Often scientists need to convey information in a non-textual way to express certain ideas that otherwise would be difficult to communicate. Using \TeX\ alone would be difficult, and out of that need packages like TikZ and PSTricks. 


For the Web, there are many solutions, but none that provide client-side rendering of diagrams for packages like PSTricks in an analogy to how MathJAX has done for \LaTeX. 


Because \LaTeX\ is so popular, PStricks became wide-spread and many academics use it to produce diagrams in academic text. Also, many programs generate PSTricks as well. Note that this platform could have supported TiKZ, but I chose PSTricks because of the difference in verbosity, and wanted to use a higher-level of abstraction. TiKZ support would be a great addition in the future!


Let's get to the point. The core of PSTricks is graphics!

\begin{center}
\begin{pspicture}(-5,-5)(5,5)
\psline{->}(0,-3.75)(0,3.75)
\psline{->}(-3.75,0)(3.75,0)
\pscircle(0,0){ 3 }	
\end{pspicture}
\end{center}

which can be produced using the following tex:

\begin{verbatim}
\begin{center}
\begin{pspicture}(-5,-5)(5,5)
\psline{->}(0,-3.75)(0,3.75)
\psline{->}(-3.75,0)(3.75,0)
\pscircle(0,0){ 3 }	
\end{pspicture}
\end{center}

\end{verbatim}


But more importantly, and probably the best part of using such a package is that you also get to mix beautiful mathematics with a consistent look for your diagrams. This can be done using \emph{rput}:

\begin{center}
\begin{pspicture}(0,-3)(8,3)

\rput(0,0){$x(t)$}
\rput(4,1.5){$f(t)$}
\rput(4,-1.5){$g(t)$}
\rput(8.2,0){$y(t)$}
\rput(1.5,-2){$h(t)$}

\psframe(1,-2.5)(7,2.5)
\psframe(3,1)(5,2)
\psframe(3,-1)(5,-2)

\rput(4,0){$X_k = \frac{1}{p} \sum \limits_{n=\langle p\rangle}x(n)e^{-ik\omega_0n}$}

\psline{->}(0.5,0)(1.5,0)
\psline{->}(1.5,1.5)(3,1.5)
\psline{->}(1.5,-1.5)(3,-1.5)

\psline{->}(6.5,1.5)(6.5,0.25)
\psline{->}(6.5,-1.5)(6.5,-0.25)
\psline{->}(6.75,0)(7.75,0)
\psline(1.5,-1.5)(1.5,1.5)
\psline(5,1.5)(6.5,1.5)
\psline(5,-1.5)(6.5,-1.5)
\psline(6,-1.5)(6.5,-1.5)

\pscircle(6.5,0){0.25}
\psline(6.25,0)(6.75,0)
\psline(6.5,0.5)(6.5,-0.5)

\end{pspicture}
\end{center}

which can be produced with the following \LaTeX\ (hint: try to copy and paste it into \href{/sandbox}{the sandbox}): 

\begin{verbatim}
\begin{center}
\begin{pspicture}(0,-3)(8,3)
\rput(0,0){$x(t)$}
\rput(4,1.5){$f(t)$}
\rput(4,-1.5){$g(t)$}
\rput(8.2,0){$y(t)$}
\rput(1.5,-2){$h(t)$}
\psframe(1,-2.5)(7,2.5)
\psframe(3,1)(5,2)
\psframe(3,-1)(5,-2)
\rput(4,0){$X_k = \frac{1}{p} \sum \limits_{n=\langle p\rangle}x(n)e^{-ik\omega_0n}$}
\psline{->}(0.5,0)(1.5,0)
\psline{->}(1.5,1.5)(3,1.5)
\psline{->}(1.5,-1.5)(3,-1.5)
\psline{->}(6.5,1.5)(6.5,0.25)
\psline{->}(6.5,-1.5)(6.5,-0.25)
\psline{->}(6.75,0)(7.75,0)
\psline(1.5,-1.5)(1.5,1.5)
\psline(5,1.5)(6.5,1.5)
\psline(5,-1.5)(6.5,-1.5)
\psline(6,-1.5)(6.5,-1.5)
\pscircle(6.5,0){0.25}
\psline(6.25,0)(6.75,0)
\psline(6.5,0.5)(6.5,-0.5)
\end{pspicture}
\end{center}
\end{verbatim}

You can specify {\tt linewidth, linecolor, fillstyle, fillcolor} on most PSTricks objects. For example:

\begin{center}
\begin{pspicture}(-2,-2)(2,2)
\psline[linecolor=green]{->}(0,0)(1.2,1.2)
\psline[linecolor=red]{->}(0,0)(-1.2,-1.2)
\psline[linecolor=purple]{->}(0,0)(1.2,-1.2)
\psline[linecolor=lightblue]{->}(0,0)(-1.2,1.2)
\end{pspicture}
\end{center}

Which can be created with the following source:

\begin{verbatim}
\begin{pspicture}(-2,-2)(2,2)
\psline[linecolor=green]{->}(0,0)(1.2,1.2)
\psline[linecolor=red]{->}(0,0)(-1.2,-1.2)
\psline[linecolor=purple]{->}(0,0)(1.2,-1.2)
\psline[linecolor=lightblue]{->}(0,0)(-1.2,1.2)
\end{pspicture}
\end{verbatim}

Fill modes can be useful to show things like integration and area:

\begin{interactive}
\begin{center}
\begin{pspicture}(-4,-3)(4,3)
\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{-1.5}{1.5}{sin(x)}
\psplot[algebraic,linewidth=2pt]{-4}{4}{sin(x)}
\psline{->}(-4,0)(4,0)    
\end{pspicture}
\end{center}
\end{interactive}
\begin{print}
\begin{center}
\begin{pspicture}(-4,-3)(4,3)
\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{-3.14}{3.14}{sin(x)}
\psplot[algebraic,linewidth=2pt]{-4}{4}{sin(x)}
\psline{->}(-4,0)(4,0)    
\end{pspicture}
\end{center}
\end{print}

Which can be created with the following source:

\begin{verbatim}
\begin{pspicture}(-4,-3)(4,3)
\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{-1.5}{1.5}{sin(x)}
\psplot[algebraic,linewidth=2pt]{-4}{4}{sin(x)}
\psline{->}(-4,0)(4,0)    
\end{pspicture}
\end{verbatim}



\psset{unit=0.5}
\begin{center}
\begin{pspicture}(-13,-1.25)(13,3)

\psplot[algebraic,linewidth=1.5pt,plotpoints=1000]{-12.56}{12.56}{2*sin(x)/x}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-12.6,0)(12.6,0)
\rput(5.7, 1){$a/b$}
\psline[linestyle=dashed](0,2)(5,2)
\psline{<->}(5,0)(5,2)
\rput(3.14, -0.5){$\frac{\pi}{a}$}
\rput(6.28, -0.5){$\frac{2\pi}{a}$}
\rput(9.42, -0.5){$\frac{3\pi}{a}$}
\rput(12.56, -0.5){$\frac{4\pi}{a}$}
\rput(-3.14, -0.5){$\frac{-\pi}{a}$}
\rput(-6.28, -0.5){$\frac{-2\pi}{a}$}
\rput(-9.42, -0.5){$\frac{-3\pi}{a}$}
\rput(-12.56, -0.5){$\frac{-4\pi}{a}$}
\rput(0, -0.5){$0$}

% begin x-axis labels:
\psline(-6.2831853, -0.1)(-6.2831853, 0.1)
\psline(-4.712388975, -0.1)(-4.712388975, 0.1)
\psline(-3.14159265, -0.1)(-3.14159265, 0.1)
\psline(-1.570796325, -0.1)(-1.570796325, 0.1)
\psline(0, -0.1)(0, 0.1)
\psline(1.570796325, -0.1)(1.570796325, 0.1)
\psline(3.14159265, -0.1)(3.14159265, 0.1)
\psline(4.712388975, -0.1)(4.712388975, 0.1)
\psline(6.2831853, -0.1)(6.2831853, 0.1)
% end x-axis labels:


\end{pspicture}
\end{center}


\begin{verbatim}
\begin{pspicture}(-13,-1.25)(13,3)
\psplot[algebraic,linewidth=1.5pt,plotpoints=1000]{-12.56}{12.56}{2*sin(x)/x}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-12.6,0)(12.6,0)
\rput(5.7, 1){$a/b$}
\psline[linestyle=dashed](0,2)(5,2)
\psline{<->}(5,0)(5,2)
\rput(3.14, -0.5){$\frac{\pi}{a}$}
\rput(6.28, -0.5){$\frac{2\pi}{a}$}
\rput(9.42, -0.5){$\frac{3\pi}{a}$}
\rput(12.56, -0.5){$\frac{4\pi}{a}$}
\rput(-3.14, -0.5){$\frac{-\pi}{a}$}
\rput(-6.28, -0.5){$\frac{-2\pi}{a}$}
\rput(-9.42, -0.5){$\frac{-3\pi}{a}$}
\rput(-12.56, -0.5){$\frac{-4\pi}{a}$}
\rput(0, -0.5){$0$}
\psline(-6.2831853, -0.1)(-6.2831853, 0.1)
\psline(-4.712388975, -0.1)(-4.712388975, 0.1)
\psline(-3.14159265, -0.1)(-3.14159265, 0.1)
\psline(-1.570796325, -0.1)(-1.570796325, 0.1)
\psline(0, -0.1)(0, 0.1)
\psline(1.570796325, -0.1)(1.570796325, 0.1)
\psline(3.14159265, -0.1)(3.14159265, 0.1)
\psline(4.712388975, -0.1)(4.712388975, 0.1)
\psline(6.2831853, -0.1)(6.2831853, 0.1)
\end{pspicture}
\end{verbatim}



\begin{center}
\psset{xunit=1,yunit=2}
\begin{pspicture}(-8,-2)(8,2)
    

\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{-3.14}{3.14}{sin(x)}
\psplot[algebraic,linewidth=2pt]{-6.2831}{6.2831}{sin(x)}

% function name
\rput(6.2831853,1.3){$\left|H(\omega)\right|$}

% x-axis
\psline(-6.6831853, 0)(6.6831853, 0)
\rput(6.6831853,-0.3){$\omega$}

% begin x-axis labels:
\psline(-6.2831853, -0.1)(-6.2831853, 0.1)
\rput(-6.2831853, -0.3){$-2\pi$}
\psline(-4.712388975, -0.1)(-4.712388975, 0.1)
\rput(-4.712388975, -0.3){$-\frac{3\pi}{2}$}
\psline(-3.14159265, -0.1)(-3.14159265, 0.1)
\rput(-3.14159265, -0.3){$-\pi$}
\psline(-1.570796325, -0.1)(-1.570796325, 0.1)
\rput(-1.570796325, -0.3){$-\frac{\pi}{2}$}
\psline(0, -0.1)(0, 0.1)
\rput(0, -0.3){$0$}
\psline(1.570796325, -0.1)(1.570796325, 0.1)
\rput(1.570796325, -0.3){$\frac{\pi}{2}$}
\psline(3.14159265, -0.1)(3.14159265, 0.1)
\rput(3.14159265, -0.3){$\pi$}
\psline(4.712388975, -0.1)(4.712388975, 0.1)
\rput(4.712388975, -0.3){$\frac{3\pi}{2}$}
\psline(6.2831853, -0.1)(6.2831853, 0.1)
\rput(6.2831853, -0.3){$2\pi$}
% end x-axis labels:
\end{pspicture}
\end{center}

\begin{verbatim}
\begin{pspicture}(-8,-2)(8,2)
\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{-3.14}{3.14}{sin(x)}
\psplot[algebraic,linewidth=2pt]{-6.2831}{6.2831}{sin(x)}
\rput(6.2831853,1.3){$\left|H(\omega)\right|$}
\psline(-6.6831853, 0)(6.6831853, 0)
\rput(6.6831853,-0.3){$\omega$}
\psline(-6.2831853, -0.1)(-6.2831853, 0.1)
\rput(-6.2831853, -0.3){$-2\pi$}
\psline(-4.712388975, -0.1)(-4.712388975, 0.1)
\rput(-4.712388975, -0.3){$-\frac{3\pi}{2}$}
\psline(-3.14159265, -0.1)(-3.14159265, 0.1)
\rput(-3.14159265, -0.3){$-\pi$}
\psline(-1.570796325, -0.1)(-1.570796325, 0.1)
\rput(-1.570796325, -0.3){$-\frac{\pi}{2}$}
\psline(0, -0.1)(0, 0.1)
\rput(0, -0.3){$0$}
\psline(1.570796325, -0.1)(1.570796325, 0.1)
\rput(1.570796325, -0.3){$\frac{\pi}{2}$}
\psline(3.14159265, -0.1)(3.14159265, 0.1)
\rput(3.14159265, -0.3){$\pi$}
\psline(4.712388975, -0.1)(4.712388975, 0.1)
\rput(4.712388975, -0.3){$\frac{3\pi}{2}$}
\psline(6.2831853, -0.1)(6.2831853, 0.1)
\rput(6.2831853, -0.3){$2\pi$}
\end{pspicture}
\end{verbatim}

\psset{unit=1cm}
\begin{center}
\begin{pspicture}(-3.5,-3.25)(3.5,2)
\psplot[algebraic,linewidth=1.5pt]{-3.14}{3.14}{cos(x/2)}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-3.25,0)(3.25,0)
\rput(3.14, -0.35){$\pi$}
\rput(-3.14, -0.35){$-\pi$}
\rput(0, -0.35){$0$}
\rput(1.25,1.25 ){$\left| H(\omega) \right| =\cos(\omega/2)$}
\end{pspicture}
\end{center}

\begin{verbatim}
\begin{pspicture}(-3.5,-3.25)(3.5,2)
\psplot[algebraic,linewidth=1.5pt]{-3.14}{3.14}{cos(x/2)}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-3.25,0)(3.25,0)
\rput(3.14, -0.35){$\pi$}
\rput(-3.14, -0.35){$-\pi$}
\rput(0, -0.35){$0$}
\rput(1.25,1.25 ){$\left| H(\omega) \right| =\cos(\omega/2)$}
\end{pspicture}
\end{verbatim}

\begin{center}
\begin{pspicture}(-3.5,-1.25)(3.5,2)
\psplot[algebraic,linewidth=1.5pt]{-3.14}{3.14}{abs(sin(x/2))}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-3.25,0)(3.25,0)
\rput(3.14, -0.35){$\pi$}
\rput(-3.14, -0.35){$-\pi$}
\rput(0, -0.35){$0$}
\rput(1,1.25 ){$\left| G(\omega) \right| =\left| \sin(\omega/2) \right|$}
\end{pspicture}
\end{center}

\begin{verbatim}
\begin{pspicture}(-3.5,-1.25)(3.5,2)
\psplot[algebraic,linewidth=1.5pt]{-3.14}{3.14}{abs(sin(x/2))}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-3.25,0)(3.25,0)
\rput(3.14, -0.35){$\pi$}
\rput(-3.14, -0.35){$-\pi$}
\rput(0, -0.35){$0$}
\rput(1,1.25 ){$\left| G(\omega) \right| =\left| \sin(\omega/2) \right|$}
\end{pspicture}
\end{verbatim}


\begin{center}
\begin{pspicture}(0,-3.5)(8,2)


\rput(0,0){$x$}
\rput(7.2,0){$y$}
\rput(5.5,-1.25){$z^{-1}$}


\rput(3.65,-2){$\alpha$}
\rput(1.5,-2.5){$H$}

% plus or minus for adder
\rput(2.1,-0.5){$-$}
\rput(1.45,0.35){$+$}

\psframe(1,-3)(6.5,1)

\pspolygon(4,-1.5)(4,-2.5)(2.5,-2)

\psline{->}(0.25,0)(1.5,0)
\psline{->}(1.75,-2)(1.75,-0.25)
\psline{->}(5.5,-2)(4,-2)
\psline(2.5,-2)(1.75,-2)
\psline{->}(2,0)(7,0)
\psline(5.5,-1.7)(5.5,-2)
\psline{->}(5.5,0)(5.5,-0.75)

\psframe(5, -1.7)(6,-0.75)

\pscircle(1.75,0){0.25}
\psline(1.5,0)(2,0)
\psline(1.75,0.25)(1.75,-0.25)


\end{pspicture}
\end{center}

Which can be produced with the following \TeX:

\begin{verbatim}
\begin{pspicture}(0,-3.5)(8,2)
\rput(0,0){$x$}
\rput(7.2,0){$y$}
\rput(5.5,-1.25){$z^{-1}$}
\rput(3.65,-2){$\alpha$}
\rput(1.5,-2.5){$H$}
\rput(2.1,-0.5){$-$}
\rput(1.45,0.35){$+$}
\psframe(1,-3)(6.5,1)
\pspolygon(4,-1.5)(4,-2.5)(2.5,-2)
\psline{->}(0.25,0)(1.5,0)
\psline{->}(1.75,-2)(1.75,-0.25)
\psline{->}(5.5,-2)(4,-2)
\psline(2.5,-2)(1.75,-2)
\psline{->}(2,0)(7,0)
\psline(5.5,-1.7)(5.5,-2)
\psline{->}(5.5,0)(5.5,-0.75)
\psframe(5, -1.7)(6,-0.75)
\pscircle(1.75,0){0.25}
\psline(1.5,0)(2,0)
\psline(1.75,0.25)(1.75,-0.25)
\end{pspicture}
\end{verbatim}