# Graph3DCylindrical1

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## Deprecated: Interactive Graphs of Functions in Cylindrical Coordinates

This PG code shows how to make an interactive graph of a function in cylindrical coordinates that is displayed using the LiveGraphics3D Java applet. It is deprecated because Java is no longer universally supported on all web browsers and platforms.

PG problem file Explanation

Problem tagging:

```DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"parserVectorUtils.pl",
"PGcourse.pl",
"LiveGraphicsCylindricalPlot3D.pl",
);

TEXT(beginproblem());
```

Initialization: We need to include the macros file `LiveGraphicsCylindricalPlot3D.pl`.

```Context("Numeric");
Context()->variables->are(x=>"Real",y=>"Real",r=>"Real",t=>"Real");

\$a = random(2,4,1);

\$plot = CylindricalPlot3D(
function => Formula("\$a*cos((r^2)/4)"),
rvar => "r",
tvar => "t",
rmin =>  0,
rmax =>  6,
tmin =>  0,
tmax =>  2*pi,
rsamples => 20,
tsamples => 15,
axesframed => 1,
xaxislabel => "X",
yaxislabel => "Y",
zaxislabel => "Z",
outputtype => 4,
);
```

Setup: We generate a string of plot data using `CylindricalPlot3D()`.

Setting `outputtype` to something other than 4 will require you to read the source code of `LiveGraphicsCylindricalPlot3D.pl` and familiarize yourself with the details of the `LiveGraphics3D` java applet. For more information on how to work with the string of plot data, see Martin Kraus's LiveGraphics3D homepage, and the excellent article by Jonathan Rogness and Martin Kraus Constructing Mathlets Quickly Using LiveGraphics3D.

```Context()->texStrings;
BEGIN_TEXT
\{
Live3Ddata(
\$plot,
image => "bell-shape.png",
size => [400,400],
tex_size => 600,
tex_center => 1,
scale => 1.1,
);
\}
END_TEXT
Context()->normalStrings;
```

Main Text: To display the string of plot data `\$plot`, we use the `Live3Ddata()` routine provided by the macro `LiveGraphics3D.pl`, which is loaded automatically.

After you construct the graph you like, don't forget to take a screen shot of it and make an image file such as `bell-shape.png` that will be used in the pdf hardcopy.

```\$showPartialCorrectAnswers = 1;

```

Answer Evaluation:

```Context()->texStrings;
BEGIN_SOLUTION
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;

COMMENT('MathObject version.');

ENDDOCUMENT();
```

Solution: