\documentclass{beamer}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[main=polish,]{babel}  
\usepackage{ragged2e}
\usepackage{booktabs}
\usepackage{tabularx}
\usepackage{tikz}
\usetikzlibrary{calc, shapes, backgrounds}
\usepackage{amsmath, amssymb}
\usepackage{url}
\usepackage{listings}
\usepackage{dsfont}
\usepackage{algorithm, algpseudocode}
\usepackage{changepage}
\usetheme{zut}
\title{Algorytm rzutowania obrazu boiska piłkarskiego uzyskanego z ruchomej kamery na płaszczyznę niewymagający wstępnej kalibracji}
\date[\today]{\today}
\author[Działowski]{Karol Działowski}
\city{Szczecin}
\institute[ZUT]{West Pomeranian University of Technology, Szczecin Poland}
\supervisor{dr.~hab.~inż.~Pawła~Forczmańskiego,~prof.~ZUT}
\goal{stworzenie algorytmu rzutowania trójwymiarowej sceny przedstawiającej boisko piłkarskie na płaszczyznę. Obraz boiska pozyskany jest za pomocą ruchomej kamery o sześciu stopniach swobody (zmiana pozycji XYZ, zmiany odpowiednich kątów patrzenia)}
%\usepackage[texcoord, grid,gridcolor=red!10,subgridcolor=green!10,gridunit=cm]{eso-pic}
\begin{document}
\begin{frame}
\addtocounter{framenumber}{1}
\titlepage
\end{frame}
\section{Blind Text}
\begin{frame}{Jabberwocky}
    \framesubtitle{Lewis Carroll}%
    \begin{tikzpicture}[overlay,remember picture]
    \node[anchor=south east,xshift=-10pt,yshift=55pt]
        at (current page.south east) {
        \includegraphics[width=30mm]{resources/jabberwocky-light}
        };
    \end{tikzpicture}%
    'Twas brillig, and the slithy toves\\
    Did gyre and gimble in the wabe;\\
    All mimsy were the borogoves,\\
    And the mome raths outgrabe.\\\bigskip
    “Beware the Jabberwock, my son!\\
    The jaws that bite, the claws that\\
    Beware the Jubjub bird, and shun\\
    The frumious Bandersnatch!”\\
\end{frame}
\begin{frame}[label=lists]{Lists and locales}
    \framesubtitle{Lorem ipsum dolor sit amet}
    \begin{columns}[onlytextwidth, T]
    \column{.5\textwidth}
        \begin{itemize}
        \item Nulla nec lacinia odio. Curabitur urna tellus.
        \begin{itemize}
            \item Fusce id sodales dolor. Sed id metus dui.
            \begin{itemize}
            \item Cupio virtus licet mi vel feugiat.
            \end{itemize}
        \end{itemize}
        \item Nulla nec lacinia odio. Curabitur urna tellus.
        \item Nulla nec lacinia odio. Curabitur urna tellus.
        \end{itemize}
    \column{.5\textwidth}
        \begin{enumerate}
        \item Donec porta, risus porttitor egestas scelerisque video.
        \item Donec porta, risus porttitor egestas scelerisque video.
        \end{enumerate}
    \end{columns}
    \bigskip
    \justifying
    {\uselanguage{polish}Tutaj jakiś fajny tekst po polsku, żeby nie było, że
    nie da się pisać po polsku z polskimi znakami.}
    {\uselanguage{english}The quick, brown fox jumps over a lazy
    dog.}
\end{frame}
\section{Structuring Elements}
\begin{frame}[label=simmonshall]{Text blocks}
    \framesubtitle{In plain, example, and \alert{alert} flavour}
    \alert{This text} is highlighted.
    \begin{block}{A plain block}
    This is a plain block containing some \alert{highlighted text}.
    \end{block}
    \begin{exampleblock}{An example block}
    This is an example block containing some \alert{highlighted text}.
    \end{exampleblock}
    \begin{alertblock}{An alert block}
    This is an alert block containing some \alert{highlighted text}.
    \end{alertblock}
\end{frame}
\begin{frame}[label=proof]{Definitions, theorems, and proofs}
    \framesubtitle{All integers divide zero}
    \begin{definition}
    $\forall a,b\in\mathds{Z}: a\mid b\iff\exists c\in\mathds{Z}:a\cdot c=b$
    \end{definition}
    \begin{theorem}
    $\forall a\in\mathds{Z}: a\mid 0$
    \end{theorem}
    \begin{proof}
    $\forall a\in\mathds{Z}: a\cdot 0=0$
    \end{proof}
\end{frame}
\section{Numerals and Mathematics}
\begin{frame}[label=math]{Numerals and Mathematics}
    \framesubtitle{Formulae, equations, and expressions}
    \begin{columns}[onlytextwidth]
    \column{.20\textwidth}
        1234567
    \column{.20\textwidth}
        \oldstylenums{1234567}
    \column{.20\textwidth}
        $\hat{x}$, $\check{x}$, $\tilde{a}$,
        $\bar{a}$, $\dot{y}$, $\ddot{y}$
    \column{.40\textwidth}
        $\int \!\! \int f(x,y,z)\,\mathsf{d}x\mathsf{d}y\mathsf{d}z$
    \end{columns}
    \begin{columns}[onlytextwidth]
    \column{.5\textwidth}
        $$\frac{1}{\displaystyle 1+
        \frac{1}{\displaystyle 2+
        \frac{1}{\displaystyle 3+x}}} +
        \frac{1}{1+\frac{1}{2+\frac{1}{3+x}}}$$
    \column{.5\textwidth}
        $$F:\left| \begin{array}{ccc}
        F''_{xx} & F''_{xy} &  F'_x \\
        F''_{yx} & F''_{yy} &  F'_y \\
        F'_x     & F'_y     & 0
        \end{array}\right| = 0$$
    \end{columns}
    \begin{columns}[onlytextwidth]
    \column{.3\textwidth}
        $$\mathop{\int \!\!\! \int}_{\mathbf{x} \in \mathds{R}^2}
        \! \langle \mathbf{x},\mathbf{y}\rangle\,\mathsf{d}\mathbf{x}$$
    \column{.33\textwidth}
        $$\overline{\overline{a\alpha}^2+\underline{b\beta}
        +\overline{\overline{d\delta}}}$$
    \column{.37\textwidth}
        $\left] 0,1\right[ + \lceil x \rfloor - \langle x,y\rangle$
    \end{columns}
    \begin{columns}[onlytextwidth]
    \column{.4\textwidth}
        \begin{eqnarray*}
        e^x &\approx& 1+x+x^2/2! + \\
            && {}+x^3/3! + x^4/4!
        \end{eqnarray*}
    \column{.6\textwidth}
        $${n+1\choose k} = {n\choose k} + {n \choose k-1}$$
    \end{columns}
\end{frame}
\section{Figures and Code Listings}
\begin{frame}[label=figs1]{Figures}
    \framesubtitle{Tables, graphs, and images}
    \begin{table}[!b]
     % Use monospaced lining figures
    \begin{tabularx}{\textwidth}{Xrrr}
        \textbf{Faculty} & \textbf{With \TeX} & \textbf{Total} &
        \textbf{\%} \\
        \toprule
        Faculty of Informatics       & 1\,716  & 2\,904  &
        59.09 \\% 1433
        Faculty of Science           & 786     & 5\,275  &
        14.90 \\% 1431
        Faculty of $\genfrac{}{}{0pt}{}{\textsf{Economics and}}{%
        \textsf{Administration}}$    & 64      & 4\,591  &
        1.39  \\% 1456
        Faculty of Arts              & 69      & 10\,000 &
        0.69  \\% 1421
        Faculty of Medicine          & 8       & 2\,014  &
        0.40  \\% 1411
        Faculty of Law               & 15      & 4\,824  &
        0.31  \\% 1422
        Faculty of Education         & 19      & 8\,219  &
        0.23  \\% 1441
        Faculty of Social Studies    & 12      & 5\,599  &
        0.21  \\% 1423
        Faculty of Sports Studies    & 3       & 2\,062  &
        0.15  \\% 1451
        \bottomrule
    \end{tabularx}
    \caption{The distribution of theses written using \TeX\ during 2010--15 at MU}
    \end{table}
\end{frame}
\begin{frame}[label=figs2]{Figures}
    %\framesubtitle{Tables, graphs, and images}
    \begin{figure}[b]
    \centering
    % Flipping a coin
    % Author: cis
    \tikzset{
        head/.style = {fill = none, label = center:\textsf{H}},
        tail/.style = {fill = none, label = center:\textsf{T}}}
    \scalebox{0.65}{\begin{tikzpicture}[
        scale = 1.5, transform shape, thick,
        every node/.style = {draw, circle, minimum size = 10mm},
        grow = down,  % alignment of characters
        level 1/.style = {sibling distance=3cm},
        level 2/.style = {sibling distance=4cm},
        level 3/.style = {sibling distance=2cm},
        level distance = 1.25cm
        ]
        \node[shape = rectangle,
        minimum width = 6cm, font = \sffamily] {Coin flipping}
        child { node[shape = circle split, draw, line width = 1pt,
                minimum size = 10mm, inner sep = 0mm, rotate = 30] (Start)
                { \rotatebox{-30}{H} \nodepart{lower} \rotatebox{-30}{T}}
        child {   node [head] (A) {}
            child { node [head] (B) {}}
            child { node [tail] (C) {}}
        }
        child {   node [tail] (D) {}
            child { node [head] (E) {}}
            child { node [tail] (F) {}}
        }
        };
        % Filling the root (Start)
        \begin{scope}[on background layer, rotate=30]
        \fill[head] (Start.base) ([xshift = 0mm]Start.east) arc (0:180:5mm)
            -- cycle;
        \fill[tail] (Start.base) ([xshift = 0pt]Start.west) arc (180:360:5mm)
            -- cycle;
        \end{scope}
        % Labels
        \begin{scope}[nodes = {draw = none}]
        \path (Start) -- (A) node [near start, left]  {$0.5$};
        \path (A)     -- (B) node [near start, left]  {$0.5$};
        \path (A)     -- (C) node [near start, right] {$0.5$};
        \path (Start) -- (D) node [near start, right] {$0.5$};
        \path (D)     -- (E) node [near start, left]  {$0.5$};
        \path (D)     -- (F) node [near start, right] {$0.5$};
        \begin{scope}[nodes = {below = 11pt}]
            \node [name = X] at (B) {$0.25$};
            \node            at (C) {$0.25$};
            \node [name = Y] at (E) {$0.25$};
            \node            at (F) {$0.25$};
        \end{scope}
        \end{scope}
    \end{tikzpicture}}
    \caption{Tree of probabilities -- Flipping a coin\footnote[frame]{%
        A derivative of a diagram from \url{texample.net} by cis, CC BY 2.5 licensed.}}
    \end{figure}
\end{frame}
\defverbatim[colored]\sleepSort{
    \begin{lstlisting}[language=C,tabsize=2]
#include <stdio.h>
#include <unistd.h>
#include <sys/types.h>
#include <sys/wait.h>
// This is a comment
int main(int argc, char **argv)
{
        while (--c > 1 && !fork());
        sleep(c = atoi(v[c]));
        printf("%d\n", c);
        wait(0);
        return 0;
}
\end{lstlisting}}
\begin{frame}{Code listings what happens \\ if the title is longer?}{An example source code in C}
    \sleepSort
\end{frame}
\begin{frame}
	\begin{algorithm}[H]
		\caption{Text Summarization Algorithm}\label{euclid}
		\begin{algorithmic}[1]
			\Procedure{Summary Construction}{}\newline
			\textbf{Input:} Text Document.\newline
			\textbf{Output:} Summary sentences.
			\State{Creating information table from a text document.}
			\State{Generate matrices.}
			\State {\textbf{Call Pocedure:} Reduct Construction \textbf{[Algorithm 2]}}
			\State {\textbf{Return:} Summary sentences}
			\EndProcedure
		\end{algorithmic}
		\label{alg_1}
	\end{algorithm}
\end{frame}
\begin{frame}{RealBoost algorithm}{With narrow margins}
    \vspace{-15pt}
    % TODO- przesunela sie data w stopce
	% https://tex.stackexchange.com/a/200172/228402
	  \begin{columns}
		\column{\dimexpr\paperwidth-90pt}
		\begin{algorithm}[H]
			\footnotesize
			\caption{Algorytm RealBoost}\label{realboost}
			\begin{algorithmic}[1]
				\Procedure{RealBoost}{$D$}
				\State{Rozpocznij od jednostajnego rozkładu wag: $w_i := 1/m, i=1, \ldots, m$.}
				\For{$t:=1,\ldots, T$}
					\State Naucz klasyfikator $f_t(x) \in \mathds{R}$ na danych uczących używając wag $w_i$, tak aby $f_t$ minimalizowało \emph{kryterium wykładnicze} $\sum_{i=1}^{m} w_i e^{-f_t(x_i)y_i}$ lub równoważnie aby $f_t$ było przybliżeniem połowy przekształcenia logit:
					\Statex $f_{t}(\mathbf{x}):=1 / 2 \ln \left\{\widehat{P}_{w}(y=1 \mid \mathbf{x}) \sqrt{P}_{w}(y=-1 \mid \mathbf{x})\right)$
					\State Aktualizuj wagi przykładów wg:
					\Statex $Z_{t}:=\sum_{i=1}^{i n} w_{i} e^{-f_{i}\left(x_{i}\right) y_{i}}$
					\Statex $w_{i}:=w_{i} e^{-f_{i}\left(\mathbf{x}_{i}\right) y_{i}} / Z_{t}, \quad i=1, \ldots, m$
				\EndFor\\
				\Return zbiorowy klasyfikator $F(\mathbf{x}):=\sum_{t=1}^{T} f_{t}(\mathbf{x})$ z decyzją obliczaną jako sgn $F(x)$.
				\EndProcedure
			\end{algorithmic}
			\label{alg_2}
		\end{algorithm}
	\end{columns}
\end{frame}
\section{Citations and Bibliography}
\begin{frame}[label=citations]{Citations}
    \framesubtitle{\TeX, \LaTeX, and Beamer}
    \justifying\TeX\ is a programming language for the typesetting
    of documents. It was created by Donald Erwin Knuth in the late
    1970s and it is documented in \emph{The \TeX
    book}~\cite{knuth84}.
    In the early 1980s, Leslie Lamport created the initial version
    of \LaTeX, a high-level language on top of \TeX, which is
    documented in \emph{\LaTeX : A Document Preparation
    System}~\cite{lamport94}. There exists a healthy ecosystem of
    packages that extend the base functionality of \LaTeX;
    \emph{The \LaTeX\ Companion}~\cite{MG94} acts as a guide
    through the ecosystem.
    In 2003, Till Tantau created the initial version of Beamer, a
    \LaTeX\ package for the creation of presentations. Beamer is
    documented in the \emph{User's Guide to the Beamer
    Class}~\cite{tantau04}.
\end{frame}
\begin{frame}[label=bibliography]{Bibliography}
    \framesubtitle{\TeX, \LaTeX, and Beamer}
    \begin{thebibliography}{9}
    \bibitem{knuth84}
        Donald~E.~Knuth.
        \emph{The \TeX book}.
        Addison-Wesley, 1984.
    \bibitem{lamport94}
        Leslie~Lamport.
        \emph{\LaTeX : A Document Preparation System}.
        Addison-Wesley, 1986.
    \bibitem{MG94}
        M.~Goossens, F.~Mittelbach, and A.~Samarin.
        \emph{The \LaTeX\ Companion}.
        Addison-Wesley, 1994.
    \bibitem{tantau04}
        Till~Tantau.
        \emph{User's Guide to the Beamer Class Version 3.01}.
        Available at \url{http://latex-beamer.sourceforge.net}.
    \bibitem{MS05}
        A.~Mertz and W.~Slough.
        Edited by B.~Beeton and K.~Berry.
        \emph{Beamer by example} In TUGboat,
            Vol. 26, No. 1., pp. 68-73.
    \end{thebibliography}
\end{frame}
\end{document}