ContourPlots

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This article has been retained as a historical document. It is not up-to-date and the formatting may be lacking. Use the information herein with caution.

This problem has been replaced with a newer version of this problem

Contour Plots


This PG code shows how to construct contour plots.

Problem Techniques Index

PG problem file Explanation 
DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGgraphmacros.pl",
"unionTables.pl",
);

TEXT(beginproblem());

$refreshCachedImages=1;

Initialization: Use unionTables.pl to display the graphs nicely. 

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

#
#  Create some graph canvases
#
foreach my $i (0..1) {
  $gr[$i] = init_graph(-5,-5,5,5,grid=>[10,10],axes=>[0,0],pixels=>[400,400]);
  $gr[$i]->lb('reset');
  $gr[$i]->lb( new Label(4.7,0.2,'x','black','center','middle'));
  $gr[$i]->lb( new Label(0.2,4.7,'y','black','center','middle'));
  $gr[$i]->new_color("nicegreen",0,110,0); # verdant green
  $gr[$i]->new_color("darkred", 159, 64, 16); # red-brown
}

#
#  Circular contours as parametrized curves
#
foreach $k (5,10,15,20,25,30,35,40,45) {
  my $a = sqrt($k);
  $fn = new Fun( 
     sub { my $t=shift(); return $a * cos($t); }, 
     sub { my $t=shift(); return $a * sin($t);}, 
     $gr[0] 
  );
  $fn->domain(0,6.3);
  $fn->color("nicegreen");
}

#
#  Hyperbolas as parametrized curves
#
foreach my $k (0,5,10,15,20,25) {
  # left and right branches
  $fn = new Fun( 
     sub { my $t=shift(); return sqrt($k+$t**2); }, 
     sub { my $t=shift(); return $t;}, 
     $gr[1] 
  );
  $fn->domain(-5,5);
  $fn->color("darkred");
  $fn = new Fun( 
     sub { my $t=shift(); return -sqrt($k+$t**2); }, 
     sub { my $t=shift(); return $t;}, 
     $gr[1] 
  );
  $fn->domain(-5,5);
  $fn->color("darkred");

  # top and bottom branches
  add_functions($gr[1],
  " sqrt(x^2+$k)  for x in <-5,5> using color:darkred and weight:2",
  "-sqrt(x^2+$k)  for x in <-5,5> using color:darkred and weight:2",
  );
}

foreach my $i (0..1) {
  $fig[$i] = image(insertGraph($gr[$i]),width=>300,height=>300,tex_size=>450);
}

Setup: We create the contour plots as a parametrized family of (parametric) curves. 

BEGIN_TEXT
$BCENTER
\{
BeginTable().
AlignedRow([$fig[0],$fig[1]]).
TableSpace(5,0).
AlignedRow(["A","B"]).
EndTable();
\}
$BR
(Click on a graph to enlarge it.)
$ECENTER
END_TEXT

Main Text: We display the contour plots nicely using tables provided by unionTables.pl. 

$showPartialCorrectAnswers = 1;

ENDDOCUMENT();

Answer Evaluation: We did not ask any questions, so there's nothing interesting here.

Problem Techniques Index



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