overview of thesis and fixing in style

arbeit/ma.md

@@ -23,10 +23,7 @@ Unless otherwise noted the following holds:
 
 # Introduction
 
-\improvement[inline]{mehr Motivation, Ziel der Arbeit, Wieso das ganze?\newline
+\improvement[inline]{Mehr Bilder}
-Wieso untersuchen wir das überhaupt? \cmark \newline
-Aufbau der Arbeit? \xmark \newline
-Mehr Bilder}
 
 Many modern industrial design processes require advanced optimization methods
 do to the increased complexity. These designs have to adhere to more and more
@@ -69,12 +66,30 @@ scheme, as suspected in \cite{anrichterEvol}.
 
 ## Outline of this thesis
 
-\improvement[inline]{Kapitel vorstellen, Inhalt? Ziel?}
+First we introduce different topics in isolation in Chapter \ref{sec:back}. We
+take an abstract look at the definition of \ac{FFD} for a one-dimensional line
+(in \ref{sec:back:ffd}) and discuss why this is a sensible deformation function
+(in \ref{sec:back:ffdgood}).
+Then we establish some background-knowledge of evolutional algorithms (in
+\ref{sec:back:evo}) and why this is useful in our domain (in
+\ref{sec:back:evogood}).
+In a third step we take a look at the definition of the different evolvability
+criteria established in \cite{anrichterEvol}.
+
+In Chapter \ref{sec:impl} we take a look at our implementation of \ac{FFD} and
+the adaptation for 3D-meshes.
+
+Next, in Chapter \ref{sec:eval}, we describe the different scenarios we use to
+evaluate the different evolvability-criteria incorporating all aspects
+introduced in Chapter \ref{sec:back}. Following that, we evaluate the results in
+Chapter \ref{sec:res} with further on discussion in Chapter \ref{sec:dis}.
+
 
 # Background
+\label{sec:back}
 
 ## What is \acf{FFD}?
-\label{sec:intro:ffd}
+\label{sec:back:ffd}
 
 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. For simplicity we only summarize
@@ -119,6 +134,7 @@ $\tau_{i+d+1}$ as can bee seen from the two coefficients in every step of the
 recursion.
 
 ### Why is \ac{FFD} a good deformation function?
+\label{sec:back:ffdgood}
 
 The usage of \ac{FFD} as a tool for manipulating follows directly from the
 properties of the polynomials and the correspondence to the control points.
@@ -156,10 +172,12 @@ All in all \ac{FFD} and \ac{DM-FFD} are still good ways to deform a high-polygon
 mesh albeit the downsides.
 
 ## What is evolutional optimization?
+\label{sec:back:evo}
 
 \change[inline]{Write this section}
 
 ## Advantages of evolutional algorithms
+\label{sec:back:evogood}
 
 \change[inline]{Needs citations}
 The main advantage of evolutional algorithms is the ability to find optima of
@@ -188,7 +206,7 @@ over time.
 
 ### Variability
 
-In \cite{anrichterEvol} variability is defined as
+In \cite{anrichterEvol} *variability* is defined as
 $$V(\vec{U}) := \frac{\textrm{rank}(\vec{U})}{n},$$
 whereby $\vec{U}$ is the $m \times n$ deformation-Matrix used to map the $m$
 control points onto the $n$ vertices.
@@ -206,7 +224,7 @@ control-points for an $d$-dimensional control mesh.
 
 ### Regularity
 
-Regularity is defined\cite{anrichterEvol} as
+*Regularity* is defined\cite{anrichterEvol} as
 $$R(\vec{U}) := \frac{1}{\kappa(\vec{U})} = \frac{\sigma_{min}}{\sigma_{max}}$$
 where $\sigma_{min}$ and $\sigma_{max}$ are the smallest and greatest right singular
 value of the deformation-matrix $\vec{U}$.
@@ -224,7 +242,7 @@ locality\cite{weise2012evolutionary,thorhauer2014locality}.
 
 ### Improvement Potential
 
-In contrast to the general nature of variability and regularity, which are
+In contrast to the general nature of *variability* and *regularity*, which are
 agnostic of the fitness-function at hand the third criterion should reflect a
 notion of potential.
 
@@ -232,7 +250,7 @@ As during optimization some kind of gradient $g$ is available to suggest a
 direction worth pursuing we use this to guess how much change can be achieved in
 the given direction.
 
-The definition for an improvement potential $P$ is\cite{anrichterEvol}:
+The definition for an *improvement potential* $P$ is\cite{anrichterEvol}:
 $$
 P(\vec{U}) := 1 - \|(\vec{1} - \vec{UU}^+)\vec(G)\|^2_F
 $$
@@ -240,6 +258,7 @@ given some approximate $n \times d$ fitness-gradient $\vec{G}$, normalized to
 $\|\vec{G}\|_F = 1$, whereby $\|\cdot\|_F$ denotes the Frobenius-Norm.
 
 # Implementation of \acf{FFD}
+\label{sec:impl}
 
 The general formulation of B-Splines has two free parameters $d$ and $\tau$
 which must be chosen beforehand.
@@ -255,7 +274,7 @@ formulas for the general case so it can be adapted quite freely.
 
 ## Adaption of \ac{FFD}
 
-As we have established in Chapter \ref{sec:intro:ffd} we can define an
+As we have established in Chapter \ref{sec:back:ffd} we can define an
 \ac{FFD}-displacement as
 \begin{equation}
 \Delta_x(u) = \sum_i N_{i,d,\tau_i}(u) \Delta_x c_i
@@ -363,6 +382,7 @@ linear equations.
 
 
 # Scenarios for testing evolvability criteria using \acf{FFD}
+\label{sec:eval}
 
 ## Test Scenario: 1D Function Approximation
 
@@ -397,6 +417,7 @@ linear equations.
 - Kriterien trotzdem gut
 
 # Evaluation of Scenarios
+\label{sec:res}
 
 ## Spearman/Pearson-Metriken
 
@@ -437,5 +458,6 @@ linear equations.
 <!-- ![Regularity vs steps](img/evolution3d/20170926_3dFit_both_regularity-vs-steps.png) -->
 
 # Schluss
+\label{sec:dis}
 
 HAHA .. als ob -.-

arbeit/ma.tex

@@ -45,6 +45,19 @@ xcolor=dvipsnames,
 \fancyhead[OR]{\textrm{\nouppercase\rightmark}}% Odd=rechte Seiten und dort rechts, also aussen das \rightmark
 \fancyfoot[RO,LE]{\thepage} % Seitenzahl : rechts ungerade, links gerade
 
+% ###### Title ######
+
+\usepackage[explicit]{titlesec}
+\newcommand{\hsp}{\hspace{20pt}}
+% \titleformat{\chapter}[hang]{\Huge\bfseries\ }{\textcolor{CadetBlue}{\thechapter} #1}{20pt}{\Huge\bfseries\ }
+\titleformat{name=\chapter,numberless}[hang]{\Huge\bfseries\ }{#1}{20pt}{\Huge\bfseries\ }
+\titleformat{\chapter}[hang]{\Huge\bfseries\ }{\color{CadetBlue}\thechapter}{20pt}{\begin{tabular}[t]{@{\color{CadetBlue}\vrule width 2pt}>{\hangindent=20pt\hsp}p{\dimexpr 1\textwidth -44pt}}#1\end{tabular}}
+
+\titleformat{name=\section,numberless}[hang]{\large\bfseries\ }{#1}{32pt}{\large\bfseries\ }
+\titleformat{\section}[hang]{\large\bfseries\ }{\color{CadetBlue}\thesection}{32pt}{\begin{tabular}[t]{p{\dimexpr 1\textwidth -44pt}}#1\end{tabular}}
+\titleformat{name=\subsection,numberless}[hang]{\bfseries\ }{#1}{27pt}{\bfseries\ }
+\titleformat{\subsection}[hang]{\bfseries\ }{\color{CadetBlue}\thesubsection}{27pt}{\begin{tabular}[t]{p{\dimexpr 1\textwidth -44pt}}#1\end{tabular}}
+
 % ### fr 1 seitig
 %\usepackage{fancyhdr} %
 %\lhead{\textsf{\noupercase\leftmark}}
@@ -148,10 +161,7 @@ Unless otherwise noted the following holds:
 
 \chapter{Introduction}\label{introduction}
 
-\improvement[inline]{mehr Motivation, Ziel der Arbeit, Wieso das ganze?\newline
+\improvement[inline]{Mehr Bilder}
-Wieso untersuchen wir das überhaupt? \cmark \newline
-Aufbau der Arbeit? \xmark \newline
-Mehr Bilder}
 
 Many modern industrial design processes require advanced optimization
 methods do to the increased complexity. These designs have to adhere to
@@ -199,13 +209,32 @@ given the different deformation scheme, as suspected in
 
 \section{Outline of this thesis}\label{outline-of-this-thesis}
 
-\improvement[inline]{Kapitel vorstellen, Inhalt? Ziel?}
+First we introduce different topics in isolation in Chapter
+\ref{sec:back}. We take an abstract look at the definition of \ac{FFD}
+for a one-dimensional line (in \ref{sec:back:ffd}) and discuss why this
+is a sensible deformation function (in \ref{sec:back:ffdgood}). Then we
+establish some background-knowledge of evolutional algorithms (in
+\ref{sec:back:evo}) and why this is useful in our domain (in
+\ref{sec:back:evogood}). In a third step we take a look at the
+definition of the different evolvability criteria established in
+\cite{anrichterEvol}.
+
+In Chapter \ref{sec:impl} we take a look at our implementation of
+\ac{FFD} and the adaptation for 3D-meshes.
+
+Next, in Chapter \ref{sec:eval}, we describe the different scenarios we
+use to evaluate the different evolvability-criteria incorporating all
+aspects introduced in Chapter \ref{sec:back}. Following that, we
+evaluate the results in Chapter \ref{sec:res} with further on discussion
+in Chapter \ref{sec:dis}.
 
 \chapter{Background}\label{background}
 
+\label{sec:back}
+
 \section{\texorpdfstring{What is \acf{FFD}?}{What is ?}}\label{what-is}
 
-\label{sec:intro:ffd}
+\label{sec:back:ffd}
 
 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. For simplicity we
@@ -254,6 +283,8 @@ coefficients in every step of the recursion.
 \subsection{\texorpdfstring{Why is \ac{FFD} a good deformation
 function?}{Why is  a good deformation function?}}\label{why-is-a-good-deformation-function}
 
+\label{sec:back:ffdgood}
+
 The usage of \ac{FFD} as a tool for manipulating follows directly from
 the properties of the polynomials and the correspondence to the control
 points. Having only a few control points gives the user a nicer
@@ -293,11 +324,15 @@ high-polygon mesh albeit the downsides.
 \section{What is evolutional
 optimization?}\label{what-is-evolutional-optimization}
 
+\label{sec:back:evo}
+
 \change[inline]{Write this section}
 
 \section{Advantages of evolutional
 algorithms}\label{advantages-of-evolutional-algorithms}
 
+\label{sec:back:evogood}
+
 \change[inline]{Needs citations} The main advantage of evolutional
 algorithms is the ability to find optima of general functions just with
 the help of a given error-function (or fitness-function in this domain).
@@ -327,7 +362,7 @@ deformations}\label{criteria-for-the-evolvability-of-linear-deformations}
 
 \subsection{Variability}\label{variability}
 
-In \cite{anrichterEvol} variability is defined as
+In \cite{anrichterEvol} \emph{variability} is defined as
 \[V(\vec{U}) := \frac{\textrm{rank}(\vec{U})}{n},\] whereby \(\vec{U}\)
 is the \(m \times n\) deformation-Matrix used to map the \(m\) control
 points onto the \(n\) vertices.
@@ -346,7 +381,7 @@ grid so each control point is not independent, but typically depends on
 
 \subsection{Regularity}\label{regularity}
 
-Regularity is defined\cite{anrichterEvol} as
+\emph{Regularity} is defined\cite{anrichterEvol} as
 \[R(\vec{U}) := \frac{1}{\kappa(\vec{U})} = \frac{\sigma_{min}}{\sigma_{max}}\]
 where \(\sigma_{min}\) and \(\sigma_{max}\) are the smallest and
 greatest right singular value of the deformation-matrix \(\vec{U}\).
@@ -366,15 +401,15 @@ locality\cite{weise2012evolutionary,thorhauer2014locality}.
 
 \subsection{Improvement Potential}\label{improvement-potential}
 
-In contrast to the general nature of variability and regularity, which
+In contrast to the general nature of \emph{variability} and
-are agnostic of the fitness-function at hand the third criterion should
+\emph{regularity}, which are agnostic of the fitness-function at hand
-reflect a notion of potential.
+the third criterion should reflect a notion of potential.
 
 As during optimization some kind of gradient \(g\) is available to
 suggest a direction worth pursuing we use this to guess how much change
 can be achieved in the given direction.
 
-The definition for an improvement potential \(P\)
+The definition for an \emph{improvement potential} \(P\)
 is\cite{anrichterEvol}: \[
 P(\vec{U}) := 1 - \|(\vec{1} - \vec{UU}^+)\vec(G)\|^2_F
 \] given some approximate \(n \times d\) fitness-gradient \(\vec{G}\),
@@ -384,6 +419,8 @@ Frobenius-Norm.
 \chapter{\texorpdfstring{Implementation of
 \acf{FFD}}{Implementation of }}\label{implementation-of}
 
+\label{sec:impl}
+
 The general formulation of B-Splines has two free parameters \(d\) and
 \(\tau\) which must be chosen beforehand.
 
@@ -399,7 +436,7 @@ adapted quite freely.
 \section{\texorpdfstring{Adaption of
 \ac{FFD}}{Adaption of }}\label{adaption-of}
 
-As we have established in Chapter \ref{sec:intro:ffd} we can define an
+As we have established in Chapter \ref{sec:back:ffd} we can define an
 \ac{FFD}-displacement as
 
 \begin{equation}
@@ -517,6 +554,8 @@ system of linear equations.
 using
 \acf{FFD}}{Scenarios for testing evolvability criteria using }}\label{scenarios-for-testing-evolvability-criteria-using}
 
+\label{sec:eval}
+
 \section{Test Scenario: 1D Function
 Approximation}\label{test-scenario-1d-function-approximation}
 
@@ -587,6 +626,8 @@ Optimierung}\label{besonderheiten-der-optimierung}
 
 \chapter{Evaluation of Scenarios}\label{evaluation-of-scenarios}
 
+\label{sec:res}
+
 \section{Spearman/Pearson-Metriken}\label{spearmanpearson-metriken}
 
 \begin{itemize}
@@ -623,6 +664,8 @@ Approximation}\label{results-of-3d-function-approximation}
 
 \chapter{Schluss}\label{schluss}
 
+\label{sec:dis}
+
 HAHA .. als ob -.-
 
 \backmatter

arbeit/settings/commands.tex

@@ -161,5 +161,5 @@
 \newcommandx{\improvement}[2][1=]{\todo[linecolor=violet,backgroundcolor=violet!25,bordercolor=violet,#1]{\textbf{Improvement:} #2}}
 \newcommandx{\thiswillnotshow}[2][1=]{\todo[disable,#1]{#2}}
 
-\renewcommand\cmark{\textcolor{OliveGreen}{\ding{51}}}
+\newcommand\cmark{\textcolor{OliveGreen}{\ding{51}}}
-\renewcommand\xmark{\textcolor{Maroon}{\ding{55}}}
+\newcommand\xmark{\textcolor{Maroon}{\ding{55}}}

arbeit/template.tex

@@ -45,6 +45,19 @@ xcolor=dvipsnames,
 \fancyhead[OR]{\textrm{\nouppercase\rightmark}}% Odd=rechte Seiten und dort rechts, also aussen das \rightmark
 \fancyfoot[RO,LE]{\thepage} % Seitenzahl : rechts ungerade, links gerade
 
+% ###### Title ######
+
+\usepackage[explicit]{titlesec}
+\newcommand{\hsp}{\hspace{20pt}}
+% \titleformat{\chapter}[hang]{\Huge\bfseries\ }{\textcolor{CadetBlue}{\thechapter} #1}{20pt}{\Huge\bfseries\ }
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+
+\titleformat{name=\section,numberless}[hang]{\large\bfseries\ }{#1}{32pt}{\large\bfseries\ }
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+\titleformat{\subsection}[hang]{\bfseries\ }{\color{CadetBlue}\thesubsection}{27pt}{\begin{tabular}[t]{p{\dimexpr 1\textwidth -44pt}}#1\end{tabular}}
+
 % ### fr 1 seitig
 %\usepackage{fancyhdr} %
 %\lhead{\textsf{\noupercase\leftmark}}