From 5b2abd2fa51de20ba40e8307573fa3d7fad779ac Mon Sep 17 00:00:00 2001 From: Stefan Dresselhaus Date: Sun, 8 Oct 2017 21:08:29 +0200 Subject: [PATCH] overview of thesis and fixing in style --- arbeit/ma.md | 44 ++++++++++++++++------ arbeit/ma.pdf | Bin 147294 -> 147528 bytes arbeit/ma.tex | 69 ++++++++++++++++++++++++++++------- arbeit/settings/commands.tex | 4 +- arbeit/template.tex | 13 +++++++ 5 files changed, 104 insertions(+), 26 deletions(-) diff --git a/arbeit/ma.md b/arbeit/ma.md index 34552d0..af9602d 100644 --- a/arbeit/ma.md +++ b/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 -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. # Schluss +\label{sec:dis} HAHA .. als ob -.- diff --git a/arbeit/ma.pdf b/arbeit/ma.pdf index 2ff5c5f2419ed154df4216bf2687618b56bee684..30dbabbf40f17ff648842bad4ddf0d121f90137e 100644 GIT binary patch delta 88493 zcmY(pQ+qCevaB21wr$&XGGZGew(-Trh;7@pZQHh;?77xC7i-@252&ZR>h0S3fg1CN zu44xUW=}N2B*$T9W)Tp8advSsGqQ#8*f>s;joaiv^1uB?Pjm$(1oR4!#xE5{r06uA z-*7M)PC!_Uy@x*L1-b)+G5ZnyWBV6DAp@DIa>qc#l4974nMg<%Aw3lYUYww0WIiee zDd@8Mxo3s%(-{cFg*5)RZU-EP^1_g~jU);D@|tn~`SREb|GVRd`OPn;vXBa46=YkHW{FdU?{w699Sfj_(*!9X{|MBj8iFp`VT-P{Jj^E#)2 zr}mVcv})xc-U@|Y3{UXIXvQ$i*Ock?E$slAm9_l-UajNZ7hvDzL*1f}i1;vYxgU&T zmvVvsb@Gp6B(?SJ56!@_rk|SGdQFu=)TNzNXXBcsCvJ`Us(sz9RFr)Z-OC+uukxcj}J3-jM1N zvXsQ<+lb}50Kkwt4fcqP96jAfyUBWtmYAmp>K{4LQQ0VBew>8k_Ho7cu%#df!t{)) z7onN$T~gkS-lv3OXrrkFvy>|*@5KbUD2i>1X7RR1CWW}qhKbC<@|Th4zw?qPYlZlq z@lNX!ZNd}u3#H){l}@<*Sk1nUUud)lByxbsIL}8v7(j1zqvf;o)vgF$5S(E{DWlBR zq~luHgPBwcRe>J;fp6#+H%OmqI30bymU~?qnN`85aOh*Igh1M@WX)mAvg=s6_zzE% zf7s_Fa``U!Ti$Ucm_S;sZy)y$X#xRPV_$CejM_R&Z-h|rI`l0t1#%bNCa-WTxBCio z2J#GL2H+P`PIBe1V&fDy!q$$(RLq%+fE%1-Ou}SYWlhwGLi2Qci%xT#9fxr%{-sYL zd{<2U{RU7EPd_tLzkb(;zIVI)Z0~PkOIUkz`B2?X-ViFe>aPO1`X{plt)lq>E*(SZ7P^ zl>&p4T|>t>@0s4H0siS+M|IG_h~wWSH&o;eZC^>T>JRcvXT3#KVcIUvNg$`I6?{4 zH?GU)lPQj_8`M1126C!KxM$*`Va^w<#16s*nY6cOPEIKA28FXnTm#GVXz+}88#t_WGHNXeL4D%b;3HNl&|9PV1^P$U zm*nE-kh7 zx}2)7K4b0C*PiEtV+uQ0#9>F@&Ap9CQ|7bg#nfya^H5N`<#g*jTe#*P)d#-m1TKT& z^L|VpW9Xp9qN#1pXnIcxuXK=VLeH&Sc$SKFJ!MA2NQwQF^Ovzsxyb1Tx(s8xs0n@N zrF|oY>%wITW#3xu=z%K|fFH1&t&qJ@Xc9G52t2-G)cljo10g zBi{^0&r=T~;eoP0diHk?;ePD}p$_#%Z17|I!;NG+F0_1Ow)$DK)W4mh4<5w|mfcRT zIP}9icZDC5FBrkoPpXl59XkofM$uEkH-Cy?Ofpg^8N zIfK9#7;=#)-v0`^8io?U`G57CtuF7J$%NGXs&NJdsY*sB^h}M-dF_&MUQ}G#0SRuJ zi477Q*LGfe8(6ef1N~x})-Tev?faQS7EORGET9V}jwYVpS1)u9>LteYKx%xmGcStt zv1Tz=$TpB<-4qA@!M4MB#v^=d4@DBaN0mpVMG62G3gDYDmIF;P?aexVt;`(y&h`-| zL@h(eNAiGN#hOAgds zCxcNDRMJFzYyT$fA?HYChz=J3z?fyIVgXp(uL8yKEsp(xVi~|~hRAp6bmOPeI-6hY z6Xs~|f^3g&SGQH_`BP29`~6q0wsLDm6E>*$wJ@c8z+yPCnt15g_Z}rItz>{+V~- z@awdr)@0vCGRraAUx52=g>yvVgEZhSI!&2?){~_9q3!II7a>#R^P^F` z0FMq(=*k5{em+0*^`8>qG~w-dgIV+_MNelMr>bhJ$)}_?s9bB!o5V5-ioBln)SQCF zRqd_r_ApT5!0kO^WJ4jyI;cC)t~*`q^&2sfa_z$U@%BSXJc&8JO%fM)4%?fp9-T)| z!4-g?;fXK%_91B1@rnSBK3OBDw-9Yhn(&?*gH(G@}~td zOs$*b?ANOZHYw51PCfbpGNgcq7UdF=5jp(utE#XdOJ4QZVxmZRq znGvlx5VR3e6dyCnfb-2SzQvm8k>^pj*B`1Put_G=fAj6GI8k&D+P9d>D-AtLlqn>t zw5~rpvxgLN-}yX%Bxlwq1>Q81r&x-hD=rEM7Jtea<#B8p2TY0N4$0)$; z-&5@GJK6%iC`Z~^n{VUXHeSd6TTaoaOc3HJ!~oJ2eVPU?xkhpt3~9VRQu17Y>sj?+tHm2QEUiT+(h(ca z!9?=UW^qX>Tupd;0dgbXYOkJ=;^=I&qa~ZMMy{Td<>~BOZ*z^eL{?f|J)+p8WW0;8 zO+oU(%WGGZ|jMu+L-g`*rm6I++D2 z3Mq1&2${tUS-clI`L|_#g6_T(SlKI(wfDSokS$Jr{-I+*rLocb(~;_#?K~o-T=3#l zl+|j7wjwn~)o(tvw7iydEemr-rBfs&xGi9GiCK0T}czUcSoffA- z2kppj(`Wa{ltmlO3$LQJ=PUySO6;L~7m6OMX2jUN_dOV#1SmBULEg;$ZOp~fyk>O2 zuJSc3ebrPtB{Hw#hVvyj30k!FibkL!)hi4j;fRUB95$?8p>p((T=k-t!+9EM6a%

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}{#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 diff --git a/arbeit/settings/commands.tex b/arbeit/settings/commands.tex index 4f0c48d..9d5746b 100644 --- a/arbeit/settings/commands.tex +++ b/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}}} -\renewcommand\xmark{\textcolor{Maroon}{\ding{55}}} +\newcommand\cmark{\textcolor{OliveGreen}{\ding{51}}} +\newcommand\xmark{\textcolor{Maroon}{\ding{55}}} diff --git a/arbeit/template.tex b/arbeit/template.tex index 1389036..2949ac6 100644 --- a/arbeit/template.tex +++ b/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\ } +\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}}