\begin{frame}
    \frametitle{\problemtitle}
    \begin{itemize}
        \item<+-> \textbf{Problem:} Given two sets of points $A$ and $B$. Determine whether there is a symmetry line separating $A$ and $B$, i.e., mirroring $A$ along that line results in $B$
    \end{itemize}
    \begin{minipage}[t]{0.55\textwidth}
        \begin{itemize}
            \item<+-> Compute the Center of Mass (COM) for both sets: $c_A=\left(\sum_{p\in A}p\right)/|A|$
            \item<+-> If there is a symmetry line, it
                \begin{itemize}
                    \item goes through $(c_A + c_B) / 2$, and
                    \item is perpendicular to $c_A - c_B$
                \end{itemize}
            \item<+>[$\rightarrow$] Check that
                \begin{itemize}
                    \item $c_A\neq c_B$,
                    \item mirroring $A$ results in $B$, and
                    \item all points in $A$ lie strictly one side of the mirror line
                \end{itemize}
        \end{itemize}
        \vspace{-1.5cm}
        \pause
        Possible pitfalls:
        \begin{itemize}
            \item Rounding after mirroring without checking for integer coordinates
            \item Sorting for comparing the mirrored $A$ with $B$
            \item Missing one of the checks above
            \item \texttt{float} instead of (\texttt{long}) \texttt{double}
        \end{itemize}
    \end{minipage}
    \begin{minipage}[t]{0.35\textwidth}
        \centering\vspace{-0.7\baselineskip}
        \includegraphics[width=\textwidth]{../statement/figure.pdf}
    \end{minipage}
\end{frame}
