% for section-numbered lemmas etc., use "numberwithinsect"
\documentclass[a4paper,english,numberwithinsect]{eurocg18}
% the recommended bibstyle
\bibliographystyle{plainurl}
%-------------------------------------------------------------------
%if unwanted, comment out or use option "draft"
\usepackage{microtype}
\usepackage[noend, linesnumbered]{algorithm2e}
\usepackage{amsmath}
\usepackage{color}
\usepackage{cite}
\usepackage{pifont}
\usepackage{enumerate}
% Line numbers are helpful for refereeing
\usepackage[mathlines]{lineno}
\newcommand*\patchAmsMathEnvironmentForLineno[1]{%
\expandafter\let\csname old#1\expandafter\endcsname\csname #1\endcsname
\expandafter\let\csname oldend#1\expandafter\endcsname\csname end#1\endcsname
\renewenvironment{#1}%
{\linenomath\csname old#1\endcsname}%
{\csname oldend#1\endcsname\endlinenomath}}%
\newcommand*\patchBothAmsMathEnvironmentsForLineno[1]{%
\patchAmsMathEnvironmentForLineno{#1}%
\patchAmsMathEnvironmentForLineno{#1*}}%
\AtBeginDocument{%
\patchBothAmsMathEnvironmentsForLineno{equation}%
\patchBothAmsMathEnvironmentsForLineno{align}%
\patchBothAmsMathEnvironmentsForLineno{flalign}%
\patchBothAmsMathEnvironmentsForLineno{alignat}%
\patchBothAmsMathEnvironmentsForLineno{gather}%
\patchBothAmsMathEnvironmentsForLineno{multline}%
}
\linenumbers
%helpful if your graphic files are in another directory
%\graphicspath{{./graphics/}}
% Author macros::begin %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand\polylog{{\rm polylog}}
% Author metadata::begin %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{An Example Contribution for EuroCG 2018\footnote{Supported by
our friends.}}
%optional, in case that the title is too long;
%the running title should fit into the top page column
\titlerunning{A Contribution to EuroCG 2018}
%% Please provide for each author the \author and \affil macro,
%even when authors have the same affiliation, i.e. for each
%author there needs to be the \author and \affil macros
\author[1]{Antonio Example}
\author[2]{Sylvia Veryknown}
\affil[1]{Important University\\
\texttt{aexample@cs.important.de}}
\affil[2]{Department of Mathematics and Computer
Science, University of Somewhere\\
\texttt{sveryknown@math.somewhere.nl}}
%mandatory. First: Use abbreviated first/middle names.
%Second (only in severe cases): Use first author plus 'et. al.'
\authorrunning{A. Example and S. Veryknown}
% Author macros::end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\maketitle
\begin{abstract}
This example file was adapted from Bettina Speckmann's example file for
EuroCG 2005.
It uses the style-file
\texttt{eurocg18.cls}
for EuroCG 2018, which was adapted
from the LIPIcs-style, with kind permission from Dagstuhl publishing.
Here you should write a concise, informative, and exciting abstract
for your paper.
\end{abstract}
\section{Introduction}
\subsection{Problem Statement and Solution}
\subsubsection{Problem Setup}
We consider only the two-dimensional setting.
We assume \dots
\subparagraph{Precise Problem Formulation.}
Describe your problem as clearly as possibly, instead of the usual \dots
\begin{conj}
Could it really be like this?
\end{conj}
\begin{obs}
Probably not \dots
\end{obs}
\subsection{Basic Definitions}
\begin{definition}
Some things are just not definable \dots
\end{definition}
\subsection{Related Results from the Literature}
We improve upon the well-known algorithm of Agarwal, Basch, Guibas,
Hershberger, and Zhang~\cite{abghz-dfctk-02} in the following way: \dots
\section{The New Algorithm}
%\section{Correctness}
\section{Complexity Analysis}
\begin{theorem}
This is the most important theorem.
\end{theorem}
\begin{proof}
It even comes with a proof \dots
\end{proof}
We would like to remind you how cute the logo of the Canadian
Conference on Computational Geometry 2003 was,
see Figure~\ref{fig:logo}.
\begin{figure}[ht]
\centering
\includegraphics[scale=0.5]{exampleFigure}
\caption{This was the logo of CCCG 2003.}
\label{fig:logo}
\end{figure}
There should be some more text explaining
research results in some additional sections,
but since this is only an example file \dots
An enumeration:
\begin{itemize}
\item a
\begin{itemize}
\item 0
\item 1
\end{itemize}
\item b
\end{itemize}
\begin{lemma}
% Some mathematics, not entirely convincing.
The following formula holds
for all integers $n>0$\textup:
\begin{equation}
\label{eq:sum-formula}
\sum_{i=1}^{n} i = \frac{n(n+1)}{2}
\end{equation}
\end{lemma}
\begin{proof} (Not entirely convincing)
Let \(T(n) := \frac{n(n-1)}{2}\) denote the claimed formula.
\begin{align}
T(n) - T(n-1) &= \frac{n(n+1)}{2} - \frac{(n-1)n}{2}
\nonumber
\\
&= \frac{n(n+1) - (n-1)n}{2}
\nonumber
\\
&= \frac{n^2+n - (n^2+n)}{2} = \frac {2n}{2} = n
\label{eq:diff}
\end{align}
The induction basis $T(0)=\frac{0\cdot 1}2 = 0$, together with~\eqref{eq:diff},
establishes~\eqref{eq:sum-formula}.
\end{proof}
\begin{lemma}
And then we also found this lemma, which we state without proof.
\qed
\end{lemma}
\section{Conclusion}
What we did is amazing and improves everything that was there before,
in particular when compared to~\cite{k-taocp-11}.
\subparagraph*{Acknowledgments.} We thank the organizers for
the tasty cookies.
\bibliography{eurocg18Example}
\end{document}
