ContourPlots
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Contour Plots
This PG code shows how to construct contour plots.
| PG problem file | Explanation |
|---|---|
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "PGgraphmacros.pl", "unionTables.pl", ); TEXT(beginproblem()); $refreshCachedImages=1; |
Initialization:
Use |
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 |
$showPartialCorrectAnswers = 1; ENDDOCUMENT(); |
Answer Evaluation: We did not ask any questions, so there's nothing interesting here. |
