Difference between revisions of "GraphTool"

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{{UnderConstruction}}
  
  +
{{historical}}
  +
  +
<p style="font-size: 120%;font-weight:bold">This problem has been replaced with many other problems:</p>
  +
* [https://openwebwork.github.io/pg-docs/sample-problems/Algebra/GraphToolCircle.html A graph tool with circle]
  +
* [https://openwebwork.github.io/pg-docs/sample-problems/Algebra/GraphToolCubic.html A graph tool with cubic]
  +
* [https://openwebwork.github.io/pg-docs/sample-problems/Algebra/GraphToolLine.html A graph tool with line]
  +
* [https://openwebwork.github.io/pg-docs/sample-problems/Algebra/GraphToolNumberLine.html A graph tool with a number line]
  +
* [https://openwebwork.github.io/pg-docs/sample-problems/Algebra/GraphToolCustomChecker.html A graph tool with custom checker]
  +
* [https://openwebwork.github.io/pg-docs/sample-problems/Algebra/GraphToolPoints.html A graph tool with points]
   
 
<h2>Graph Tool</h2>
  
<h2>Graph Tool</h2>
Line 48: Line 56:
 
<td style="background-color:#ffffdd;border:black 1px dashed;">
  
<td style="background-color:#ffffdd;border:black 1px dashed;">
 
<pre>
  
<pre>
−
$h = non_zero_random(-5, 5);
  
  +
# Define the answer checker for the graph tool.
−
$k = non_zero_random(-5, 5);
  
  +
# This checker allows the student to graph the correct circle multiple
−
$r = random(1, 4);
  
  +
# times. The idea is that the graph is graded based on appearance.
  +
# No matter how many times the student graphs the correct circle,
  +
# the resulting graph appears the same.
   
−
Context()->variables->add("y" => "Real");
  
  +
$gt_checker = sub {
−
$circle_eq_lhs = Formula("(x-$h)^2 + (y-$k)^2")->reduce;
  
  +
my ($correct, $student, $ans, $value) = @_;
  +
return 0 if $ans->{isPreview};
   
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# This grader allows the student to graph the correct circle multiple times. The idea is that
  
  +
my $score = 0;
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# the graph is graded based on appearance. No matter how many times the student graphs the
  
  +
my @errors;
−
# correct circle, the resulting graph appears the same.
  
  +
my $count = 1;
−
$gt = GraphTool("{circle, solid, ($h, $k), ($h + $r, $k)}")->with(
  
−
bBox => [-11, 11, 11, -11],
  
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cmpOptions => {
  
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list_checker => sub
  
−
{
  
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my ($correct, $student, $ans, $value) = @_;
  
−
return 0 if $ans->{isPreview};
  
   
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my $score = 0;
  
  +
# Get the center and point that define the correct circle and
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my @errors;
  
  +
# compute the square of the radius.
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my $count = 1;
  
   
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# Get the center and point that define the correct circle and compute the square of
  
  +
my ($cx, $cy) = $correct->[0]->extract(3)->value;
−
# the radius.
  
  +
my ($px, $py) = $correct->[0]->extract(4)->value;
−
my ($cx, $cy) = $correct->[0]->extract(3)->value;
  
  +
my $r_squared = ($cx - $px) ** 2 + ($cy - $py) ** 2;
−
my ($px, $py) = $correct->[0]->extract(4)->value;
  
−
my $r_squared = ($cx - $px) ** 2 + ($cy - $py) ** 2;
  
   
−
my $pointOnCircle = sub
 +
my $pointOnCircle = sub {
−
{
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my $point = shift;
−
my $point = shift;
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my ($x, $y) = $point->value;
−
my ($x, $y) = $point->value;
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return ($x - $cx) ** 2 + ($y - $cy) ** 2 == $r_squared;
−
return ($x - $cx) ** 2 + ($y - $cy) ** 2 == $r_squared;
 +
};
−
};
  
   
−
for (@$student)
  
  +
# Iterate through the objects the student graphed and check to
−
{
  
  +
# see if each is the correct circle.
−
my $nth = Value::List->NameForNumber($count++);
  
  +
for (@$student) {
  +
my $nth = Value::List->NameForNumber($count++);
  +
  +
# This checks if the student input matches the circle, type
  +
# (solid or dashed), the center of the circle and
  +
# checks if a point is on the circle.
   
−
$score += 1, next
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$score += 1, next
−
if ($_->extract(1) eq $correct->[0]->extract(1) &&
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if ($_->extract(1) eq $correct->[0]->extract(1) &&
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$_->extract(2) eq $correct->[0]->extract(2) &&
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$_->extract(2) eq $correct->[0]->extract(2) &&
−
$_->extract(3) == $correct->[0]->extract(3) &&
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$_->extract(3) == $correct->[0]->extract(3) &&
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$pointOnCircle->($_->extract(4)));
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$pointOnCircle->($_->extract(4)));
   
−
push(@errors, "The $nth object graphed is not a " . $correct->[0]->extract(1)),
  
  +
# The following gives additional information to the student.
−
next if ($_->extract(1) ne $correct->[0]->extract(1));
  
  +
  +
push(@errors, "The $nth object graphed is not a circle"),
  +
next if ($_->extract(1) ne $correct->[0]->extract(1));
   
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push(@errors, "The $nth object graphed should be a " . $correct->[0]->extract(2) . " circle."),
 +
push(@errors, "The $nth object graphed should be a " .
−
next if ($_->extract(2) ne $correct->[0]->extract(2));
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$correct->[0]->extract(2) . " circle."),
  +
next if ($_->extract(2) ne $correct->[0]->extract(2));
   
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push(@errors, "The $nth object graphed is incorrect.");
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push(@errors, "The $nth object graphed is incorrect.");
−
}
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}
   
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return ($score, @errors);
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return ($score, @errors);
−
}
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};
−
}
 +
  +
  +
$h = non_zero_random(-5, 5);
  +
$k = non_zero_random(-5, 5);
  +
$r = random(1, 4);
  +
  +
Context()->variables->add("y" => "Real");
  +
$circle_eq_lhs = Formula("(x-$h)^2 + (y-$k)^2")->reduce;
  +
  +
$gt = GraphTool("{circle, solid, ($h, $k), ($h + $r, $k)}")->with(
  +
bBox => [-11, 11, 11, -11],
  +
cmpOptions => { list_checker => $gt_checker }
 
);
  
);
 
</pre>
  
</pre>
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<b>Setup:</b>
 
<b>Setup:</b>
 
<ul>
  
<ul>
−  
  +
<li>The subroutine <pre>$gt_checker</pre> at the top is the answer checker. It checks if the student input matches the correct answer. </li>
  +
<li>The variables <tt>$h, $k</tt> and <tt>$r</tt> randomly pick a center and radius of the circle.</li>
  +
<li>The lines:
  +
<pre>
  +
Context()->variables->add("y" => "Real");
  +
$circle_eq_lhs = Formula("(x-$h)^2 + (y-$k)^2")->reduce;
  +
</pre>
  +
are used to print out nicely the equation of the circle. </li>
  +
<li>The command <tt>GraphTool</tt> creates the graph tool (the axes and input buttons for the various types of graphs). The first argument is a string surrounded by {}. The arguments are:
  +
<ul>
  +
<li>The type of geometric figure (circle, line, parabola or fill)</li>
  +
<li>The type of figure (solid or dashed)</li>
  +
<li>Other information about the figure. For example, with the circle, the center and another point on the circle. See [https://webwork.maa.org/pod/pg/macros/parserGraphTool.html#GRAPH-OBJECTS Graph Objects] for more details.</li>
  +
</ul>
  +
</li>
  +
<li>Other parameters of the <tt>GraphTool</tt> can be set using <tt>with</tt>. The following include other features:
  +
<ul>
  +
<li><tt>bbox</tt>: this is an array reference of four values <tt>xmin, ymax, xmax, ymin</tt> indicating the upper left and lower right corners of the visible graph.</li>
  +
<li><tt>cmpOptions</tt>: this is a hash of options passed to the <tt>cmp</tt> method for checking the answer. The example here:
  +
<pre>
  +
cmpOptions => { list_checker => $gt_checker }
  +
</pre>
  +
has the checker use the one we defined above. </li>
  +
</ul></li>
  +
<li>More documentation can be found at: [https://webwork.maa.org/pod/pg/macros/parserGraphTool.html]</li>
 
</ul>
  
</ul>
−
</p>
  
−
<p>
  
−
Notes: on using this and related Contexts.
  
 
</p>
  
</p>
   
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<pre>
  
<pre>
 
BEGIN_PGML
  
BEGIN_PGML
  +
Graph the circle given by the following equation.
   
−
[@ image(insertGraph($graph_image), width => 300, tex_size => 1000) @]*
  
  +
[`[$circle_eq_lhs] = [$r ** 2]`]
   
  +
[_]{$gt}
 
END_PGML
  
END_PGML
 
</pre>
  
</pre>
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<p>
  
<p>
 
<b>Main Text:</b>
  
<b>Main Text:</b>
−
This is how to insert the tikz image. Note the <tt>width</tt> and <tt>tex_size</tt> parameters can change the size of the image on the web and as hardcopy.
 
  +
This asks to graph the circle given by the equation. And the code:
  +
<pre>
  +
[_]{$gt}
  +
</pre>
  +
inserts the GraphTool.
 
</p>
  
</p>
 
</td>
  
</td>
 
</tr>
  
</tr>
   
−
<!-- Answer section -->
 +
<!-- Solution section -->
   
 
<tr valign="top">
  
<tr valign="top">
 
<td style="background-color:#eeddff;border:black 1px dashed;">
  
<td style="background-color:#eeddff;border:black 1px dashed;">
 
<pre>
  
<pre>
  +
BEGIN_PGML_SOLUTION
  +
The equation of the circle of the form:
  +
  +
[`[$circle_eq_lhs] = [$r ** 2]`]
  +
  +
has a center at [`([$h],[$k])`] and radius [$r]. To enter the graph, click the circle tool, then click the center at [`([$h],[$k])`] and then click a second point that is [$r] units from the center. This is easist going left, right, up or down from the center.
  +
END_PGML_SOLUTION
  +
 
ENDDOCUMENT();
  
ENDDOCUMENT();
 
</pre>
  
</pre>
 
<td style="background-color:#eeccff;padding:7px;">
  
<td style="background-color:#eeccff;padding:7px;">
 
<p>
  
<p>
−
This doesn't have a question, so we aren't checking an answer.
 
  +
This is the solution.
 
</p>
  
</p>
 
</td>
  
</td>
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<ul>
  
<ul>
−
<li>POD documentation: [https://webwork.maa.org/pod/pg/macros/PGtikz.html PGtikz.pl]</li>
 +
<li>POD documentation: [https://webwork.maa.org/pod/pg/macros/parserGraphTool.html]</li>
−
<li>PG macro: [https://github.com/openwebwork/pg/blob/PG-2.16/macros/PGtikz.pl PGtikz.pl]</li>
  
−
<!--<li>PG macro: [https://github.com/openwebwork/pg/blob/master/macros/PGtikz.pl PGtikz.pl]</li>-->
  
 
</ul>
  
</ul>

Latest revision as of 10:11, 29 June 2023

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 many other problems:

Graph Tool


This example shows how to get student input in the form of a graph (a circle) by using interactive graphing tools.

Problem Techniques Index

PG problem file Explanation 
DOCUMENT();
loadMacros(
  "PGstandard.pl",
  "MathObjects.pl",
  "PGML.pl",
  "parserGraphTool.pl"
);
TEXT(beginproblem());

Initialization: It is important to include the parseGraphTool.pl macro. 

# Define the answer checker for the graph tool.
# This checker allows the student to graph the correct circle multiple 
# times.  The idea is that the graph is graded based on appearance.  
# No matter how many times the student graphs the correct circle, 
# the resulting graph appears the same.

$gt_checker = sub {
    my ($correct, $student, $ans, $value) = @_;
    return 0 if $ans->{isPreview};

    my $score = 0;
    my @errors;
    my $count = 1;

    # Get the center and point that define the correct circle and 
    # compute the square of the radius.

    my ($cx, $cy) = $correct->[0]->extract(3)->value;
    my ($px, $py) = $correct->[0]->extract(4)->value;
    my $r_squared = ($cx - $px) ** 2 + ($cy - $py) ** 2;

    my $pointOnCircle = sub {
        my $point = shift;
        my ($x, $y) = $point->value;
        return ($x - $cx) ** 2 + ($y - $cy) ** 2  == $r_squared;
    };

    # Iterate through the objects the student graphed and check to
    # see if each is the correct circle.
    for (@$student) {
        my $nth = Value::List->NameForNumber($count++);
        
        # This checks if the student input matches the circle, type
        # (solid or dashed), the center of the circle and
        # checks if a point is on the circle. 

        $score += 1, next
        if ($_->extract(1) eq $correct->[0]->extract(1) &&
            $_->extract(2) eq $correct->[0]->extract(2) &&
            $_->extract(3) == $correct->[0]->extract(3) &&
            $pointOnCircle->($_->extract(4)));

        # The following gives additional information to the student.
        
        push(@errors, "The $nth object graphed is not a circle"),
        next if ($_->extract(1) ne $correct->[0]->extract(1));

        push(@errors, "The $nth object graphed should be a " .
                      $correct->[0]->extract(2) . " circle."),
        next if ($_->extract(2) ne $correct->[0]->extract(2));

        push(@errors, "The $nth object graphed is incorrect.");
    }

    return ($score, @errors);
};


$h = non_zero_random(-5, 5);
$k = non_zero_random(-5, 5);
$r = random(1, 4);

Context()->variables->add("y" => "Real");
$circle_eq_lhs = Formula("(x-$h)^2 + (y-$k)^2")->reduce;

$gt = GraphTool("{circle, solid, ($h, $k), ($h + $r, $k)}")->with(
    bBox => [-11, 11, 11, -11],
    cmpOptions => { list_checker => $gt_checker }
);

Setup:

  • The subroutine 
    $gt_checker
    at the top is the answer checker. It checks if the student input matches the correct answer.
  • The variables $h, $k and $r randomly pick a center and radius of the circle.
  • The lines: 
    Context()->variables->add("y" => "Real");
$circle_eq_lhs = Formula("(x-$h)^2 + (y-$k)^2")->reduce;
    are used to print out nicely the equation of the circle.
  • The command GraphTool creates the graph tool (the axes and input buttons for the various types of graphs). The first argument is a string surrounded by {}. The arguments are:
    • The type of geometric figure (circle, line, parabola or fill)
    • The type of figure (solid or dashed)
    • Other information about the figure. For example, with the circle, the center and another point on the circle. See Graph Objects for more details.
  • Other parameters of the GraphTool can be set using with. The following include other features:
    • bbox: this is an array reference of four values xmin, ymax, xmax, ymin indicating the upper left and lower right corners of the visible graph.
    • cmpOptions: this is a hash of options passed to the cmp method for checking the answer. The example here: 
      cmpOptions => { list_checker => $gt_checker }
      has the checker use the one we defined above.
  • More documentation can be found at: [1]

 
BEGIN_PGML
Graph the circle given by the following equation.

    [`[$circle_eq_lhs] = [$r ** 2]`]

[_]{$gt}
END_PGML

Main Text: This asks to graph the circle given by the equation. And the code: 

[_]{$gt}

inserts the GraphTool. 

BEGIN_PGML_SOLUTION
The equation of the circle of the form:

[`[$circle_eq_lhs] = [$r ** 2]`]

has a center at [`([$h],[$k])`] and radius [$r].   To enter the graph, click the circle tool, then click the center at [`([$h],[$k])`] and then click a second point that is [$r] units from the center.  This is easist going left, right, up or down from the center.
END_PGML_SOLUTION

ENDDOCUMENT();

This is the solution.

Problem Techniques Index


  • POD documentation: [2]
Retrieved from "https://webwork.maa.org/mediawiki_new/index.php?title=GraphTool&oldid=23694"