\documentclass[a4paper,twoside,10pt]{article}
\usepackage{tutorial}
\input{tutorial.def}

\begin{document}

% TITLE
\date{}
\title{{\LARGE {\sffamily\bfseries Getting started with CGAL
Polyhedron}}\\ the example of subdivision surfaces}
\author{
\sffamily Pierre Alliez\footnote{GEOMETRICA, INRIA Sophia-Antipolis}
\and 
\sffamily Andreas Fabri\footnote{GeometryFactory, Sophia-Antipolis}
\and 
\sffamily Lutz Kettner\footnote{Max-Planck Institut für Informatik, Saarbrücken}
\and
\sffamily Le-Jeng Shiue\footnote{SurfLab, University of Florida}
\and
\sffamily Radu Ursu\footnote{GEOMETRICA, INRIA Sophia-Antipolis}}
\maketitle

\thispagestyle{empty}

% ABSTRACT

\abstract{This document gives a rapid description for a user to get
started with the halfedge data structure provided by the Computational
Geometry Algorithm Library (CGAL). Assuming the reader to be familiar
with the C++ template mechanisms and the key concepts of the Standard
Template Library (STL), we describe three different approaches with
increasing level of sophistication for implementing mesh subdivision
schemes. The simplest approach uses simple Euler operators to
implement the $\sqrt{3}$ subdivision scheme applicable to triangle
meshes. A second approach overloads the incremental builder already
provided by CGAL to implement the quad-triangle subdivision scheme
applicable to polygon meshes. The third approach is more generic and
offers an efficient way to design its own subdivision scheme through
the definition of rule template. Catmull-Clark, Loop and Doo-Sabin
schemes are illustrated using the latter approach. Two companion
applications, one developed on windows with MS .NET, MFC and OpenGL,
and the other developed with Qt and OpenGL, implement the subdivision
schemes listed herein, as well as several functionalities for
interaction, visualization and raster/vectorial output.}

\vskip 3mm

\noindent {\bf Keywords:}
                 CGAL library,
                 tutorial, 
                 halfedge data structure, 
                 polygon surface mesh,
                 subdivision surfaces,
                 quad-triangle subdivision scheme,
                 $\sqrt{3}$,
                 Loop,
                 Doo-Sabin,
                 Catmull-Clark,
                 OpenGL.

% INTRODUCTION                 
\section{Introduction}  

Motivations:

\begin{itemize}
\item stop reinventing the wheel
\item the use of an optimized and robust computational 
      geometry library guarantees a much easier implementation, as
      well as fast and robust results
\item feel the power of generic programming
\end{itemize}               

% PREREQUISITES
\section{Prerequisites}

C++ and generic programming
STL
Concepts of iterators and circulators in general.

% HALFEDGE DATA STRUCTURE
\section{Halfedge data structure}

Description. 

Why it is so convenient (circulation around vertices, inside facets,
along a boundary, etc).

Euler operators.

% STL CONCEPTS APPLIED TO MESHES
\section{STL concepts applied to meshes}

Concepts of iterators and circulators in general on a mesh.

% POLYHEDRON DATA STRUCTURE
\section{Polyhedron data structure}

% SUBDIVISION SURFACES
\section{Subdivision surfaces}

A nice example to illustrate (i) iteration and circulation on a
halfedge data structure, (ii) modification of the connectivity, and
iii) modification of the geometry.

\subsection{Concept}

A subdivision surface is the limit surface of a subdivision process
applied over a control mesh...etc.

\subsection{Using Euler operators}

$\sqrt{3}$

\subsection{Using incremental builder}

quad-triangle

\subsection{Using a rule template}

Doo-Sabin, Catmull-Clark, Loop.

% APPLICATION DEMO
\section{Application demo}

List of features, snapshots.

\subsection{Compiling on Windows}

\subsection{Compiling on Linux}

% CONCLUSION
\section{Conclusion}

% REFERENCES
\bibliographystyle{alpha}
\bibliography{tutorial}


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