VectorFieldGraph3D1

Graphing a Vector Field in Space

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This PG code shows how to make an interactive graph of a vector field displayed with the LiveGraphics3D Java applet.

• Download file: File:VectorFieldGraph3D1.txt (change the file extension from txt to pg when you save it)
• File location in NPL: FortLewis/Authoring/Templates/VectorCalc/VectorFieldGraph3D1/VectorFieldGraph3D1.pg

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PG problem file	Explanation
Problem tagging data	Problem tagging:
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "parserVectorUtils.pl", "PGcourse.pl", "LiveGraphicsVectorField3D.pl", ); TEXT(beginproblem());	Initialization: We need to include the macros file LiveGraphicsVectorField3D.pl.
Context("Numeric"); 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 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 $BCENTER \{ Live3Ddata( $plot, image => "exploding-vector-field.png", size => [400,400], tex_size => 600, tex_center => 1, scale => 1.25, ); \} $ECENTER 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 automatically loaded by LiveGraphicsVectorField3D.pl. After you construct the vector field you like, don't forget to take a screen shot of it and make an image file such as exploding-vector-field.png that will be used in the pdf hardcopy.
$showPartialCorrectAnswers = 1;	Answer Evaluation:
Context()->texStrings; BEGIN_SOLUTION ${PAR}SOLUTION:${PAR} Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT('MathObject version.'); ENDDOCUMENT();	Solution:

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