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\title{\epsfig{file=dhbw-logo.eps, scale=2.0}  \\[0.3cm]
       Theoretical Computer Science \texttt{I}: Logic \\[0.3cm]
      --- Winter 2017 ---     \\[0.3cm]
      DHBW Mannheim}
\author{Prof.~Dr.~Karl Stroetmann}

\date{\today \\[02.5cm]
\begin{minipage}[t]{1.0\linewidth}
\noindent
These lecture notes, the corresponding \LaTeX\ sources and the programs discussed in these lecture notes are available at
\\[0.2cm]
\hspace*{\fill}
\href{https://github.com/karlstroetmann/Logic}{\texttt{https://github.com/karlstroetmann/Logic}}.
\hspace*{\fill}
\\[0.2cm]
The \href{https://github.com/karlstroetmann/Logic/blob/master/Lecture-Notes/logic.pdf}{lecture notes} are
constantly revised.   Provided you have installed  \href{http://git-scm.com/download}{\texttt{git}} on your
computer, you can clone my repository using the command
\\[0.2cm]
\hspace*{1.3cm}
\texttt{git clone https://github.com/karlstroetmann/Logic.git}.
\\[0.2cm]
Then, the repository can be updated using the command
\\[0.2cm]
\hspace*{1.3cm}
\texttt{git pull}.
\end{minipage}
}

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\begin{document}

\maketitle
\tableofcontents
\include{introduction}
\include{setlx}
\include{grenzen}
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\include{praedikatenlogik}

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%%% End:


text:
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\begin{document}
% Old cover page
%\title{\textbf{CMPMP2Y --- MSc Dissertation: \\ Procedural Generation of Dungeons}}
%\author{Olivier Legat \\ (Supervisor: Prof. Andy Day)}
%\maketitle

% New cover page
\includepdf[pages=1]{CoverSheet.pdf}

\begin{abstract}
The use of procedural content generation (PCG) is not un-common amongst games, it appears in many applications. PCG algorithms notably present the advantage of providing potentially infinite and un-predictable content for the players, which can significantly add value to the game. However, implementing a good PCG algorithm that generates convincing results is not a trivial task. PCG revolves around the concept of randomness that is usually implemented by using pseudo-random number generators. Different PCG methods can be used to create content for specific kinds of environments. These methods can vary greatly depending on the type of environment desired. This thesis focuses on generating content for dungeon-like or maze-like environments by identifying the most suitable methods and algorithms. The methods used for generating maze involve finding a random spanning tree of a graph, hence the Prim's and Kruskal's algorithms can be used. Further on, we can obtain a dungeon-like environment from a maze by applying modifications to it such as adding loops and rooms.
\end{abstract}

\setcounter{page}{1}
\pagenumbering{roman}

\pagebreak
\chapter*{Acknowledgement}
\begin{quotation}
This dissertation would have never been completed if not for the help of several people who offered their services and help to me.
\end{quotation}
\begin{quotation}
First and foremost, I would like to thank my parents, Thierry and Carol whom I hold dearly to me, for their love, their financial and moral support, and for never losing faith in me throughout the year despite the circumstances.
\end{quotation}
\begin{quotation}
I would like to express my deepest gratitude to my supervisor Professor Andy Day for accepting my self-proposed topic without a second doubt and later providing his advice, guidance and feedback on my progress.
\end{quotation}
\begin{quotation}
I would also like the thank Dr. Wenjia Wang, the MSc Dissertation Module organiser, who has taught me how to write a proper MSc thesis. His help was a valuable asset to completing my work on time.
\end{quotation}
\begin{quotation}
I want to thank Dr. Rudy Lapeer and Dr Stephen Laycock for teaching me all there is to know about Graphics, Rendering and Real-time Virtual Environments.
\end{quotation}
\begin{quotation}
I send my humble thanks to Abiishiek Vijaykumar for spending many hours thoroughly proof-reading my entire dissertation. Without his help this write-up would have certainly not met to the standard of a MSc Dissertation.
\end{quotation}
\begin{quotation}
I would like to thank all my fellow friends in Norwich whom have stood with me through the tough times, helped me in every way they could and given me the strength to keep going.
\end{quotation}

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\tableofcontents
\pagebreak

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\include{software}
\include{conclusion}

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\pagebreak
\appendix
\include{appendix}

\end{document}

domain: tex


text:
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\section*{Problema e descrizione della soluzione}
Data la struttura \textit{QuadTrees}, definita come:

\begin{minted}{haskell}
  data QT a = C a
            | Q (QT a) (QT a) (QT a) (QT a)
       deriving (Show, Eq)
\end{minted}

Dato un \texttt{QT t}, si richiede che questo abbia un \textit{bound}: ogni \texttt{t} ha un colore \texttt{C :: Integer} (sia assunto che il colore sia intero), questo deve rientrare tra un $c_{min}$ e un $c_{max}$ scelti dall'utilizzatore della funzione.

Il ``bound'' viene definito dalla funzione \texttt{bound}:
\begin{minted}{haskell}
	bound :: Ord a => a -> a -> a -> a
	bound cm cM a
            | a > cM = cM
            | a < cm = cm
            | otherwise = a
\end{minted}
dove \texttt{cm} e \texttt{cM} sono rispettivamente $c_{min}$ e $c_{max}$ ed \texttt{a} è il ``colore''.

La soluzione proposta si avvale di \texttt{Functor} per utilizzare \texttt{fmap}, al fine di non dover definire una funzione ``mapQT'' per manipolare (e involontariamente \textit{``unwrappare''}) \texttt{QT t}.

Tale funzione sarebbe definita similmente a:
\begin{minted}{haskell}
    mapQT :: (a -> b) -> QT a -> QT b
    mapQT f (C x) = C $ f x
    mapQT f (Q ss sd is id) = Q (mapQT f ss) (mapQT f sd)
                                (mapQT f is) (mapQT f id)
\end{minted}

Viene quindi sostituita dall'istanziazione automatica per il \texttt{Functor} come segue:
\begin{minted}{haskell}
    instance Functor QT where
      fmap f (C x) = C $ f x
      fmap f (Q ss sd is id) = Q (fmap f ss) (fmap f sd)
                                 (fmap f is) (fmap f id)
\end{minted}
La soluzione adottata è quella di ``derivare'' \texttt{Functor} nella definizione di \texttt{QT}, provocando il medesimo effetto descritto sopra.

In questa maniera la soluzione viene data per composizione:
\begin{minted}{haskell}
  boundPicture :: Integral t => t -> t -> QT t -> QT t
  boundPicture cm cM a = (bound cm cM) <$> a
   where bound cm cM a
            | a > cM = cM
            | a < cm = cm
            | otherwise = a
\end{minted}

Il risultato quindi è una applicazione della ``map'' ad un caso non più specifico come per le liste
ma applicato ad un tipo di dato ricorsivo. L'istanziazione del funtore permette quindi di ``istruire'' \texttt{Prelude} su come manipolare il dato per \texttt{fmap} (o, in questo caso, \texttt{<\$>}).

\section*{Assunzioni}
Viene assunto che il \texttt{QT t} rispetti le caratteristiche:
\begin{enumerate}
	\item chi passa alla funzione \texttt{boundPicture} passi un albero QT che rispetti le regole richieste;
	\item che \texttt{Color} sia per l'appunto di tipo \texttt{Integer}.
\end{enumerate}
L'unica assunzione che non porta a particolari problemi di esecuzione è che \texttt{t} non rispetti la ``forma normale'' per \texttt{QT}.

\section*{Test}
Si possono trovare alcuni test esemplificativi nel file \texttt{test.hs}.

\section*{Soluzione}
La soluzione si può trovare all'interno del file \texttt{esercizio.hs}.

\section*{Ambiente di lavoro}
Il sorgente viene quindi eseguito in ambiente con ``ghci'' alla versione 8.0.2.

\end{document}


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\twoaffiliations$for(institute)${$institute$}$endfor$
$else$$if(threegroups)$
\threeaffiliations$for(institute)${$institute$}$endfor$
$else$$if(fourgroups)$
\fouraffiliations$for(institute)${$institute$}$endfor$
$else$$if(fivegroups)$
\fiveaffiliations$for(institute)${$institute$}$endfor$
$else$$if(sixgroups)$
\sixaffiliations$for(institute)${$institute$}$endfor$
$else$
\affiliation{$for(institute)$$institute$$sep$\\ $endfor$}
$endif$$endif$$endif$$endif$$endif$
$else$
\affiliation{~}$endif$

$if(date)$
\note{$date$}$endif$

$if(authornote)$
\authornote{%
$authornote$
}$endif$

$if(abstract)$
% Abstract page
\abstract{%
$abstract$
}$endif$

$if(keywords)$
\keywords{$for(keywords)$$keywords$$sep$, $endfor$}$endif$

$for(include-before)$
% Other custom includes
$include-before$

$endfor$

\ifdocmode
\usepackage{longtable}
\fi

\ifjoumode
% Journal specific commands may go here:
$if(joucommands.leftheader)$
\leftheader{$joucommands.leftheader$}$endif$
$if(joucommands.journal)$
\journal{$joucommands.journal$}$endif$
$if(joucommands.volume)$
\volume{$joucommands.volume$}$endif$
$if(joucommands.ccoppy)$
\ccoppy{$joucommands.ccoppy$}$endif$
$if(joucommands.copnum)$
\copnum{$joucommands.copnum$}$endif$
% two column long table. has to be done at the end
\usepackage{longtable}
\makeatletter
\let\oldlt\longtable
\let\endoldlt\endlongtable
\def\longtable{\@ifnextchar[\longtable@i \longtable@ii}
\def\longtable@i[#1]{%

\begin{figure}[btph]\onecolumn \begin{minipage}{0.5\textwidth} \oldlt[#1]}
\def\longtable@ii{\begin{figure}[btph]\onecolumn \begin{minipage}{0.5\textwidth} \oldlt}
\def\endlongtable{%
\endoldlt
\end{minipage}

\twocolumn
\end{figure}}
\makeatother
\fi

% table caption width
\makeatletter
\newcommand\LastLTentrywidth{1em}
\newlength\longtablewidth
\setlength{\longtablewidth}{1in}
\newcommand\getlongtablewidth{%
\begingroup
\ifcsname LT@\roman{LT@tables}\endcsname
\global\longtablewidth=0pt
\renewcommand\LT@entry[2]{\global\advance\longtablewidth by ##2\relax\gdef\LastLTentrywidth{##2}}%
\@nameuse{LT@\roman{LT@tables}}%
\fi
\endgroup}

%% pandoc-tablenos: environment to disable table caption prefixes
\makeatletter
\newcounter{tableno}
\newenvironment{tablenos:no-prefix-table-caption}{
  \caption@ifcompatibility{}{
    \let\oldthetable\thetable
    \let\oldtheHtable\theHtable
    \renewcommand{\thetable}{tableno:\thetableno}
    \renewcommand{\theHtable}{tableno:\thetableno}
    \stepcounter{tableno}
    \captionsetup{labelformat=empty}
  }
}{
  \caption@ifcompatibility{}{
    \captionsetup{labelformat=default}
    \let\thetable\oldthetable
    \let\theHtable\oldtheHtable
    \addtocounter{table}{-1}
  }
}
\makeatother

\begin{document}
$if(title)$\maketitle$endif$

$body$

$if(bibliography)$
\printbibliography$if(biblio-title)$[title=$biblio-title$]$endif$

$endif$
$for(include-after)$
$include-after$

$endfor$

$if(lot)$
\listoftables
$endif$
$if(lof)$
\listoffigures
$endif$

$if(biblatex)$$else$
\noindent
\vspace{-2em}
\setlength{\parindent}{-0.5in}
\setlength{\leftskip}{0.5in}
\setlength{\parskip}{15pt}
$endif$

\end{document}


text:
\hypertarget{_j_g_t_l___map_interface_8h}{
\section{JGTL\_\-Map\-Interface.h File Reference}
\label{_j_g_t_l___map_interface_8h}\index{JGTL_MapInterface.h@{JGTL\_\-MapInterface.h}}
}
{\tt \#include $<$utility$>$}\par
{\tt \#include $<$cstdlib$>$}\par
{\tt \#include \char`\"{}JGTL\_\-Located\-Exception.h\char`\"{}}\par
\subsection*{Namespaces}
\begin{CompactItemize}
\item
namespace \hyperlink{namespace_j_g_t_l}{JGTL}
\end{CompactItemize}
\subsection*{Classes}
\begin{CompactItemize}
\item
class \hyperlink{class_j_g_t_l_1_1_map_interface}{JGTL::Map\-Interface$<$ Key, Data $>$}
\begin{CompactList}\small\item\em This class acts as a base class for the Map construct. \item\end{CompactList}\end{CompactItemize}
\subsection*{Defines}
\begin{CompactItemize}
\item
\#define \hyperlink{_j_g_t_l___map_interface_8h_df99d6b59685be518d4e47848e9fbfee}{DEBUG\_\-MAP\_\-INTERFACE}~(0)
\end{CompactItemize}

\subsection{Define Documentation}
\hypertarget{_j_g_t_l___map_interface_8h_df99d6b59685be518d4e47848e9fbfee}{
\index{JGTL_MapInterface.h@{JGTL\_\-Map\-Interface.h}!DEBUG_MAP_INTERFACE@{DEBUG\_\-MAP\_\-INTERFACE}}
\index{DEBUG_MAP_INTERFACE@{DEBUG\_\-MAP\_\-INTERFACE}!JGTL_MapInterface.h@{JGTL\_\-Map\-Interface.h}}
\subsubsection[DEBUG\_\-MAP\_\-INTERFACE]{\setlength{\rightskip}{0pt plus 5cm}\#define DEBUG\_\-MAP\_\-INTERFACE~(0)}}
\label{_j_g_t_l___map_interface_8h_df99d6b59685be518d4e47848e9fbfee}


text:
\hypertarget{classmov__io_1_1_close_l_w_mov_parser}{}\doxysection{mov\+\_\+io\+::Close\+LWMov\+Parser Class Reference}
\label{classmov__io_1_1_close_l_w_mov_parser}\index{mov\_io::CloseLWMovParser@{mov\_io::CloseLWMovParser}}
Inheritance diagram for mov\+\_\+io\+::Close\+LWMov\+Parser\+:\begin{figure}[H]
\begin{center}
\leavevmode
\includegraphics[height=2.000000cm]{classmov__io_1_1_close_l_w_mov_parser}
\end{center}
\end{figure}
\doxysubsection*{Public Member Functions}
\begin{DoxyCompactItemize}
\item
QString \mbox{\hyperlink{classmov__io_1_1_close_l_w_mov_parser_a935484ac8b155c942b64a3b1bb43c4bf}{header}} () const override
\item
void \mbox{\hyperlink{classmov__io_1_1_close_l_w_mov_parser_afbf7e64856d24e13ed55eba51b48d67d}{operator()}} (\mbox{\hyperlink{classtipc_1_1_message}{Message}} \&stream) override
\end{DoxyCompactItemize}

\doxysubsection{Detailed Description}

\doxysubsection{Member Function Documentation}
\mbox{\Hypertarget{classmov__io_1_1_close_l_w_mov_parser_a935484ac8b155c942b64a3b1bb43c4bf}\label{classmov__io_1_1_close_l_w_mov_parser_a935484ac8b155c942b64a3b1bb43c4bf}}
\index{mov\_io::CloseLWMovParser@{mov\_io::CloseLWMovParser}!header@{header}}
\index{header@{header}!mov\_io::CloseLWMovParser@{mov\_io::CloseLWMovParser}}
\doxysubsubsection{\texorpdfstring{header()}{header()}}
{\footnotesize\ttfamily QString mov\+\_\+io\+::\+Close\+LWMov\+Parser\+::header (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}, {\ttfamily [override]}, {\ttfamily [virtual]}}

Implements \mbox{\hyperlink{classtipc_1_1_message_parser}{tipc\+::\+Message\+Parser}}.

\begin{DoxyCode}{0}
\DoxyCodeLine{00112 \{ \textcolor{keywordflow}{return} \textcolor{stringliteral}{"{}\$closeLWMov"{}}; \}}

\end{DoxyCode}
\mbox{\Hypertarget{classmov__io_1_1_close_l_w_mov_parser_afbf7e64856d24e13ed55eba51b48d67d}\label{classmov__io_1_1_close_l_w_mov_parser_afbf7e64856d24e13ed55eba51b48d67d}}
\index{mov\_io::CloseLWMovParser@{mov\_io::CloseLWMovParser}!operator()@{operator()}}
\index{operator()@{operator()}!mov\_io::CloseLWMovParser@{mov\_io::CloseLWMovParser}}
\doxysubsubsection{\texorpdfstring{operator()()}{operator()()}}
{\footnotesize\ttfamily void mov\+\_\+io\+::\+Close\+LWMov\+Parser\+::operator() (\begin{DoxyParamCaption}\item[{\mbox{\hyperlink{classtipc_1_1_message}{Message}} \&}]{stream }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [override]}, {\ttfamily [virtual]}}

Implements \mbox{\hyperlink{classtipc_1_1_message_parser}{tipc\+::\+Message\+Parser}}.

\begin{DoxyCode}{0}
\DoxyCodeLine{00288                                               \{}
\DoxyCodeLine{00289   \textcolor{keywordtype}{unsigned} \textcolor{keywordtype}{int} id;}
\DoxyCodeLine{00290   msg >> \textcolor{keywordtype}{id} >> clr;}
\DoxyCodeLine{00291 }
\DoxyCodeLine{00292   \textcolor{keywordflow}{try} \{}
\DoxyCodeLine{00293     writers.take(\textcolor{keywordtype}{id});}
\DoxyCodeLine{00294     msg << QString(\textcolor{stringliteral}{"{}ok"{}});}
\DoxyCodeLine{00295   \} \textcolor{keywordflow}{catch} (...) \{}
\DoxyCodeLine{00296     msg << QString(\textcolor{stringliteral}{"{}err"{}});}
\DoxyCodeLine{00297   \}}
\DoxyCodeLine{00298 \}}

\end{DoxyCode}

The documentation for this class was generated from the following files\+:\begin{DoxyCompactItemize}
\item
E\+:/opentoonz/toonz/sources/t32bitsrv/t32movmsg.\+h\item
E\+:/opentoonz/toonz/sources/t32bitsrv/t32movmsg.\+cpp\end{DoxyCompactItemize}


text:
% DA INCREMENTARE PER
\paragraph{MD001 - Indice di Gulpease}\mbox{}\\[0,3cm]
\begin{table}[H]
	\centering
	\begin{tabular}{cccc}
	\rowcolor{greySWEight}
	\textcolor{white}{\textbf{Documento}} &
	\textcolor{white}{\textbf{Abbreviazione}} &
	\textcolor{white}{\textbf{Valore Indice}}&
	\textcolor{white}{\textbf{Riscontro}}\\

	\textbf{Analisi dei Requisiti} & ADR & 60.38 & \textcolor{ForestGreen}{Ottimale} \\
	\textbf{Glossario} & GLO & 59.20 & \textcolor{ForestGreen}{Ottimale} \\
	\textbf{Piano di Qualifica} & PDQ & 55.70 & \textcolor{ForestGreen}{Ottimale} \\
	\textbf{Piano di Progetto} & PDP & 54,72 & \textcolor{YellowOrange}{Accettabile} \\
	\textbf{Norme di Progetto} & NDP & 56,96 & \textcolor{ForestGreen}{Ottimale} \\

	\end{tabular}
	\caption{Indice di Gulpease nel periodo di codifica}
\end{table}

\begin{figure}[H]
	\includegraphics[width=1\linewidth]{sez/App_Esito/Qualifica/graph/gulpeaseRQ.pdf}
	\caption{Andamento dell'indice di Gulpease fino al periodo di codifica}
\end{figure}
\newpage


text:
% logo (avec texte) : logocs (fichier beamerthemecslogo)
% exemple : \pgfuseimage{logocs}

\documentclass{beamer}
\usetheme[Cecile]{cs}
%
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{mathptmx}
\usepackage[scaled=0.9]{helvet}
\usepackage{manfnt}
\usepackage{pifont}
%\usepackage{courier}

\usepackage{graphicx}

\usepackage{xspace}
\usepackage[francais]{babel}

\hypersetup{pdfpagemode=FullScreen, pdffitwindow}

\title{Exemple d'utilisation de \textbf{beamercs}}
\author{Frédéric Boulanger}
\date{\today}
\institute[Supélec]{CentraleSupélec -- Département Informatique}

\begin{document}

\titlegraphic{\logocstext}

\frame{\titlepage}

\begin{frame}[fragile]
  \frametitle{Un style beamer pour CentraleSupélec}

  \begin{block}{Utilisation}
    \begin{verbatim}
\documentclass{beamer}
\usetheme{cs}
    \end{verbatim}
  \end{block}

  \begin{block}{Commandes}
	\begin{itemize}
	  \item \verb|\logocs[<scale>]| \\
	        pour afficher le logo de CentraleSupélec sans texte\\
			\centerline{\logocs}

	  \item \verb|\logocstext[<scale>]| \\
	        pour afficher le logo de CentraleSupélec avec texte\\
			\centerline{\logocstext}

      \item \verb|\timestamp| \\
            pour afficher la date de compilation du document \\
            \centerline{\timestamp}
	\end{itemize}
  \end{block}

\end{frame}

\end{document}


text:
\hypertarget{classstd_1_1tr1_1_1gtest__internal_1_1_get_3_012_01_4}{}\section{std\+::tr1\+::gtest\+\_\+internal\+::Get$<$ 2 $>$ Class Template Reference}
\label{classstd_1_1tr1_1_1gtest__internal_1_1_get_3_012_01_4}\index{std::tr1::gtest\_internal::Get$<$ 2 $>$@{std::tr1::gtest\_internal::Get$<$ 2 $>$}}

{\ttfamily \#include $<$gtest-\/tuple.\+h$>$}

\subsection*{Static Public Member Functions}
\begin{DoxyCompactItemize}
\item
{\footnotesize template$<$class Tuple $>$ }\\static \mbox{\hyperlink{classstd_1_1tr1_1_1gtest__internal_1_1_get_3_012_01_4_a8dfe7b5c1c915f10181e3fb5952ba6d8}{G\+T\+E\+S\+T\+\_\+\+A\+D\+D\+\_\+\+R\+E\+F\+\_\+}} (\mbox{\hyperlink{gtest-tuple_8h_a1b7f133d8aa02e0b7afed7b66781eeb7}{G\+T\+E\+S\+T\+\_\+\+T\+U\+P\+L\+E\+\_\+\+E\+L\+E\+M\+E\+N\+T\+\_\+}}(2, Tuple)) Field(Tuple \&t)
\item
{\footnotesize template$<$class Tuple $>$ }\\static \mbox{\hyperlink{classstd_1_1tr1_1_1gtest__internal_1_1_get_3_012_01_4_a76127c9c03c1f0caa61fb87d4d756b5b}{G\+T\+E\+S\+T\+\_\+\+B\+Y\+\_\+\+R\+E\+F\+\_\+}} (\mbox{\hyperlink{gtest-tuple_8h_a1b7f133d8aa02e0b7afed7b66781eeb7}{G\+T\+E\+S\+T\+\_\+\+T\+U\+P\+L\+E\+\_\+\+E\+L\+E\+M\+E\+N\+T\+\_\+}}(2, Tuple)) Const\+Field(const Tuple \&t)
\end{DoxyCompactItemize}

\subsection{Member Function Documentation}
\mbox{\Hypertarget{classstd_1_1tr1_1_1gtest__internal_1_1_get_3_012_01_4_a8dfe7b5c1c915f10181e3fb5952ba6d8}\label{classstd_1_1tr1_1_1gtest__internal_1_1_get_3_012_01_4_a8dfe7b5c1c915f10181e3fb5952ba6d8}}
\index{std::tr1::gtest\_internal::Get$<$ 2 $>$@{std::tr1::gtest\_internal::Get$<$ 2 $>$}!GTEST\_ADD\_REF\_@{GTEST\_ADD\_REF\_}}
\index{GTEST\_ADD\_REF\_@{GTEST\_ADD\_REF\_}!std::tr1::gtest\_internal::Get$<$ 2 $>$@{std::tr1::gtest\_internal::Get$<$ 2 $>$}}
\subsubsection{\texorpdfstring{GTEST\_ADD\_REF\_()}{GTEST\_ADD\_REF\_()}}
{\footnotesize\ttfamily template$<$class Tuple $>$ \\
static \mbox{\hyperlink{classstd_1_1tr1_1_1gtest__internal_1_1_get}{std\+::tr1\+::gtest\+\_\+internal\+::\+Get}}$<$ 2 $>$\+::G\+T\+E\+S\+T\+\_\+\+A\+D\+D\+\_\+\+R\+E\+F\+\_\+ (\begin{DoxyParamCaption}\item[{\mbox{\hyperlink{gtest-tuple_8h_a1b7f133d8aa02e0b7afed7b66781eeb7}{G\+T\+E\+S\+T\+\_\+\+T\+U\+P\+L\+E\+\_\+\+E\+L\+E\+M\+E\+N\+T\+\_\+}}(2, Tuple)}]{ }\end{DoxyParamCaption}) \&\hspace{0.3cm}{\ttfamily [inline]}, {\ttfamily [static]}}

\mbox{\Hypertarget{classstd_1_1tr1_1_1gtest__internal_1_1_get_3_012_01_4_a76127c9c03c1f0caa61fb87d4d756b5b}\label{classstd_1_1tr1_1_1gtest__internal_1_1_get_3_012_01_4_a76127c9c03c1f0caa61fb87d4d756b5b}}
\index{std::tr1::gtest\_internal::Get$<$ 2 $>$@{std::tr1::gtest\_internal::Get$<$ 2 $>$}!GTEST\_BY\_REF\_@{GTEST\_BY\_REF\_}}
\index{GTEST\_BY\_REF\_@{GTEST\_BY\_REF\_}!std::tr1::gtest\_internal::Get$<$ 2 $>$@{std::tr1::gtest\_internal::Get$<$ 2 $>$}}
\subsubsection{\texorpdfstring{GTEST\_BY\_REF\_()}{GTEST\_BY\_REF\_()}}
{\footnotesize\ttfamily template$<$class Tuple $>$ \\
static \mbox{\hyperlink{classstd_1_1tr1_1_1gtest__internal_1_1_get}{std\+::tr1\+::gtest\+\_\+internal\+::\+Get}}$<$ 2 $>$\+::G\+T\+E\+S\+T\+\_\+\+B\+Y\+\_\+\+R\+E\+F\+\_\+ (\begin{DoxyParamCaption}\item[{\mbox{\hyperlink{gtest-tuple_8h_a1b7f133d8aa02e0b7afed7b66781eeb7}{G\+T\+E\+S\+T\+\_\+\+T\+U\+P\+L\+E\+\_\+\+E\+L\+E\+M\+E\+N\+T\+\_\+}}(2, Tuple)}]{ }\end{DoxyParamCaption}) const \&\hspace{0.3cm}{\ttfamily [inline]}, {\ttfamily [static]}}

The documentation for this class was generated from the following file\+:\begin{DoxyCompactItemize}
\item
packages/\+Microsoft.\+googletest.\+v140.\+windesktop.\+msvcstl.\+static.\+rt-\/dyn.\+1.\+8.\+0/build/native/include/gtest/internal/\mbox{\hyperlink{gtest-tuple_8h}{gtest-\/tuple.\+h}}\end{DoxyCompactItemize}


text:
\documentclass{standalone}

%----------------------------------------------------------------------------------------------%
%                                 Packages and basic declarations
%----------------------------------------------------------------------------------------------%

\usepackage[utf8]{inputenc}
\usepackage{pgfplots}
\usepackage{tikz}

%----------------------------------------------------------------------------------------------%
%----------------------------------------------------------------------------------------------%
%                                            DOCUMENT STARTS
%----------------------------------------------------------------------------------------------%
%----------------------------------------------------------------------------------------------%

\begin{document}

%Tikz picture starts%

\begin{tikzpicture}

%Tikz axis starts%

\begin{axis}[width=30cm,
title={Normalized total energy release rate $\frac{G_{TOT}}{G_{0}}$ as function of crack angular semi-aperture  $\Delta\theta$, calculated with Abaqus built-in J-Integral post-processing routine (*CONTOUR INTEGRAL)},
title style={font=\fontsize{16}{8}\selectfont},
xlabel style={at={(axis description cs:0.5,-0.02)},anchor=north,font=\fontsize{16}{8}\selectfont},
ylabel style={at={(axis description cs:-0.01,.5)},anchor=south,font=\fontsize{16}{8}\selectfont},
xlabel={$\Delta\theta\left[^{\circ}\right]$},ylabel={$\frac{G_{TOT}}{G_{0}}\left[-\right]$},
xmin=0.0,
xmax=180.0,
ymin=0.0,
ymax=0.716675920144,
tick align=outside,
tick label style={font=\normalsize},
xtick={0.0,10.0,20.0,30.0,40.0,50.0,60.0,70.0,80.0,90.0,100.0,110.0,120.0,130.0,140.0,150.0,160.0,170.0,180.0},
xmajorgrids,
x grid style={lightgray!92.026143790849673!black},
ymajorgrids,
y grid style={lightgray!92.026143790849673!black},
line width=0.35mm,
legend style={draw=white!80.0!black,font=\fontsize{6}{6}\selectfont},
legend entries={{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 1},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 2},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 3},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 4},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 5},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 6},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 7},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 8},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 9},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 10},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 11},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 12},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 13},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 14},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 15},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 16},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 17},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 18},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 19},{$\frac{G_{TOT}}{G_{0}}$, FEM, Contour 20},{$\frac{G_{TOT}}{G_{0}}$, BEM}},
legend cell align={left}
]

\addplot[red!0.0!blue,smooth,mark=*]
table{
10.1165133448 0.174522655812
19.8836864193 0.345618132196
29.6513572437 0.494351475266
40.1161769391 0.608582167498
49.8838221503 0.660647023568
60.3486418456 0.656954836773
70.1163109626 0.613222949771
79.8834883059 0.553894763999
89.651164253 0.453902293575
100.116516703 0.320344841503
109.883687216 0.197546925281
119.651363163 0.0988133779648
130.116182859 0.0322838768885
139.883817825 0.00513765829388
149.651466451 0.000263955864549
};

\addplot[red!5.26315789474!blue,smooth,mark=*]
table{
10.1165133448 0.178494287366
19.8836864193 0.340347933053
29.6513572437 0.478234639468
40.1161769391 0.590478242094
49.8838221503 0.655375903699
60.3486418456 0.679721733082
70.1163109626 0.661892650618
79.8834883059 0.601345260404
89.651164253 0.49409633506
100.116516703 0.350071497835
109.883687216 0.216346361884
119.651363163 0.10828968026
130.116182859 0.035343065393
139.883817825 0.00556508957652
149.651466451 0.000362968927496
};

\addplot[red!10.5263157895!blue,smooth,mark=*]
table{
10.1165133448 0.180556480673
19.8836864193 0.34378501945
29.6513572437 0.482435710411
40.1161769391 0.594526799252
49.8838221503 0.658889983612
60.3486418456 0.682548495375
70.1163109626 0.665178046437
79.8834883059 0.606923177051
89.651164253 0.499751010097
100.116516703 0.354733004355
109.883687216 0.219632442266
119.651363163 0.110047381492
130.116182859 0.0359758428304
139.883817825 0.00566680798117
149.651466451 0.000361463403152
};

\addplot[red!15.7894736842!blue,smooth,mark=*]
table{
10.1165133448 0.180403725614
19.8836864193 0.343173981869
29.6513572437 0.480984431358
40.1161769391 0.592235163125
49.8838221503 0.655987048032
60.3486418456 0.67956893512
70.1163109626 0.662580291604
79.8834883059 0.607152406502
89.651164253 0.501126471593
100.116516703 0.356414203428
109.883687216 0.221008010798
119.651363163 0.111040864797
130.116182859 0.0363678897209
139.883817825 0.00575087277839
149.651466451 0.000352651882499
};

\addplot[red!21.0526315789!blue,smooth,mark=*]
table{
10.1165133448 0.180174593024
19.8836864193 0.342486564589
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733824.5	-8.986861\\


text:
\hypertarget{scene_8cpp}{}\doxysection{src/server/tests/scene/scene.cpp File Reference}
\label{scene_8cpp}\index{src/server/tests/scene/scene.cpp@{src/server/tests/scene/scene.cpp}}
{\ttfamily \#include \char`\"{}catch2/catch.\+hpp\char`\"{}}\newline
{\ttfamily \#include \char`\"{}scene/scene\+\_\+factory.\+h\char`\"{}}\newline
{\ttfamily \#include \char`\"{}shared/apis/datetime/datetime\+\_\+manager.\+h\char`\"{}}\newline
{\ttfamily \#include \char`\"{}shared/apis/logging/log\+\_\+manager.\+h\char`\"{}}\newline
{\ttfamily \#include \char`\"{}shared/scene/scenes/loading\+\_\+scene.\+h\char`\"{}}\newline
{\ttfamily \#include \char`\"{}shared/scene/scenes/world\+\_\+generation\+\_\+scene.\+h\char`\"{}}\newline
{\ttfamily \#include $<$vector$>$}\newline
\doxysubsection*{Functions}
\begin{DoxyCompactItemize}
\item
\mbox{\hyperlink{classpbr_1_1server_1_1scene_1_1scene__factory}{scene\+::scene\+\_\+factory}} \mbox{\hyperlink{scene_8cpp_abd4f170f6f0f275abef764f8ad7eb666}{create\+\_\+scene\+\_\+factory}} ()
\item
\mbox{\hyperlink{scene_8cpp_a2ea8828ea8be7123026db5173ebbc102}{T\+E\+S\+T\+\_\+\+C\+A\+SE}} (\char`\"{}create\+\_\+scene -\/ invalid type -\/ returns nullptr\char`\"{}, \char`\"{}\mbox{[}server/scene\mbox{]}\char`\"{})
\begin{DoxyCompactList}\small\item\em create\+\_\+scene \end{DoxyCompactList}\item
\mbox{\hyperlink{scene_8cpp_a48faaf9d06a4afbed1f571ba7b0889e9}{T\+E\+S\+T\+\_\+\+C\+A\+SE}} (\char`\"{}create\+\_\+scene -\/ loading scene type -\/ returns loading scene type\char`\"{}, \char`\"{}\mbox{[}server/scene\mbox{]}\char`\"{})
\item
\mbox{\hyperlink{scene_8cpp_a9e9dfaaa6c6570579fe08ea83e4bb5b4}{T\+E\+S\+T\+\_\+\+C\+A\+SE}} (\char`\"{}create\+\_\+scene -\/ world generation scene type -\/ returns world generation scene type\char`\"{}, \char`\"{}\mbox{[}server/scene\mbox{]}\char`\"{})
\end{DoxyCompactItemize}

\doxysubsection{Function Documentation}
\mbox{\Hypertarget{scene_8cpp_abd4f170f6f0f275abef764f8ad7eb666}\label{scene_8cpp_abd4f170f6f0f275abef764f8ad7eb666}}
\index{scene.cpp@{scene.cpp}!create\_scene\_factory@{create\_scene\_factory}}
\index{create\_scene\_factory@{create\_scene\_factory}!scene.cpp@{scene.cpp}}
\doxysubsubsection{\texorpdfstring{create\_scene\_factory()}{create\_scene\_factory()}}
{\footnotesize\ttfamily \mbox{\hyperlink{classpbr_1_1server_1_1scene_1_1scene__factory}{scene\+::scene\+\_\+factory}} create\+\_\+scene\+\_\+factory (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})}

Definition at line 13 of file scene.\+cpp.

\mbox{\Hypertarget{scene_8cpp_a2ea8828ea8be7123026db5173ebbc102}\label{scene_8cpp_a2ea8828ea8be7123026db5173ebbc102}}
\index{scene.cpp@{scene.cpp}!TEST\_CASE@{TEST\_CASE}}
\index{TEST\_CASE@{TEST\_CASE}!scene.cpp@{scene.cpp}}
\doxysubsubsection{\texorpdfstring{TEST\_CASE()}{TEST\_CASE()}\hspace{0.1cm}{\footnotesize\ttfamily [1/3]}}
{\footnotesize\ttfamily T\+E\+S\+T\+\_\+\+C\+A\+SE (\begin{DoxyParamCaption}\item[{\char`\"{}create\+\_\+scene -\/ invalid type -\/ returns nullptr\char`\"{}}]{,  }\item[{\char`\"{}\char`\"{}}]{\mbox{[}server/scene\mbox{]} }\end{DoxyParamCaption})}

create\+\_\+scene

Definition at line 26 of file scene.\+cpp.

\mbox{\Hypertarget{scene_8cpp_a48faaf9d06a4afbed1f571ba7b0889e9}\label{scene_8cpp_a48faaf9d06a4afbed1f571ba7b0889e9}}
\index{scene.cpp@{scene.cpp}!TEST\_CASE@{TEST\_CASE}}
\index{TEST\_CASE@{TEST\_CASE}!scene.cpp@{scene.cpp}}
\doxysubsubsection{\texorpdfstring{TEST\_CASE()}{TEST\_CASE()}\hspace{0.1cm}{\footnotesize\ttfamily [2/3]}}
{\footnotesize\ttfamily T\+E\+S\+T\+\_\+\+C\+A\+SE (\begin{DoxyParamCaption}\item[{\char`\"{}create\+\_\+scene -\/ loading scene type -\/ returns loading scene type\char`\"{}}]{,  }\item[{\char`\"{}\char`\"{}}]{\mbox{[}server/scene\mbox{]} }\end{DoxyParamCaption})}

Definition at line 35 of file scene.\+cpp.

\mbox{\Hypertarget{scene_8cpp_a9e9dfaaa6c6570579fe08ea83e4bb5b4}\label{scene_8cpp_a9e9dfaaa6c6570579fe08ea83e4bb5b4}}
\index{scene.cpp@{scene.cpp}!TEST\_CASE@{TEST\_CASE}}
\index{TEST\_CASE@{TEST\_CASE}!scene.cpp@{scene.cpp}}
\doxysubsubsection{\texorpdfstring{TEST\_CASE()}{TEST\_CASE()}\hspace{0.1cm}{\footnotesize\ttfamily [3/3]}}
{\footnotesize\ttfamily T\+E\+S\+T\+\_\+\+C\+A\+SE (\begin{DoxyParamCaption}\item[{\char`\"{}create\+\_\+scene -\/ world generation scene type -\/ returns world generation scene type\char`\"{}}]{,  }\item[{\char`\"{}\char`\"{}}]{\mbox{[}server/scene\mbox{]} }\end{DoxyParamCaption})}

Definition at line 45 of file scene.\+cpp.


text:
\documentclass{article}
\usepackage[a4paper,margin= 2cm]{geometry}
\usepackage{graphicx}

\title{\LARGE{\bf{Task 1 Overview}}}
\author{\Large{\bf{Kirtan Patel - AE19B038}}}
\date{}

\begin{document}

\maketitle

\section{The Amplitude Magnification Frequency Response Graph}
This Graph shows the relation between the Amplitude Magnification Function and the Frequency of the Sytem. The Frequency $\omega$ is given as a ratio over the natural frequency of the system $\omega_{n}$.
\[x(t) = \delta_{static}~|G(i\omega)|~e^{i(\omega t - \phi)}\]
where
\[|G(i \omega)|^2 = \frac{1}{(1 - r^2)^2 + (2 \zeta r)^2}\]
\begin{figure}
\centering
\includegraphics[scale = 0.56]{Amplitude Frequency_Response.png}
\caption{Frequency Response of Amplitude Magnification}
\label{fig1.}
\end{figure}

This Graph helps us analyse the nature of vibrations experienced by the system under study. Studying the graph, we can observe that:
\begin{enumerate}
	\item For an undamped system($\zeta$=0),and G$\rightarrow$ $\infty$ as r $\rightarrow$ 1
	\item Any amount of damping($\zeta$$>$0)reduces the magnification factor (G) for all values of the forcing frequency.
	\item In the degenerate case of a constant force (when r=0), the value of $|G|$
	\item The reduction in $|G|$ in the presence of damping is very significant at or near resonance.
\end{enumerate}

In System Design, we use this data to design the structure such that the frequency of vibrations handled by the structure are not near the natural frequency of the structure and hence limit the Magnification of the Transferred Vibrations.\\

The graph even helps us predict the values of Magnification Factor for intermediate Frequency Ratios by interpolation. Hence, this graph is widely used in the study and design of systems which are subjected to vibrations
\pagebreak

\section{Sinusoidal Multivariable Function Plot}
This Graph shows the sinusoidal relation expressed as
\[z(x,y) = \frac{sin(5x).cos(5y)}{5}\]

This Graph helps us analyse the nature of multivariable functions.It contains multiple Saddle Points and can be used in visualizing the concept.\\

\begin{figure} [!ht] %to keep the image where we place it.
\centering
\includegraphics[scale=0.3]{Octave_3D Plot.png}
\caption{Sinusoidal Multivariable Function Plot}
\label{fig2.}
\end{figure}

\subsection{Saddle Point}
Given the function z=f(x,y), the point $(x_{0},y_{0},f(x_{0},y_{0}))$ is a saddle point if both $f_{x}(x_{0},y_{0})=0$ and $f_{y}(x_{0},y_{0})=0$, but f does not have a local extremum at $(x_{0},y_{0})$.\\

While we have to be careful to not misinterpret the results of this fact it is very useful in helping us to identify relative extrema. Because of this fact we know that if we have all the critical points of a function then we also have every possible relative extrema for the function. The fact tells us that all relative extrema must be critical points so we know that if the function does have relative extrema then they must be in the collection of all the critical points. Remember however, that it will be completely possible that at least one of the critical points won’t be a relative extrema.\\

In machine learning for example, local/global minimums/maximums are important as the indicate the validity and accuracy of the function.
\end{document}


text:
\section{Lista plików}
Tutaj znajduje się lista wszystkich plików z ich krótkimi opisami\-:\begin{DoxyCompactList}
\item\contentsline{section}{src/\hyperlink{_animation_8cpp}{Animation.\-cpp} }{\pageref{_animation_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_animation_8h}{Animation.\-h} }{\pageref{_animation_8h}}{}
\item\contentsline{section}{src/\hyperlink{_animation_timer_thread_8cpp}{Animation\-Timer\-Thread.\-cpp} }{\pageref{_animation_timer_thread_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_animation_timer_thread_8h}{Animation\-Timer\-Thread.\-h} }{\pageref{_animation_timer_thread_8h}}{}
\item\contentsline{section}{src/\hyperlink{_animation_waiting_thread_8cpp}{Animation\-Waiting\-Thread.\-cpp} }{\pageref{_animation_waiting_thread_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_animation_waiting_thread_8h}{Animation\-Waiting\-Thread.\-h} }{\pageref{_animation_waiting_thread_8h}}{}
\item\contentsline{section}{src/\hyperlink{_camera_8cpp}{Camera.\-cpp} }{\pageref{_camera_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_camera_8h}{Camera.\-h} }{\pageref{_camera_8h}}{}
\item\contentsline{section}{src/\hyperlink{_camera_controller_8cpp}{Camera\-Controller.\-cpp} }{\pageref{_camera_controller_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_camera_controller_8h}{Camera\-Controller.\-h} }{\pageref{_camera_controller_8h}}{}
\item\contentsline{section}{src/\hyperlink{_constants_8h}{Constants.\-h} }{\pageref{_constants_8h}}{}
\item\contentsline{section}{src/\hyperlink{_cross_8cpp}{Cross.\-cpp} }{\pageref{_cross_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_cross_8h}{Cross.\-h} }{\pageref{_cross_8h}}{}
\item\contentsline{section}{src/\hyperlink{_cross_rules_8cpp}{Cross\-Rules.\-cpp} }{\pageref{_cross_rules_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_cross_rules_8h}{Cross\-Rules.\-h} }{\pageref{_cross_rules_8h}}{}
\item\contentsline{section}{src/\hyperlink{_direction_8h}{Direction.\-h} }{\pageref{_direction_8h}}{}
\item\contentsline{section}{src/\hyperlink{_drawable_8h}{Drawable.\-h} }{\pageref{_drawable_8h}}{}
\item\contentsline{section}{src/\hyperlink{_exceptions_8h}{Exceptions.\-h} }{\pageref{_exceptions_8h}}{}
\item\contentsline{section}{src/\hyperlink{main_8cpp}{main.\-cpp} }{\pageref{main_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_main_window_8cpp}{Main\-Window.\-cpp} }{\pageref{_main_window_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_main_window_8h}{Main\-Window.\-h} }{\pageref{_main_window_8h}}{}
\item\contentsline{section}{src/\hyperlink{_map_element_8h}{Map\-Element.\-h} }{\pageref{_map_element_8h}}{}
\item\contentsline{section}{src/\hyperlink{_map_factory_8cpp}{Map\-Factory.\-cpp} }{\pageref{_map_factory_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_map_factory_8h}{Map\-Factory.\-h} }{\pageref{_map_factory_8h}}{}
\item\contentsline{section}{src/\hyperlink{_moveable_8h}{Moveable.\-h} }{\pageref{_moveable_8h}}{}
\item\contentsline{section}{src/\hyperlink{_pedestrian_8cpp}{Pedestrian.\-cpp} }{\pageref{_pedestrian_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_pedestrian_8h}{Pedestrian.\-h} }{\pageref{_pedestrian_8h}}{}
\item\contentsline{section}{src/\hyperlink{_position_8h}{Position.\-h} }{\pageref{_position_8h}}{}
\item\contentsline{section}{src/\hyperlink{_priority_rules_8h}{Priority\-Rules.\-h} }{\pageref{_priority_rules_8h}}{}
\item\contentsline{section}{src/\hyperlink{_road_8cpp}{Road.\-cpp} }{\pageref{_road_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_road_8h}{Road.\-h} }{\pageref{_road_8h}}{}
\item\contentsline{section}{src/\hyperlink{_scene_8cpp}{Scene.\-cpp} }{\pageref{_scene_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_scene_8h}{Scene.\-h} }{\pageref{_scene_8h}}{}
\item\contentsline{section}{src/\hyperlink{_shortest_path_8cpp}{Shortest\-Path.\-cpp} }{\pageref{_shortest_path_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_shortest_path_8h}{Shortest\-Path.\-h} }{\pageref{_shortest_path_8h}}{}
\item\contentsline{section}{src/\hyperlink{_simulator_8cpp}{Simulator.\-cpp} }{\pageref{_simulator_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_simulator_8h}{Simulator.\-h} }{\pageref{_simulator_8h}}{}
\item\contentsline{section}{src/\hyperlink{_spawn_8cpp}{Spawn.\-cpp} }{\pageref{_spawn_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_spawn_8h}{Spawn.\-h} }{\pageref{_spawn_8h}}{}
\item\contentsline{section}{src/\hyperlink{_spawning_pedestrians_runnable_8cpp}{Spawning\-Pedestrians\-Runnable.\-cpp} }{\pageref{_spawning_pedestrians_runnable_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_spawning_pedestrians_runnable_8h}{Spawning\-Pedestrians\-Runnable.\-h} }{\pageref{_spawning_pedestrians_runnable_8h}}{}
\item\contentsline{section}{src/\hyperlink{_spawning_vehicles_runnable_8cpp}{Spawning\-Vehicles\-Runnable.\-cpp} }{\pageref{_spawning_vehicles_runnable_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_spawning_vehicles_runnable_8h}{Spawning\-Vehicles\-Runnable.\-h} }{\pageref{_spawning_vehicles_runnable_8h}}{}
\item\contentsline{section}{src/\hyperlink{test_8cpp}{test.\-cpp} }{\pageref{test_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_types_8h}{Types.\-h} }{\pageref{_types_8h}}{}
\item\contentsline{section}{src/\hyperlink{_vehicle_8cpp}{Vehicle.\-cpp} }{\pageref{_vehicle_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_vehicle_8h}{Vehicle.\-h} }{\pageref{_vehicle_8h}}{}
\item\contentsline{section}{src/\hyperlink{_vehicle_creator_8cpp}{Vehicle\-Creator.\-cpp} }{\pageref{_vehicle_creator_8cpp}}{}
\item\contentsline{section}{src/\hyperlink{_vehicle_creator_8h}{Vehicle\-Creator.\-h} }{\pageref{_vehicle_creator_8h}}{}
\item\contentsline{section}{src/\hyperlink{_vehicle_state_8h}{Vehicle\-State.\-h} }{\pageref{_vehicle_state_8h}}{}
\end{DoxyCompactList}


text:
\documentclass[convert=pdf2svg,multi=false]{standalone}
\usepackage{tikz}
  \usetikzlibrary{positioning}
\begin{document}
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text:
\begin{titlepage}
    \centering
    \includegraphics[width=0.25\textwidth]{\bannerLogo}\par\vspace{0.5cm}
    {\scshape\LARGE \textbf{Reporte técnico}}\par\vspace{0.3cm}
    {\Huge \bfseries \textcolor{greenBanner}{\productToTestName}}\par\vspace{1cm}
    \vfill
    \vfill
    \includegraphics[width=\textwidth,height=10cm,keepaspectratio]{\actualMachine}\par\vspace{1cm}
    \vfill
    \begin{tcolorbox}[colback=red!5!white,colframe=red!75!black]
        \centering
        Este documento contiene información confidencial y de propiedad exclusiva.\\
        Este documento no debe imprimirse ni compartirse.
    \end{tcolorbox}
    \vfill
    {\large \startDate}\par
    \vfill
    \clearpage
\end{titlepage}


text:
\hypertarget{group___n_i_s_t_const-_thomson}{}\section{Thomson cross section}
\label{group___n_i_s_t_const-_thomson}\index{Thomson cross section@{Thomson cross section}}
\subsection*{Variables}
\begin{DoxyCompactItemize}
\item
\mbox{\hyperlink{group___n_i_s_t_const-_macros_ga2b0fc1d7452373f816175dd86ce26729}{N\+I\+S\+T\+C\+O\+N\+S\+T\+\_\+\+C\+O\+N\+S\+T\+A\+NT}} \mbox{\hyperlink{group___n_i_s_t_const-_thomson_gab8adbacb38cef2b9b883e8bbe6a4b524}{N\+I\+S\+T\+Const\+::\+Thomson\+Cross\+Section}} = 0.\+66524587158e-\/28
\end{DoxyCompactItemize}

\subsection{Detailed Description}

\subsection{Variable Documentation}
\mbox{\Hypertarget{group___n_i_s_t_const-_thomson_gab8adbacb38cef2b9b883e8bbe6a4b524}\label{group___n_i_s_t_const-_thomson_gab8adbacb38cef2b9b883e8bbe6a4b524}}
\index{Thomson cross section@{Thomson cross section}!Thomson\+Cross\+Section@{Thomson\+Cross\+Section}}
\index{Thomson\+Cross\+Section@{Thomson\+Cross\+Section}!Thomson cross section@{Thomson cross section}}
\subsubsection{\texorpdfstring{Thomson\+Cross\+Section}{ThomsonCrossSection}}
{\footnotesize\ttfamily \mbox{\hyperlink{group___n_i_s_t_const-_macros_ga2b0fc1d7452373f816175dd86ce26729}{N\+I\+S\+T\+C\+O\+N\+S\+T\+\_\+\+C\+O\+N\+S\+T\+A\+NT}} N\+I\+S\+T\+Const\+::\+Thomson\+Cross\+Section = 0.\+66524587158e-\/28}

$\sigma_e \ (m^2)$ Thomson cross section in meters squared.


text:
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\lfoot{Verbale 2019-02-13}
\cfoot{}
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We have already seen the logical and binary operator $\land$ and the unary logical negation operator $\shortsim$.

\subsection{The logical or ($\lor$) operator}
The next operator we will introduce is the logical or operator $\lor$. The motivation for considering this operator is as follows. In colloquial language, a statement of the form ``$A$ or $B$'' is usually taken to mean ``either $A$ or $B$ is true.'' However, this excludes the scenario where $A$ and $B$ are both true. Taking this to account, the truth table for $\lor$ is the following:

\begin{table}[h]
\centering
\begin{tabular}{|l|l|l|}
\hline
$p$ & $q$ & $p \lor q$ \\ \hline
$T$ & $T$ & $T$ \\ \hline
$T$ & $F$ & $T$ \\ \hline
$F$ & $T$ & $T$ \\ \hline
$F$ & $F$ & $F$ \\ \hline
\end{tabular}
\end{table}

\subsection{The NAND and NOR operators}
The NAND and NOR operators, $\uparrow$ and $\downarrow$ respectively can be defined in terms of previously defined operators. The NAND operator $\uparrow$ is defined as
\[p \uparrow q \equiv \shortsim(p \land q)\]
and the NOR operator $\downarrow$ is defined as
\[p \downarrow q \equiv \shortsim(p \lor q).\]

In other words, NAND and NOR are simply the logical negations of the results of the logical and and logical or, respectively. The reader should create truth tables for these operators if they want more practice in creating truth tables.

\subsection{The XOR and XNOR operator}
As we have stated before, the or operator does not reflect colloquial language of the term, which more precisely reflects the term ``either-or''. This operator is true whenever exactly one of its arguments is true, and false otherwise. It is denoted by $\oplus$. The truth table for this operator is written below:

\begin{table}[h]
\centering
\begin{tabular}{|l|l|l|}
\hline
$p$ & $q$ & $p \lor q$ \\ \hline
$T$ & $T$ & $F$ \\ \hline
$T$ & $F$ & $T$ \\ \hline
$F$ & $T$ & $T$ \\ \hline
$F$ & $F$ & $F$ \\ \hline
\end{tabular}
\end{table}

The XNOR operator $\odot$ is defined to be the negation of the XOR operator. Later (In chapter 4) we will see that this operator plays an important role in defining what are called biconditional statements.

\subsection{The implies ($\implies$) operator}

The truth table of the implies operator $\implies$ is defined below.

\begin{table}[h]
\centering
\begin{tabular}{|l|l|l|}
\hline
$p$ & $q$ & $p \implies q$ \\ \hline
$T$ & $T$ & $T$ \\ \hline
$T$ & $F$ & $T$ \\ \hline
$F$ & $T$ & $F$ \\ \hline
$F$ & $F$ & $T$ \\ \hline
\end{tabular}
\end{table}

The motivation of this operator is to tabulate situations that can happen given that any given implication statement is true. Suppose that the following statement is true no matter what

\begin{center}
If it is raining outside, then Bob will carry an umbrella.
\end{center}

Then consider the statements ``it is raining outside'' and ``Bob is carrying an umbrella''. Consider the following scenarios.

\begin{itemize}
	\item It is possible for it to be both raining outside and for Bob to be carrying an umbrella at the same time, for the statement above is always true. So both statements being true is possible.
	\item It is possible for it to be not raining outside and yet for Bob to be carrying an umbrella. For what if Bob carried an umbrella all the time? The statement above does not discount that possibility. So for the first statement to be true and the second to be false is possible.
	\item It is not possible for it to be raining outside and Bob to not be carrying an umbrella, as the statement given forbids this possibility.
	\item It is possible for it to be not raining outside and for Bob to be not carrying an umbrella. For the statement does not say anything about Bob when it is not raining outside.
\end{itemize}

For every case where the two statements are possible we let the implication operator record true, and for the one case where the two statements are not possible we let the implication operator record false.


text:
\section{Yuyan}

Please present main results on manifold ...

\subsection{Manifold Learning}
Suppose there a dataset $\mathbf X =(\mathbf x_1,...,\mathbf x_n)$ and each $\mathbf x_i\in \mathbb R^d$. In many  practical problem, the $\mathbf x_i$ locates on a low dimension manifold $\mathcal M$ in $\mathbb R^d$. The goal of Manifold Learning is to find the parameter coordinate of $\mathcal M$, so we can present the points $\mathbf x_1,...,\mathbf x_n$ in a essential form.
\subsubsection{Isomap}
The main idea of isomap is to keep the geodesic distance of $\mathcal M$ during dimensionality reduction.

The Figure \ref{fig:isomapmnist} is the effect of Isomap for MNist, it shows different digit in the MNist dataset is separable.
%\begin{figure}
	%\centering
	%\includegraphics[width=0.7\linewidth]{../figures/IsomapMnist}
	%\caption{The effect of Isomap for MNist}
	%\label{fig:isomapmnist}
%\end{figure}


text:
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\label{struct_reflection_1_1_function_wrapper_base_1_1_make_indexes_3_010_00_01_indexes_8_8_8_01_4}\index{Reflection\+::\+Function\+Wrapper\+Base\+::\+Make\+Indexes$<$ 0, Indexes... $>$@{Reflection\+::\+Function\+Wrapper\+Base\+::\+Make\+Indexes$<$ 0, Indexes... $>$}}
\subsection*{公開型}
\begin{DoxyCompactItemize}
\item
typedef \hyperlink{struct_reflection_1_1_function_wrapper_base_1_1_args_indexes}{Args\+Indexes}$<$ Indexes... $>$ {\bfseries Type}\hypertarget{struct_reflection_1_1_function_wrapper_base_1_1_make_indexes_3_010_00_01_indexes_8_8_8_01_4_ac7d811c386c8a4606539aa9bbd2afbed}{}\label{struct_reflection_1_1_function_wrapper_base_1_1_make_indexes_3_010_00_01_indexes_8_8_8_01_4_ac7d811c386c8a4606539aa9bbd2afbed}

\end{DoxyCompactItemize}

この構造体詳解は次のファイルから抽出されました\+:\begin{DoxyCompactItemize}
\item
C\+:/\+Users/\+Owner/\+Documents/\+Visual Studio 2013/\+Projects/\+Q\+G\+J2015\+Spring/\hyperlink{_reflector_helper_8hpp}{Reflector\+Helper.\+hpp}\end{DoxyCompactItemize}