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\documentclass[11pt]{article} % of: {report} \usepackage{ipe,a4wide} \newcommand{\tree}{{\cal T}} \newtheorem{lemma}{Lemma} \newtheorem{corollary}{Corollary}

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Presentation on theme: "\documentclass[11pt]{article} % of: {report} \usepackage{ipe,a4wide} \newcommand{\tree}{{\cal T}} \newtheorem{lemma}{Lemma} \newtheorem{corollary}{Corollary}"— Presentation transcript:

1 \documentclass[11pt]{article} % of: {report} \usepackage{ipe,a4wide} \newcommand{\tree}{{\cal T}} \newtheorem{lemma}{Lemma} \newtheorem{corollary}{Corollary} \newtheorem{theorem}{Theorem} \newtheorem{defi}{Definition}

2 \begin{document} \title{Good orders for incremental (re)construction\thanks{This research is supported by the NSERC and by the ESPRIT IV LTR Project No. 21957 (CGAL). }} \author{Jack Snoeyink\\ Dept. of Computer Science\\ University of British Columbia \and Marc van Kreveld\\ Dept. of Computer Science\\ Utrecht University\\ } \date{} \maketitle

3 \begin{abstract} Voronoi diagrams, Delaunay triangulations, and vertical decompositions in the plane are structures that are canonically defined for a set of $n$ points or line segments. Construction requires $\Theta(n\log n)$ time in the worst case. The method is simple and our implementation can be seen at {\footnotesize {\tt}} \end{abstract}

4 \chapter{Dynamic programming} % Nodig: \documentclass{report} \section{Introduction} \subsection{Background} \subsubsection{The early years} \paragraph{Example.}

5 {\bf dikgedrukt} {\it scheefgedrukt}, {\em benadrukt} \footnotesize \small \large \Large \LARGE {\sf sans serif font} {\tt typewriter font} \smallskip \medskip \bigskip \\ % Commentaar Line breaks onbelangrijk; lege regel(s) geeft nieuwe alinea

6 \begin{itemize} \item Het is mooi. \item Het werkt snel. \item Het is robuust. \end{itemize} enumerate: \item description: \item[Vooraf:]

7 $n$, $T$, $t \in S$ $k \choose 2$ $\frac{n-4}{n+i-1}$ $O(n \log n)$ $n^2$, $k^{11}$, $P_i$, $M_{i,j}$ $\sum_{i=1}^{n} i^2 $ $\triangle$, $\alpha$, $\rightarrow$, $\Rightarrow$ \[ \sum_{i=1}^{n-3} … \]

8 \begin{defi} Een {\em graaf} is een verzameling $V$ met knopen en een verzameling $E$ van edges, met voor een edge $e=(u,v)$ waarbij $u,v \in V$. \end{defi}

9 \begin{figure}[htb] \begin{center} \Ipe{mis.ipe} \end{center} \caption{An independent set with 31 vertices out of a triangulation with 100 vertices.} \label{fig:independentset} \end{figure} … in Figure~\ref{fig:independentset} …

10 \begin{table}[htb] \begin{center} \begin{tabular}{|l|r|r|} \hline & size with method A & size with method B \\ \hline Test 1 & 1,345 & 1,245 \\ Test 2 & 923 & 999 \\ \hline \end{tabular} \end{center} \caption{Results for …} \label{tab:comparison} \end{table} … in Table~\ref{tab:comparison} …

11 \bibliographystyle{plain} \bibliography{socg} \end{document} socg.bib is een file met entries in bibtex format N.B. Bibtex format entries zijn overal op het Web te vinden, bijv. Digital Bibliography & Library Project:

12 @Article{af-panp-84, author = {John Ahn and Herbert Freeman}, title = {A program for automatic name placement}, journal = {Cartographica}, volume = 21, number = {2--3}, year = 1984, pages = {101--109}, update = {97.07 agarwal} } … in~\cite{af-panp-83}, …

13 @inproceedings{af-panp-83, author = {John Ahn and Herbert Freeman}, title = {A Program for Automatic Name Placement}, booktitle = {Proc. Auto-Carto 6}, year = 1983, pages = {444--453} } @book{mf-gdspa-89, author = "H. Matthews and I. Foster", title = "Geographical Data -- Sources, Presentation, and Analysis", publisher = "Oxford University Press", year = 1989, address = "London", update = "95.12 kreveld" }

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