\chapter{برخی نمودارها و شکل‌های مختلف}
\section{دیاگرام جبری}

\[
\xymatrix{
	A \ar@<.5ex>[r]^f\ar@<-.5ex>[r]_g & B\ar[d]_{c'}\ar[r]^c & C\ar[ld]^{\overline{c}} \\
	& C' & 
}
\]

\[
\xymatrix{
	& X\ar@<.5ex>[r]^{f}\ar@<-.5ex>[r]_{g} & Y\\
	A \ar[r]_{u_k\qquad}\ar[ru]^k& \mathop{\sqcup}\limits_{k\in pos_S(A,X)}A\ar@{-->}_h[u]
}
\]

\[
\xymatrix{
	\ar[dd]_{g\circ f} & _T\!B \ar[d]_{f}\ar[r] & _T\! pos(A,B)\ar[d]^{_T\! pos(A,f)} & \ar[dd]^{_T\! pos(A,g\circ f)}\\
	& _T\!C\ar[r]\ar[d]_{g} & _T\! pos(A,C)\ar[d]^{_T\! pos(A,g)} & \\
	& _T\!D\ar[r] \ar[r] & _T\! pos(A,D) &
}
\]



\begin{align}\begin{CD}
S^{{\mathcal{W}}_\Lambda}\otimes T @>j>> T\\
@VVV @VV{{\rm End ~} P}V\\
(S\otimes T)/I @= (Z\otimes T)/J
\end{CD}\end{align}
یک دیاگرام دیگر:
\begin{align}\begin{CD} 
{\rm cov~}(\mathcal{L}) @>>> {\rm non~}(\mathcal{K}) @>>> {\rm  cf~}(\mathcal{K}) @>>>
{\rm cf~}(\mathcal{L})\\
@VVV @AAA @AAA @VVV\\
{\rm add~}(\mathcal{L}) @>>> {\rm add~}(\mathcal{K}) @>>> {\rm cov~}(\mathcal{K}) @>>>
{\rm non~}(\mathcal{L})
\end{CD}\end{align}
\section{برخی از نمونه‌ شکل‌ها و نمودارهایی که توسط بسته tkz قابل ترسیم می‌باشند}

\section{رسم نمودار}
این بخش از فایلی که توسط آقای وفا خلیقی نوشته شده، برداشته شده است. 
\subsection{رسم نمودارهای قطبی}
برای رسم این دسته از نمودارها از بسته \lr{pst-plot} استفاده می‌کنیم.
%\begin{figure}[!ht]
%\centering
%\scalebox{.5} % Change this value to rescale the drawing.
%{
%\begin{pspicture}(3,3)(-3,-3)
% \psaxes{<->}(0,0)(3,3)(-3,-3)
% \psplot[polarplot,algebraic=true,linecolor=yellow,linewidth=1pt,
% plotpoints=2000]{0}{TwoPi 4 mul}{2*(sin(2*x))}
%  \psplot[polarplot,algebraic=true,linecolor=red,linewidth=1pt,
% plotpoints=2000]{0}{TwoPi 4 mul}{2*(cos(2*x))}
% \end{pspicture} 
% }
%\end{figure}
%
%\begin{figure}[!ht]
%\centering
%\scalebox{.5} % Change this value to rescale the drawing.
%{
%\begin{pspicture}(3,3)(-3,-5)
% \psaxes{<->}(0,0)(3,3)(-3,-5)
% \psplot[polarplot,algebraic=true,linecolor=blue,linewidth=1pt,
% plotpoints=2000]{0}{TwoPi 4 mul}{2}
%  \psplot[polarplot,algebraic=true,linecolor=green,linewidth=1pt,
% plotpoints=2000]{0}{TwoPi 4 mul}{2*(1-sin(x))}
% \end{pspicture} 
% }
%\end{figure}
\subsection{نمودارهای دکارتی با استفاده از بسته tikz}
می دانید 
همیشه برای کار با بسته ی  tikz یک محور مختصات مجازی داریم.
پس سریع یک  مبدا هر جا که می‌خواهید در نظر بگیرید و هر چیزی را که می‌خواهید نسبت به آن تعیین موقعیت کنید.

تابلوی جادویی‌ای که باید در آن شروع به کشیدن کنید، چیست؟

\lstset{framexleftmargin=5mm, frame=shadowbox, rulesepcolor=\color{blue}, language=Tex}
\begin{latin}
	\begin{lstlisting}[frame=trBL]
	\begin{tikzpicture}
	
	\end{tikzpicture}
	\end{lstlisting}
\end{latin}
اما برای این‌که شروع به رسم کنید، باید بدانید که از چه دستوراتی برای رسم در این محیط می‌توانید استفاده کنید.

ضمنا لازم به ذکر است که هر خط دستور که می‌نویسید باید با ;(سمیکولن) آن‌را تمام کنید.

\begin{description}
	\item[draw]
	برای اشکال پایه که با دستور فوق می‌خواهید رسم کنید به دو جفت مختصات نیاز دارید که بین آن‌ها نوع شکل را مشخص می‌کنید، البته دقیق .بعد از دستور هم تنظیماتی اختیاری وجود دارند که با آن‌ها آشنا خواهید شد.
	
	\lstset{framexleftmargin=5mm, frame=shadowbox, numbers=left, rulesepcolor=\color{blue}, language=Tex}
	\begin{latin}
		\begin{lstlisting}[frame=trBL]
		\begin{tikzpicture}
		\draw[color=cm1, ] (x1, y1) fig (x2, y2);
		\draw[step=.5cm,gray,very thin] (x1, y1) grid (x2, y2);
		\clip[draw] (x1, y1) fig (x2, y2);
		\end{tikzpicture}
		\end{lstlisting}
	\end{latin}
	
	در دستور فوق در جفت پرانتزها مختصات را قرار می‌دهیم که برای مستطیل اولی مختصات راس چپ‌ِ پایین و دومی مختصات راس راستِ بالا است و در دایره اولی مختصات مرکز و دومی شعاع است. بین دو پرانتز به جای fig می‌توانید از اشکال --(خط ساده)، circle (دایره)، rectangle (مستطیل) و arc (زاویه) استفاده کنید. برای تنظیمات اختیاری هم می‌توانید با مطالعه ی ‌‌راهنمای tikz بیشتر آشنا شوید(هر چند که ما هم چندتا از آن‌ها را معرفی می‌کنیم.
	
	برای رسم شبکه در زمینه شکل از دستور grid استفاده می‌شود که خط سوم کد فوق شامل این دستور است.
	
	برای گرفتن یک نمای خاص با هر یک از شکل‌های یاد شده از دستور کلیپ می‌توان استفاده کرد(مطابق خط چهارم کد فوق).
	
	ما همه چیز را نگفتیم اگر می‌خواهید بیشتر بدانید تا حد امکان به کد زیر و خروجی آن دقت کنید.
	
	\lstset{framexleftmargin=5mm, frame=shadowbox, numbers=left, rulesepcolor=\color{blue}, language=Tex}
	\begin{latin}
		\begin{lstlisting}[frame=trBL]
		\begin{center}
		\begin{tikzpicture}[scale=1.5]
		\clip[draw] (.5,.5) circle (2.5);
		\draw[step=.5cm, gray,color=brown] (0,0) grid (2,2);
		\draw (-1.5,0) -- (1.5,0);
		\draw [color=red,<->] (0,-1.5) -- (0,1.5);
		\draw[color=blue] (0,0) circle (1.5cm);
		\draw (0,0) rectangle (0.5,0.5);
		\draw (-0.5,-0.5) rectangle (-1,-1);
		\draw [color=green] (5mm,0mm) arc (0:90:5mm);
		\shadedraw[left color=gray,right color=green, draw=
		green!50!black](0,0) -- (3mm,0mm) arc (0:30:3mm) -- cycle;
		\end{tikzpicture}
		\end{center}
		\end{lstlisting}
	\end{latin}
	
	
	\begin{center}
		\begin{tikzpicture}[scale=1.5]
		\clip[draw] (.5,.5) circle (2.5);
		\draw[step=.5cm, gray,color=brown] (0,0) grid (2,2);
		\draw (-1.5,0) -- (1.5,0);
		\draw [color=red,<->] (0,-1.5) -- (0,1.5);
		\draw[color=blue] (0,0) circle (1.5cm);
		\draw (0,0) rectangle (0.5,0.5);
		\draw (-0.5,-0.5) rectangle (-1,-1);
		\draw [color=green] (5mm,0mm) arc (0:90:5mm);
		\shadedraw[left color=gray,right color=green, draw=green!50!black](0,0) -- (3mm,0mm) arc (0:30:3mm) -- cycle;
		\end{tikzpicture}
	\end{center}
	
	اما این همه‌ی هنر این دستور نیست شما تقریبا هر نمودار در فضای ۲بعدی و مختصات دکارتی رامی‌توانید با دستور plot در دستور draw بکشید، برای نمونه می‌توانید دو تا کد زیر و خروجی‌شان را ملاحظه کنید.\footnote{تنها چیزی که لازم است یادآوری کنم این است که دقت کنید هر خط با سمیکولن تمام می‌شود پس اگرانتهای خطی خالی ست بدانید که ادامه دستور در خط بعد آمده، این رااز این بابت گفتم که بتوانید کد رابرای خودتان تشریح کنید}
	\begin{center}
		\begin{tikzpicture}[scale=.6]
		\draw[->] (-7,0) -- (7,0) node[right] {$x$};
		\draw[->] (0,-5) -- (0,7) node[above] {$y$};
		\draw[color=blue] plot[domain=-6.5:-1.18, samples=70, smooth] (\x, {((\x)^2+1)/((\x)^2-1)}) node[right] {};
		\draw[color=blue] plot[domain=1.18:6.5, samples=70, smooth] (\x, {((\x)^2+1)/((\x)^2-1)}) node[right] {};
		\draw[color=blue] plot[domain=-.8:.8, samples=70, smooth] (\x, {((\x)^2+1)/((\x)^2-1)}) node[right] {};
		\draw[color=blue] plot[domain=-6.5:6.5] (\x, { 1}) node[right] {};
		\draw[blue] (1,-4.5) -- (1,6.5) node[above] {};
		\draw[blue] (-1,-4.5) -- (-1,6.5) node[above] {};
		\fill[blue] (0,-1) circle (.1) (2,1.67) circle (.1) (-2,1.67) circle (.1) (.5,-1.67) circle (.1) (-.5,-1.67) circle (.1) (0,1) circle (.1);
		\end{tikzpicture}
	\end{center}
	\lstset{framexleftmargin=5mm, frame=shadowbox, numbers=left, rulesepcolor=\color{blue}, language=Tex}
	\begin{latin}
		\begin{lstlisting}[frame=trBL]
		\begin{center}
		\begin{tikzpicture}[scale=.8]
		\draw[->] (-7,0) -- (7,0) node[right] {$x$};
		\draw[->] (0,-5) -- (0,7) node[above] {$y$};
		\draw[color=blue] plot[domain=-6.5:-1.18, samples=70, smooth] 
		(\x, {((\x)^2+1)/((\x)^2-1)}) node[right] {};
		\draw[color=blue] plot[domain=1.18:6.5, samples=70, smooth] 
		(\x, {((\x)^2+1)/((\x)^2-1)}) node[right] {};
		\draw[color=blue] plot[domain=-.8:.8, samples=70, smooth] 
		(\x, {((\x)^2+1)/((\x)^2-1)}) node[right] {};
		\draw[color=blue] plot[domain=-6.5:6.5] 
		(\x,{1}) node[right] {};
		\draw[blue] (1,-4.5) -- (1,6.5) node[above] {};
		\draw[blue] (-1,-4.5) -- (-1,6.5) node[above] {};
		\fill[blue] (0,-1) circle (.1) (2,1.67) circle (.1) 
		(-2,1.67) circle (.1) (.5,-1.67) circle (.1) 
		(-.5,-1.67) circle (.1) (0,1) circle (.1);
		\end{tikzpicture}
		\end{center}
		\end{lstlisting}
	\end{latin}
	نمونه‌ی دیگر یک نمودار مثلثاتی ست که تنها یک تفاوت کوچک برای رسمش هست که مختصات رابه رادیان تبدیل می‌کند\footnote{واقعا فکر می‌کنید اگر با گذاشتن کد و خروجی آن را هم می‌گفتم تا زحمت چک کردن هم به خودتان ندهید کار خوبی بود؟!}.
	\begin{center}
		\begin{tikzpicture}[scale=1, domain=-3.3:3.3]
		\draw[->] (-3.5,0) -- (3.5,0) node[right] {$x$};
		\draw[->] (0,-5) -- (0,5) node[above] {$y$};
		\draw[color=blue] plot[ samples=100, smooth]  (\x, {3*cos(2*\x r)}) node[right] {};
		\fill[blue] (-3.14,3) circle (.08) (-1.57,-3) circle (.08) (-.775,0) circle (.08) (0,3) circle (.08) (.775,0) circle (.08) (1.57,-3) circle (.08) (3.14,3) circle (.08);
		\draw[blue,dashed] (-1.57,0) -- (-1.57,-3) -- (1.57,-3) -- (1.57,0) (-3.14,0) --(-3.14,3)--(3.14,3)--(3.14,0);
		\foreach \x/\xtext in {-3.14/-\pi, -1.57/-\frac{\pi}{2}, -.775/-\frac{\pi}{4}, 0/0, .775/\frac{\pi}{4}, 1.57/\frac{\pi}{2}, 3.14/\pi}
		\draw[shift={(\x,0)}] (0pt,0pt) -- (0pt,0pt) node[below] {$\xtext$};
		\end{tikzpicture}
	\end{center}
	\lstset{framexleftmargin=5mm, frame=shadowbox, numbers=left, rulesepcolor=\color{blue}, language=Tex}
	\begin{latin}
		\begin{lstlisting}[frame=trBL]
		\begin{center}
		\begin{tikzpicture}[scale=1, domain=-3.3:3.3]
		\draw[->] (-3.5,0) -- (3.5,0) node[right] {$x$};
		\draw[->] (0,-5) -- (0,5) node[above] {$y$};
		\draw[color=blue] plot[ samples=100, smooth] 
		(\x, {3*cos(2*\x r)}) node[right] {};
		\fill[blue] (-3.14,3) circle (.08) (-1.57,-3) circle (.08)
		(-.775,0) circle (.08) (0,3) circle (.08) 
		(.775,0) circle (.08) (1.57,-3) circle (.08) 
		(3.14,3) circle (.08);
		\draw[blue,dashed] (-1.57,0) -- (-1.57,-3) -- (1.57,-3)
		-- (1.57,0) (-3.14,0) --(-3.14,3)--(3.14,3)--(3.14,0);
		\foreach \x/\xtext in {-3.14/-\pi, -1.57/-\frac{\pi}{2},
		-.775/-\frac{\pi}{4}, 0/0, .775/\frac{\pi}{4},
		1.57/\frac{\pi}{2}, 3.14/\pi}
		\draw[shift={(\x,0)}] (0pt,0pt) -- (0pt,0pt)
		node[below] {$\xtext$};
		\end{tikzpicture}
		\end{center}
		\end{lstlisting}
	\end{latin}
	
	\item[fill]
	دستور fill هم مشابه دستور draw است، فقط این‌که طبیعتا از آن انتظار داریم همه‌ی اشکال را تو پر بکشد.\footnote{فکر می‌کنم تا همین جا کافی باشد اگر بیشتر از این نمونه خواستید، و از راهنمای tikz نتوانستید استفاده کنید با ما تماس بگیرید، تا در حد توان تجربیات‌مان را تقدیم‌تان کنیم.} البته کاربردش را هم می‌توانید در کدهای بالا ببینید.
\end{description}

\begin{center}
	\begin{tikzpicture}[scale=1]
	\draw[blue] (.5,0) rectangle (7,4) node[right] {\rl{دانشکده}};
	\draw[blue] (2.5,2) circle (1.5) node[] {$A$\ \rl{حسابداری}};
	\draw[blue] (5,2) circle (1.5) node[] {$B$\ \rl{مدیریت}};
	\end{tikzpicture}
	
	\begin{tikzpicture}[domain=-4:4]
	%\draw[very thin,color=gray] (-5,-1.1) grid (9,5);
	\draw[->] (-5.2,0) -- (4.2,0) node[right] {$x$};
	\draw[->] (0,-1.2) -- (0,4.2) node[above] {$f(x)$};
	\draw[color=red] plot (\x,\x) node[right] {$f(x) =x$};
	\draw[color=blue] plot (\x,{sin(\x r)}) node[right] {$f(x) = \sin x$};
	\draw[color=orange] plot (\x,{0.05*exp(\x)}) node[right] {$f(x) = \frac{1}{20} \mathrm e^x$};
	\draw[color=green] plot (\x,{5*sin(\x r)}) node[right] {$5\times f(x) = \sin x$};
	\draw[color=green] plot (\x,{(\x^2)/3}) node[right] {$f(x) = \sin^2/ 3$};
	\end{tikzpicture}
\end{center}

%\section{بسته tabvar برای رسم جداول تعیین علامت}
%در این قسمت فقط می‌تونید نمونه‌ها رو ببینید، چون واقعا چیز زیادی برا گفتن نداره.
%
%\[\begin{tabvar}{ C|CCCCCCCC} 
%x &-\infty & &1 & &\frac{5}{3}& & +\infty
%\\ \hline
%f'(x)& &+& \barre{0} &- &\barre{0} &+ & &
%\\ \hline
%f(x) &  &\niveau{2}{2}\text{صعودی} &\niveau{0}{ 1}\barre{\text{ماکزیمم}}&\niveau{2}{2}\text{نزولی}&\niveau{0}{1}\barre{\text{مینیمم}}
% &\niveau{2}{2}\text{صعودی}&
%\end{tabvar}\]
%
%\[\begin{tabvar}{C|CCCCCCCCC} 
%x &-\infty & &-1& &0& &+1 & &+\infty 
%\\ \hline
%f'(x) & &+&\barre{0} &-&\dbarre{}&-&\barre{0}&+&
%\\ \hline
%f''(x)& &-&\barre{}&-&\dbarre{}&+&\barre{}&+&
%\\ \hline
%\niveau{2}{2}\TVcenter{f(x)}& &\niveau{2}{2}\TVcenter{\text{صعودی محدب}}&\niveau{0}{1}\barre{\text{ماکزیمم}}&\niveau{2}{2}\TVcenter{\text{نزولی محدب}}&\dbarre{}&\TVcenter{\text{نزولی مقعر}}
%&\niveau{0}{1}\barre{\text{مینیمم}}&\niveau{2}{2}\TVcenter{\text{صعودی مقعر}}&
%\end{tabvar}\]
%
%\[\begin{tabvar}{C|CCCCCCCCC} 
%x &-\infty & &-1& &1& &5& &+\infty \\ \hline
%(1+x)^2& &+&\barre{0}&+&\barre{}&+&\barre{}&+& \\ \hline
%1-x& &+&\barre{}&+&\barre{0}&-&\barre{}&-&\\ \hline
%x-5& & -&\barre{}&-&\barre{}&-&\barre{0}&+&\\ \hline
%f'(x) & &-&\barre{0} &-&\barre{0}&+&\barre{0}&-&\\ \hline
%\niveau{3}{3}\TVcenter{f(x)}& &\decroit &\niveau{0}{2}\barre{}&\niveau{3}{3}\decroit &
%\niveau{0}{2}\barre{\text{مینیمم}}&\niveau{3}{3}\TVcenter{\croit} & \niveau{0}{2}\barre{\text{ماکزیمم}}&\niveau{3}{3}{\decroit} &
%\end{tabvar}\]

تمام شکل‌ها و نمودارهایی که در ادامه خواهید دید  تنها توسط بسته tkz رسم شده‌اند.
\section{دیاگرام جبری}
%\begin{figure}[!ht]
%\centering
%\scalebox{.7}
%{
%\begin{pspicture}(0,0)
%\pscircle[linewidth=.015,dimen=outer](0,0){.4}
%\rput(0,0){$1$}
%\psline[linewidth=.01cm,arrowsize=.1cm,arrowlength=1.5,arrowinset=.2]{-}(-.255,-.255)(-1.15,-1.1)
%\rput(-1.2,-.6){$u_3=0$}
%\psline[linewidth=.01cm,arrowsize=.1cm,arrowlength=1.5,arrowinset=.2]{-}(.26,-.255)(1.2,-1.1)
%\rput(1.6,-.6){$g_3=0$}
%\pscircle[linewidth=.015,dimen=outer](1.4,-1.4){.4}
%\rput(1.4,-1.4){$4$}
%\pscircle[linewidth=.015,dimen=outer](-1.4,-1.4){.4}
%\rput(-1.4,-1.4){$0$}
%\psline[linewidth=.01cm,arrowsize=.1cm,arrowlength=1.5,arrowinset=.2]{-}(-1.65,-1.67)(-2.52,-2.52)
%\pscircle[linewidth=.015,dimen=outer](-2.8,-2.8){.4}
%\rput(-2.8,-2.8){$2$}
%\rput(-2.5,-2){$u_2=0$}
%\psline[linewidth=.01cm,arrowsize=.1cm,arrowlength=1.5,arrowinset=.2]{-}(-2.35,-3.37)(-3.35,-3.37)
%\psline[linewidth=.01cm,arrowsize=.1cm,arrowlength=1.5,arrowinset=.2]{-}(-1.1,-1.65)(-.23,-2.52)
%\rput(0,-2){$g_2=0$}
%\pscircle[linewidth=.015,dimen=outer](0,-2.8){.4}
%\rput(0,-2.8){$3$}
%\end{pspicture} 
%}
%\end{figure}


%\begin{center}
%\begin{tikzpicture}
%\GraphInit[vstyle=Shade]
%\SetVertexNoLabel
%\grTriangularGrid[RA=1,form=2]{6}%
%\end{tikzpicture}
%\end{center}


%\begin{center}
%\begin{tikzpicture}
%\GraphInit[vstyle=Shade]
%\SetVertexLabel
%\grTriangularGrid[prefix=G,Math,RA=1.2]{8}%
%\end{tikzpicture}
%\end{center}
%
%\begin{center}
%\begin{tikzpicture}%
%\GraphInit[vstyle=Art]
%\SetGraphArtColor{black!50}{darkgray}
%\tikzset{VertexStyle/.append style = {
%minimum size = 2pt}}
%\grLCF[RA=3]{1,-3}{4}%
%\end{tikzpicture}
%\end{center}



%\begin{center}
%\begin{tikzpicture}
%\useasboundingbox (-1,-1) rectangle (11,11);
%\tikzset{VertexStyle/.style = {shape = circle,
%ball color = orange,
%text = black,
%inner sep = 2pt,
%outer sep = 0pt,
%minimum size = 24 pt}}
%\tikzset{EdgeStyle/.style = {thick,
%double = orange,
%double distance = 1pt}}
%\tikzset{LabelStyle/.style = {draw,
%fill = yellow,
%text = red}}
%\node[VertexStyle](A){A};
%\node[VertexStyle,right= of A](B){B};
%\node[VertexStyle,right= of B](C){C};
%\node[VertexStyle,above= 7 cm of B](D){D};
%\draw[EdgeStyle](B) to node[LabelStyle]{1} (D) ;
%\tikzset{EdgeStyle/.append style = {bend left}}
%\draw[EdgeStyle](A) to node[LabelStyle]{2} (B);
%\draw[EdgeStyle](B) to node[LabelStyle]{3} (A);
%\draw[EdgeStyle](B) to node[LabelStyle]{4} (C);
%\draw[EdgeStyle](C) to node[LabelStyle]{5} (B);
%\draw[EdgeStyle](A) to node[LabelStyle]{6} (D);
%\draw[EdgeStyle](D) to node[LabelStyle]{7} (C);
%\end{tikzpicture}
%\end{center}

%\begin{tikzpicture}
%\SetGraphUnit{4}
%\Vertex{a}
%\EA(a){b}
%\SO[unit=2](a){c}
%\EA(c){d}
%{\SetGraphUnit{2}
%\SO(c){e}}
%\EA(e){f}
%\Edge(a)(b)
%\tikzset{EdgeStyle/.style = {-,bend left}}
%\Edge(c)(d)
%\tikzset{EdgeStyle/.style = {<->,bend right=90}}
%\Edge(e)(f)
%\end{tikzpicture}


\newpage

\begin{figure}[H]
	\usetikzlibrary{matrix}
	\begin{center}
			\begin{tikzpicture}
		\matrix (m) [matrix of math nodes,row sep=3em,column sep=4em,minimum width=2em]
		{
			F_t(x) & F(x) \\
			A_t & A \\};
		\path[-stealth]
		(m-1-1) edge node [left] {$\mathcal{B}_X$} (m-2-1)
		edge [double] node [below] {$\mathcal{B}_t$} (m-1-2)
		(m-2-1.east|-m-2-2) edge node [below] {$\mathcal{B}_T$}
		node [above] {$\exists$} (m-2-2)
		(m-1-2) edge node [right] {$\mathcal{B}_T$} (m-2-2)
		edge [dashed,-] (m-2-1);
		\end{tikzpicture}
		\caption{commutative-diagram1}
%	\end{center}
%\end{figure}
%\begin{figure}
%	 \usetikzlibrary{matrix}
%	\begin{center}
		\begin{tikzpicture}
		\matrix (m) [matrix of math nodes, row sep=3em,
		column sep=3em]{
			& f^\ast E_V& & \vphantom{f^\ast}E_V \\
			f^\ast E & & \vphantom{f^\ast}E & \\
			& U & & V \\
			M & & N & \\};
		\path[-stealth]
		(m-1-2) edge (m-1-4) edge (m-2-1)
		edge [densely dotted] (m-3-2)
		(m-1-4) edge (m-3-4) edge (m-2-3)
		(m-2-1) edge [-,line width=6pt,draw=white] (m-2-3)
		edge (m-2-3) edge (m-4-1)
		(m-3-2) edge [densely dotted] (m-3-4)
		edge [densely dotted] (m-4-1)
		(m-4-1) edge (m-4-3)
		(m-3-4) edge (m-4-3)
		(m-2-3) edge [-,line width=6pt,draw=white] (m-4-3)
		edge (m-4-3);
		\end{tikzpicture} 
		\caption{commutative-diagram2}
	\end{center}
\end{figure}
\newpage
\subsection{نمودارهایی برای مقایسه}
\begin{figure}[H]
	\begin{center}
		\begin{tikzpicture}
		\begin{axis}[
		y axis line style = { opacity = 0 },
		axis x line       = none,
		tickwidth         = 0pt,
		enlarge y limits  = 0.1,
		enlarge x limits  = 0.15,
		xbar, xmin=0,
		width=13cm, height=3.5cm,
		symbolic y coords={\rl{واریانس خارج از نمونه}},
		ytick=data,
		nodes near coords, nodes near coords align={horizontal},
		]
		\addplot coordinates {(.8334,\rl{واریانس خارج از نمونه})};
		\addplot coordinates {(.9274,\rl{واریانس خارج از نمونه})};
		\addplot coordinates {(.7788,\rl{واریانس خارج از نمونه})};
		\end{axis}
		\end{tikzpicture}
		\begin{tikzpicture}
		\begin{axis}[
		y axis line style = { opacity = 0 },
		axis x line       = none,
		tickwidth         = 0pt,
		enlarge y limits  = 0.01,
		enlarge x limits  = 0.21,
		xbar, xmin=0,
		width=12cm, height=3.5cm,
		symbolic y coords={\rl{نسبت شارپ}},
		ytick=data,
		nodes near coords, nodes near coords align={horizontal},
		]
		\addplot coordinates {(.1763,\rl{نسبت شارپ})};
		\addplot coordinates {(.1570,\rl{نسبت شارپ})};
		\addplot coordinates {(.1835,\rl{نسبت شارپ})};
		\end{axis}
		\end{tikzpicture}
		\begin{tikzpicture}
		\begin{axis}[
		y axis line style = { opacity = 0 },
		axis x line       = none,
		tickwidth         = 0pt,
		enlarge y limits  = 0.1,
		enlarge x limits  = 0.23,
		xbar, xmin=0,
		width=12cm, height=3.5cm,
		symbolic y coords={\rl{حجم معاملاتی}},
		ytick=data,
		nodes near coords, nodes near coords align={horizontal},
		legend style={at={(0.5,-0.15)},
			anchor=north,legend columns=-1},
		]
		\addplot coordinates {(.0421,\rl{حجم معاملاتی})};
		\addplot coordinates {(.0595,\rl{حجم معاملاتی})};
		\addplot coordinates {(.0365,\rl{حجم معاملاتی})};
		\legend{MVSRE, MVSRB, MVIR}
		\end{axis}
		\end{tikzpicture}
	\end{center}
	\caption{نمودار مربوط به سه روش}
	\label{fig8}
\end{figure}

\begin{figure}[H]
\begin{tikzpicture}
\begin{axis}[ 
xbar=0pt,% space of 0pt between adjacent bars
bar width=2pt,
%width=\textwidth,
%height=11cm,
minor y tick num=4,
%ytick=data,
enlargelimits=0.15
x tick label style={
	/pgf/number format/1000 sep=},
ylabel=Population,
enlargelimits=0.15,
legend style={at={(0.5,-0.15)},
	anchor=north,legend columns=-1},
ybar=1pt,% configures ‘bar shift’
bar width=4pt,
%nodes near coords,
point meta=y  % the displayed number
]
\addplot
coordinates {(1930,50) (1940,33)
	(1950,40)   (1960,50) (1970,70)(1980,10) (1990,4) (2010,18) (2020,45) (2030,95)};
\addplot
coordinates {(1930,50) (1940,33)
	(1950,25)   (1960,36) (1970,50)(1980,5) (1990,29) (2010,10) (2020,49) (2030,55)};
\addplot
coordinates {(1930,38) (1940,42)
	(1950,43) (1960,45) (1970,65)(1980,65) (1990,69) (2010,25) (2020,75) (2030,10)};
\addplot
coordinates {(1930,82) (1940,34)
	(1950,43) (1960,67) (1970,63)(1980,83) (1990,52) (2010,78) (2020,19) (2030,86)};
\legend{\rl{روش 4}, \rl{روش 3}, \rl{روش 2}, \rl{روش 1}}
\end{axis}
\end{tikzpicture}
% Preamble: \pgfplotsset{width=7cm,compat=1.14}
\begin{tikzpicture}
\begin{axis}[
ybar,
enlargelimits=0.15,
legend style={at={(0.5,-0.15)},
	anchor=north,legend columns=-1},
ylabel={participants},
symbolic x coords={tool8,tool9,tool10},
xtick=data,
nodes near coords,
nodes near coords align={vertical},
]
\addplot coordinates {(tool8,7) (tool9,9) (tool10,4)};
\addplot coordinates {(tool8,4) (tool9,4) (tool10,4)};
\addplot coordinates {(tool8,1) (tool9,1) (tool10,1)};
\legend{used,understood,not understood}
\end{axis}
\end{tikzpicture}
\end{figure}
\begin{figure}[H]
	\begin{center}
		{
			\begin{tikzpicture}
			%	\begin{loglogaxis}
			\begin{axis}
			[ width=13cm, height=10cm,
			xlabel=\textsc{k},
			ylabel=vsi
			]
			% 	\axispath\draw
			% 	(7.49165,-10.02171)
			% 	|-  (8.31801,-11.32467)
			% 	node[near start,left] {$\frac{dy}{dx} = -1.58$};
			\addplot plot coordinates {
				(10,  4.039)
				(12,  5.9)
				(14,  10)
				(16, 7.0)
				(18, 3.8)
				(20,     3.2)
				(22,    3.844)
				(24,   7.0)
			};
			
			\addplot plot coordinates {
				(10,  3.4)
				(12,  5.5)
				(14,  9.01)
				(16, 7.2)
				(18, 3.1)
				(20,     2.9)
				(22,    4.1)
				(24,   6.9)
			};
			\addplot plot coordinates {
				(10,  3.039)
				(12,  5.196)
				(14,  9.658)
				(16, 7.873)
				(18, 3.437)
				(20,     2.472)
				(22,    4.044)
				(24,   6.22)
			};
			\legend{ 	
				\rl{مدل اول}\\ 		\rl{مدل دوم} \\ 		\rl{مدل سوم} \\}
			\end{axis}
			%		\end{loglogaxis}
			\end{tikzpicture}}
	\end{center}
\end{figure}
 
\begin{figure}[H]
\begin{tikzpicture}
\begin{axis}[
ybar stacked,
enlargelimits=0.15,
legend style={at={(0.5,-0.20)},
	anchor=north,legend columns=-1},
ylabel={\#participants},
symbolic x coords={tool1, tool2, tool3, tool4,
	tool5, tool6, tool7},
xtick=data,
x tick label style={rotate=45,anchor=east},
]
\addplot+[ybar] plot coordinates {(tool1,0) (tool2,2)
	(tool3,2) (tool4,3) (tool5,0) (tool6,2) (tool7,0)};
\addplot+[ybar] plot coordinates {(tool1,0) (tool2,0)
	(tool3,0) (tool4,3) (tool5,1) (tool6,1) (tool7,0)};
\addplot+[ybar] plot coordinates {(tool1,6) (tool2,6)
	(tool3,8) (tool4,2) (tool5,6) (tool6,5) (tool7,6)};
\addplot+[ybar] plot coordinates {(tool1,4) (tool2,2)
	(tool3,0) (tool4,2) (tool5,3) (tool6,2) (tool7,4)};
\legend{never, rarely, sometimes, often}
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{axis}[
ybar stacked,
bar width=15pt,
nodes near coords,
enlargelimits=0.15,
legend style={at={(0.5,-0.20)},
	anchor=north,legend columns=-1},
ylabel={\#participants},
symbolic x coords={tool1, tool2, tool3, tool4,
	tool5, tool6, tool7},
xtick=data,
x tick label style={rotate=45,anchor=east},
]
\addplot+[ybar] plot coordinates {(tool1,0) (tool2,2)
	(tool3,2) (tool4,3) (tool5,0) (tool6,2) (tool7,0)};
\addplot+[ybar] plot coordinates {(tool1,0) (tool2,0)
	(tool3,0) (tool4,3) (tool5,1) (tool6,1) (tool7,0)};
\addplot+[ybar] plot coordinates {(tool1,6) (tool2,6)
	(tool3,8) (tool4,2) (tool5,6) (tool6,5) (tool7,6)};
\addplot+[ybar] plot coordinates {(tool1,4) (tool2,2)
	(tool3,0) (tool4,2) (tool5,3) (tool6,2) (tool7,4)};
\legend{never, rarely, sometimes, often}
\end{axis}
\end{tikzpicture}
\end{figure}
 
\begin{figure}[H]
	\begin{tikzpicture}
	\begin{axis}[ 
	xbar=0pt,% space of 0pt between adjacent bars
	bar width=2pt,
	width=16cm,
	height=12cm,
	minor y tick num=4,
	%ytick=data,
	enlargelimits=0.15
	x tick label style={
		/pgf/number format/1000 sep=},
	ylabel=Population,
	enlargelimits=0.15,
	legend style={at={(0.5,-0.15)},
		anchor=north,legend columns=-1},
	ybar=1pt,% configures ‘bar shift’
	bar width=7pt,
	grid=both,
	%nodes near coords,
	point meta=y *10^-7 % the displayed number
	]
	\addplot
	coordinates {(1930,-50e6) (1940,33e6)
		(1950,40e6)   (1960,50e6) (1970,-70e6)(1980,10e6) (1990,4e6) (2010,-18e6) (2020,45e6) (2030,-95e6)};
	\addplot
	coordinates {(1930,50e6) (1940,-33e6)
		(1950,25e6)   (1960,-36e6) (1970,50e6)(1980,5e6) (1990,29e6) (2010,10e6) (2020,49e6) (2030,-55e6)};
	\addplot
	coordinates {(1930,38e6) (1940,-42e6)
		(1950,43e6) (1960,-45e6) (1970,65e6)(1980,65e6) (1990,69e6) (2010,25e6) (2020,75e6) (2030,-10e6)};
	\legend{Model 1, Model 2, Model 3}
	\end{axis}
	\end{tikzpicture}
\end{figure}
 
\newpage
\begin{figure}[H]
	\begin{center}
		\begin{tikzpicture}
		\begin{scope}[blend group = soft light]
		\fill[red!50!white]   ( 90:1.2) circle (2);
		\fill[green!50!white] (210:1.2) circle (2);
		\fill[blue!50!white]  (330:1.2) circle (2);
		\end{scope}
		\node at ( 90:2)    {الف};
		\node at ( 210:2)   {ب};
		\node at ( 330:2)   {ج};
		\node [font=\Large] {د};
		\end{tikzpicture}
		\caption{نمودار ون}
	\end{center}
\end{figure}
\newpage

\section{نمودار توابع}
\begin{figure}[H]
	\begin{center}
		\begin{tikzpicture}[>=latex]
		% Draw the lines at multiples of pi/12
		\foreach \ang in {0,...,31} {
			\draw [lightgray] (0,0) -- (\ang * 180 / 16:4);
		}
		
		% Concentric circles and radius labels
		\foreach \s in {0, 1, 2, 3} {
			\draw [lightgray] (0,0) circle (\s + 0.5);
			\draw (0,0) circle (\s);
			\node [fill=white] at (\s, 0) [below] {\scriptsize $\s$};
		}
		
		% Add the labels at multiples of pi/4
		\foreach \ang/\lab/\dir in {
			0/0/right,
			1/{\pi/4}/{above right},
			2/{\pi/2}/above,
			3/{3\pi/4}/{above left},
			4/{\pi}/left,
			5/{5\pi/4}/{below left},
			7/{7\pi/4}/{below right},
			6/{3\pi/2}/below} {
			\draw (0,0) -- (\ang * 180 / 4:4.1);
			\node [fill=white] at (\ang * 180 / 4:4.2) [\dir] {\scriptsize $\lab$};
		}
		
		% The double-lined circle around the whole diagram
		\draw [style=double] (0,0) circle (4);
		
		\fill [fill=red!50!black, opacity=0.5] plot [domain=-pi/2:pi/2]
		(xy polar cs:angle=\x r, radius= {2-2*sin(\x r)});
		\draw [thick, color=red, domain=0:2*pi, samples=200, smooth]
		plot (xy polar cs:angle=\x r, radius={2-2*sin(\x r)});
		\node [fill=white] at (2,1) {$r=2-2\sin\theta$};
		\end{tikzpicture} 
		\caption{polar-plot}
	\end{center}
\end{figure}
%\newpage
%\begin{figure}[H]
%	\begin{center}
%		\begin{tikzpicture}
%		\begin{axis}[
%		xlabel=$x$,
%		ylabel=$y$]
%		\addplot[smooth,mark=*,blue] plot coordinates {
%			(0,2)
%			(2,3)
%			(3,1)
%		};
%		\addlegendentry{Case 1}
%		
%		\addplot[smooth,color=red,mark=x]
%		plot coordinates {
%			(0,0)
%			(1,1)
%			(2,1)
%			(3,2)
%		};
%		\addlegendentry{Case 2}
%		\end{axis}
%		\end{tikzpicture}
%		
%		
%		\begin{tikzpicture}
%		\begin{loglogaxis}[
%		xlabel=\textsc{Dof},
%		ylabel=$L_2$ Error
%		]
%		\axispath\draw
%		(7.49165,-10.02171)
%		|-  (8.31801,-11.32467)
%		node[near start,left] {$\frac{dy}{dx} = -1.58$};
%		\addplot plot coordinates {
%			(5,     8.312e-02)
%			(17,    2.547e-02)
%			(49,    7.407e-03)
%			(129,   2.102e-03)
%			(321,   5.874e-04)
%			(769,   1.623e-04)
%			(1793,  4.442e-05)
%			(4097,  1.207e-05)
%			(9217,  3.261e-06)
%		};
%		
%		\addplot plot coordinates {
%			(7,     8.472e-02)
%			(31,    3.044e-02)
%			(111,   1.022e-02)
%			(351,   3.303e-03)
%			(1023,  1.039e-03)
%			(2815,  3.196e-04)
%			(7423,  9.658e-05)
%			(18943, 2.873e-05)
%			(47103, 8.437e-06)
%		};
%		
%		\addplot plot coordinates {
%			(9, 7.881e-02)
%			(49,    3.243e-02)
%			(209,   1.232e-02)
%			(769,   4.454e-03)
%			(2561,  1.551e-03)
%			(7937,  5.236e-04)
%			(23297, 1.723e-04)
%			(65537, 5.545e-05)
%			(178177,    1.751e-05)
%		};
%		
%		\addplot plot coordinates {
%			(11,    6.887e-02)
%			(71,    3.177e-02)
%			(351,   1.341e-02)
%			(1471,  5.334e-03)
%			(5503,  2.027e-03)
%			(18943, 7.415e-04)
%			(61183, 2.628e-04)
%			(187903,    9.063e-05)
%			(553983,    3.053e-05)
%		};
%		
%		\addplot plot coordinates {
%			(13,    5.755e-02)
%			(97,    2.925e-02)
%			(545,   1.351e-02)
%			(2561,  5.842e-03)
%			(10625, 2.397e-03)
%			(40193, 9.414e-04)
%			(141569,    3.564e-04)
%			(471041,    1.308e-04)
%			(1496065,   4.670e-05)
%		};
%		\legend{$d=2$\\$d=3$\\$d=4$\\$d=5$\\$d=6$\\}
%		\end{loglogaxis}
%		\end{tikzpicture}
%		\caption{pgfplot}
%	\end{center}
%\end{figure}

\newpage
\begin{figure}[H]
	\begin{center}
		\begin{tikzpicture}[scale=2]
		\shade[top color=blue,bottom color=gray!50] 
		(0,0) parabola (1.5,2.25) |- (0,0);
		\draw (1.05cm,2pt) node[above] 
		{$\displaystyle\int_0^{3/2} \!\!x^2\mathrm{d}x$};
		
		\draw[style=help lines] (0,0) grid (3.9,3.9)
		[step=0.25cm]      (1,2) grid +(1,1);
		
		\draw[->] (-0.2,0) -- (4,0) node[right] {$x$};
		\draw[->] (0,-0.2) -- (0,4) node[above] {$f(x)$};
		
		\foreach \x/\xtext in {1/1, 1.5/1\frac{1}{2}, 2/2, 3/3}
		\draw[shift={(\x,0)}] (0pt,2pt) -- (0pt,-2pt) node[below] {$\xtext$};
		
		\foreach \y/\ytext in {1/1, 2/2, 2.25/2\frac{1}{4}, 3/3}
		\draw[shift={(0,\y)}] (2pt,0pt) -- (-2pt,0pt) node[left] {$\ytext$};
		
		\draw (-.5,.25) parabola bend (0,0) (2,4) node[below right] {$x^2$};
		\end{tikzpicture}	
		\caption{}
	\end{center}
\end{figure}
%
%\newpage
%\GraphInit[vstyle = Shade]
%\tikzset{
%	LabelStyle/.style = { rectangle, rounded corners, draw,
%		minimum width = 2em, fill = yellow!50,
%		text = red, font = \bfseries },
%	VertexStyle/.append style = { inner sep=5pt,
%		font = \Large\bfseries},
%	EdgeStyle/.append style = {->, bend left} }
%\begin{figure}
%	\begin{center}
%		\begin{tikzpicture}
%		\SetGraphUnit{5}
%		\Vertex{B}
%		\WE(B){A}
%		\EA(B){C}
%		\Edge[label = 1](A)(B)
%		\Edge[label = 2](B)(C)
%		\Edge[label = 3](C)(B)
%		\Edge[label = 4](B)(A)
%		\Loop[dist = 4cm, dir = NO, label = 5](A.west)
%		\Loop[dist = 4cm, dir = SO, label = 6](C.east)
%		\tikzset{EdgeStyle/.append style = {bend left = 50}}
%		\Edge[label = 7](A)(C)
%		\Edge[label = 8](C)(A)
%		\end{tikzpicture}
%		\caption{graph1}
%	\end{center}
%\end{figure}
\newpage

\begin{figure}[H]
	\usetikzlibrary{arrows,intersections}
	\begin{center}
		\begin{tikzpicture}[
		thick,
		>=stealth',
		dot/.style = {
			draw,
			fill = white,
			circle,
			inner sep = 0pt,
			minimum size = 4pt
		}
		]
		\coordinate (O) at (0,0);
		\draw[->] (-0.3,0) -- (8,0) coordinate[label = {below:$x$}] (xmax);
		\draw[->] (0,-0.3) -- (0,5) coordinate[label = {right:$f(x)$}] (ymax);
		\path[name path=x] (0.3,0.5) -- (6.7,4.7);
		\path[name path=y] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
		\scope[name intersections = {of = x and y, name = i}]
		\fill[gray!20] (i-1) -- (i-2 |- i-1) -- (i-2) -- cycle;
		\draw      (0.3,0.5) -- (6.7,4.7) node[pos=0.8, below right] {Sekante};
		\draw[red] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
		\draw (i-1) node[dot, label = {above:$P$}] (i-1) {} -- node[left]
		{$f(x_0)$} (i-1 |- O) node[dot, label = {below:$x_0$}] {};
		\path (i-2) node[dot, label = {above:$Q$}] (i-2) {} -- (i-2 |- i-1)
		node[dot] (i-12) {};
		\draw           (i-12) -- (i-12 |- O) node[dot,
		label = {below:$x_0 + \varepsilon$}] {};
		\draw[blue, <->] (i-2) -- node[right] {$f(x_0 + \varepsilon) - f(x_0)$}
		(i-12);
		\draw[blue, <->] (i-1) -- node[below] {$\varepsilon$} (i-12);
		\path       (i-1 |- O) -- node[below] {$\varepsilon$} (i-2 |- O);
		\draw[gray]      (i-2) -- (i-2 -| xmax);
		\draw[gray, <->] ([xshift = -0.5cm]i-2 -| xmax) -- node[fill = white]
		{$f(x_0 + \varepsilon)$}  ([xshift = -0.5cm]xmax);
		\endscope
		\end{tikzpicture}		
		\caption{linear-regression}
	\end{center}
\end{figure}
\newpage
\section{نمودار درختی}
\begin{figure}[H]
	\usetikzlibrary{positioning,shadows,arrows}
	\begin{center}
		\begin{tikzpicture}[
		fact/.style={rectangle, draw=none, rounded corners=1mm, fill=blue, drop shadow,
			text centered, anchor=north, text=white},
		state/.style={circle, draw=none, fill=orange, circular drop shadow,
			text centered, anchor=north, text=white},
		leaf/.style={circle, draw=none, fill=red, circular drop shadow,
			text centered, anchor=north, text=white},
		level distance=0.5cm, growth parent anchor=south
		]
		\node (State00) [state] {$S_{00}$} [->]
		child{
			node (Fact01) [fact] {$T_{01}$}
			child{ [sibling distance=9cm]
				node (State01) [state] {$S_{01}$}
				child{
					node (Fact02) [fact] {$T_{02}$}
					child{ [sibling distance=4cm]
						node (State02) [state] {$S_{02}$}
						child{
							node (Fact03) [fact] {$T_{03}$}
							child{
								node (State03) [leaf] {$S_{03}$}
							}
						}
						child{
							node (Fact04) [fact] {$T_{04}$}
							child{ [sibling distance=1.2cm]
								node (State04) [state] {$S_{04}$}
								child{
									node (Fact05) [fact] {$T_{05}$}
									child{
										node (State05) [leaf] {$S_{05}$}
									}
								}
								child{
									node (Fact06) [fact] {$T_{06}$}
									child{
										node (State06) [leaf] {$S_{06}$}
									}
								}
								child{
									node (Fact07) [fact] {$T_{07}$}
									child{
										node (State07) [leaf] {$S_{07}$}
									}
								}
								child{
									node (Fact08) [fact] {$T_{08}$}
									child{
										node (State08) [leaf] {$S_{08}$}
									}
								}
								child{
									node (Fact09) [fact] {$T_{09.0}$}
									child{
										node (Fact09-1) [fact] {$T_{09.1}$}
										child{
											node (State09) [leaf] {$S_{09}$}
										}
									}
								}
							}
						}
					}
				}
				child{ [sibling distance=4cm]
					node (Fact10) [fact] {$T_{10}$}
					child{
						node (State10) [state] {$S_{10}$}
						child{
							node (Fact11) [fact] {$T_{11}$}
							child{
								node (State11) [leaf] {$S_{11}$}
							}
						}
						child{
							node (Fact12) [fact] {$T_{12}$}
							child{
								node (State12) [state] {$S_{12}$}
							}
						}
					}
				}
			}
		}   
		;
		\end{tikzpicture}		
		\caption{نمودار درختی}
	\end{center}
\end{figure}
\newpage

\section{شکل‌های دیگر }



\begin{figure}[H]
	\usetikzlibrary[topaths]
	\newcount\mycount
	\begin{center}
		\begin{tikzpicture}[transform shape]
		%the multiplication with floats is not possible. Thus I split the loop in two.
		\foreach \number in {1,...,8}{
			% Computer angle:
			\mycount=\number
			\advance\mycount by -1
			\multiply\mycount by 45
			\advance\mycount by 0
			\node[draw,circle,inner sep=0.25cm] (N-\number) at (\the\mycount:5.4cm) {};
		}
		\foreach \number in {9,...,16}{
			% Computer angle:
			\mycount=\number
			\advance\mycount by -1
			\multiply\mycount by 45
			\advance\mycount by 22.5
			\node[draw,circle,inner sep=0.25cm] (N-\number) at (\the\mycount:5.4cm) {};
		}
		\foreach \number in {1,...,15}{
			\mycount=\number
			\advance\mycount by 1
			\foreach \numbera in {\the\mycount,...,16}{
				\path (N-\number) edge[->,bend right=3] (N-\numbera)  edge[<-,bend
				left=3] (N-\numbera);
			}
		}
		\end{tikzpicture}
		\caption{Complete-graph}
	\end{center}
\end{figure}

\newcounter{density}
\setcounter{density}{20}
\begin{figure}[H]
	\begin{center}
		\begin{tikzpicture}
		\def\couleur{LimeGreen}
		\path[coordinate] (0,0)  coordinate(A)
		++( 120:6cm) coordinate(B)
		++(60:6cm) coordinate(C)
		++(0:6cm) coordinate(D)
		++(-60:6cm) coordinate(E)
		++(240:6cm) coordinate(F)
		;
		\draw[fill=\couleur!\thedensity] (A) -- (B) -- (C) --(D) -- (E) -- (F)-- cycle;
		\foreach \x in {1,...,40}{%
			\pgfmathsetcounter{density}{\thedensity+2}
			\setcounter{density}{\thedensity}
			\path[coordinate] coordinate(X) at (A){};
			\path[coordinate] (A) -- (B) coordinate[pos=.10](A)
			-- (C) coordinate[pos=.10](B)
			-- (D) coordinate[pos=.10](C)
			-- (E) coordinate[pos=.10](D)
			-- (F) coordinate[pos=.10](E)
			-- (X) coordinate[pos=.10](F);
			\draw[fill=\couleur!\thedensity] (A)--(B)--(C)-- (D) --(E) -- (F) -- cycle;
		}
		\end{tikzpicture}
		\setcounter{density}{20}
		\begin{tikzpicture}
		\def\couleur{OrangeRed}
		\path[coordinate] (0,0)  coordinate(A)
		++( 90:12cm) coordinate(B)
		++(0:12cm) coordinate(C)
		++(-90:12cm) coordinate(D);
		\draw[fill=\couleur!\thedensity] (A) -- (B) -- (C) --(D) -- cycle;
		\foreach \x in {1,...,22}{%
			\pgfmathsetcounter{density}{\thedensity+20}
			\setcounter{density}{\thedensity}
			\path[coordinate] coordinate(X) at (A){};
			\path[coordinate] (A) -- (B) coordinate[pos=.10](A)
			-- (C) coordinate[pos=.10](B)
			-- (D) coordinate[pos=.10](C)
			-- (X) coordinate[pos=.10](D);
			\draw[fill=\couleur!\thedensity] (A)--(B)--(C)-- (D) -- cycle;
		}
		\end{tikzpicture}
		\caption{rotated-plygones}
	\end{center}
\end{figure}
\newpage
\begin{figure}[H]
	\usetikzlibrary{positioning}
	\begin{center}
		\newcommand\pgfmathsinandcos[3]{%
			\pgfmathsetmacro#1{sin(#3)}%
			\pgfmathsetmacro#2{cos(#3)}%
		}
		\newcommand\LongitudePlane[3][current plane]{%
			\pgfmathsinandcos\sinEl\cosEl{#2} % elevation
			\pgfmathsinandcos\sint\cost{#3} % azimuth
			\tikzset{#1/.style={cm={\cost,\sint*\sinEl,0,\cosEl,(0,0)}}}
		}
		\newcommand\LatitudePlane[3][current plane]{%
			\pgfmathsinandcos\sinEl\cosEl{#2} % elevation
			\pgfmathsinandcos\sint\cost{#3} % latitude
			\pgfmathsetmacro\yshift{\cosEl*\sint}
			\tikzset{#1/.style={cm={\cost,0,0,\cost*\sinEl,(0,\yshift)}}} %
		}
		\newcommand\DrawLongitudeCircle[2][1]{
			\LongitudePlane{\angEl}{#2}
			\tikzset{current plane/.prefix style={scale=#1}}
			% angle of "visibility"
			\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
			\draw[current plane,thin,black] (\angVis:1) arc (\angVis:\angVis+180:1);
			\draw[current plane,thin,dashed] (\angVis-180:1) arc (\angVis-180:\angVis:1);
		}%this is fake: for drawing the grid
		\newcommand\DrawLongitudeCirclered[2][1]{
			\LongitudePlane{\angEl}{#2}
			\tikzset{current plane/.prefix style={scale=#1}}
			% angle of "visibility"
			\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
			\draw[current plane,red,thick] (150:1) arc (150:180:1);
			%\draw[current plane,dashed] (-50:1) arc (-50:-35:1);
		}%for drawing the grid
		\newcommand\DLongredd[2][1]{
			\LongitudePlane{\angEl}{#2}
			\tikzset{current plane/.prefix style={scale=#1}}
			% angle of "visibility"
			\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
			\draw[current plane,black,dashed, ultra thick] (150:1) arc (150:180:1);
		}
		\newcommand\DLatred[2][1]{
			\LatitudePlane{\angEl}{#2}
			\tikzset{current plane/.prefix style={scale=#1}}
			\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
			% angle of "visibility"
			\pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
			\draw[current plane,dashed,black,ultra thick] (-50:1) arc (-50:-35:1);
			
		}
		\newcommand\fillred[2][1]{
			\LongitudePlane{\angEl}{#2}
			\tikzset{current plane/.prefix style={scale=#1}}
			% angle of "visibility"
			\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
			\draw[current plane,red,thin] (\angVis:1) arc (\angVis:\angVis+180:1);
			
		}
		
		\newcommand\DrawLatitudeCircle[2][1]{
			\LatitudePlane{\angEl}{#2}
			\tikzset{current plane/.prefix style={scale=#1}}
			\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
			% angle of "visibility"
			\pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
			\draw[current plane,thin,black] (\angVis:1) arc (\angVis:-\angVis-180:1);
			\draw[current plane,thin,dashed] (180-\angVis:1) arc (180-\angVis:\angVis:1);
		}%Defining functions to draw limited latitude circles (for the red mesh)
		\newcommand\DrawLatitudeCirclered[2][1]{
			\LatitudePlane{\angEl}{#2}
			\tikzset{current plane/.prefix style={scale=#1}}
			\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
			% angle of "visibility"
			\pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
			%\draw[current plane,red,thick] (-\angVis-50:1) arc (-\angVis-50:-\angVis-20:1);
			\draw[current plane,red,thick] (-50:1) arc (-50:-35:1);
			
		}
		
		\tikzset{%
			>=latex,
			inner sep=0pt,%
			outer sep=2pt,%
			mark coordinate/.style={inner sep=0pt,outer sep=0pt,minimum size=3pt,
				fill=black,circle}%
		}
		\begin{tikzpicture}[scale=1,every node/.style={minimum size=1cm}]
		%% some definitions
		
		\def\R{4} % sphere radius
		
		\def\angEl{25} % elevation angle
		\def\angAz{-100} % azimuth angle
		\def\angPhiOne{-50} % longitude of point P
		\def\angPhiTwo{-35} % longitude of point Q
		\def\angBeta{30} % latitude of point P and Q
		
		%% working planes
		
		\pgfmathsetmacro\H{\R*cos(\angEl)} % distance to north pole
		\LongitudePlane[xzplane]{\angEl}{\angAz}
		\LongitudePlane[pzplane]{\angEl}{\angPhiOne}
		\LongitudePlane[qzplane]{\angEl}{\angPhiTwo}
		\LatitudePlane[equator]{\angEl}{0}
		\fill[ball color=white!10] (0,0) circle (\R); % 3D lighting effect
		\coordinate (O) at (0,0);
		\coordinate[mark coordinate] (N) at (0,\H);
		\coordinate[mark coordinate] (S) at (0,-\H);
		\path[xzplane] (\R,0) coordinate (XE);
		
		%defining points outsided the area bounded by the sphere
		\path[qzplane] (\angBeta:\R+5.2376) coordinate (XEd);
		\path[pzplane] (\angBeta:\R) coordinate (P);%fino alla sfera
		\path[pzplane] (\angBeta:\R+5.2376) coordinate (Pd);%sfora di una quantità pari a 10 dopo la sfera
		\path[pzplane] (\angBeta:\R+5.2376) coordinate (Td);%sfora di una quantità pari a 10 dopo la sfera
		\path[pzplane] (\R,0) coordinate (PE);
		\path[pzplane] (\R+4,0) coordinate (PEd);
		\path[qzplane] (\angBeta:\R) coordinate (Q);
		\path[qzplane] (\angBeta:\R) coordinate (Qd);%sfora di una quantità pari a 10 dopo la sfera
		
		\path[qzplane] (\R,0) coordinate (QE);
		\path[qzplane] (\R+4,0) coordinate (QEd);%sfora di una quantità 10 dalla sfera sul piano equat.
		
		
		\DrawLongitudeCircle[\R]{\angPhiOne} % pzplane
		\DrawLongitudeCircle[\R]{\angPhiTwo} % qzplane
		\DrawLatitudeCircle[\R]{\angBeta}
		\DrawLatitudeCircle[\R]{0} % equator
		%labelling north and south
		\node[above=8pt] at (N) {$\mathbf{N}$};
		\node[below=8pt] at (S) {$\mathbf{S}$};
		
		\draw[-,dashed, thick] (N) -- (S);
		\draw[->] (O) -- (P);
		\draw[dashed] (XE) -- (O) -- (PE);
		\draw[dashed] (O) -- (QE);
		%connecting Points outside the sphere
		\draw[-,dashed,black,very thick] (O) -- (Pd);
		\draw[-,dashed,black,very thick] (O) -- (PEd);
		\draw[-,dashed,black,very thick] (O) -- (QEd);
		\draw[-,dashed,black,very thick] (O) -- (XEd);
		\draw[dashed] (XE) -- (O) -- (PE);
		%draw black thick flat grid
		\draw[-,ultra thick,black] (Pd) -- (PEd) node[below, left] {$P_1$};%verticale sinistro
		\draw[-,ultra thick,black] (PEd) -- (QEd)node[below, right] {$P_3$};%orizzontale inferiore
		\draw[-,ultra thick,black] (Pd)-- (XEd)node[above, right] {$P_2$};%orizzontale superiore	
		\draw[-,ultra thick,black] (XEd) -- (QEd);	
		
		\draw[pzplane,->,thin] (0:0.5*\R) to[bend right=15]
		node[midway,right] {$\lambda$} (\angBeta:0.5*\R);
		\path[pzplane] (0.5*\angBeta:\R) node[right] {$$};
		\path[qzplane] (0.5*\angBeta:\R) node[right] {$$};
		\draw[equator,->,thin] (\angAz:0.5*\R) to[bend right=30]
		node[pos=0.4,above] {$\phi_1$} (\angPhiOne:0.5*\R);
		\draw[equator,->,thin] (\angAz:0.6*\R) to[bend right=35]
		node[midway,below] {$\phi_2$} (\angPhiTwo:0.6*\R);
		\path[xzplane] (0:\R) node[below] {$$};
		\path[xzplane] (\angBeta:\R) node[below left] {$$};
		\foreach \t in {0,2,...,30} { \DrawLatitudeCirclered[\R]{\t} }
		\foreach \t in {130,133,...,145} { \DrawLongitudeCirclered[\R]{\t} }
		
		%drawing grids on the spere invoking DLongredd and DrawLongitudeCirclered
		
		\foreach \t in {130,145,...,145} { \DLongredd[\R+3]{\t} }
		\foreach \t in {130,133,...,145} { \DrawLongitudeCirclered[\R+3]{\t} }
		
		\foreach \t in {0,30,...,30} { \DLatred[\R+3]{\t} }
		\foreach \t in {0,2,...,30} { \DrawLatitudeCirclered[\R+3]{\t} }
		
		%labelling
		\draw[-latex,thick](4,-5.5)node[left]{}
		to[out=0,in=270] (5.8,-2.3);
		\draw[thick](3.6,-6)node[left]{$[\mathsf{Rectilinear}]$};
		\end{tikzpicture}
		\caption {Spherical}
	\end{center}
\end{figure}

\newpage
\begin{figure}[H]
	\begin{center}
		\begin{tikzpicture}
		% \x runs over the angles at which to draw the circles defining the
		% torus
		\foreach \x in {90,89,...,-90} { % change 89 to 80 or 45 for speed
			% \elrad is the x-radius of the ellipse (technically, a circle seen
			% from side on at angle \x).  The 'max' is because at small angles
			% then the real ellipse is too thin and the torus doesn't ``fill
			% out'' nicely.
			\pgfmathsetmacro\elrad{20*max(cos(\x),.1)}
			% We draw the torus from the back to the front to get the right
			% layering effect.  To tint it, we define colours according to the
			% angle, but need different colours for the left and right pieces.
			% It'd be nice if the xcolor colour specification could take something
			% computed by pdfmath, such as {red!\tint} but it doesn't appear to
			% work, so we define the colours explicitly.
			\pgfmathsetmacro\ltint{.9*abs(\x-45)/180}
			\pgfmathsetmacro\rtint{.9*(1-abs(\x+45)/180)}
			\definecolor{currentcolor}{rgb}{\ltint, 0, \ltint}
			% This draws the right-hand circle.
			\draw[color=currentcolor,fill=currentcolor] 
			(xyz polar cs:angle=\x,y radius=.75,x radius=1.5) 
			ellipse (\elrad pt and 20pt);
			% This sets the colour correctly for the left-hand circle ...
			\definecolor{currentcolor}{rgb}{\rtint, 0, \rtint}
			% ... and draws it
			\draw[color=currentcolor,fill=currentcolor] 
			(xyz polar cs:angle=180-\x,radius=.75,x radius=1.5) 
			ellipse (\elrad pt and 20pt);
			% End of foreach statement
		}
		% Spheres are *much* easier!
		\shadedraw[shading=ball,ball color=purple, white] (6.5,0) circle (1.5);
		% As are the subsets of Euclidean space
		\draw[fill=cyan] (-1,-4) rectangle (1,-3);
		\draw[fill=cyan] (5.5,-4) rectangle (7.5,-3);
		% The next three draw the maps, slightly curved for aesthetics.
		\draw[->] (0,-2.8) .. controls (-.2,-2.2) .. (0,-1.6) 
		node[pos=0.5, auto=left] {\(\psi\)};
		\draw[->] (6.5,-1.6) .. controls (6.7,-2.2) .. (6.5,-2.8) 
		node[pos=0.5, auto=left] {\(\phi^{-1}\)};
		\draw[->] (2.5,0) .. controls (3.5,.2) .. (4.5,0) 
		node[pos=0.5, auto=left] {\(f\)};
		% Now we want to draw the codomains of the charts.  Sticking cosines
		% and sines directly into the coordinates doesn't seem to work so
		% we define macros to hold the sines and cosines of the angles.
		% \elrad is the angle on the torus at which to start.
		\pgfmathsetmacro\elrad{cos(-135)}
		% the circle drawn at the specific angle on the torus looks like an
		% ellipse, \xrad and \yrad compute its major and minor semi-axes.
		\pgfmathsetmacro\xrad{1.5cm-20pt*\elrad}
		\pgfmathsetmacro\yrad{.75cm-20pt*sin(-135)}
		% This draws the codomain of the chart on the torus.
		\path[fill=cyan, fill opacity=.35] 
		(xyz polar cs:angle=-135,radius=.75,x radius=1.5) 
		++(20pt*\elrad,0) arc (0:45:20*\elrad pt and 20pt) 
		arc (-135:-45:\xrad pt and \yrad pt) 
		arc (45:-45:-20*\elrad pt and 20pt) 
		arc (-45:-135:\xrad pt and \yrad pt) 
		arc (-45:0:20*\elrad pt and 20pt);
		% Now we do the same for the sphere.
		% We do this by drawing some great circles (aka ellipses) on the
		% sphere and then ``clipping'' an overlaid (and slightly trans:parent)
		% sphere by those great circles.  Each great circle actually specifies
		% one side of the ``clip'' so to make sure that the clip is big enough
		% the arcs are completed by big rectangles (otherwise the clipping
		% would join the end points directly).
		\pgfmathsetmacro\tell{-sin(10)}
		\pgfmathsetmacro\bell{sin(50)}
		\pgfmathsetmacro\rell{1.5 * sin(50)}
		\begin{scope}
		\clip (6.5,0) +(-1.5,0) arc (-180:0:1.5 and 1.5*\tell) 
		-- ++(0,-1.5) -- ++(-3,0) -- ++(0,1.5);
		\clip (6.5,0) +(-1.5,0) arc (-180:0:1.5 and 1.5*\bell) 
		-- ++(0,1.5) -- ++(-3,0) -- ++(0,-1.5);
		\clip (6.5,0) +(0,1.5)  arc (90:-90:\rell cm and 1.5 cm) 
		-- ++(-1.5,0) -- ++(0,3) -- ++(1.5,0);
		\clip (6.5,0) +(0,1.5)  arc (90:-90:-\rell cm and 1.5 cm) 
		-- ++(1.5,0) -- ++(0,3) -- ++(-1.5,0);
		\fill[cyan, fill opacity=0.35] (6.5,0) circle (1.5);
		\end{scope}
		\end{tikzpicture}
		
		\begin{tikzpicture}
		\draw[fill=cyan] (0,0) rectangle (1,-1);
		\draw[gray,fill=cyan!40!white] (8,0) rectangle (9,-1);
		\draw[gray,fill=cyan!40!white] (0,-5) rectangle (1,-6);
		\draw[fill=cyan] (8,-5) rectangle (9,-6);
		\foreach \x in {90,89,...,-90} { % change 89 to 80 for speed
			% \elrad is the x-radius of the ellipse (technically, a circle seen
			% from side on at angle \x).  The 'max' is because at small angles
			% then the real ellipse is too thin and the torus doesn't ``fill
			% out'' nicely.
			\pgfmathsetmacro\elrad{20*max(cos(\x),.1)}
			\pgfmathsetmacro\lscale{1-abs(\x-45)/180}
			\pgfmathsetmacro\rscale{abs(\x+45)/180}
			% We draw the torus from the back to the front to get the right
			% layering effect.  To tint it, we define colours according to the
			% angle, but need different colours for the left and right pieces.
			% It'd be nice if the xcolor colour specification could take something
			% computed by pdfmath, such as {red!\tint} but it doesn't appear to
			% work, so we define the colours explicitly.
			\pgfmathsetmacro\ltint{.9*abs(\x-45)/180}
			\pgfmathsetmacro\rtint{.9*(1-abs(\x+45)/180)}
			\definecolor{currentcolor}{rgb}{\ltint, 0, \ltint}
			% This draws the right-hand circle.
			\draw[color=currentcolor,fill=currentcolor] (4.3cm,-.5cm) 
			+(xyz polar cs:angle=\x,y radius=.75,x radius=1.5) 
			ellipse (\elrad*\lscale pt and 20*\lscale pt);
			% This sets the colour correctly for the left-hand circle ...
			\definecolor{currentcolor}{rgb}{\rtint, 0, \rtint}
			% ... and draws it
			\draw[color=currentcolor,fill=currentcolor] (4.3cm,-.5cm) 
			+(xyz polar cs:angle=180-\x,radius=.75,x radius=1.5) 
			ellipse (\elrad*\rscale pt and 20*\rscale pt);
			% End of foreach statement
		}
		\shadedraw[shading=ball,ball color=red] (3,-5.5) 
		.. controls (3.5,-5.5) and (4,-4.5) .. (4.5,-4.5) 
		.. controls (5,-4.5) and (6,-5) .. (6,-5.5) 
		.. controls (6,-6) and (5,-6.5) .. (4.5,-6.5) 
		.. controls (4,-6.5) and (3.5, -5.5) .. (3,-5.5);
		\draw[->] (1.2,-0.5) -- node[auto=left] {\(\phi\)} (2.4,-0.5);
		\draw[->, color=gray] (1.2,-5.5) -- (2.4,-5.5);
		\draw[->, color=gray] (6.4,-0.5) -- (7.8,-0.5);
		\draw[->] (6.4,-5.5) -- node[auto=left] {\(\psi\)} (7.8,-5.5);
		\draw[->] (4.5,-1.8) -- node[auto=left] {\(f\)} (4.5,-4);
		\end{tikzpicture}
		\caption{smoot-map}
	\end{center}
\end{figure}
\newpage
\tikzset{isometricXYZ/.style={x={(-0.866cm,-0.5cm)}, y={(0.866cm,-0.5cm)}, z={(0cm,1cm)}}}

%: isometric South West : Z , South East : X , North : Y
\tikzset{isometricZXY/.style={x={(0.866cm,-0.5cm)}, y={(0cm,1cm)}, z={(-0.866cm,-0.5cm)}}}

%: isometric South West : Y , South East : Z , North : X
\tikzset{isometricYZX/.style={x={(0cm,1cm)}, y={(-0.866cm,-0.5cm)}, z={(0.866cm,-0.5cm)}}}
\begin{figure}[H]
	\begin{center}
		\begin{tikzpicture} [scale=4, isometricZXY, line join=round,
		opacity=.75, text opacity=1.0,%
		>=latex,
		inner sep=0pt,%
		outer sep=2pt,%
		]
		\def\h{5}
		
		\newcommand{\quadrant}[2]{
			\foreach \t in {#1} \foreach \f in {175,165,...,5}
			\draw [fill=#2]
			({sin(\f - \h)*cos(\t - \h)}, {sin(\f - \h)*sin(\t - \h)}, {cos(\f - \h)})
			-- ({sin(\f - \h)*cos(\t + \h)}, {sin(\f - \h)*sin(\t + \h)}, {cos(\f - \h)})
			-- ({sin(\f + \h)*cos(\t + \h)}, {sin(\f + \h)*sin(\t + \h)}, {cos(\f + \h)})
			-- ({sin(\f + \h)*cos(\t - \h)}, {sin(\f + \h)*sin(\t - \h)}, {cos(\f + \h)})
			-- cycle;
		}
		
		%Quadrants
		\quadrant{220,230,...,300}{black}
		\quadrant{-60,-50,...,20}{white}
		\quadrant{30,40,...,120}{black}
		\quadrant{130,140,...,210}{none}
		
		%Movement arrows
		\foreach \t in {225,235,...,295}
		\foreach \f in {50,40,...,0}
		\draw [red, opacity=1.0, ->, thick]
		({sin(\f - \h)*cos(\t - \h)}, {sin(\f - \h)*sin(\t - \h)}, {cos(\f - \h)})
		-- ({(1 + 0.2*cos(90 - \f))*sin(\f - \h)*cos(\t - \h)},
		{(1 + 0.2*cos(90 - \f))*sin(\f - \h)*sin(\t - \h)},
		{(1 + 0.2*cos(90 - \f))*cos(\f - \h)});
		
		\foreach \t in {125,135,...,205}
		\foreach \f in {110,100,...,0}
		\draw [black, ->, thick]
		({(1 + 0.2*cos(90 - \f))*sin(\f - \h)*cos(\t - \h)},
		{(1 + 0.2*cos(90 - \f))*sin(\f - \h)*sin(\t - \h)},
		{(1 + 0.2*cos(90 - \f))*cos(\f - \h)})
		-- ({sin(\f - \h)*cos(\t - \h)},{sin(\f - \h)*sin(\t - \h)},{cos(\f - \h)});
		\foreach \t in {35,45,...,115}
		\foreach \f in {130,120,...,0}
		\draw [red, opacity=1.0 ,->, thick]
		({sin(\f - \h)*cos(\t - \h)}, {sin(\f - \h)*sin(\t - \h)}, {cos(\f - \h)})
		-- ({(1 + 0.2*cos(90 - \f))*sin(\f - \h)*cos(\t - \h)},
		{(1 + 0.2*cos(90 - \f))*sin(\f - \h)*sin(\t - \h)},
		{(1 + 0.2*cos(90 - \f))*cos(\f - \h)});
		
		\foreach \t in {-55,-45,...,25}
		\foreach \f in {130,120,...,0}
		\draw [black, ->, thick]
		({(1 + 0.2*cos(90 - \f))*sin(\f - \h)*cos(\t - \h)},
		{(1 + 0.2*cos(90 - \f))*sin(\f - \h)*sin(\t - \h)},
		{(1 + 0.2*cos(90 - \f))*cos(\f - \h)})
		-- ({sin(\f - \h)*cos(\t - \h)},{sin(\f - \h)*sin(\t - \h)},{cos(\f - \h)});
		
		%Annotations
		\path ({1.5*sin(100)*cos(75)}, {1.5*sin(100)*sin(75)}, {1.5*cos(100)}) node [right] {Compression};
		\path ({1.5*sin(70)*cos(-15)}, {1.5*sin(70)*sin(-15)}, {1.5*cos(70)})  node [right] {Dilatation};
		\path ({1.25*sin(50)*cos(165)},{1.25*sin(50)*sin(165)},{1.25*cos(50)}) node [left]  {Dilatation};
		\path ({1.25*sin(30)*cos(255)},{1.25*sin(30)*sin(255)},{1.25*cos(30)}) node [left]  {Compression};
		
		%P and T axis
		\begin{scope}[ultra thick]
		\draw[->] ({1.75*sin(90)*cos(75)}, {1.75*sin(90)*sin(75)}, {1.75*cos(90)})
		-- ({2*sin(90)*cos(75)},{2*sin(90)*sin(75)},{2*cos(90)}) node [above] {T-axis};
		\draw[->] ({1.75*sin(90)*cos(255)},{1.75*sin(90)*sin(255)},{1.75*cos(90)})
		-- ({2*sin(90)*cos(255)},{2*sin(90)*sin(255)},{2*cos(90)}) node [below] {T-axis};
		\draw[<-] ({1.5*sin(90)*cos(-15)}, {1.5*sin(90)*sin(-15)}, {1.5*cos(90)})
		-- ({1.75*sin(90)*cos(-15)},{1.75*sin(90)*sin(-15)},{1.75*cos(90)}) node [right] {P-axis};
		\draw[<-] ({1.5*sin(90)*cos(165)}, {1.5*sin(90)*sin(165)}, {1.5*cos(90)})
		-- ({1.75*sin(90)*cos(165)},{1.75*sin(90)*sin(165)},{1.75*cos(90)}) node [left] {P-axis};
		\end{scope}
		
		% Label
		\node [anchor=north, yshift=-2mm] at (current bounding box.south)
		{Seismic focal mechanism and Pression-Tension axis.};
		\end{tikzpicture}
		\caption{seismic-focal}
	\end{center}
\end{figure}
\newpage
\begin{figure}[H]
	\usetikzlibrary{lindenmayersystems,shadings}
	\begin{center}
		\pgfdeclarelindenmayersystem{Koch curve}{
			\rule{F -> F-F++F-F}}
		\pgfdeclarelindenmayersystem{Sierpinski triangle}{
			\rule{F -> G-F-G}
			\rule{G -> F+G+F}}
		\pgfdeclarelindenmayersystem{Fractal plant}{
			\rule{X -> F-[[X]+X]+F[+FX]-X}
			\rule{F -> FF}}
		\pgfdeclarelindenmayersystem{Hilbert curve}{
			\rule{L -> +RF-LFL-FR+}
			\rule{R -> -LF+RFR+FL-}}
		\begin{tabular}{cc}
			\begin{tikzpicture}
			\shadedraw[shading=color wheel] 
			[l-system={Koch curve, step=2pt, angle=60, axiom=F++F++F, order=4}]
			lindenmayer system -- cycle;
			\end{tikzpicture}
			&
			\begin{tikzpicture}
			\shadedraw [top color=white, bottom color=blue!80, draw=blue!80!black]
			[l-system={Sierpinski triangle, step=2pt, angle=60, axiom=F, order=8}]
			lindenmayer system -- cycle;
			\end{tikzpicture}
			\\
			\begin{tikzpicture}
			\shadedraw [bottom color=white, top color=red!80, draw=red!80!black]
			[l-system={Hilbert curve, axiom=L, order=5, step=6pt, angle=90}]
			lindenmayer system; 
			\end{tikzpicture}
			&
			\begin{tikzpicture}
			\draw [green!50!black, rotate=90]
			[l-system={Fractal plant, axiom=X, order=6, step=2pt, angle=25}]
			lindenmayer system; 
			\end{tikzpicture}
		\end{tabular}
		\caption{lindenmayer-systems}
	\end{center}
\end{figure}