TeX Implementation

We have provided some useful elements to expose basic interactive functionality for an end user. The first of these is the {\tt slider} command. 


Arguments for the {\tt slider} command are:

\begin{verbatim}
 \slider{min}{max}{variable}{latex}{default}
\end{verbatim}

The min and max values are for specifying the minimum and maximum of the range of the slider. 


The {\tt latex} argument is what to display next to the slider to indicate to the end user what variable the slider is changing. Finally, the most important is the {\tt variable} argument. The {\tt variable} specifies the variable that is changed based on the values of the slider, and can be used in the equations of {\tt psplot} commands. 


Note that using these ``extended'' features are not backwards compatible, a.k.a they don't work on paper!

\begin{interactive}
\psset{unit=1cm}

\begin{center}
\begin{pspicture}(-3.5,-1)(3.75,3.5)

\slider{1}{8}{n}{$N$}{4}

\psplot[algebraic,linewidth=1.5pt,plotpoints=1000]{-3.14}{3.14}{cos(n*x/2)+1.3}
\psaxes[showorigin=false,labels=none, Dx=1.62](0,0)(-3.25,0)(3.25,2.5)

\psline[linestyle=dashed](-3.14,0.3)(3.14,0.3)
\psline[linestyle=dashed](-3.14,2.3)(3.14,2.3)
\rput(3.6,2.3){$\frac{1}{1-\alpha}$}
\rput(3.6,0.3){$\frac{1}{1+\alpha}$}


\rput(3.14, -0.35){$\pi$}
\rput(1.62, -0.35){$\pi/2$}
\rput(-1.62, -0.35){$-\pi/2$}
\rput(-3.14, -0.35){$-\pi$}
\rput(0, -0.35){$0$}

\end{pspicture}
\end{center}
\end{interactive}


\begin{print}
\psset{unit=1cm}

\begin{center}
\begin{pspicture}(-3.5,-1)(3.75,3.5)

\psplot[algebraic,linewidth=1.5pt,plotpoints=1000]{-3.14}{3.14}{cos(4*x/2)+1.3}
\psaxes[showorigin=false,labels=none, Dx=1.62](0,0)(-3.25,0)(3.25,2.5)

\psline[linestyle=dashed](-3.14,0.3)(3.14,0.3)
\psline[linestyle=dashed](-3.14,2.3)(3.14,2.3)
\rput(3.6,2.3){$\frac{1}{1-\alpha}$}
\rput(3.6,0.3){$\frac{1}{1+\alpha}$}


\rput(3.14, -0.35){$\pi$}
\rput(1.62, -0.35){$\pi/2$}
\rput(-1.62, -0.35){$-\pi/2$}
\rput(-3.14, -0.35){$-\pi$}
\rput(0, -0.35){$0$}

\end{pspicture}
\end{center}
\end{print}

Which can be created using the following \TeX:


\begin{verbatim}
\begin{pspicture}(-3.5,-1)(3.75,3.5)

\slider{1}{8}{n}{$N$}{4}

\psplot[algebraic,linewidth=1.5pt,plotpoints=1000]{-3.14}{3.14}{cos(n*x/2)+1.3}
\psaxes[showorigin=false,labels=none, Dx=1.62](0,0)(-3.25,0)(3.25,2.5)
\psline[linestyle=dashed](-3.14,0.3)(3.14,0.3)
\psline[linestyle=dashed](-3.14,2.3)(3.14,2.3)
\rput(3.6,2.3){$\frac{1}{1-\alpha}$}
\rput(3.6,0.3){$\frac{1}{1+\alpha}$}
\rput(3.14, -0.35){$\pi$}
\rput(1.62, -0.35){$\pi/2$}
\rput(-1.62, -0.35){$-\pi/2$}
\rput(-3.14, -0.35){$-\pi$}
\rput(0, -0.35){$0$}
\end{pspicture}
\end{verbatim}




You can also add more than one slider (variable):

\begin{interactive}
\psset{unit=0.5cm}
\begin{center}
\begin{pspicture}(-13,-5)(13,10)

\slider{1}{8}{a}{amplitude}{4}
\slider{1}{8}{n}{frequency}{4}

\psplot[algebraic,linewidth=1.5pt,plotpoints=1000]{-12.56}{12.56}{a*sin(n*x)/(n*x)}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-12.6,0)(12.6,0)

\rput(0, -0.5){$0$}

\end{pspicture}
\end{center}
\end{interactive}


\begin{print}
\psset{unit=0.5cm}
\begin{center}
\begin{pspicture}(-13,-5)(13,10)

\psplot[algebraic,linewidth=1.5pt,plotpoints=1000]{-12.56}{12.56}{4*sin(4*x)/(4*x)}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-12.6,0)(12.6,0)

\rput(0, -0.5){$0$}

\end{pspicture}
\end{center}
\end{print}

which can be created with the following:

\begin{verbatim}
\begin{pspicture}(-13,-5)(13,10)
\slider{1}{8}{a}{amplitude}{4}
\slider{1}{8}{n}{frequency}{4}
\psplot[algebraic,linewidth=1.5pt,plotpoints=1000]{-12.56}{12.56}{a*sin(n*x)/(n*x)}
\psaxes[showorigin=false,labels=none, Dx=3.14](0,0)(-12.6,0)(12.6,0)
\rput(0, -0.5){$0$}
\end{pspicture}
\end{verbatim}


slider

{\tt userline} is just like {\tt psline}, except you can have extra arguments on the end to represent a user action. Suppose you'd like a vector to follow the user's cursor or finger on a computer or touch device. You can simply do


\begin{verbatim}
\userline[linewidth=1.5 pt]{->}(0,0)(2,2)
\end{verbatim}

This places a vector at $(0,0)$ and initial value of the head at $(2,2)$. This will produce the following interaction

\begin{interactive}

\begin{center}
\begin{pspicture}(-2,-2)(2,2)
\psframe(-2,-2)(2,2)
\userline[linewidth=1.5 pt]{->}(0,0)(2,2)
\end{pspicture}
\end{center}

\end{interactive}

\begin{print}

\begin{center}
\begin{pspicture}(-2,-2)(2,2)
\psframe(-2,-2)(2,2)
\psline[linewidth=1.5 pt]{->}(0,0)(2,2)
\end{pspicture}
\end{center}

\end{print}

This can be produced with the following source:

\begin{verbatim}
\begin{pspicture}(-2,-2)(2,2)
\psframe(-2,-2)(2,2)
\userline[linewidth=1.5 pt]{->}(0,0)(2,2)
\end{pspicture}
\end{verbatim}


If you specify more arguments, you can create functions for the head and and tail of the vector, which each takes the current $x$ and $y$ position of the users finger or cursor and they move. 


2 extra arguments provide functions for the head, 4 extra arguments allows you to control both and tail

\begin{verbatim}
\userline[linewidth=2pt,linecolor=green]{->}(0,0)(2,2){-x}{-y}
\userline[linewidth=2pt,linecolor=red]{->}(0,0)(2,2){0}{y}
\userline[linewidth=2pt,linecolor=purple]{->}(0,0)(2,2){-x}{cos(y)}
\userline[linewidth=2pt,linecolor=lightblue]{->}(0,0)(2,2)(sin(x)}{-y}
\end{verbatim}

and produce the following interaction

\begin{interactive}

\begin{center}
\begin{pspicture}(-2,-2)(2,2)
\psframe(-2,-2)(2,2)
\userline[linewidth=2pt,linecolor=green]{->}(0,0)(2,2){-x}{-y}
\userline[linewidth=2pt,linecolor=red]{->}(0,0)(2,2){0}{y}
\userline[linewidth=2pt,linecolor=purple]{->}(0,0)(2,2){-x}{cos(y)}
\userline[linewidth=2pt,linecolor=lightblue]{->}(0,0)(2,2)(sin(x)}{-y}
\end{pspicture}
\end{center}

\end{interactive}

\begin{print}

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

\end{print}

Then you can have fun with math!

\begin{interactive}

\begin{center}
\begin{pspicture}(-5,-5)(5,5)

\rput(0.3,3.75){ $Im$ }
\psline{->}(0,-3.75)(0,3.75)
\rput(3.75,0.3){ $Re$ }
\psline{->}(-3.75,0)(3.75,0)
\pscircle(0,0){ 3 }
      
\userline[linewidth=1.5 pt]{->}(1.500,0.000)(2.121,2.121)
\userline[linewidth=1.5 pt,linecolor=blue]{->}(0,0.000)(2.121,2.121){(x>0) ? 3 * cos( atan(-y/x) ) : -3 * cos( atan(-y/x) ) }{ (x>0) ? -3 * sin( atan(-y/x) ) : 3 * sin( atan(-y/x) )}
\userline[linewidth=1.5 pt,linestyle=dashed](-1.500,0.000)(2.121,2.121){x}{0}{x}{y}
\userline[linewidth=1.5 pt,linestyle=dashed](-1.500,0.000)(2.121,2.121){0}{y}{x}{y}

\end{pspicture}
\end{center}


\end{interactive}

\begin{print}

\begin{center}
\begin{pspicture}(-5,-5)(5,5)

\rput(0.3,3.75){ $Im$ }
\psline{->}(0,-3.75)(0,3.75)
\rput(3.75,0.3){ $Re$ }
\psline{->}(-3.75,0)(3.75,0)
\pscircle(0,0){ 3 }
      
\psline[linewidth=1.5 pt]{->}(1.500,0.000)(2.121,2.121)
\psline[linewidth=1.5 pt,linecolor=blue]{->}(0,0.000)(2.121,2.121)
\psline[linewidth=1.5 pt,linestyle=dashed](-1.500,0.000)(2.121,2.121)
\psline[linewidth=1.5 pt,linestyle=dashed](-1.500,0.000)(2.121,2.121)

\end{pspicture}
\end{center}

\end{print}


\begin{verbatim}
\begin{pspicture}(-5,-5)(5,5)
\rput(0.3,3.75){ $Im$ }
\psline{->}(0,-3.75)(0,3.75)
\rput(3.75,0.3){ $Re$ }
\psline{->}(-3.75,0)(3.75,0)
\pscircle(0,0){ 3 }
      
\userline[linewidth=1.5 pt]{->}(1.500,0.000)(2.121,2.121)
\userline[linewidth=1.5 pt,linecolor=blue]{->}(0,0.000)(2.121,2.121){(x>0) ? 3 * cos( atan(-y/x) ) : -3 * cos( atan(-y/x) ) }{ (x>0) ? -3 * sin( atan(-y/x) ) : 3 * sin( atan(-y/x) )}
\userline[linewidth=1.5 pt,linestyle=dashed](-1.500,0.000)(2.121,2.121){x}{0}{x}{y}
\userline[linewidth=1.5 pt,linestyle=dashed](-1.500,0.000)(2.121,2.121){0}{y}{x}{y}
\end{pspicture}
\end{verbatim}


userline

The {\tt uservariable} command represents a variable that changes with user interaction such as touch or mouse events over the graphic.

\begin{verbatim}
\uservariable{variable}(x1,y1){f(x,y)}
\end{verbatim}

{\tt variable} is the variable that you can use in {\tt psplot} and {\tt userline} parameters and equations. Eventually it should be something you can use everywhere, but for the scope of this project, we kept it limited.


{\tt x1} and {\tt y1} are the initial values of {\tt x} and {\tt y} for the function $f(x,y)$ that is that last argument for the command. If there are no user interactions, the function is evaluated with the specified inital values.


On any user event, such as a touch or mouse event, the function $f(x,y)$ is evaluated and any dependent commands, namely {\tt psplot} and {\tt userline} are immediately notified and re-rendered with updated execution contexts.


Here is an example of teaching somebody integration, for example, you can represent $\int_a^b f(x) dx$ as:

\begin{interactive}

\begin{center}
\begin{pspicture}(-4,-3)(4,3)
    
\uservariable{alpha}(0,0){x}

\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{-4}{alpha}{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 produced with the following \TeX:

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

The next example allows you to move the height of the graph and also demonstrates how to specify an interval:

\begin{interactive}
\begin{center}
\begin{pspicture}(-4,-3)(4,3)

\uservariable{alpha}(0,0){x}
\uservariable{beta}(0,0){y}

\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{alpha-3}{alpha}{beta + sin(x)}
\psplot[algebraic,linewidth=2pt]{-4}{4}{beta + 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}{0}{sin(x)}
\psplot[algebraic,linewidth=2pt]{-4}{4}{sin(x)}

\psline{->}(-4,0)(4,0)

\end{pspicture}
\end{center}
\end{print}

which can be produced with the following source:

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

9.8 extended interactivity