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%%%%%%%%%%%%%%% Hauptteil %%%%%%%%%%%%%%%
% Insgesamt ca. 60-100 Seiten Davon mindesten 50% Eigene Arbeit
\mainmatter %Abstrakte Gliederungsebene: Hauptteil des Buches
\pagestyle{fancy}
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\chapter*{How to read this Thesis}

As a guide through the nomenclature used in the formulas we prepend this
chapter.

Unless otherwise noted the following holds:

\begin{itemize}
\tightlist
\item
  lowercase letters \(x,y,z\)\\
   refer to real variables and represent a point in 3D-Space.
\item
  lowercase letters \(u,v,w\)\\
   refer to real variables between \(0\) and \(1\) used as coefficients
  in a 3D B-Spline grid.
\item
  other lowercase letters\\
   refer to other scalar (real) variables.
\item
  lowercase \textbf{bold} letters (e.g. \(\vec{x},\vec{y}\))\\
   refer to 3D coordinates
\item
  uppercase \textbf{BOLD} letters (e.g. \(D, M\))\\
   refer to Matrices
\end{itemize}

\chapter{Introduction}\label{introduction}

In this Master Thesis we try to extend a previously proposed concept of
predicting the evolvability of \acf{FFD} given a
Deformation-Matrix\cite{anrichterEvol}. In the original publication the
author used random sampled points weighted with \acf{RBF} to deform the
mesh and defined three different criteria that can be calculated prior
to using an evolutional optimisation algorithm to asses the quality and
potential of such optimisation.

We will replicate the same setup on the same meshes but use \acf{FFD}
instead of \acf{RBF} to create a deformation and evaluate if the
evolution-criteria still work as a predictor given the different
deformation.

\section{\texorpdfstring{What is \acf{FFD}?}{What is ?}}\label{what-is}

First of all we have to establish how a \ac{FFD} works and why this is a
good tool for deforming meshes in the first place.

\section{Was ist evolutionäre
Optimierung?}\label{was-ist-evolutionuxe4re-optimierung}

\section{Wieso ist evo-Opt so cool?}\label{wieso-ist-evo-opt-so-cool}

\section{Evolvierbarkeitskriterien}\label{evolvierbarkeitskriterien}

\begin{itemize}
\tightlist
\item
  Konditionszahl etc.
\end{itemize}

\chapter{Hauptteil}\label{hauptteil}

\section{Was ist FFD?}\label{was-ist-ffd}

\begin{itemize}
\tightlist
\item
  Definition
\item
  Wieso Newton-Optimierung?
\item
  Was folgt daraus?
\end{itemize}

\section{Szenarien vorstellen}\label{szenarien-vorstellen}

\subsection{1D}\label{d}

\subsubsection{Optimierungszenario}\label{optimierungszenario}

\begin{itemize}
\tightlist
\item
  Ebene -\textgreater{} Template-Fit
\end{itemize}

\subsubsection{Matching in 1D}\label{matching-in-1d}

\begin{itemize}
\tightlist
\item
  Trivial
\end{itemize}

\subsubsection{Besonderheiten der
Auswertung}\label{besonderheiten-der-auswertung}

\begin{itemize}
\tightlist
\item
  Analytische Lösung einzig beste
\item
  Ergebnis auch bei Rauschen konstant?
\item
  normierter 1-Vektor auf den Gradienten addieren

  \begin{itemize}
  \tightlist
  \item
    Kegel entsteht
  \end{itemize}
\end{itemize}

\subsection{3D}\label{d-1}

\subsubsection{Optimierungsszenario}\label{optimierungsszenario}

\begin{itemize}
\tightlist
\item
  Ball zu Mario
\end{itemize}

\subsubsection{Matching in 3D}\label{matching-in-3d}

\begin{itemize}
\tightlist
\item
  alternierende Optimierung
\end{itemize}

\subsubsection{Besonderheiten der
Optimierung}\label{besonderheiten-der-optimierung}

\begin{itemize}
\tightlist
\item
  Analytische Lösung nur bis zur Optimierung der ersten Punkte gültig
\item
  Kriterien trotzdem gut
\end{itemize}

\chapter{Evaluation}\label{evaluation}

\section{Spearman/Pearson-Metriken}\label{spearmanpearson-metriken}

\begin{itemize}
\tightlist
\item
  Was ist das?
\item
  Wieso sollte uns das interessieren?
\item
  Wieso reicht Monotonie?
\item
  Haben wir das gezeigt?
\item
  Stastik, Bilder, blah!
\end{itemize}

\chapter{Schluss}\label{schluss}

HAHA .. als ob -.-

\backmatter
\cleardoublepage

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\chapter*{Appendix}
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%%%%%%%%%%%%%%% Literaturverzeichnis %%%%%%%%%%%%%%%
    \bibliographystyle{natdin} % 	\bibliographystyle{natdin}
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\end{document}
