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Contour Plots with a Color Gradient

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This PG code shows how to construct a contour plot with a color gradient.

  • Download file: File:ContourPlot1.txt (change the file extension from txt to pg when you save it)
  • File location in NPL: FortLewis/Authoring/Templates/DiffCalcMV/

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PG problem file Explanation

Problem tagging data

Problem tagging:




$refreshCachedImages = 1;

Initialization: We will use for constructing the graph. Don't forget to have the browser cache refreshed by setting $refreshCachedImages = 1;


#  Create a graph canvas
$gr = init_graph(-5,-5,5,5,axes=>[0,0],pixels=>[300,300]);
$gr->lb( new Label(4.7,0.2,'x','black','center','middle'));
$gr->lb( new Label(0.2,4.7,'y','black','center','middle'));

#  A subroutine for adding the color gradient to the graph object
sub makegradient # ($graph, $steps, $r0, $g0, $b0, $r1, $g1, $b1)
  my ($graph, $steps, $r0, $g0, $b0, $r1, $g1, $b1) = @_;
  my $dr = ($r1 - $r0) / $steps;
  my $dg = ($g1 - $g0) / $steps;
  my $db = ($b1 - $b0) / $steps;

  my $r = $r0;
  my $g = $g0;
  my $b = $b0;
  for my $i (0..$steps-1)
    $r += $dr;
    $g += $dg;
    $b += $db;
  return $graph;

#  Add to $gr a 10 step color gradient
$gr = &makegradient($gr, 10, 
0,0,225,    # RGB blue
255,255,255 # RGB white

#  Circular contours as parametrized curves
foreach my $k (5,10,15,20,25,30,35,40,45) {
  my $a = sqrt($k);
  $fn = new Fun( 

#  Fill with gradient colors between contours
foreach my $i (0..9) {
  my $a = sqrt(2)/2 * sqrt(5*$i) - 0.1; 
  $gr->fillRegion([ $a, $a, "gradient$i"]);
  $gr->fillRegion([-$a, $a, "gradient$i"]);
  $gr->fillRegion([-$a,-$a, "gradient$i"]);
  $gr->fillRegion([ $a,-$a, "gradient$i"]);

#  Label the contours
foreach my $k (5,15,25,35,45) {
  $gr->lb(  new Label(0.707*sqrt($k),0.707*sqrt($k),$k,'black','center','middle'));

$pop = PopUp(["Choose","True","False"],"False");

Setup: By default, graph objects only know a few named colors, so if you want to have a color gradient, you'll need to add a bunch of named colors to the graph. The makegradient subroutine adds colors named gradient0, gradient1, ... to the graph object. Colors need to be specified in RGB format, and the makegradient subroutine takes in a graph object, the number of distinct colors you want in the gradient, a starting color (in this case blue) and an ending color (in this case white).

Unfortunately, we have to do everything manually, including constructing the contour curves as parametric curves, filling the spaces between curves with colors from the color gradient, and labeling each contour curve.

\{ $pop->menu() \}  This could be a contour plot 
for \( f(x,y) = x^2 - y^2 \).
\{ image(insertGraph($gr),width=>300,height=>300,tex_size=>450) \}

Main Text: We ought to have asked a more interesting question.

$showPartialCorrectAnswers = 0;

ANS( $pop->cmp() );

Answer Evaluation:

Solution explanation goes here.

COMMENT('MathObject version.');



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