Added pos_vel_accel file.
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% Tutorial slides on Python.
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% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>
% Copyright (c) 2005-2009, Prabhu Ramachandran
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% Title page
\title[3D Plotting]{3D data Visualization}
\author[FOSSEE] {FOSSEE}
\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
\date[] {1 November, 2009\\Day 2, Session 5}
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%\pgfdeclareimage[height=0.75cm]{iitblogo}{iitblogo}
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\AtBeginSection[]
{
\begin{frame}<beamer>
\frametitle{Outline}
\tableofcontents[currentsection,currentsubsection]
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}
%% Delete this, if you do not want the table of contents to pop up at
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{
\begin{frame}<beamer>
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% DOCUMENT STARTS
\begin{document}
\begin{frame}
\maketitle
\end{frame}
\begin{frame}
\frametitle{Outline}
\tableofcontents
% You might wish to add the option [pausesections]
\end{frame}
\section{3D Data Visualization}
\begin{frame}
\frametitle{What is visualization?}
\Large
\begin{center}
Visual representation of data
\end{center}
\end{frame}
%% \begin{frame}
%% \frametitle{Is this new?}
%% \begin{center}
%% We have moved from:
%% \end{center}
%% \begin{columns}
%% \column{}
%% \hspace*{-1in}
%% \includegraphics[width=1.75in,height=1.75in, interpolate=true]{data/3832}
%% \column{}\hspace*{-0.25in}
%% To
%% \column{}
%% \hspace*{-1in}
%% \includegraphics[width=1.75in, height=1.75in, interpolate=true]{data/torus}
%% \end{columns}
%% \end{frame}
\begin{frame}
\frametitle{3D visualization}
\Large
\begin{center}
Harder but important
\end{center}
\end{frame}
\begin{frame}
\frametitle{Is this Graphics?}
\Large
\begin{center}
Visualization is about data!
\end{center}
\end{frame}
\begin{frame}
\frametitle{Examples: trajectory in space}
\Large
\begin{center}
\pgfimage[width=2.5in]{MEDIA/m2/mlab/plot3d_ex}
\end{center}
\end{frame}
\begin{frame}
\frametitle{Examples: Fire in a room}
\Large
\begin{center}
Demo of data
\end{center}
\inctime{10}
\end{frame}
\section{Tools available}
\subsection{mlab}
\begin{frame}
{Overview}
\Large
\begin{itemize}
\item Simple
\item Convenient
\item Full-featured
\end{itemize}
\end{frame}
\begin{frame}[fragile]
\frametitle{Getting started}
\myemph{\Large Vanilla:}
\begin{lstlisting}[language=bash]
$ ipython -wthread
\end{lstlisting}
\myemph{\Large with Pylab:}
\begin{lstlisting}[language=bash]
$ ipython -pylab -wthread
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Using mlab}
\begin{lstlisting}
In []:from enthought.mayavi import mlab
\end{lstlisting}
\vspace*{0.5in}
\myemph{\Large Try these}
\vspace*{0.25in}
\begin{lstlisting}
In []: mlab.test_<TAB>
In []: mlab.test_contour3d()
In []: mlab.test_contour3d??
\end{lstlisting}
\end{frame}
\begin{frame}
{Exploring the view}
\begin{columns}
\column{0.6\textwidth}
\pgfimage[width=3in]{MEDIA/m2/contour3d}
\column{0.4\textwidth}
\begin{itemize}
\item Mouse
\item Keyboard
\item Toolbar
\item Mayavi icon\pgfimage[width=0.2in]{MEDIA/m2/m2_icon}
\end{itemize}
\end{columns}
\end{frame}
\begin{frame}[fragile]
\frametitle{\mlab\ plotting functions}
\begin{columns}
\column{0.25\textwidth}
\myemph{\Large 0D data}
\column{0.5\textwidth}
\pgfimage[width=2in]{MEDIA/m2/mlab/points3d_ex}
\end{columns}
\begin{lstlisting}
In []: t = linspace(0, 2*pi, 50)
In []: u = cos(t) * pi
In []: x, y, z = sin(u), cos(u), sin(t)
\end{lstlisting}
\emphbar{\PythonCode{In []: mlab.points3d(x, y, z)}}
\end{frame}
\begin{frame}
\begin{columns}
\column{0.25\textwidth}
\myemph{\Large 1D data}
\column{0.5\textwidth}
\pgfimage[width=2.5in]{MEDIA/m2/mlab/plot3d_ex}
\end{columns}
\emphbar{\PythonCode{In []: mlab.plot3d(x, y, z, t)}}
Plots lines between the points
\end{frame}
\begin{frame}[fragile]
\begin{columns}
\column{0.25\textwidth}
\myemph{\Large 2D data}
\column{0.5\textwidth}
\pgfimage[width=2in]{MEDIA/m2/mlab/surf_ex}
\end{columns}
\begin{lstlisting}
In []: x, y = mgrid[-3:3:100j,-3:3:100j]
In []: z = sin(x*x + y*y)
\end{lstlisting}
\emphbar{\PythonCode{In []: mlab.surf(x, y, z)}}
\alert{Assumes the points are rectilinear}
\end{frame}
\begin{frame}[fragile]
\frametitle{mgrid}
\begin{lstlisting}
In []: mgrid[0:3,0:3]
Out[]:
array([[[0, 0, 0],
[1, 1, 1],
[2, 2, 2]],
[[0, 1, 2],
[0, 1, 2],
[0, 1, 2]]])
In []: mgrid[-1:1:5j]
Out[]: array([-1., -0.5, 0., 0.5, 1.])
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Example}
\begin{lstlisting}
In []: x, y = mgrid[-1:1:5j, -1:1:5j]
In []: z = x*x + y*y
In []: z
Out[]:
array([[ 2. , 1.25, 1. , 1.25, 2. ],
[ 1.25, 0.5 , 0.25, 0.5 , 1.25],
[ 1. , 0.25, 0. , 0.25, 1. ],
[ 1.25, 0.5 , 0.25, 0.5 , 1.25],
[ 2. , 1.25, 1. , 1.25, 2. ]])
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\myemph{\Large 2D data: \texttt{mlab.mesh}}
\vspace*{0.25in}
\emphbar{\PythonCode{In []: mlab.mesh(x, y, z)}}
\alert{Points needn't be regular}
\vspace*{0.25in}
\begin{lstlisting}
In []: phi, theta = mgrid[0:pi:20j,
... 0:2*pi:20j]
In []: x = sin(phi)*cos(theta)
In []: y = sin(phi)*sin(theta)
In []: z = cos(phi)
In []: mlab.mesh(x, y, z,
... representation=
... 'wireframe')
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\begin{columns}
\column{0.25\textwidth}
\myemph{\Large 3D data}
\column{0.5\textwidth}
\pgfimage[width=1.5in]{MEDIA/m2/mlab/contour3d}\\
\end{columns}
\begin{lstlisting}
In []: x, y, z = mgrid[-5:5:64j,
... -5:5:64j,
... -5:5:64j]
In []: mlab.contour3d(x*x*0.5 + y*y +
z*z*2)
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\myemph{\Large 3D vector data: \PythonCode{mlab.quiver3d}}
\vspace*{0.25in}
\pgfimage[width=2in]{MEDIA/m2/mlab/quiver3d_ex}\\
\begin{lstlisting}
In []: mlab.test_quiver3d()
\end{lstlisting}
\emphbar{\PythonCode{obj = mlab.quiver3d(x, y, z, u, v, w)}}
\inctime{20}
\end{frame}
\subsection{Mayavi2}
\begin{frame}
\frametitle{Introduction to Mayavi}
\begin{itemize}
\item Most scientists not interested in details of visualization
\item Visualization of data files with a nice UI
\item Interactive visualization of data (think Matlab)
\item Embedding visualizations in applications
\item Customization
\end{itemize}
\pause
\begin{block}{The Goal}
Provide a \alert{flexible} library/app for all of these needs!
\end{block}
\end{frame}
\begin{frame}
{Overview of features}
\vspace*{-0.3in}
\begin{center}
\hspace*{-0.2in}\pgfimage[width=5in]{MEDIA/m2/m2_app3_3}
\end{center}
\end{frame}
\begin{frame}
\frametitle{Mayavi in applications}
\vspace*{-0.3in}
\begin{center}
\hspace*{-0.2in}\pgfimage[width=4.5in]{MEDIA/m2/m2_envisage}
\end{center}
\end{frame}
\begin{frame}
\frametitle{Live in your dialogs}
\vspace*{0.1in}
\begin{center}
\hspace*{-0.2in}\pgfimage[width=2.5in]{MEDIA/m2/mlab_tui}
\end{center}
\end{frame}
\begin{frame}
{Exploring the documentation}
\begin{center}
\pgfimage[width=4in]{MEDIA/m2/m2_ug_doc}
\end{center}
\end{frame}
\begin{frame}
\frametitle{Summary}
\begin{itemize}
\item \url{http://code.enthought.com/projects/mayavi}
\item Uses VTK (\url{www.vtk.org})
\item BSD license
\item Linux, win32 and Mac OS X
\item Highly scriptable
\item Embed in Traits UIs (wxPython and PyQt4)
\item Envisage Plugins
\item Debian/Ubuntu/Fedora
\item \alert{Pythonic}
\end{itemize}
\inctime{10}
\end{frame}
\begin{frame}
{Getting hands dirty!}
\begin{block}{Motivational problem}
Atmospheric data of temperature over the surface of the earth.
Let temperature ($T$) vary linearly with height ($z$):
\begin{center}
$T = 288.15 - 6.5z$
\end{center}
\end{block}
\end{frame}
\begin{frame}[fragile]
\frametitle{Simple solution}
\begin{lstlisting}
lat = linspace(-89, 89, 37)
lon = linspace(0, 360, 37)
z = linspace(0, 100, 11)
\end{lstlisting}
\pause
\begin{lstlisting}
x, y, z = mgrid[0:360:37j,-89:89:37j,
0:100:11j]
t = 288.15 - 6.5*z
mlab.contour3d(x, y, z, t)
mlab.outline()
mlab.colorbar()
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Exercise: Lorenz equation}
\begin{columns}
\column{0.25\textwidth}
\begin{eqnarray*}
\frac{d x}{dt} &=& s (y-x)\\
\frac{d y}{d t} &=& rx -y -xz\\
\frac{d z}{d t} &=& xy - bz\\
\end{eqnarray*}
\column{0.25\textwidth}
Let $s=10,$
$r=28,$
$b=8./3.$
\end{columns}
\structure{\Large Region of interest}
\begin{lstlisting}
x, y, z = mgrid[-50:50:20j,-50:50:20j,
-10:60:20j]
\end{lstlisting}
\inctime{20}
\end{frame}
\begin{frame}[fragile]
\frametitle{Solution}
\begin{lstlisting}
def lorenz(x,y,z,s=10.,r=28.,b=8./3.):
u = s*(y-x)
v = r*x-y-x*z
w = x*y-b*z
return u,v,w
x,y,z = mgrid [-50:50:20j,-50:50:20j,
-10:60:20j ]
u,v,w = lorenz( x , y , z )
# Your plot here
#
mlab.show()
\end{lstlisting}
\end{frame}
\begin{frame}
\frametitle{We have covered:}
\begin{itemize}
\item Need of visualization.
\item Using mlab to create 3 D plots.
\item Mayavi Toolkit.
\end{itemize}
\end{frame}
\end{document}