Added doc on mesh optimizer

contrib/MeshOptimizer/doc/figures/log_barrier/Makefile

+%.pdf : %.tex
+	pdflatex --shell-escape $<
+clean :
+	${RM} *.gnuplot *.table *.aux *.log

contrib/MeshOptimizer/doc/figures/log_barrier/log_barrier.tex

+\documentclass{standalone}
+\usepackage{tikz}
+\begin{document}
+\begin{tikzpicture}[yscale = 0.25, xscale = 2]
+  \draw[thick, ->] (0,0) -- (3.2,0) node[right] {$m$};
+  \draw[thick, ->] (0,0) -- (0,17) node[left] {$F_{\epsilon,\omega}$};
+%  \node at (2, 12) {$F_{\epsilon,\omega}(m) = (m - \omega)^2 + \log\Big(\frac{m - \epsilon} {\omega - \epsilon}\Big)^2$};
+  \foreach \y in {0, 5, 10, 15}
+    \draw[thick, shift={(0, \y)}] node[left] {$\y$}(-1pt, 0pt) -- (0pt,0pt) ;
+  \foreach \x in {0, 1, 2, 3}
+    \draw[thick, shift={(\x, 0)}] node[below] {$\x$}(0pt, -8pt) -- (0pt,0pt) ;
+  \clip(-1,-2) rectangle(3.5, 17);
+  \draw[very thick, dashed](0.2, 0) node[below]{$\epsilon$}-- (0.2, 20);
+  \draw[thick, domain = 0.2:3, samples=300] plot[id=opti] function{(log((x - 0.2)/ 0.8))**2 + (x - 1)**2}; 
+\end{tikzpicture}
+\end{document}

contrib/MeshOptimizer/doc/figures/log_barrier/log_barrier_max.tex

+\documentclass{standalone}
+% Paper size: 3.58in,2.03in
+\usepackage{tikz}
+\begin{document}
+\begin{tikzpicture}[yscale = 0.25, xscale = 2]
+  \draw[thick, ->] (0,0) -- (3.2,0) node[right] {$m$};
+  \draw[thick, ->] (0,0) -- (0,17) node[left] {$F_{\epsilon,\omega}$};
+%  \node at (1.4, 12) {$F_{\epsilon,\omega}(m) = (m - \omega)^2 + \log\Big(\frac{m - \epsilon} {\omega - \epsilon}\Big)^2$};
+  \foreach \y in {0, 5, 10, 15}
+    \draw[thick, shift={(0, \y)}] node[left] {$\y$}(-1pt, 0pt) -- (0pt,0pt) ;
+  \foreach \x in {0, 1, 2, 3}
+    \draw[thick, shift={(\x, 0)}] node[below] {$\x$}(0pt, -8pt) -- (0pt,0pt) ;
+  \clip(-1,-2) rectangle(3.5, 17);
+  \draw[very thick, dashed](2.75, 0) node[below]{$\epsilon$}-- (2.75, 20);
+  \draw[thick, domain = 0:2.75, samples=300] plot[id=opti] function{(log((x - 2.75)/ -1.75))**2 + (x - 1)**2}; 
+\end{tikzpicture}
+\end{document}

contrib/MeshOptimizer/doc/figures/opti_process/Makefile

+opti_process.pdf : opti_process.tex
+	pdflatex --shell-escape $<
+clean :
+	${RM} *.gnuplot *.table *.aux *.log

contrib/MeshOptimizer/doc/figures/opti_process/opti2.dat

+-2.64148E+00 0  
+-2.43013E+00 1  
+-1.70784E+00 2  
+-1.48840E+00 3  
+-1.24431E+00 4  
+-1.22296E+00 5  
+-1.46493E+00 6  
+-1.37456E+00 7  
+-1.06042E+00 8  
+-1.08719E+00 9  
+-7.98080E-01 10 
+-6.91630E-01 11 
+-5.29097E-01 12 
+-7.59110E-01 13 
+-7.96486E-01 14 
+-5.83650E-01 15 
+-5.67035E-01 16 
+-5.54370E-01 17 
+-5.58354E-01 18 
+-4.42153E-01 19 
+-5.31631E-01 20 
+-3.67621E-01 21 
+-2.35836E-01 22 
+-3.03352E-01 23 
+-1.23011E-01 24 
+-3.10858E-01 25 
+-2.79462E-01 26 
+-3.07822E-01 27 
+-3.90367E-01 28 
+-2.83299E-01 29 
+-3.25716E-01 30 
+-2.32968E-01 31 
+-6.45337E-02 32 
+-7.54033E-02 33 
+ 1.03627E-01 34 
+ 1.10993E-01 35 
+ 1.57424E-01 36 
+ 1.12755E-01 37 
+ 1.15172E-01 38 
+ 1.96417E-01 39 
+ 1.59601E-01 40 
+ 2.11292E-01 41 
+ 1.83952E-01 42 
+ 2.25986E-01 43 
+ 2.67051E-01 44 
+ 1.72728E-01 45 
+ 2.87346E-01 46 
+ 2.34241E-01 47 
+ 2.50449E-01 48 
+ 1.53213E-01 49 
+ 2.73509E-01 50 
+ 2.20303E-01 51 
+ 1.71445E-01 52 
+ 2.94302E-01 53 
+ 2.40149E-01 54 
+ 1.62477E-01 55 
+ 2.70177E-01 56 
+ 1.97067E-01 57 
+ 1.49844E-01 58 
+ 3.15566E-01 59 
+ 2.14724E-01 60 
+ 2.78222E-01 61 
+ 3.41295E-01 62 
+ 3.99265E-01 63 
+ 4.07313E-01 64 
+ 4.55684E-01 65 
+ 4.37392E-01 66 
+ 4.56385E-01 67 
+ 4.88812E-01 68 
+ 4.47293E-01 69 
+ 5.02562E-01 70 

contrib/MeshOptimizer/doc/figures/opti_process/opti_process.tex

+\documentclass{standalone}
+\usepackage{tikz}
+\begin{document}
+\begin{tikzpicture}[yscale = 0.06, xscale = 1.8, thick]
+  %\node at (-1.4, 40) {\Large $\displaystyle J^{\min} = \min_{e,j} \frac{J_{ej}}{J_e^0}$};
+  \draw[dashed, green!70!black](0.5, 0) node[below]{$\bar{\epsilon}$}-- (0.5, 75);
+  \begin{scope}[black]
+    \draw(-3,0) -- (2,0) node[right] {};
+    \foreach \x in {-2, -1, 0, 1, 2}
+      \draw[shift={(\x, 0)}] node[below] {$\x$}(0pt, -20pt) -- (0pt,0pt) ;
+  \end{scope}
+  \begin{scope}[red, yscale = 3]
+    \draw[dashed](-2.9, 0) node[below]{$\epsilon_0$}-- (-2.9, 25) ;
+    \draw[dashed](-0.358, 0) node[below]{$\epsilon_1$}-- (-0.358, 25);
+    \draw[dashed](0.193, 0) node[below]{$\epsilon_2$}-- (0.193, 25);
+    \begin{scope}
+      \clip(-3.5, 0) rectangle(2.4, 25);
+      \draw[domain = -3:2, samples=500] plot[id=opti1] function{(log((x + 2.9)/ 3.9))**2 + (x - 1)**2}; 
+      \draw[domain = -3:2, samples=500] plot[id=opti2] function{(log((x + 0.358)/ 1.358))**2 + (x - 1)**2}; 
+      \draw[domain = -3:2, samples=500] plot[id=opti3] function{(log((x - 0.193)/ 0.807))**2 + (x - 1)**2}; 
+    \end{scope}
+    \node at (-2.50, 25) {$f_{\epsilon_0,\omega}$};
+    \node at (-0.10, 25) {$f_{\epsilon_1,\omega}$};
+    \node at (0.45, 25) {$f_{\epsilon_2,\omega}$};
+    \foreach \y in {0, 5, 10, 15, 20}
+      \draw[shift={(2, \y)}] node[right] {$\y$}(0pt, 0pt) -- (1pt,0pt) ;
+    \draw[->] (2,0) -- (2,25) node[right] {$f_{\epsilon,\omega}$};
+  \end{scope}
+  \begin{scope}[blue]
+    \draw plot file {opti2.dat} node[right]{$m$};
+    \node at (-2.641, 0) {$\bullet$};
+    \node at (-0.3257, 30) {$\bullet$};
+    \node at (0.214, 60) {$\bullet$};
+    \node at (0.5025, 70) {$\bullet$};
+    \draw[->] (-3,0) -- (-3,75) node[left] {Iterations};
+    \foreach \y in {0, 30, 60}
+      \draw[shift={(-3, \y)}] node[left] {$\y$}(-1pt, 0pt) -- (0pt,0pt) ;
+  \end{scope}
+\end{tikzpicture}
+\end{document}