Space Curve Graph

Parametric equations: graphing a parametric curve in space

Complete Code

POD for Macro Files

plotly3D.pl

PG problem file

Explanation

DOCUMENT();

loadMacros('PGstandard.pl', 'PGML.pl', 'plotly3D.pl', 'PGcourse.pl');

Preamble

The macro plotly3D.pl is used to produce the graph.

$graph = Graph3D(
    height => 300,
    width  => 300,
    title  => 'Spiral in 3D',
);

$graph->addCurve([ 't * cos(t)', 't * sin(t)', 't' ], [ 0, 6 * pi, 150 ]);

Setup

A plotly3D graph is created with the Graph3D function. There are many options as decribed in plotly3D macro documentation. In this example, only the height, width, and title are provided.

A parametric curve is added to the graph with the addCurve method, which takes takes 2 array references with each array of length 3. The entries of the first array will be used as the body of JavaScript functions with parameter t whose values are the x, y, and z coordinates, respectively, of a point on the curve. For example, t * cos(t) would be converted into the JavaScript function (t) => t * cos(t) for the x-coordinate. The entries of the second array are the minimum and maximum values for the parameter t, and the number of samples to use for t.

BEGIN_PGML
[@ $graph->Print @]*
END_PGML

ENDDOCUMENT();

Statement

Insert the graph into the problem.