do you expect a sharp texture?
+%
+% useful commands: calcODF, ebsd('phaseName').orientations, textureindex, calcMIndex
+
+odf_Forsterite = calcODF(ebsd('Forsterite').orientations,'halfwidth',10*degree)
+
+J_index_Forsterite = textureindex(odf_Forsterite)
+
+M_index_Forsterite = calcMIndex(odf_Forsterite)
+
+%% Exercise 3 - pole figures
+%
+% Visualize the <100>, <010> and <001> pole figures of the Forsterite phase
+%
+% useful commands: plotPDF, mtexColorbar
+
+h = Miller({1,0,0}, {0,1,0}, {0,0,1}, ebsd('Forsterite').CS,'uvw');
+plotPDF(odf_Forsterite,h,'colorrange','equal');
+mtexColorbar
+
+%% Exercise 4 - band contrast
+%
+% plot a gray valued image of the band contrast (bc) of the ebsd data
+%
+% useful commands: reduce, mtexColorMap
+
+ebsd = reduce(ebsd,2)
+
+plot(ebsd,ebsd.bc)
+mtexColorMap gray
+mtexColorbar
+
+%% Exercise 5 - orientation gradient
+%
+% Visualize the orientation gradient within the Forsterite phase 
+%
+% a) plot the misorientation angle to the reference orientation
+% (104,90,175)
+%
+% b) plot the misorientation angle to the mean orientation
+% (104,90,175)
+%
+% c) use an ipf key with inverse pole figure direction such that the mean
+% orientation is colored white
+%
+% useful commands: angle, caxis, ipdfHSVOrientationMapping, 
+
+figure(1)
+reference_o = orientation('Euler',104*degree,90*degree,175*degree,ebsd('Forsterite').CS)
+ori = ebsd('Forsterite').orientations;
+plot(ebsd('Forsterite'), angle(ori,reference_o)./degree)
+% set scaling to the angles range 0 - 3 degree
+caxis([0 3]);
+mtexColorbar
+
+figure(2)
+plot(ebsd('Forsterite'),angle(ori,mean(ori))./degree)
+mtexColorbar
+caxis([0 3])
+
+
+figure(3)
+oM = ipdfHSVOrientationMapping(ebsd('Forsterite').CS);
+oM.inversePoleFigureDirection = mean(ebsd('Forsterite').orientations) * oM.whiteCenter;
+oM.maxAngle = 3.5*degree;
+
+plot(ebsd('Forsterite'),oM.orientation2color(ebsd('Forsterite').orientations))
+
+%% Exercise 6 - Grain modelling 
+% 
+% Model grains and plot them on top of the band contrast map. Repeat this
+% for different threshold angles 2 .. 15 degree. Analyse the grain size
+% distributions. How many grains do only contain one pixel?
+%
+% useful commands: calcGrains, grains.boundary, grains.grainSize
+
+[grains,ebsd.grainId,ebsd.mis2mean] = calcGrains(ebsd,'angle',15*degree)
+
+plot(ebsd,ebsd.bc)
+hold on
+plot(grains.boundary)
+hold off
+
+% percentage of one pixel grains
+nnz(grains.grainSize == 2) / length(grains) * 100
+
+%% Exercise 7 - removing small grains
+%
+% a) remove the EBSD data that belong to the one pixel grains or set those
+% to notIndexed
+%
+% b) recompute grains, graidIds and mis2mean
+%
+% c) plot a phase map and overlay it with the grain boundaries
+%
+% useful commands: ebsd(grains)
+
+ebsd = ebsd(grains(grains.grainSize > 1));
+
+[grains,ebsd.grainId,ebsd.mis2mean] = calcGrains(ebsd)
+
+%%
+
+plot(ebsd)
+hold on
+plot(grains.boundary,'linewidth',2)
+hold off
+
+
+%% Exercise 8 - kernel average misorientation (KAM)
+%
+% Plot the kernel average misorientation and overlay it with the grain
+% boundaries
+%
+% Note KAM is defined using EBSD data, it is the kernel average
+% misorientation for each EBSD measurement
+% options : 'threshold',10*degree and 'secondOrder'
+% Kernels for square EBSD grids
+% X = center point *= points used for Kernel
+% 1st order KAM (default)    2nd order KAM (option 'secondOrder')
+%                                      *
+%           *                         ***
+%          *X*                       **X**
+%           *                         ***
+%                                      *
+%
+% useful commands: ebsd.KAM('threshold',xx*degree)
+
+% compute and visualize the KAM
+kam = ebsd('Forsterite').KAM('threshold',3*degree)./degree;
+plot(ebsd('Forsterite'),kam)
+mtexColorbar
+% caxis - allows you focus the scale of the angle range of interest
+% example 0 to 3 degrees
+caxis([0 1])
+
+% plot grain boundary outline
+hold on
+plot(grains('Forsterite').boundary,'linewidth',2,'color','w','figSize','large')
+hold off
+
+
+%% Exercise 9
+%
+% Find the largest grain and 
+% a) plot it
+% b) mark its center of gravity
+% c) determine its phase, area, equivalent diameter
+% b) grain equivalent diameter
+% c) grain orientation spread (GOS) in degrees
+%
+% useful commands: grains.area, centroid(grains), grains.GOS,
+% grains.aspectRatio, grains.mis2mean
+
+[~,id] = max(grains.area)
+
+lGrain = grains(id)
+
+% grain centroid
+[centroid_x,centroid_y] = centroid(lGrain)
+
+% grain axial ratio
+lGrain.aspectRatio
+
+% grain area
+lGrain.area
+
+% grain equivalent diameter
+2 * lGrain.equivalentRadius
+
+% grain equivalent perimeter
+lGrain.equivalentPerimeter
+
+% grain orientation spread (GOS) in degrees
+lGrain.GOS / degree
+
+% plot ebsd orientation pixels
+plot(ebsd(lGrain),ebsd(lGrain).mis2mean.angle./degree)
+mtexColorbar
+% caxis - allows you focus the scale of the angle range of interest
+% example 0 to 5 degrees
+caxis([0 3])
+
+hold on
+% plot grain boundary outline
+plot(lGrain.boundary,'linewidth',2)
+
+% plot grain centroid
+plot(centroid_x,centroid_y,'o','MarkerEdgeColor',...
+  'k','MarkerFaceColor','r','MarkerSize',10)
+hold off
+
+
+%% Exercise 10 - misorientation line profile
+% select a line through the Forsterite grain and plot a misorientation
+% profile
+%
+% a) with respect to the first orienation 
+% b) with respect to the neighbouring orientation
+%
+% useful commands:  ginput, spatialProfile
+
+
+close all
+
+% plot grain boundary outline with mis2mean
+figure(1)
+plot(ebsd('fo'),angle(ori,mean(ori))./degree)
+caxis([0 3])
+mtexColorbar
+hold on
+plot(grains.boundary,'linewidth',2)
+hold off
+
+% Displays a cursor over the map and waits for 2 mouse clicks for the start
+% and for the end of the line, respectively
+[X_line, Y_line] = ginput(2);
+profile_line = [X_line(1) Y_line(1); X_line(2) Y_line(2)];
+
+hold on
+% draw profile line
+line(profile_line(:,1),profile_line(:,2),'linewidth',4,'color',[0 0 0 0.5])
+hold off
+
+% extract orientations and distance along profile_line
+[ebsd_line, distance]= spatialProfile(ebsd('Fo'),profile_line);
+ori_line = ebsd_line.orientations;
+
+% Misorientation with respect the first point along profile
+m_lineSec1 = angle(ori_line(1),ori_line)/degree;
+
+% Misorientation with respect the neighbouring point along profile
+m_lineSec2 = angle(ori_line(1:end-1),ori_line(2:end))/degree;
+
+% plot Misorientation angle profile
+figure(2)
+plot(distance,m_lineSec1,'color','b','linewidth',2)
+hold on
+plot(0.5*(distance(1:end-1)+distance(2:end)),m_lineSec2,'color','r','linewidth',2)
+xlabel('Position (microns)')
+ylabel('Misorientation angle in degrees')
+title('Misorientation angle profile')
+legend('wrt to 1st orientation','orientation gradient','Location','NorthWest')
+
+
+%% Exercise 11
+%
+% Plot the axes of the misorientations along the profile line. Colorize the
+% axes according
+%
+% a) the position on the profile line
+% b) the rotational angle
+% c) make a contour plot of the misorientation axes weighted by the
+% misorientation angle
+%
+% useful commands:  axis, angle, contourf
+
+mAxis = axis(ori_line(1:end-1),ori_line(2:end));
+mAngle = angle(ori_line(1:end-1),ori_line(2:end));
+
+plot(mAxis,mAngle,'contourf')
+
diff --git a/15_brasil/matlab/Forsterite.ctf b/scripts/Forsterite.ctf
similarity index 100%
rename from 15_brasil/matlab/Forsterite.ctf
rename to scripts/Forsterite.ctf
diff --git a/15_brasil/matlab/Gaussian.m b/scripts/Gaussian.m
similarity index 100%
rename from 15_brasil/matlab/Gaussian.m
rename to scripts/Gaussian.m
diff --git a/15_brasil/matlab/colorCodingExample.m b/scripts/colorCodingExample.m
similarity index 100%
rename from 15_brasil/matlab/colorCodingExample.m
rename to scripts/colorCodingExample.m
diff --git a/15_brasil/matlab/ebsdExample.m b/scripts/ebsdExample.m
similarity index 100%
rename from 15_brasil/matlab/ebsdExample.m
rename to scripts/ebsdExample.m
diff --git a/15_brasil/matlab/exercises.m b/scripts/exercises.m
similarity index 100%
rename from 15_brasil/matlab/exercises.m
rename to scripts/exercises.m
diff --git a/15_brasil/matlab/grainExample.m b/scripts/grainExample.m
similarity index 100%
rename from 15_brasil/matlab/grainExample.m
rename to scripts/grainExample.m
diff --git a/15_brasil/matlab/grainExercises.m b/scripts/grainExercises.m
similarity index 100%
rename from 15_brasil/matlab/grainExercises.m
rename to scripts/grainExercises.m
diff --git a/15_brasil/matlab/misorientationExample.m b/scripts/misorientationExample.m
similarity index 100%
rename from 15_brasil/matlab/misorientationExample.m
rename to scripts/misorientationExample.m
diff --git a/15_brasil/matlab/odfExample.m b/scripts/odfExample.m
similarity index 100%
rename from 15_brasil/matlab/odfExample.m
rename to scripts/odfExample.m
diff --git a/15_brasil/matlab/pm-17_1.cpr b/scripts/pm-17_1.cpr
similarity index 100%
rename from 15_brasil/matlab/pm-17_1.cpr
rename to scripts/pm-17_1.cpr
diff --git a/15_brasil/matlab/pm-17_1.crc b/scripts/pm-17_1.crc
similarity index 100%
rename from 15_brasil/matlab/pm-17_1.crc
rename to scripts/pm-17_1.crc
diff --git a/15_brasil/matlab/poleFigureExample.m b/scripts/poleFigureExample.m
similarity index 100%
rename from 15_brasil/matlab/poleFigureExample.m
rename to scripts/poleFigureExample.m
diff --git a/15_brasil/matlab/randomPoints.m b/scripts/randomPoints.m
similarity index 100%
rename from 15_brasil/matlab/randomPoints.m
rename to scripts/randomPoints.m
diff --git a/15_brasil/matlab/reduce.m b/scripts/reduce.m
similarity index 100%
rename from 15_brasil/matlab/reduce.m
rename to scripts/reduce.m
diff --git a/15_brasil/matlab/tensorExample.m b/scripts/tensorExample.m
similarity index 100%
rename from 15_brasil/matlab/tensorExample.m
rename to scripts/tensorExample.m
diff --git a/15_brasil/matlab/twinning.ctf b/scripts/twinning.ctf
similarity index 100%
rename from 15_brasil/matlab/twinning.ctf
rename to scripts/twinning.ctf
diff --git a/15_brasil/matlab/twinningExample.m b/scripts/twinningExample.m
similarity index 100%
rename from 15_brasil/matlab/twinningExample.m
rename to scripts/twinningExample.m