Three-D Vector Field Graph

Vector Calculus: graph of a 3D vector field

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Complete Code

Download file: VectorFieldGraph3D1.pg

POD for Macro Files

PG problem file

Explanation

DOCUMENT();
loadMacros(
    'PGstandard.pl',                'PGML.pl',
    'LiveGraphicsVectorField3D.pl', 'PGcourse.pl'
);

Preamble

We need to include the macros file LiveGraphicsVectorField3D.pl.

Context()->variables->are(x => 'Real', y => 'Real', z => 'Real');

$plot = VectorField3D(
    Fx              => Formula('x'),
    Fy              => Formula('y'),
    Fz              => Formula('z'),
    xvar            => 'x',
    yvar            => 'y',
    zvar            => 'z',
    xmin            => -1,
    xmax            => 1,
    ymin            => -1,
    ymax            => 1,
    zmin            => -1,
    zmax            => 1,
    xsamples        => 4,
    ysamples        => 4,
    zsamples        => 4,
    axesframed      => 1,
    xaxislabel      => 'X',
    yaxislabel      => 'Y',
    zaxislabel      => 'Z',
    vectorcolor     => "RGBColor[0.0,0.0,1.0]",
    vectorscale     => 0.2,
    vectorthickness => 0.01,
    outputtype      => 4,
);

Setup

The VectorField3D() routine returns a string of plot data consisting of a list of line segments (the vectors) along with other plot options. The arguments RGBColor[a,b,c] are numbers a, b, and c between 0 and 1 inclusive. You can uniformly scale all of the vectors in the vector field by the same amount using vectorscale. The outputtype feature controls how much of the string of plot data is generated, and setting it equal to 4 generates all of the plot information necessary to be displayed.

Setting outputtype to something other than 4 will require you to read the source code of LiveGraphicsVectorField3D.pl and familiarize yourself with the details of the LiveGraphics3D javascript applet.

BEGIN_PGML

The following is the 3D vector field give by
>> [`` \vec{v} = \left<x,y,z\right> ``] <<

>> [@ Live3Ddata(
    $plot,
    image => alias("exploding-vector-field.png"),
    size => [400,400],
    tex_size => 600,
    tex_center => 1,
    scale => 1.25,
); @]* <<
END_PGML

Statement

This just shows the plot.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.