3DGraphsParametricSurfaces

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Interactive Graphs of Parametric Surfaces in Three Dimensions


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

  • Example 1: A sphere.
  • Example 2: A Moebius band with some orientation vectors.


Example 1: A sphere.

Problem Techniques Index

PG problem file Explanation
DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"parserVectorUtils.pl",
"PGcourse.pl",
"LiveGraphicsParametricSurface3D.pl",
);

TEXT(beginproblem());

Initialization: We need to include the macros file LiveGraphicsParametricSurface3D.pl.

Context("Numeric");

Context()->variables->are(x=>"Real",y=>"Real",z=>"Real",u=>"Real",v=>"Real");

$plot = ParametricSurface3D(
Fx => Formula("3*cos(u)*sin(v)"),
Fy => Formula("3*sin(u)*sin(v)"),
Fz => Formula("3*cos(v)"),
uvar => 'u', # theta
vvar => 'v', # phi
umin => 0,
umax =>  2*pi,
vmin =>  0,
vmax =>  pi,
usamples => 15,
vsamples => 15,
axesframed => 1,
xaxislabel => "X",
yaxislabel => "Y",
zaxislabel => "Z",
mesh => 0,
outputtype => 4,
);

Setup: We generate a string of plot data using ParametricSurface3D().

Setting outputtype to something other than 4 will require you to read the source code of LiveGraphicsParametricSurface3D.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 => "sphere.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 sphere.png that will be used in the pdf hardcopy.

$showPartialCorrectAnswers = 1;

ENDDOCUMENT();

Answer Evaluation: Nothing happening here.

Problem Techniques Index




Example 2: A Moebius band with some orientation vectors.

Problem Techniques Index

PG problem file Explanation
DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"parserVectorUtils.pl",
"PGcourse.pl",
"LiveGraphicsParametricSurface3D.pl",
);

TEXT(beginproblem());

Initialization: We need to include the macros file LiveGraphicsParametricSurface3D.pl.

Context("Numeric");

Context()->variables->are(x=>"Real",y=>"Real",z=>"Real",u=>"Real",v=>"Real");

$plot1 = ParametricSurface3D(
Fx => Formula("cos(v)+u*cos(v/2)*cos(v)"),
Fy => Formula("sin(v)+u*cos(v/2)*sin(v)"),
Fz => Formula("u*sin(v/2)"),
uvar => 'u', 
vvar => 'v', 
umin =>  -0.4,
umax =>   0.4,
vmin =>  0,
vmax =>  2*pi,
usamples => 1,
vsamples => 90,
axesframed => 0,
xaxislabel => "X",
yaxislabel => "Y",
zaxislabel => "Z",
mesh => 0,
outputtype => 1,
);

$plot = 
$beginplot .
"{" .
$plot1 .
"," .
"{RGBColor[0,1,0],Thickness[0.012],Line[{{-1,0,0},{-0.5,0,0}}],
Line[{{-0.5,0,0},{-0.6,0.1,0}}],Line[{{-0.5,0,0},{-0.6,-0.1,0}}]}" .
"," .
"{RGBColor[1,0,0],Thickness[0.012],Line[{{-1,0,0},{-1.5,0,0}}],
Line[{{-1.5,0,0},{-1.4,0.1,0}}],Line[{{-1.5,0,0},{-1.4,-0.1,0}}]}" .
"," .
"{RGBColor[0,0,0],Thickness[0.012],Line[{{0,1,0},{0,0.646,0.353}}],
Line[{{0,0.646,0.353},{0,0.646,0.253}}],Line[{{0,0.646,0.353},{0,0.746,0.353}}]}" .
"," .
"{RGBColor[0,0,0],Thickness[0.012],Line[{{1,0,0},{1,0,0.5}}],
Line[{{1,0,0.5},{1,0.1,0.4}}],Line[{{1,0,0.5},{1,-0.1,0.4}}]}" .
"," .
"{RGBColor[0,0,0],Thickness[0.012],Line[{{0,-1,0},{0,-1.353,0.353}}],
Line[{{0,-1.353,0.353},{0,-1.353,0.253}}],Line[{{0,-1.353,0.353},{0,-1.246,0.353}}]}" .
"}" .
",Axes->False,AxesLabel->{X,Y,Z},Boxed->False" .
"," .
"ViewPoint->{1.618,-2.236,1.956},ViewVertical->{-0.276,0.561,2.6213}" .
$endplot;


Setup: We generate a string of plot data using ParametricSurface3D().

Setting outputtype to something other than 4 will require you to read the source code of LiveGraphicsParametricSurface3D.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 => "moebius-band.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 moebius-band.png that will be used in the pdf hardcopy.

$showPartialCorrectAnswers = 1;

ENDDOCUMENT();

Answer Evaluation: Nothing happening here.

Problem Techniques Index

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