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overview of thesis and fixing in style

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Stefan Dresselhaus
2017-10-08 21:08:29 +02:00
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44
arbeit/ma.md
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@@ -23,10 +23,7 @@ Unless otherwise noted the following holds:
# Introduction
\improvement[inline]{mehr Motivation, Ziel der Arbeit, Wieso das ganze?\newline
Wieso untersuchen wir das überhaupt? \cmark \newline
Aufbau der Arbeit? \xmark \newline
Mehr Bilder}
\improvement[inline]{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 -.-

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arbeit/ma.tex
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@@ -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
Wieso untersuchen wir das überhaupt? \cmark \newline
Aufbau der Arbeit? \xmark \newline
Mehr Bilder}
\improvement[inline]{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
are agnostic of the fitness-function at hand the third criterion should
reflect a notion of potential.
In contrast to the general nature of \emph{variability} and
\emph{regularity}, which are agnostic of the fitness-function at hand
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

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@@ -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}}}
\renewcommand\xmark{\textcolor{Maroon}{\ding{55}}}
\newcommand\cmark{\textcolor{OliveGreen}{\ding{51}}}
\newcommand\xmark{\textcolor{Maroon}{\ding{55}}}

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arbeit/template.tex
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@@ -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\ }
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\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}}