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File:  [LON-CAPA] / loncom / homework / functionplotresponse.pm
Revision 1.24: download - view: text, annotated - select for diffs
Sat Nov 6 16:12:39 2010 UTC (13 years, 5 months ago) by www
Branches: MAIN
CVS tags: HEAD
Starting to implement the spline rule tag

# LearningOnline Network with CAPA
# option list style responses
#
# $Id: functionplotresponse.pm,v 1.24 2010/11/06 16:12:39 www Exp $
#
# Copyright Michigan State University Board of Trustees
#
# This file is part of the LearningOnline Network with CAPA (LON-CAPA).
#
# LON-CAPA is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# LON-CAPA is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with LON-CAPA; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
#
# /home/httpd/html/adm/gpl.txt
#
# http://www.lon-capa.org/
#

package Apache::functionplotresponse;
use strict;
use Apache::response();
use Apache::lonlocal;
use Apache::lonnet;

BEGIN {
  &Apache::lonxml::register('Apache::functionplotresponse',('functionplotresponse','backgroundplot','spline','splinerule'));
}

#
# There can be a number of applets on a page, each called ggbApplet_$id, 
# where $id is the "_"-concatenated part and responseid
#

sub geogebra_startcode {
    my ($id)=@_;
    return (<<ENDSTARTCODE);
<applet name="ggbApplet_$id" code="geogebra.GeoGebraApplet" archive="geogebra.jar"
         codebase="/adm/geogebra/"  width="714" height="447" MAYSCRIPT>
       <param name="java_arguments" value="-Xmx512m -Djnlp.packEnabled=true"/>
ENDSTARTCODE
}

sub geogebra_endcode {
    return &Apache::lonhtmlcommon::java_not_enabled()."</applet>\n";
}

#
# This is the internal GeoGebra bytecode which defines the spline functions
#
sub geogebra_spline_program {
    return (<<ENDSPLINEPROGRAM);
<param name="ggbBase64" value="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"/>
ENDSPLINEPROGRAM
}

#
# The standard set of parameters inside <applet>
#
sub geogebra_default_parameters {
   my ($id)=@_;
   return(<<ENDDEFAULTPARAMETERS);
        <param name="image" value="/adm/lonIcons/lonanim.gif"  />
        <param name="boxborder" value="false"  />
        <param name="centerimage" value="true"  />
        <param name="java_arguments" value="-Xmx512m" />
        <param name="cache_archive" value="geogebra.jar, geogebra_main.jar, geogebra_gui.jar, geogebra_cas.jar, geogebra_export.jar, geogebra_properties.jar" />
        <param name="cache_version" value="3.2.44.0, 3.2.44.0, 3.2.44.0, 3.2.44.0, 3.2.44.0, 3.2.44.0" />
        <param name="framePossible" value="false" />

        <param name="showResetIcon" value="false" />
        <param name="showAnimationButton" value="false" />
        <param name="enableRightClick" value="false" />
        <param name="errorDialogsActive" value="true" />
        <param name="enableLabelDrags" value="false" />
        <param name="showMenuBar" value="false" />
        <param name="showToolBar" value="false" />
        <param name="showToolBarHelp" value="false" />
        <param name="showAlgebraInput" value="false" />
        <param name="enableShiftDragZoom" value="false" />
        <param name="allowRescaling" value="false" />
        <param name="enableLabelDrags" value="false" />
        <param name="ggbOnInitParam" value="applet_$id" />
ENDDEFAULTPARAMETERS
}

#
# This subroutine is called by LON-CAPA at </problem>
# Each applet on the page will call function ggbOnInit when it is done loading
# This function in turn will call the respective function registered by start_init_script
# Which one of the registered functions is called is determined by ggbOnInitParam, which GeoGebra passes to ggbOnInit
#

sub init_script {
   if ($#Apache::functionplotresponse::callscripts>=0) {
      my $script='';
      foreach my $id (@Apache::functionplotresponse::callscripts) {
          $script.="if (param=='applet_$id') { loaded_$id=true; }\n";
      }
      $script.="if (".join(' && ',map { "loaded_$_" } (@Apache::functionplotresponse::callscripts)).
               ") { setTimeout('ggbInitAll()',20) }";
      my $calls=join("\n",map { "ggbInit_$_();" } (@Apache::functionplotresponse::callscripts)); 
      return (<<ENDGGBINIT);
<script type="text/javascript">
// <![CDATA[
// Function that each applet will call when loaded
// It will pass "its" parameter
// Set flags for when an applet is loaded, wait till all are loaded, and then some
function ggbOnInit(param) {
$script
}
function ggbInitAll() {
$calls
}
// ]]>
</script>
ENDGGBINIT
   }
}

#
# Each Geogebra applet is supposed to call this when parameters change
# Changes the hidden fields on the web page
#
sub update_script {
    my ($id)=@_;
    return (<<ENDUPDATESCRIPT);
<script type="text/javascript">
// <![CDATA[
function updatePointCoordinates_$id(coordinateName) {
            var x = document.ggbApplet_$id.getXcoord(coordinateName);
            var y = document.ggbApplet_$id.getYcoord(coordinateName);
            document.lonhomework.elements["HWVAL_$id\_" + coordinateName + "_x"].value = x;
            document.lonhomework.elements["HWVAL_$id\_" + coordinateName + "_y"].value = y;
        }
// ]]>
</script>
ENDUPDATESCRIPT
}

#
# Register the above update-handler for a variable
#

sub update_register {
   my ($id,$variable)=@_;
   return "document.ggbApplet_$id.registerObjectUpdateListener('$variable','updatePointCoordinates_$id');\n";
}

#
# Set a coordinate variable
#
sub set_coordinate {
   my ($id,$variable,$x,$y)=@_;
   return (<<ENDSETVARIABLE);
document.ggbApplet_$id.evalCommand("$variable=($x,$y)");
ENDSETVARIABLE
}

#
# Input field name for a coordinate variable
#

sub field_name {
    my ($id,$variable,$name)=@_;
    return "HWVAL_$id\_$variable\_$name";
}

#
# Generate an input field for a coordinate variable
#

sub generate_input_field {
    my ($id,$variable,$x,$y)=@_;
    $Apache::functionplotresponse::inputfields.=
       "<input type='hidden' name='".&field_name($id,$variable,'x')."' value='$x' />\n".
       "<input type='hidden' name='".&field_name($id,$variable,'y')."' value='$y' />\n";
}

#
# Initialize a new coordinate variable at set a listener on it
#
sub new_coordinate {
    my ($id,$variable,$x,$y)=@_;
    if (defined($Apache::functionplotresponse::previous{&field_name($id,$variable,'x')})) {
       $x=$Apache::functionplotresponse::previous{&field_name($id,$variable,'x')};
    }
    if (defined($Apache::functionplotresponse::previous{&field_name($id,$variable,'y')})) {
       $y=$Apache::functionplotresponse::previous{&field_name($id,$variable,'y')};
    }
    &generate_input_field($id,$variable,$x,$y);
    return &set_coordinate($id,$variable,$x,$y).&update_register($id,$variable);
}

#
# This registers the init-function call for ggbOnInit, which LON-CAPA will place at </problem>
# It then starts the right headers
#
sub start_init_script {
    my ($id)=@_;
# Add id to the list of ggbInit_$id functions that need to be called
    push(@Apache::functionplotresponse::callscripts,$id);
# ... and open this function
    return (<<ENDSTARTINIT);
<script type="text/javascript">
// <![CDATA[
// variable that will eventually be passed back to the server
var coordinateMap_$id = [];
// flag for not loaded yet
var loaded_$id=false;
// Init-function for applet
function ggbInit_$id() {
ENDSTARTINIT
}

#
# This sets the axes inside ggbInit_$id
#

sub axes_script {
    my ($id,$xmin,$xmax,$ymin,$ymax,$xvisible,$yvisible,$gvisible)=@_;
    return (<<ENDAXESSCRIPT);
            // changes (xmin, xmax, ymin, ymax)
            document.ggbApplet_$id.setCoordSystem($xmin,$xmax,$ymin,$ymax);

            // makes the (x,y) axis (in)visible
            document.ggbApplet_$id.setAxesVisible($xvisible,$yvisible);
            // makes the grid (in)visible
            document.ggbApplet_$id.setGridVisible($gvisible);
ENDAXESSCRIPT
}

sub axes_label {
    my ($id,$xlabel,$ylabel)=@_;
    unless ($xlabel || $ylabel) { return ''; }
    my $return='document.ggbApplet_'.$id.'.evalCommand("topRight=Corner[3]");';
    if ($xlabel) {
       $return.=(<<ENDXAXISLABELSCRIPT);
document.ggbApplet_$id.evalCommand("Xlabel=(x(topRight)-AxisStepX[],AxisStepY[]/6)");
document.ggbApplet_$id.setVisible("Xlabel",false);
document.ggbApplet_$id.evalCommand("Text[\\"$xlabel\\", Xlabel]");
ENDXAXISLABELSCRIPT
    }
    if ($ylabel) {
       $return.=(<<ENDYAXISLABELSCRIPT);
document.ggbApplet_$id.evalCommand("Ylabel=(AxisStepX[]/6,y(topRight)-AxisStepY[]/3)");
document.ggbApplet_$id.setVisible("Ylabel",false);
document.ggbApplet_$id.evalCommand("Text[\\"$ylabel\\", Ylabel]");
ENDYAXISLABELSCRIPT
    }
    return $return;
}

sub plot_script {
   my ($id,$function,$fixed)=@_;
   if ($fixed) {
# Use stupid trick to nail this to a location
# Oddly, it seems like only one plot cannot be nailed to a location
# Non-nailed-down plots apparently get overwritten
      return (<<ENDPLOTSCRIPT);
            document.ggbApplet_$id.evalCommand("a=1");
            document.ggbApplet_$id.setVisible("a",false);
            // This MUST be a DEPENDENT OBJECT in order to be locked down:
            document.ggbApplet_$id.evalCommand("y=a*($function)");
ENDPLOTSCRIPT
   } else {
       return "document.ggbApplet_$id.evalCommand('y=$function')";
   }
}

#
# Subroutine that generates code for spline $label based on stored information
#

sub generate_spline {
   my ($id,$label)=@_;
   my $result='';
   my $order=$Apache::functionplotresponse::splineorder{$label};
   my $x=$Apache::functionplotresponse::splineinitx{$label};
   my $y=$Apache::functionplotresponse::splineinity{$label};
   my $sx=$Apache::functionplotresponse::splinescalex{$label};
   my $sy=$Apache::functionplotresponse::splinescaley{$label};
   my @coords=();
   foreach my $i (1..$order) {
       $result.=&new_coordinate($id,$label.'P'.$i,$x,$y);
       $x+=$sx/(2.*($order-1));
       push(@coords,$label.'P'.$i);
       $result.=&new_coordinate($id,$label.'S'.$i,$x,$y+$sy);
       $x+=$sx/(2.*($order-1));
       push(@coords,$label.'S'.$i);
   }
   $result.='document.ggbApplet_'.$id.'.evalCommand("Spline'.$order.'['.join(',',@coords).']");'."\n";
   return $result;
}
#
# <backgroundplot function="..." fixed="yes/no" />
#
sub start_backgroundplot {
   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
   my $result='';
   my $internalid = $Apache::inputtags::part.'_'.$Apache::inputtags::response[-1];
   my $function=&Apache::lonxml::get_param('function',$parstack,$safeeval);
   my $fixed=(&Apache::lonxml::get_param('fixed',$parstack,$safeeval)=~/on|true|yes|1/i?1:0);
 
   unless ($function) { $function="0"; }
   if ($target eq 'web') {
      $result.=&plot_script($internalid,$function,$fixed);
   } elsif ($target eq 'edit') {
        $result=&Apache::edit::tag_start($target,$token,'Background Function Plot').
             &Apache::edit::text_arg('Function:','function',
                                     $token,'16').
             &Apache::edit::select_arg('Fixed location:','fixed',
                                  ['yes','no'],$token).
             &Apache::edit::end_row();
  } elsif ($target eq 'modified') {
    my $constructtag=&Apache::edit::get_new_args($token,$parstack,
                                                 $safeeval,'function','fixed');
    if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
  }
  return $result;
}

sub end_backgroundplot {
   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
   my $result='';
   if ($target eq 'edit') {
       $result=&Apache::edit::end_table();
   }
   return $result;
}

#
# <splinerule ... />
#
sub start_splinerule {
   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
   my $result='';
   my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval);
   $Apache::functionplotresponse::counter++;
   if ($label=~/\W/) {
      &Apache::lonxml::warning(&mt('Spline Rule indices should only contain alphanumeric characters.'));
   }
   $label=~s/\W//gs;
   unless ($label) {
      $label='R'.$Apache::functionplotresponse::counter;
   } else {
      $label='R'.$label;
   }
   if ($Apache::functionplotresponse::splineorder{$label}) {
       &Apache::lonxml::error(&mt('Spline Rule indices must be unique.'));
   }


   if ($target eq 'grade') {
# Simply remember - in order - for later
      my $beginninglabel=&Apache::lonxml::get_param('beginninglabel',$parstack,$safeeval);
      my $endinglabel=&Apache::lonxml::get_param('endinglabel',$parstack,$safeeval);
      if (($beginninglabel=~/\W/) || ($endinglabel=~/W/)) {
          &Apache::lonxml::warning(&mt('Spline Rule labels must be alphanumeric.'));
      }
      $beginninglabel=~s/\W//gs;
      $endinglabel=~s/\W//gs;
      my $relationship=&Apache::lonxml::get_param('relationship',$parstack,$safeeval);
      $relationship=~s/\W//gs;
      $relationship=lc($relationship);
      unless ($relationship=~/^(eq|ge|gt|le|lt|ne)$/) {
          &Apache::lonxml::warning(&mt('Spline Rule relationship not defined.'));
          $relationship='eq';
      }
      my $derivative=&Apache::lonxml::get_param('derivative',$parstack,$safeeval);
      unless (($derivative==0) || ($derivative==1) || ($derivative==2)) {
         &Apache::lonxml::warning(&mt('Spline Rule derivative not defined.'));
         $derivative=0;
      }
      push(@Apache::functionplotresponse::splinerules,join(':',(
           $label,
           $derivative,
           &Apache::lonxml::get_param('beginningvalue',$parstack,$safeeval),
           $beginninglabel,
           &Apache::lonxml::get_param('endingvalue',$parstack,$safeeval),
           $endinglabel,
           $relationship,
           &Apache::lonxml::get_param('value',$parstack,$safeeval)
          )));
   } elsif ($target eq 'edit') {
      $result=&Apache::edit::tag_start($target,$token,'Spline Evaluation Rule').
              &Apache::edit::end_row();
   }
   return $result;
}

sub end_splinerule {
   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
   my $result='';
   if ($target eq 'edit') {
       $result=&Apache::edit::end_table();
   }
   return $result;
}


#
# <spline index="..." order="1,2,3,4" initx="..." inity="..." scalex="..." scaley="..." />
#
# Unfortunately, GeoGebra seems to want all splines after everything else, so we need to store them
#
sub start_spline {
   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
   my $result='';
   if ($target eq 'web') {
      my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval);
      $Apache::functionplotresponse::counter++;
      if ($label=~/\W/) {
         &Apache::lonxml::warning(&mt('Spline indices should only contain alphanumeric characters.'));
      }
      $label=~s/\W//gs;
      unless ($label) { 
         $label='S'.$Apache::functionplotresponse::counter; 
      } else {
         $label='S'.$label;
      }
      if ($Apache::functionplotresponse::splineorder{$label}) {
         &Apache::lonxml::error(&mt('Spline indices must be unique.'));
      }

      my $order=&Apache::lonxml::get_param('order',$parstack,$safeeval);
      if ($order<2) { $order=2; }
      if ($order>8) { $order=8; }
      $Apache::functionplotresponse::splineorder{$label}=$order;

      my $x=&Apache::lonxml::get_param('initx',$parstack,$safeeval);
      unless ($x) { $x=0; }
      $Apache::functionplotresponse::splineinitx{$label}=$x;

      my $y=&Apache::lonxml::get_param('inity',$parstack,$safeeval);
      unless ($y) { $y=0; }
      $Apache::functionplotresponse::splineinity{$label}=$y;

      my $sx=&Apache::lonxml::get_param('scalex',$parstack,$safeeval);
      unless ($sx) { $sx=$order; }
      $Apache::functionplotresponse::splinescalex{$label}=$sx;

      my $sy=&Apache::lonxml::get_param('scaley',$parstack,$safeeval);
      unless ($sy) { $sy=2; }
      $Apache::functionplotresponse::splinescaley{$label}=$sy;
   } elsif ($target eq 'edit') {
        $result=&Apache::edit::tag_start($target,$token,'Spline').
             &Apache::edit::text_arg('Index:','index',
                                     $token,'4').'&nbsp;'.
             &Apache::edit::select_arg('Order:','order',
                                  ['2','3','4','5','6','7','8','9'],$token).'&nbsp;'.
             &Apache::edit::text_arg('Initial x-value:','initx',
                                     $token,'4').'&nbsp;'.
             &Apache::edit::text_arg('Initial y-value:','inity',
                                     $token,'4').'&nbsp;'.
             &Apache::edit::text_arg('Scale x:','scalex',
                                     $token,'4').'&nbsp;'.
             &Apache::edit::text_arg('Scale y:','scaley',
                                     $token,'4').
             &Apache::edit::end_row();
  } elsif ($target eq 'modified') {
    my $constructtag=&Apache::edit::get_new_args($token,$parstack,
                                                 $safeeval,'index','order','initx','inity',
                                                           'scalex','scaley');
    if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
  }
  return $result;
}

sub end_spline {
   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
   my $result='';
   if ($target eq 'edit') {
       $result=&Apache::edit::end_table();
   }
   return $result;
}
 
sub end_init_script {
    return (<<ENDENDINIT);
}
// ]]>
</script>
ENDENDINIT
}

#
# Storing and restoring spline coordinates from part answers
#
sub decode_previous_answer {
   my ($answer)=@_;
   foreach my $coordinate (split(/\,/,$answer)) {
      my ($key,$value)=split(/\=/,$coordinate);
      $Apache::functionplotresponse::previous{$key}=$value;
   }
}

sub get_answer_from_form_fields {
   my ($id)=@_;
   my $answer='';
   my %coords=();
   foreach my $field (keys(%env)) {
      if ($field=~/^form\.HWVAL\_$id/) {
         $field=~/^form\.(.*)$/;
         $coords{$1}=$env{$field};
      }
   }
   $answer=join(',',map { $_.'='.$coords{$_} } (sort(keys(%coords))));
   return ($answer,%coords);
}

#
# The following functions calculate the cubic-hermite splines server-side
#

sub cubic_hermite {
   my ($t,$p1,$s1,$p2,$s2)=@_;
   return (2.*$t*$t*$t-3.*$t*$t+1.)*$p1 + 5.*($t*$t*$t-2.*$t*$t+$t)*($s1-$p1)+
          (-2.*$t*$t*$t+3.*$t*$t)  *$p2 + 5.*($t*$t*$t-$t*$t)      *($s2-$p2);
}

#
# d/dt(...)
# 

sub ddt_cubic_hermite {
   my ($t,$p1,$s1,$p2,$s2)=@_;
   return (6.*$t*$t-6.*$t) *$p1 + 5.*(3.*$t*$t-4.*$t+1.)*($s1-$p1)+
          (-6.*$t*$t+6.*$t)*$p2 + 5.*(3.*$t*$t-2.*$t)   *($s2-$p2);
}

#
# d^2/dt^2(...)
#

sub d2dt2_cubic_hermite {
   my ($t,$p1,$s1,$p2,$s2)=@_;
   return (12.*$t-6.) *$p1 + 5.*(6.*$t-4.)*($s1-$p1)+
          (-12.*$t+6.)*$p2 + 5.*(6.*$t-2.)*($s2-$p2);
}

#
# Array index calculation
#
sub array_index {
   my ($xmin,$xmax,$x)=@_;
   return int(($x-$xmin)/($xmax-$xmin)*200.+0.5);
}

#
# Actual x-value of array index
#

sub index_x {
   my ($xmin,$xmax,$i)=@_;
   return $i*($xmax-$xmin)/200.+$xmin;
}

#
# Assume function to be linear between array points
# Return the two indices and the scale factor
#

sub indices_scale {
   my ($xmin,$xmax,$x)=@_;
   my $i=&array_index($xmin,$xmax,$x);
   my $xr=&index_x($xmin,$xmax,$i);
   if ($xr<$x) {
# Desired x is right of array index
      if ($i>=200) { return (200,200,0); }
      return($i,$i+1,200.*($x-$xr)/($xmax-$xmin));
   } elsif ($xr>$x) {
# Desired x is left of array index
      if ($i<=0) { return (0,0,0); }
      return($i-1,$i,1.-200.*($xr-$x)/($xmax-$xmin));
   } else {
# Desired x is at array index (unlikely, but ...)
      if ($i>=200) { return (200,200,0); }
      if ($i<=0) { return (0,0,0); }
      return ($i,$i,0);
   }
}

#
# Function value
#

sub func_val {
   my ($xmin,$xmax,$x)=@_;
   my ($il,$ih,$factor)=&indices_scale($xmin,$xmax,$x);
   my $fl=$Apache::functionplotresponse::func[$il];
   my $fh=$Apache::functionplotresponse::func[$ih];
   unless (defined($fl) || defined($fh)) { return undef; }
   unless (defined($fl)) { return $fh; }
   unless (defined($fh)) { return $fl; }
   return $fl+$factor*($fh-$fl);
}

#
# First derivative
#

sub dfuncdx_val {
   my ($xmin,$xmax,$x)=@_;
   my ($il,$ih,$factor)=&indices_scale($xmin,$xmax,$x);
   my $fl=$Apache::functionplotresponse::dfuncdx[$il];
   my $fh=$Apache::functionplotresponse::dfuncdx[$ih];
   unless (defined($fl) || defined($fh)) { return undef; }
   unless (defined($fl)) { return $fh; }
   unless (defined($fh)) { return $fl; }
   return $fl+$factor*($fh-$fl);
}

#
# Second derivative
#

sub d2funcdx2_val {
   my ($xmin,$xmax,$x)=@_;
   my ($il,$ih,$factor)=&indices_scale($xmin,$xmax,$x);
   my $fl=$Apache::functionplotresponse::d2funcdx2[$il];
   my $fh=$Apache::functionplotresponse::d2funcdx2[$ih];
   unless (defined($fl) || defined($fh)) { return undef; }
   unless (defined($fl)) { return $fh; }
   unless (defined($fh)) { return $fl; }
   return $fl+$factor*($fh-$fl);
}

#
# Populate the arrays
#

sub populate_arrays {
    my ($id,$xmin,$xmax)=@_;
    for (my $i=0; $i<=200; $i++) {
       $Apache::functionplotresponse::func[$i]=undef;
       $Apache::functionplotresponse::dfuncdx[$i]=undef;
       $Apache::functionplotresponse::d2funcd2x[$i]=undef;
    }
    unless ($xmax>$xmin) { return 'no_func'; }
# Run over all splines in response
    foreach my $label (split(/\,/,$env{"form.HWVAL_AllSplines_$id"})) {
        my $xiold=-1;
# Run over all points in spline
        for (my $i=1; $i<$env{"form.HWVAL_SplineOrder_".$id."_".$label}; $i++) {
            my $ni=$i+1;
            my @xparms=($env{'form.HWVAL_'.$id.'_'.$label.'P'.$i.'_x'},
                        $env{'form.HWVAL_'.$id.'_'.$label.'S'.$i.'_x'},
                        $env{'form.HWVAL_'.$id.'_'.$label.'P'.$ni.'_x'},
                        $env{'form.HWVAL_'.$id.'_'.$label.'S'.$ni.'_x'});
            my @yparms=($env{'form.HWVAL_'.$id.'_'.$label.'P'.$i.'_y'},
                        $env{'form.HWVAL_'.$id.'_'.$label.'S'.$i.'_y'},
                        $env{'form.HWVAL_'.$id.'_'.$label.'P'.$ni.'_y'},
                        $env{'form.HWVAL_'.$id.'_'.$label.'S'.$ni.'_y'});
# Run in small steps over spline parameter
            for (my $t=0; $t<=1; $t+=0.00025) {
                my $xi=&array_index($xmin,$xmax,&cubic_hermite($t,@xparms));
                if ($xi<$xiold) { return 'no_func'; }
                if (($xi>$xiold) && ($xi>=0) && ($xi<=200)) {
                   if (defined($Apache::functionplotresponse::func[$xi])) { return 'no_func'; }
                   $xiold=$xi;
# Function value
                   $Apache::functionplotresponse::func[$xi]=&cubic_hermite($t,@yparms);
# dy/dx=dy/dt/(dx/dt)
                   my $dxdt=&ddt_cubic_hermite($t,@xparms);
                   if ($dxdt) {
                      $Apache::functionplotresponse::dfuncdx[$xi]=&ddt_cubic_hermite($t,@yparms)/$dxdt;
                   }
# d^2y/dx^2
                   my $d2xdt2=&d2dt2_cubic_hermite($t,@xparms);
                   if ($d2xdt2) {
                      $Apache::functionplotresponse::d2funcd2x[$xi]=&d2dt2_cubic_hermite($t,@yparms)/$d2xdt2;
                   }
                }
            }
        }
    }
}

#
# Implentation of <functionplotresponse>
#

sub start_functionplotresponse {
  my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  my $result='';
# To remember the splines - somehow, they need to come last
  undef %Apache::functionplotresponse::splineorder;
  undef %Apache::functionplotresponse::splineinitx;
  undef %Apache::functionplotresponse::splineinity;
  undef %Apache::functionplotresponse::splinescalex;
  undef %Apache::functionplotresponse::splinescaley;
# Remember input fields, etc
  undef %Apache::functionplotresponse::previous;
  $Apache::functionplotresponse::inputfields='';
  $Apache::functionplotresponse::counter=0;
# Remember rules
  undef @Apache::functionplotresponse::splinerules;
# Part and ID
  my $partid=$Apache::inputtags::part;
  my $id=&Apache::response::start_response($parstack,$safeeval);
# Internal ID to mark the applet and its coordinates
  my $internalid = $partid.'_'.$id;
# Previous answer
  &decode_previous_answer($Apache::lonhomework::history{"resource.$partid.$id.submission"});

# Parameters of <functionplotresponse>
  my $xmin=&Apache::lonxml::get_param('xmin',$parstack,$safeeval);
  $xmin=(defined($xmin)?$xmin:-10);
  my $xmax=&Apache::lonxml::get_param('xmax',$parstack,$safeeval);
  $xmax=(defined($xmax)?$xmax:10);
  my $ymin=&Apache::lonxml::get_param('ymin',$parstack,$safeeval);
  $ymin=(defined($ymin)?$ymin:-10);
  my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval);
  $ymax=(defined($ymax)?$ymax:10);
  my $xaxisvisible=(&Apache::lonxml::get_param('xaxisvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false');
  my $yaxisvisible=(&Apache::lonxml::get_param('yaxisvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false');
  my $gridvisible=(&Apache::lonxml::get_param('gridvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false');
  my $xlabel=&Apache::lonxml::get_param('xlabel',$parstack,$safeeval);
  my $ylabel=&Apache::lonxml::get_param('ylabel',$parstack,$safeeval);
  if ($target eq 'edit') {
    $result.=&Apache::edit::start_table($token)
       .'<tr><td><span class="LC_nobreak">'.&mt('Function Plot Question').'</span></td>'
       .'<td><span class="LC_nobreak">'.&mt('Delete?').' '
       .&Apache::edit::deletelist($target,$token)
       .'</span></td>'
       ."<td>&nbsp;"
       .&Apache::edit::end_row()
       .&Apache::edit::start_spanning_row()
       ."\n";
    $result.=&Apache::edit::text_arg('Label x-axis:','xlabel',
                                     $token,'6').'&nbsp;'.
             &Apache::edit::text_arg('Minimum x-value:','xmin',
                                     $token,'4').'&nbsp;'.
             &Apache::edit::text_arg('Maximum x-value:','xmax',
                                     $token,'4').'&nbsp;'.
             &Apache::edit::select_arg('x-axis visible:','xaxisvisible',
                                  ['yes','no'],$token).'&nbsp;&nbsp;'.
             &Apache::edit::text_arg('Label y-axis:','ylabel',
                                     $token,'6').'&nbsp;'.
             &Apache::edit::text_arg('Minimum y-value:','ymin',
                                     $token,'4').'&nbsp;'.
             &Apache::edit::text_arg('Maximum y-value:','ymax',
                                     $token,'4').'&nbsp;'.
             &Apache::edit::select_arg('y-axis visible:','yaxisvisible',
                                  ['yes','no'],$token).'&nbsp;&nbsp;'.
             &Apache::edit::select_arg('Grid visible:','gridvisible',
                                  ['yes','no'],$token).
             &Apache::edit::end_row().&Apache::edit::start_spanning_row();
  } elsif ($target eq 'modified') {
    my $constructtag=&Apache::edit::get_new_args($token,$parstack,
                                                 $safeeval,'xlabel','xmin','xmax','ylabel','ymin','ymax',
                                                           'xaxisvisible','yaxisvisible','gridvisible');
    if ($constructtag) { $result = &Apache::edit::rebuild_tag($token); }

  } elsif ($target eq 'meta') {
       $result=&Apache::response::meta_package_write('functionplotresponse');
  } elsif ($target eq 'web') {
# paste in the update routine to receive stuff back from the applet
     $result.=&update_script($internalid);
# start the initscript for this applet
     $result.=&start_init_script($internalid);
# put the axis commands inside
     $result.=&axes_script($internalid,$xmin,$xmax,$ymin,$ymax,$xaxisvisible,$yaxisvisible,$gridvisible);
     $result.=&axes_label($internalid,$xlabel,$ylabel);
# init script is left open
  }
  return $result;
}

sub splinerulecheck {
   my ($rule)=@_;
   return 0;
}


sub end_functionplotresponse {
  my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  &Apache::response::end_response;

  my $result;
  my $id=$Apache::inputtags::response[-1];
  my $partid=$Apache::inputtags::part;
  my $internalid = $partid.'_'.$id;

    if ($target eq 'edit') { $result=&Apache::edit::end_table(); }
    if ($target eq 'grade'
         && &Apache::response::submitted()
         && $Apache::lonhomework::type eq 'exam') {

        #&Apache::response::scored_response($partid,$id);

    } elsif ($target eq 'grade'
         && &Apache::response::submitted()
         && $Apache::lonhomework::type ne 'exam') {
        my ($response,%coords)=&get_answer_from_form_fields($internalid);
        $Apache::lonhomework::results{"resource.$partid.$id.submission"}=$response;
        my %previous=&Apache::response::check_for_previous($response,$partid,$id);
#
# Actually grade
#
        my $xmin=&Apache::lonxml::get_param('xmin',$parstack,$safeeval);
        $xmin=(defined($xmin)?$xmin:-10);
        my $xmax=&Apache::lonxml::get_param('xmax',$parstack,$safeeval);
        $xmax=(defined($xmax)?$xmax:10);
        my $ad='';
        if (&populate_arrays($internalid,$xmin,$xmax) eq 'no_func') {
           $ad='NOT_FUNCTION';
        } else {
# We have a function that we can actually grade, go through the spline rules.
           undef  %Apache::functionplotresponse::splinerulelabels;
           foreach my $rule (@Apache::functionplotresponse::splinerules) {
              unless (&splinerulecheck($rule)) {
                 $ad='INCORRECT';
                 last;
              }
           }
# If it's not wrong, it's correct 
           unless ($ad) { $ad='EXACT_ANS' };
        }

#
# Store grading info
#
        $Apache::lonhomework::results{"resource.$partid.$id.awarddetail"}=$ad;
        &Apache::response::handle_previous(\%previous,$ad);
   } elsif ($target eq 'web') {
# Now is the time to render all of the stored splines
     foreach my $label (keys(%Apache::functionplotresponse::splineorder)) {
        $result.=&generate_spline($internalid,$label);
     }
# close the init script
     $result.=&end_init_script();
# register all splines in this response 
     $result.='<input type="hidden" name="HWVAL_AllSplines_'.$internalid.'" value="'.
                 join(',',keys(%Apache::functionplotresponse::splineorder)).'" />'."\n";
     foreach my $label (keys(%Apache::functionplotresponse::splineorder)) {
        $result.='<input type="hidden" name="HWVAL_SplineOrder_'.$internalid.'_'.$label.'" value="'.
                 $Apache::functionplotresponse::splineorder{$label}.'" />'."\n";
     }
# generate the input fields
     $result.=$Apache::functionplotresponse::inputfields;
# actually start the <applet>-tag
     $result.=&geogebra_startcode($internalid);
# load the spline bytecode
     $result.=&geogebra_spline_program();
# set default parameters
     $result.=&geogebra_default_parameters($internalid);
# close the <applet>-tag
     $result.=&geogebra_endcode();
  }
  return $result;
}

1;

__END__
 
=head1 NAME

Apache::functionplotresponse.pm;

=head1 SYNOPSIS

Handles tags associated with accepting function plots.

This is part of the LearningOnline Network with CAPA project
described at http://www.lon-capa.org.

=head1 HANDLER SUBROUTINE

start_functionplotresponse()

=head1 OTHER SUBROUTINES

=over

=item end_functionplotresponse()

=back

=cut
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