GraphTool: Difference between revisions

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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>
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<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.
 
$gt_checker = sub {
    my ($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;


Context()->variables->add("y" => "Real");
    my $pointOnCircle = sub {
$circle_eq_lhs = Formula("(x-$h)^2 + (y-$k)^2")->reduce;
        my $point = shift;
        my ($x, $y) = $point->value;
        return ($x - $cx) ** 2 + ($y - $cy) ** 2 == $r_squared;
    };


# This grader allows the student to graph the correct circle multiple times.  The idea is that
    # Iterate through the objects the student graphed and check to
# the graph is graded based on appearance.  No matter how many times the student graphs the
    # see if each is the correct circle.
# correct circle, the resulting graph appears the same.
    for (@$student) {
$gt = GraphTool("{circle, solid, ($h, $k), ($h + $r, $k)}")->with(
        my $nth = Value::List->NameForNumber($count++);
bBox => [-11, 11, 11, -11],
       
cmpOptions => {
        # This checks if the student input matches the circle, type
list_checker => sub
        # (solid or dashed), the center of the circle and
{
        # checks if a point is on the circle.
my ($correct, $student, $ans, $value) = @_;
            return 0 if $ans->{isPreview};


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


# Get the center and point that define the correct circle and compute the square of
        # The following gives additional information to the student.
# the radius.
       
my ($cx, $cy) = $correct->[0]->extract(3)->value;
        push(@errors, "The $nth object graphed is not a circle"),
my ($px, $py) = $correct->[0]->extract(4)->value;
        next if ($_->extract(1) ne $correct->[0]->extract(1));
my $r_squared = ($cx - $px) ** 2 + ($cy - $py) ** 2;


my $pointOnCircle = sub
        push(@errors, "The $nth object graphed should be a " .
{
                      $correct->[0]->extract(2) . " circle."),
my $point = shift;
        next if ($_->extract(2) ne $correct->[0]->extract(2));
my ($x, $y) = $point->value;
return ($x - $cx) ** 2 + ($y - $cy) ** 2  == $r_squared;
};


for (@$student)
        push(@errors, "The $nth object graphed is incorrect.");
{
    }
my $nth = Value::List->NameForNumber($count++);


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


push(@errors, "The $nth object graphed is not a " . $correct->[0]->extract(1)),
next if ($_->extract(1) ne $correct->[0]->extract(1));


push(@errors, "The $nth object graphed should be a " . $correct->[0]->extract(2) . " circle."),
$h = non_zero_random(-5, 5);
next if ($_->extract(2) ne $correct->[0]->extract(2));
$k = non_zero_random(-5, 5);
$r = random(1, 4);


push(@errors, "The $nth object graphed is incorrect.");
Context()->variables->add("y" => "Real");
}
$circle_eq_lhs = Formula("(x-$h)^2 + (y-$k)^2")->reduce;


return ($score, @errors);
$gt = GraphTool("{circle, solid, ($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 15:11, 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://wiki.openwebwork.org/index.php?title=GraphTool&oldid=23694"