day2/3Dplotting.tex
author Santosh G. Vattam <vattam.santosh@gmail.com>
Sat, 24 Oct 2009 11:19:08 +0530
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Minor correction to session 2 day 1 slides.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Tutorial slides on Python.
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%
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% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>
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% Copyright (c) 2005-2009, Prabhu Ramachandran
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\documentclass[compress,14pt]{beamer}
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% \documentclass[handout]{beamer}
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% \usepackage{pgfpages}
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% \pgfpagesuselayout{4 on 1}[a4paper,border, shrink=5mm,landscape]
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\usepackage{tikz}
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\newcommand{\hyperlinkmovie}{}
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%\usepackage{movie15}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Note that in presentation mode 
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% \paperwidth  364.19536pt
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% \paperheight 273.14662pt
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% h/w = 0.888
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\mode<presentation>
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{
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  \usetheme{Warsaw}
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  %\usetheme{Boadilla}
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  %\usetheme{default}
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  \useoutertheme{split}
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  \setbeamercovered{transparent}
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}
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% To remove navigation symbols
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\setbeamertemplate{navigation symbols}{}
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\usepackage{amsmath}
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\usepackage[english]{babel}
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\usepackage[latin1]{inputenc}
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\usepackage{times}
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\usepackage[T1]{fontenc}
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% Taken from Fernando's slides.
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\usepackage{ae,aecompl}
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\usepackage{mathpazo,courier,euler}
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\usepackage[scaled=.95]{helvet}
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\usepackage{pgf}
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\definecolor{darkgreen}{rgb}{0,0.5,0}
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\usepackage{listings}
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\lstset{language=Python,
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    basicstyle=\ttfamily\bfseries,
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    commentstyle=\color{red}\itshape,
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  stringstyle=\color{darkgreen},
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  showstringspaces=false,
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  keywordstyle=\color{blue}\bfseries}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% My Macros
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\setbeamercolor{postit}{bg=yellow,fg=black}
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\setbeamercolor{emphbar}{bg=blue!20, fg=black}
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\newcommand{\emphbar}[1]
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{\begin{beamercolorbox}[rounded=true]{emphbar} 
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      {#1}
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 \end{beamercolorbox}
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}
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%{\centerline{\fcolorbox{gray!50} {blue!10}{
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%\begin{minipage}{0.9\linewidth}
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%    {#1} 
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%\end{minipage}
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%    }}}
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\newcommand{\myemph}[1]{\structure{\emph{#1}}}
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\newcommand{\PythonCode}[1]{\lstinline{#1}}
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\newcommand{\tvtk}{\texttt{tvtk}}
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\newcommand{\mlab}{\texttt{mlab}}
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\newcounter{time}
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\setcounter{time}{0}
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\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\vspace*{0.1in}\tiny \thetime\ m}}
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\newcommand\BackgroundPicture[1]{%
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  \setbeamertemplate{background}{%
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      \parbox[c][\paperheight]{\paperwidth}{%
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      \vfill \hfill
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 \hfill \vfill
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}}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Configuring the theme
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%\setbeamercolor{normal text}{fg=white}
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%\setbeamercolor{background canvas}{bg=black}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Title page
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\title[]{3D data Visualization}
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\author[FOSSEE Team] {FOSSEE}
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\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
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\date[] {1, November 2009\\Day 2, Session 3}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\pgfdeclareimage[height=0.75cm]{iitblogo}{iitblogo}
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%\logo{\pgfuseimage{iitblogo}}
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\AtBeginSection[]
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{
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  \begin{frame}<beamer>
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    \frametitle{Outline}      
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    \tableofcontents[currentsection,currentsubsection]
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  \end{frame}
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}
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%% Delete this, if you do not want the table of contents to pop up at
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%% the beginning of each subsection:
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\AtBeginSubsection[]
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{
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  \begin{frame}<beamer>
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    \frametitle{Outline}
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    \tableofcontents[currentsection,currentsubsection]
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  \end{frame}
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}
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\AtBeginSection[]
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{
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  \begin{frame}<beamer>
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    \frametitle{Outline}
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    \tableofcontents[currentsection,currentsubsection]
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  \end{frame}
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% DOCUMENT STARTS
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\begin{document}
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\begin{frame}
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  \maketitle
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\end{frame}
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\begin{frame}
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  \frametitle{Outline}
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  \tableofcontents
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  % You might wish to add the option [pausesections]
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\end{frame}
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\section{3D Data Visualization}
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\begin{frame}
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    \frametitle{What is visualization?}
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    \Large
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    \begin{center}
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    Visual representation of data
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    \end{center}
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\end{frame}
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\begin{frame}
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    \frametitle{3D visualization}
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    \Large
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    \begin{center}
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        Harder but important
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    \end{center}
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\end{frame}
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\begin{frame}
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    \frametitle{Is this Graphics?}
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    \Large
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    \begin{center}
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        Visualization is about data!
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    \end{center}
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\end{frame}
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\begin{frame}
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    \frametitle{Examples: trajectory in space}
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    \Large
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    \begin{center}
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        \pgfimage[width=2.5in]{MEDIA/m2/mlab/plot3d_ex}
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    \end{center}
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\end{frame}
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\begin{frame}
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    \frametitle{Examples: Fire in a room}
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    \Large
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    \begin{center}
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        Demo of data
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    \end{center}
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\inctime{10}
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\end{frame}
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\section{Tools at your disposal}
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\subsection{Mayavi2}
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\begin{frame}
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  \frametitle{Introduction to Mayavi}
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  \begin{itemize}
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  \item Most scientists not interested in details of visualization
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  \item Visualization of data files with a nice UI
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  \item Interactive visualization of data (think Matlab)
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  \item Embedding visualizations in applications
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  \item Customization
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  \end{itemize}
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  \pause
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  \begin{block}{The Goal}
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      Provide a \alert{flexible} library/app for every one of these needs!
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  \end{block}
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\end{frame}
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\begin{frame}
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    {Overview of features}
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      \vspace*{-0.3in}
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  \begin{center}    
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    \hspace*{-0.2in}\pgfimage[width=5in]{MEDIA/m2/m2_app3_3}
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  \end{center}    
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\end{frame}
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\begin{frame}
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    \frametitle{Mayavi in applications}
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      \vspace*{-0.3in}
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  \begin{center}    
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    \hspace*{-0.2in}\pgfimage[width=4.5in]{MEDIA/m2/m2_envisage}
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  \end{center}
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\end{frame}
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\begin{frame}
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    \frametitle{Live in your dialogs}
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      \vspace*{0.1in}
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  \begin{center}    
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    \hspace*{-0.2in}\pgfimage[width=2.5in]{MEDIA/m2/mlab_tui}
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  \end{center}
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\end{frame}
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\begin{frame}
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    {Exploring the documentation}
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    \begin{center}
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    \pgfimage[width=4in]{MEDIA/m2/m2_ug_doc}
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    \end{center}
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\end{frame}
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\begin{frame}
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  \frametitle{Summary}
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      \begin{itemize}
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          \item \url{http://code.enthought.com/projects/mayavi}
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          \item Uses VTK (\url{www.vtk.org})
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          \item BSD license
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          \item Linux, win32 and Mac OS X
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          \item Highly scriptable
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          \item Embed in Traits UIs (wxPython and PyQt4)
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          \item Envisage Plugins
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          \item Debian/Ubuntu/Fedora
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          \item \alert{Pythonic}
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      \end{itemize}
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      \inctime{10}
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\end{frame}
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\subsection{mlab}
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\begin{frame}
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    {Overview}
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    \Large
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    \begin{itemize}
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        \item Simple
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        \item Convenient
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        \item Full-featured
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    \end{itemize}
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\end{frame}
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\begin{frame}[fragile]
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    \frametitle{Getting started}
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    \myemph{\Large Vanilla:}
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    \begin{lstlisting}[language=bash]
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        $ ipython -wthread
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    \end{lstlisting}
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    \myemph{\Large with Pylab:}
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    \begin{lstlisting}[language=bash]
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        $ ipython -pylab -wthread
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    \end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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    \frametitle{Using mlab}
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    \begin{lstlisting}
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>>> from enthought.mayavi import mlab
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    \end{lstlisting}
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    \vspace*{0.5in}
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    \myemph{\Large Try these}
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    \vspace*{0.25in}
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    \begin{lstlisting}
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>>> mlab.test_<TAB>
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>>> mlab.test_contour3d()
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>>> mlab.test_contour3d??
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    \end{lstlisting}
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\end{frame}
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\begin{frame}
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    {Exploring the view}
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    \begin{columns}
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        \column{0.6\textwidth}
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    \pgfimage[width=3in]{MEDIA/m2/contour3d}
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        \column{0.4\textwidth}
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        \begin{itemize}
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            \item Mouse
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            \item Keyboard
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            \item Toolbar
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            \item Mayavi icon\pgfimage[width=0.2in]{MEDIA/m2/m2_icon}
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        \end{itemize}
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    \end{columns}
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\end{frame}
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\begin{frame}[fragile]
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    \frametitle{\mlab\ plotting functions}
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    \begin{columns}
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        \column{0.25\textwidth}
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        \myemph{\Large 0D data}
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        \column{0.5\textwidth}
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    \pgfimage[width=2in]{MEDIA/m2/mlab/points3d_ex}
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    \end{columns}
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    \begin{lstlisting}
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>>> from numpy import *
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>>> t = linspace(0, 2*pi, 50)
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>>> u = cos(t)*pi
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>>> x, y, z = sin(u), cos(u), sin(t)
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    \end{lstlisting}
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    \emphbar{\PythonCode{>>> mlab.points3d(x, y, z)}}
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\end{frame}
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\begin{frame}
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  \begin{columns}
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        \column{0.25\textwidth}
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        \myemph{\Large 1D data}
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        \column{0.5\textwidth}
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        \pgfimage[width=2.5in]{MEDIA/m2/mlab/plot3d_ex}
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  \end{columns}
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  \emphbar{\PythonCode{>>> mlab.plot3d(x, y, z, t)}}
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    Plots lines between the points
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\end{frame}
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\begin{frame}[fragile]
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    \begin{columns}
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        \column{0.25\textwidth}
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   356
        \myemph{\Large 2D data}
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        \column{0.5\textwidth}
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        \pgfimage[width=2in]{MEDIA/m2/mlab/surf_ex}
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    \end{columns}            
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    \begin{lstlisting}
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   361
>>> x = mgrid[-3:3:100j,-3:3:100j]
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   362
>>> z = sin(x*x + y*y)
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    \end{lstlisting}
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diff changeset
   364
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   365
    \emphbar{\PythonCode{>>> mlab.surf(x, y, z)}}
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   367
    \alert{Assumes the points are rectilinear}
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   369
\end{frame}
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\begin{frame}[fragile]
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   372
    \myemph{\Large 2D data: \texttt{mlab.mesh}}
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   373
    \vspace*{0.25in}
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   374
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   375
    \emphbar{\PythonCode{>>> mlab.mesh(x, y, z)}}
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   376
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   377
    \alert{Points needn't be regular}
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diff changeset
   378
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   379
    \vspace*{0.25in}
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   380
\begin{lstlisting}
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   381
>>> phi, theta = numpy.mgrid[0:pi:20j, 
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   382
...                         0:2*pi:20j]
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diff changeset
   383
>>> x = sin(phi)*cos(theta)
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   384
>>> y = sin(phi)*sin(theta)
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diff changeset
   385
>>> z = cos(phi)
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parents:
diff changeset
   386
>>> mlab.mesh(x, y, z, 
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diff changeset
   387
...           representation=
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diff changeset
   388
...           'wireframe')
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   389
\end{lstlisting}
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diff changeset
   390
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\end{frame}
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parents:
diff changeset
   392
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parents:
diff changeset
   393
\begin{frame}[fragile]
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parents:
diff changeset
   394
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   395
  \begin{columns}
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   396
        \column{0.25\textwidth}
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   397
        \myemph{\Large 3D data}
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   398
        \column{0.5\textwidth}
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   399
        \pgfimage[width=1.5in]{MEDIA/m2/mlab/contour3d}\\        
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parents:
diff changeset
   400
    \end{columns}
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   401
\begin{lstlisting}
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   402
>>> x, y, z = ogrid[-5:5:64j, 
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   403
...                -5:5:64j, 
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   404
...                -5:5:64j]
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Shantanu <shantanu@fossee.in>
parents:
diff changeset
   405
>>> mlab.contour3d(x*x*0.5 + y*y + 
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   406
                   z*z*2)
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   407
\end{lstlisting}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   408
\end{frame}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   409
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   410
\begin{frame}[fragile]
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   411
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   412
    \myemph{\Large 3D vector data: \PythonCode{mlab.quiver3d}}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   413
    \vspace*{0.25in}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   414
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   415
    \pgfimage[width=2in]{MEDIA/m2/mlab/quiver3d_ex}\\
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   416
    
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   417
\begin{lstlisting}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   418
>>> mlab.test_quiver3d()
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   419
\end{lstlisting}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   420
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   421
\emphbar{\PythonCode{obj = mlab.quiver3d(x, y, z, u, v, w)}}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   422
\inctime{20}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   423
\end{frame}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   424
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   425
\begin{frame}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   426
    {Getting hands dirty!}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   427
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   428
        \begin{block}{Motivational problem}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   429
        Atmospheric data of temperature over the surface of the earth.
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   430
        Let temperature ($T$) vary linearly with height ($z$):
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   431
        \begin{center}            
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   432
        $T = 288.15 - 6.5z$
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   433
        \end{center}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   434
        \end{block}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   435
\end{frame}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   436
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   437
\begin{frame}[fragile]
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   438
    \frametitle{Simple solution}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   439
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   440
    \begin{lstlisting}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   441
lat = linspace(-89, 89, 37)
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   442
lon = linspace(0, 360, 37)
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   443
z = linspace(0, 100, 11)
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   444
    \end{lstlisting}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   445
\pause
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   446
    \begin{lstlisting}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   447
x, y, z = mgrid[0:360:37j,-89:89:37j,
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   448
                0:100:11j]
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   449
t = 288.15 - 6.5*z
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   450
mlab.contour3d(x, y, z, t)
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   451
mlab.outline()
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   452
mlab.colorbar()
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   453
    \end{lstlisting}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   454
\end{frame}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   455
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   456
\begin{frame}[fragile]
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   457
    \frametitle{Exercise: Lorenz equation}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   458
    \begin{columns}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   459
        \column{0.25\textwidth}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   460
        \begin{eqnarray*}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   461
        \frac{d x}{dt} &=& s (y-x)\\
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   462
        \frac{d y}{d t} &=& rx -y -xz\\
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   463
        \frac{d z}{d t} &=& xy - bz\\
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   464
        \end{eqnarray*}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   465
        \column{0.25\textwidth}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   466
        Let $s=10,$
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   467
        $r=28,$ 
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   468
        $b=8./3.$
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   469
    \end{columns}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   470
    \structure{\Large Region of interest}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   471
  \begin{lstlisting}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   472
x, y, z = mgrid[-50:50:20j,-50:50:20j,
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   473
                -10:60:20j]
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   474
  \end{lstlisting}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   475
\inctime{20}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   476
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   477
\end{frame}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   478
\begin{frame}[fragile]
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   479
    \frametitle{Solution}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   480
  \begin{lstlisting}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   481
def lorenz(x,y,z,s=10.,r=28.,b=8./3.):
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   482
    u = s*(y-x)
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   483
    v = r*x-y-x*z
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   484
    w = x*y-b*z
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   485
    return u,v,w
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   486
x,y,z = mgrid [-50:50:20j,-50:50:20j,
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   487
                    -10:60:20j ]
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   488
u,v,w = lorenz( x , y , z )
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   489
# Your plot here
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   490
#
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   491
mlab.show()
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   492
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   493
  \end{lstlisting}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   494
\end{frame}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   495
  
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   496
\end{document}
66b117b7edc7 Added slides for 3D data visualization session 3 day 2.
Shantanu <shantanu@fossee.in>
parents:
diff changeset
   497