fixed equations, added todo for cites

arbeit/bibma.bib

@@ -5,6 +5,7 @@
   publisher    = "IEEE",
   title        = "Evolvability as a Quality Criterion for Linear Deformation Representations in Evolutionary Optimization",
   year         = "2016",
+  note={\url{http://graphics.uni-bielefeld.de/publications/cec16.pdf}, \url{https://pub.uni-bielefeld.de/publication/2902698}},
 }
 @article{spitzmuller1996bezier,
   title="Partial derivatives of Bèzier surfaces",
@@ -15,10 +16,12 @@
   pages="67--72",
   year="1996",
   publisher="Elsevier",
+  url={https://doi.org/10.1016/0010-4485(95)00044-5},
 }
 @article{hsu1991dmffd,
   title={A direct manipulation interface to free-form deformations},
   author={Hsu, William M},
   journal={Master's thesis, Brown University},
-  year={1991}
+  year={1991},
+  url={https://cs.brown.edu/research/pubs/theses/masters/1991/hsu.pdf},
 }

arbeit/files/erklaerung.aux

@@ -27,7 +27,7 @@
 \setcounter{r@tfl@t}{0}
 \setcounter{subfigure}{0}
 \setcounter{subtable}{0}
-\setcounter{@todonotes@numberoftodonotes}{1}
+\setcounter{@todonotes@numberoftodonotes}{3}
 \setcounter{Item}{0}
 \setcounter{Hfootnote}{2}
 \setcounter{bookmark@seq@number}{16}

arbeit/ma.md

@@ -16,7 +16,7 @@ Unless otherwise noted the following holds:
   refer to other scalar (real) variables.
 - lowercase **bold** letters (e.g. $\vec{x},\vec{y}$)  
   refer to 3D coordinates
-- uppercase **BOLD** letters (e.g. $D, M$)  
+- uppercase **BOLD** letters (e.g. $\vec{D}, \vec{M}$)  
   refer to Matrices
 
 # Introduction
@@ -42,23 +42,19 @@ Given an arbitrary number of points $p_i$ alongside a line, we map a scalar
 value $\tau_i \in [0,1[$ to each point with $\tau_i < \tau_{i+1} \forall i$.
 Given a degree of the target polynomial $d$ we define the curve $N_{i,d,\tau_i}(u)$ as follows:
 
-$$
+\begin{equation} \label{eqn:ffd1d1}
-\begin{equation}
-\label{ffd1d1}
 N_{i,0,\tau}(u) = \begin{cases} 1, & u \in [\tau_i, \tau_{i+1}[ \\ 0, & \mbox{otherwise} \end{cases}
 \end{equation}
-$$
+
 and
-$$
+
-\begin{equation}
+\begin{equation} \label{eqn:ffd1d2}
-\label{ffd1d2}
 N_{i,d,\tau}(u) = \frac{u-\tau_i}{\tau_{i+d}} N_{i,d-1,\tau}(u) + \frac{\tau_{i+d+1} - u}{\tau_{i+d+1}-\tau_{i+1}} N_{i+1,d-1,\tau}(u)
 \end{equation}
-$$
 
 If we now multiply every $p_i$ with the corresponding $N_{i,d,\tau_i}(u)$ we get the contribution of each
 point $p_i$ to the final curve-point parameterized only by $u \in [0,1[$.
-As can be seen from equation \ref{ffd1d2} we only access points $[i..i+d]$ for any given $i$^[one more for each recursive step.], which
+As can be seen from \eqref{eqn:ffd1d2} we only access points $[i..i+d]$ for any given $i$^[one more for each recursive step.], which
 gives us, in combination with choosing $p_i$ and $\tau_i$ in order, only a local interference of $d+1$ points.
 
 We can even derive this equation straightforward for an arbitrary $N$^[*Warning:* in the case of $d=1$ the recursion-formula yields a $0$ denominator, but $N$ is also $0$. The right solution for this case is a derivative of $0$]:
@@ -82,11 +78,12 @@ model follows in an intuitive manner. The deformation is smooth as the underlyin
 vertices of the model as needed. Moreover the changes are always local so one risks not any change that a user cannot immediately see.
 
 But there are also disadvantages of this approach. The user loses the ability to directly influence vertices and even seemingly simple tasks as
-creating a plateau can be difficult to achieve\cite[chapter~3.2]{hsu1991dmffd}.
+creating a plateau can be difficult to achieve\cite[chapter~3.2]{hsu1991dmffd}\todo{cite [24] aus \ref{anrichterEvol}}.
 
 This disadvantages led to the formulation of \acf{DM-FFD}\cite[chapter~3.3]{hsu1991dmffd} in which the user directly interacts with the surface-mesh.
 All interactions will be applied proportionally to the control-points that make up the parametrization of the interaction-point
 itself yielding a smooth deformation of the surface *at* the surface without seemingly arbitrary scattered control-points.
+Moreover this increases the efficiency of an evolutionary optimization\todo{cite [25] aus \ref{anrichterEvol}}, which we will use later on.
 
 But this approach also has downsides as can be seen in \cite[figure~7]{hsu1991dmffd}\todo{figure hier einfügen?}, as the tessellation of
 the invisible grid has a major impact on the deformation itself.

arbeit/ma.tex

@@ -140,7 +140,7 @@ Unless otherwise noted the following holds:
   lowercase \textbf{bold} letters (e.g. \(\vec{x},\vec{y}\))\\
    refer to 3D coordinates
 \item
-  uppercase \textbf{BOLD} letters (e.g. \(D, M\))\\
+  uppercase \textbf{BOLD} letters (e.g. \(\vec{D}, \vec{M}\))\\
    refer to Matrices
 \end{itemize}
 
@@ -171,24 +171,22 @@ scalar value \(\tau_i \in [0,1[\) to each point with
 \(\tau_i < \tau_{i+1} \forall i\). Given a degree of the target
 polynomial \(d\) we define the curve \(N_{i,d,\tau_i}(u)\) as follows:
 
-\[
+\begin{equation} \label{eqn:ffd1d1}
-\begin{equation}
-\label{ffd1d1}
 N_{i,0,\tau}(u) = \begin{cases} 1, & u \in [\tau_i, \tau_{i+1}[ \\ 0, & \mbox{otherwise} \end{cases}
 \end{equation}
-\] and \[
+
-\begin{equation}
+and
-\label{ffd1d2}
+
+\begin{equation} \label{eqn:ffd1d2}
 N_{i,d,\tau}(u) = \frac{u-\tau_i}{\tau_{i+d}} N_{i,d-1,\tau}(u) + \frac{\tau_{i+d+1} - u}{\tau_{i+d+1}-\tau_{i+1}} N_{i+1,d-1,\tau}(u)
 \end{equation}
-\]
 
 If we now multiply every \(p_i\) with the corresponding
 \(N_{i,d,\tau_i}(u)\) we get the contribution of each point \(p_i\) to
 the final curve-point parameterized only by \(u \in [0,1[\). As can be
-seen from equation \ref{ffd1d2} we only access points \([i..i+d]\) for
+seen from \eqref{eqn:ffd1d2} we only access points \([i..i+d]\) for any
-any given \(i\)\footnote{one more for each recursive step.}, which gives
+given \(i\)\footnote{one more for each recursive step.}, which gives us,
-us, in combination with choosing \(p_i\) and \(\tau_i\) in order, only a
+in combination with choosing \(p_i\) and \(\tau_i\) in order, only a
 local interference of \(d+1\) points.
 
 We can even derive this equation straightforward for an arbitrary
@@ -222,7 +220,7 @@ any change that a user cannot immediately see.
 But there are also disadvantages of this approach. The user loses the
 ability to directly influence vertices and even seemingly simple tasks
 as creating a plateau can be difficult to
-achieve\cite[chapter~3.2]{hsu1991dmffd}.
+achieve\cite[chapter~3.2]{hsu1991dmffd}\todo{cite [24] aus \ref{anrichterEvol}}.
 
 This disadvantages led to the formulation of
 \acf{DM-FFD}\cite[chapter~3.3]{hsu1991dmffd} in which the user directly
@@ -230,7 +228,9 @@ interacts with the surface-mesh. All interactions will be applied
 proportionally to the control-points that make up the parametrization of
 the interaction-point itself yielding a smooth deformation of the
 surface \emph{at} the surface without seemingly arbitrary scattered
-control-points.
+control-points. Moreover this increases the efficiency of an
+evolutionary optimization\todo{cite [25] aus \ref{anrichterEvol}}, which
+we will use later on.
 
 But this approach also has downsides as can be seen in
 \cite[figure~7]{hsu1991dmffd}\todo{figure hier einfügen?}, as the

arbeit/settings/commands.tex

@@ -173,3 +173,4 @@
 \newcommand\data[1]{\marginpar{\vspace{-35pt}\begin{center}
                      \includegraphics[width=1cm]{img/cd}
                     \end{center}\vspace{-15pt}\centering\footnotesize\texttt{#1}}}
+\renewcommand\vec[1]{\textbf{#1}}