# 3DGraphsParametricCurves

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## Interactive Graphs of Parametric Curves in Three Dimensions

This PG code shows how to generate interactive graphs of parametric curves from MathObjects formulas. It uses the Java applet LiveGraphics3D to display the interactive graph.

PG problem file Explanation
DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"parserVectorUtils.pl",
"PGcourse.pl",
"LiveGraphicsParametricCurve3D.pl",
);

TEXT(beginproblem());

Initialization: We need to include the macros file LiveGraphicsParametricCurve3D.pl.

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

\$plot = ParametricCurve3D(
Fx => Formula("t*cos(t)"),
Fy => Formula("t*sin(t)"),
Fz => Formula("t"),
tvar => "t",
tmin =>  0,
tmax =>  10,
tsamples => 50,
axesframed => 1,
xaxislabel => "X",
yaxislabel => "Y",
zaxislabel => "Z",
outputtype => 4,
);

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

Setting outputtype to something other than 4 will require you to read the source code of LiveGraphicsParametricCurve3D.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 => "spiral.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 spiral.png that will be used in the pdf hardcopy.

\$showPartialCorrectAnswers = 1;

ENDDOCUMENT();

Answer Evaluation: Nothing happening here.