--- loncom/homework/functionplotresponse.pm	2010/11/10 22:41:29	1.31
+++ loncom/homework/functionplotresponse.pm	2010/11/19 20:03:13	1.41
@@ -1,7 +1,7 @@
 # LearningOnline Network with CAPA
 # option list style responses
 #
-# $Id: functionplotresponse.pm,v 1.31 2010/11/10 22:41:29 www Exp $
+# $Id: functionplotresponse.pm,v 1.41 2010/11/19 20:03:13 www Exp $
 #
 # Copyright Michigan State University Board of Trustees
 #
@@ -31,9 +31,11 @@ use strict;
 use Apache::response();
 use Apache::lonlocal;
 use Apache::lonnet;
-
+ 
 BEGIN {
-  &Apache::lonxml::register('Apache::functionplotresponse',('functionplotresponse','backgroundplot','spline','functionplotrule'));
+  &Apache::lonxml::register('Apache::functionplotresponse',('functionplotresponse','backgroundplot','spline',
+                                                            'functionplotrule','functionplotruleset',
+                                                            'functionplotelements'));
 }
 
 #
@@ -45,7 +47,7 @@ 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>
+         codebase="/adm/geogebra/"  width="722" height="447" MAYSCRIPT>
        <param name="java_arguments" value="-Xmx512m -Djnlp.packEnabled=true"/>
 ENDSTARTCODE
 }
@@ -72,9 +74,8 @@ sub geogebra_default_parameters {
         <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="cache_archive" value="geogebra.jar, geogebra_main.jar, geogebra_gui.jar, geogebra_cas.jar, geogebra_algos.jar, geogebra_export.jar, geogebra_javascript.jar, jlatexmath.jar, jlm_greek.jar, jlm_cyrillic.jar, geogebra_properties.jar" />
+	<param name="cache_version" value="3.9.115.0, 3.9.115.0, 3.9.115.0, 3.9.115.0, 3.9.115.0, 3.9.115.0, 3.9.115.0, 3.9.115.0, 3.9.115.0, 3.9.115.0, 3.9.115.0" />
         <param name="framePossible" value="false" />
 
         <param name="showResetIcon" value="false" />
@@ -157,16 +158,40 @@ sub update_register {
 }
 
 #
-# Set a coordinate variable
+# Set a point coordinate variable
 #
-sub set_coordinate {
+sub set_point_coordinate {
    my ($id,$variable,$x,$y)=@_;
    return (<<ENDSETVARIABLE);
 document.ggbApplet_$id.evalCommand("$variable=($x,$y)");
+document.ggbApplet_$id.setLabelVisible("$variable",false);
 ENDSETVARIABLE
 }
 
 #
+# Set a slope coordinate variable
+#
+sub set_slope_coordinate {
+   my ($id,$variable,$xrel,$yrel,$xmin,$xmax,$ymin,$ymax,$pointname)=@_;
+   my $xvariable=$variable.'x';
+   my $yvariable=$variable.'y';
+   my $domain=$xmax-$xmin;
+   my $range=$ymax-$ymin;
+   my $xinterval=$domain/100.;
+   my $yinterval=$range/200.;
+   return (<<ENDSETSVARIABLE);
+document.ggbApplet_$id.evalCommand("$xvariable=Slider[0,$domain,$xinterval]");
+document.ggbApplet_$id.setVisible("$xvariable", false);
+document.ggbApplet_$id.evalCommand("$xvariable=$xrel");
+document.ggbApplet_$id.evalCommand("$yvariable=Slider[-$range,$range,$yinterval]");
+document.ggbApplet_$id.setVisible("$yvariable", false);
+document.ggbApplet_$id.evalCommand("$yvariable=$yrel");
+document.ggbApplet_$id.evalCommand("$variable=($xvariable+x($pointname),$yvariable+y($pointname))");
+document.ggbApplet_$id.setLabelVisible("$variable", false);
+ENDSETSVARIABLE
+}
+
+#
 # Input field name for a coordinate variable
 #
 
@@ -187,9 +212,9 @@ sub generate_input_field {
 }
 
 #
-# Initialize a new coordinate variable at set a listener on it
+# Initialize a new point coordinate variable at set a listener on it
 #
-sub new_coordinate {
+sub new_point_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')};
@@ -198,7 +223,37 @@ sub new_coordinate {
        $y=$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);
+    return &set_point_coordinate($id,$variable,$x,$y).&update_register($id,$variable);
+}
+
+#
+# Initialize a new slope coordinate variable at set a listener on it
+#
+sub new_slope_coordinate {
+    my ($id,$variable,$x,$y,$pointname,$xp,$yp,$xmin,$xmax,$ymin,$ymax)=@_;
+#
+# $variable: name of the slope point
+# $x, $y: coordinates of the slope point
+# $pointname: name of the associated point point
+# $xp $yp: coordinates of the point point
+#
+    if (defined($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')};
+    }
+    if (defined($Apache::functionplotresponse::previous{&field_name($id,$pointname,'x')})) {
+       $xp=$Apache::functionplotresponse::previous{&field_name($id,$pointname,'x')};
+    }
+    if (defined($Apache::functionplotresponse::previous{&field_name($id,$pointname,'y')})) {
+       $yp=$Apache::functionplotresponse::previous{&field_name($id,$pointname,'y')};
+    }
+
+    &generate_input_field($id,$variable,$x,$y);
+    my $xrel=$x-$xp;
+    my $yrel=$y-$yp;
+    return &set_slope_coordinate($id,$variable,$xrel,$yrel,$xmin,$xmax,$ymin,$ymax,$pointname).&update_register($id,$variable);
 }
 
 #
@@ -261,17 +316,21 @@ ENDYAXISLABELSCRIPT
 }
 
 sub plot_script {
-   my ($id,$function,$fixed)=@_;
+   my ($id,$function,$fixed,$label,$xmin,$xmax)=@_;
+   $label=~s/\W//g;
+   if (($label) && ($label!~/^[A-Za-z]/)) {
+      $label='C'.$label;
+   }
+   my $visible=0;
+   if ($label) {
+      $visible="1";
+   } else {
+      $Apache::functionplotresponse::counter++;
+      $label='C'.$Apache::functionplotresponse::counter;
+   }
    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*($function)");
-ENDPLOTSCRIPT
+      return "document.ggbApplet_$id.evalCommand('$label=Function[$function,$xmin,$xmax]')".
+             ($visible?'':"document.ggbApplet.setLabelVisible('$label', false);");
    } else {
        return "document.ggbApplet_$id.evalCommand('y=$function')";
    }
@@ -282,7 +341,7 @@ ENDPLOTSCRIPT
 #
 
 sub generate_spline {
-   my ($id,$label)=@_;
+   my ($id,$label,$xmin,$xmax,$ymin,$ymax)=@_;
    my $result='';
    my $order=$Apache::functionplotresponse::splineorder{$label};
    my $x=$Apache::functionplotresponse::splineinitx{$label};
@@ -291,10 +350,11 @@ sub generate_spline {
    my $sy=$Apache::functionplotresponse::splinescaley{$label};
    my @coords=();
    foreach my $i (1..$order) {
-       $result.=&new_coordinate($id,$label.'P'.$i,$x,$y);
+       $result.=&new_point_coordinate($id,$label.'P'.$i,$x,$y);
+       my $xp=$x;
        $x+=$sx/(2.*($order-1));
        push(@coords,$label.'P'.$i);
-       $result.=&new_coordinate($id,$label.'S'.$i,$x,$y+$sy);
+       $result.=&new_slope_coordinate($id,$label.'S'.$i,$x,$y+$sy,$label.'P'.$i,$xp,$y,$xmin,$xmax,$ymin,$ymax);
        $x+=$sx/(2.*($order-1));
        push(@coords,$label.'S'.$i);
    }
@@ -309,21 +369,25 @@ sub start_backgroundplot {
    my $result='';
    my $internalid = $Apache::inputtags::part.'_'.$Apache::inputtags::response[-1];
    my $function=&Apache::lonxml::get_param('function',$parstack,$safeeval);
+   my $label=&Apache::lonxml::get_param('label',$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);
+      my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-3);
+      $result.=&plot_script($internalid,$function,$fixed,$label,$xmin,$xmax);
    } elsif ($target eq 'edit') {
         $result=&Apache::edit::tag_start($target,$token,'Background Function Plot').
              &Apache::edit::text_arg('Function:','function',
                                      $token,'16').
+             &Apache::edit::text_arg('Label on Plot:','label',
+                                     $token,'8').
              &Apache::edit::select_arg('Fixed location:','fixed',
                                   ['yes','no'],$token).
              &Apache::edit::end_row();
   } elsif ($target eq 'modified') {
     my $constructtag=&Apache::edit::get_new_args($token,$parstack,
-                                                 $safeeval,'function','fixed');
+                                                 $safeeval,'function','label','fixed');
     if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
   }
   return $result;
@@ -376,7 +440,7 @@ sub start_functionplotrule {
           &Apache::lonxml::warning(&mt('Rule relationship not defined.'));
           $relationship='eq';
       }
-      my $derivative=&Apache::lonxml::get_param('derivative',$parstack,$safeeval);
+      my $derivative=&Apache::lonxml::get_param('derivativeorder',$parstack,$safeeval);
       unless (($derivative==0) || ($derivative==1) || ($derivative==2)) {
          &Apache::lonxml::warning(&mt('Rule derivative not defined.'));
          $derivative=0;
@@ -388,29 +452,34 @@ sub start_functionplotrule {
            $beginninglabel,
            &Apache::lonxml::get_param('xfinal',$parstack,$safeeval),
            $endinglabel,
+           &Apache::lonxml::get_param('minimumlength',$parstack,$safeeval),
+           &Apache::lonxml::get_param('maximumlength',$parstack,$safeeval),
            $relationship,
-           &Apache::lonxml::get_param('value',$parstack,$safeeval)
+           &Apache::lonxml::get_param('value',$parstack,$safeeval),
+           &Apache::lonxml::get_param('percenterror',$parstack,$safeeval)
           )));
    } elsif ($target eq 'edit') {
         $result=&Apache::edit::tag_start($target,$token,'Function Plot Evaluation Rule').
-             &Apache::edit::text_arg('Index:','index',
-                                     $token,'4').'&nbsp;'.
-             &Apache::edit::select_arg(&mt('Function:'),'derivative',
+             &Apache::edit::text_arg('Index/Name:','index',
+                                     $token,'10').'&nbsp;'.
+             &Apache::edit::select_arg(&mt('Function:'),'derivativeorder',
                                   [['0','Function itself'],
                                    ['1','First derivative'],
-                                   ['2','Second derivative']],$token).'&nbsp;'.
-
+                                   ['2','Second derivative']],$token).'<br />'.
              &Apache::edit::text_arg('(Initial) x-value:','xinitial',
-                                      $token,'4').
+                                      $token,'8').
              &Apache::edit::select_or_text_arg('(Initial) x-value label:','xinitiallabel',
-                                               [['start','Start of Plot']],$token,'8').'&nbsp;'.
+                                               [['start','Start of Plot']],$token,'8').'<br />'.
 
              &Apache::edit::text_arg('Optional final x-value for ranges:','xfinal',
-                                      $token,'4').
+                                      $token,'8').
              &Apache::edit::select_or_text_arg('Optional final x-value label:','xfinallabel',
-                                               [['end','End of Plot']],$token,'8').'&nbsp;'.
-
-             &Apache::edit::select_arg(&mt('Relationship:'),'relationship',
+                                               [['end','End of Plot']],$token,'8').'<br />'.
+             &Apache::edit::text_arg('Optional minimum length for range:','minimumlength',
+                                     $token,'8').
+             &Apache::edit::text_arg('Optional maximum length for range:','maximumlength',
+                                     $token,'8').'<br />'.
+             &Apache::edit::select_or_text_arg(&mt('Relationship:'),'relationship',
                                   [['eq','equal'],
                                    ['ne','not equal'],
                                    ['ge','greater than or equal'],
@@ -418,14 +487,16 @@ sub start_functionplotrule {
                                    ['lt','less than'],
                                    ['le','less than or equal']],$token).
              $result.= &Apache::edit::select_or_text_arg('Value:','value',
-                                               [['undef','not defined']],$token,'4').
+                                               [['undef','not defined']],$token,'8').
              &Apache::edit::text_arg('Percent error:','percenterror',
-                                     $token,'4').
+                                     $token,'8').
              &Apache::edit::end_row();
   } elsif ($target eq 'modified') {
     my $constructtag=&Apache::edit::get_new_args($token,$parstack,
-                                                 $safeeval,'index','derivative','xinitial','xinitiallabel','xfinal','xfinallabel','relationship',
-                                                           'value','percenterror');
+                                                 $safeeval,'index','derivativeorder',
+                                                           'xinitial','xinitiallabel','xfinal','xfinallabel',
+                                                           'minimumlength','maximumlength',
+                                                           'relationship','value','percenterror');
     if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
    }
    return $result;
@@ -586,7 +657,11 @@ sub d2dt2_cubic_hermite {
 #
 sub array_index {
    my ($xmin,$xmax,$x)=@_;
-   return int(($x-$xmin)/($xmax-$xmin)*400.+0.5);
+   if ($x ne '') {
+      return int(($x-$xmin)/($xmax-$xmin)*400.+0.5);
+   } else {
+      return undef;
+   }
 }
 
 #
@@ -596,6 +671,7 @@ sub array_index {
 sub populate_arrays {
     my ($id,$xmin,$xmax)=@_;
     for (my $i=0; $i<=400; $i++) {
+       $Apache::functionplotresponse::actualxval[$i]=undef;
        $Apache::functionplotresponse::func[$i]=undef;
        $Apache::functionplotresponse::dfuncdx[$i]=undef;
        $Apache::functionplotresponse::d2funcd2x[$i]=undef;
@@ -617,11 +693,13 @@ sub populate_arrays {
                         $env{'form.HWVAL_'.$id.'_'.$label.'S'.$ni.'_y'});
 # Run in small steps over spline parameter
             for (my $t=0; $t<=1; $t+=0.0001) {
-                my $xi=&array_index($xmin,$xmax,&cubic_hermite($t,@xparms));
+                my $xreal=&cubic_hermite($t,@xparms);
+                my $xi=&array_index($xmin,$xmax,$xreal);
                 if ($xi<$xiold) { return 'no_func'; }
                 if (($xi>$xiold) && ($xi>=0) && ($xi<=400)) {
                    if (defined($Apache::functionplotresponse::func[$xi])) { return 'no_func'; }
                    $xiold=$xi;
+                   $Apache::functionplotresponse::actualxval[$xi]=$xreal;
 # Function value
                    my $funcval=&cubic_hermite($t,@yparms);
                    $Apache::functionplotresponse::func[$xi]=$funcval;
@@ -638,14 +716,10 @@ sub populate_arrays {
                    my $dxdt=&ddt_cubic_hermite($t,@xparms);
                    if ($dxdt) {
                       $Apache::functionplotresponse::dfuncdx[$xi]=&ddt_cubic_hermite($t,@yparms)/$dxdt;
-                   }
-# Faa di Bruno
-# d^2y/dx^2=(d^2y/dt^2)/(dx/dt)^2+(dy/dt)/(d^2x/dt^2)
-                   my $d2xdt2=&d2dt2_cubic_hermite($t,@xparms);
-                   if (($dxdt) && ($d2xdt2)) {
+# Second derivative
                       $Apache::functionplotresponse::d2funcdx2[$xi]=
-                         &d2dt2_cubic_hermite($t,@yparms)/($dxdt*$dxdt)
-                        +&ddt_cubic_hermite($t,@yparms)/$d2xdt2;
+                         ($dxdt*&d2dt2_cubic_hermite($t,@yparms)-&ddt_cubic_hermite($t,@yparms)*&d2dt2_cubic_hermite($t,@xparms))/
+                         ($dxdt*$dxdt*$dxdt);
                    }
                 }
             }
@@ -654,7 +728,7 @@ sub populate_arrays {
 }
 
 #
-# Implentation of <functionplotresponse>
+# Implementation of <functionplotresponse>
 #
 
 sub start_functionplotresponse {
@@ -672,6 +746,12 @@ sub start_functionplotresponse {
   $Apache::functionplotresponse::counter=0;
 # Remember rules
   undef @Apache::functionplotresponse::functionplotrules;
+# Remember failed rules
+  if ($target eq 'grade') {
+     undef @Apache::functionplotresponse::failedrules;
+  }
+# Delete previous awards
+  undef $Apache::functionplotresponse::awarddetail;
 # Part and ID
   my $partid=$Apache::inputtags::part;
   my $id=&Apache::response::start_response($parstack,$safeeval);
@@ -681,22 +761,7 @@ sub start_functionplotresponse {
   &decode_previous_answer($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)?$ymax:10);
-  if ($xmax<=$xmin) {
-     &Apache::lonxml::warning('Maximum x-value needs to be larger than minimum value.');
-     $xmax=$xmin+20;
-  }
-  if ($ymax<=$ymin) {
-     &Apache::lonxml::warning('Maximum y-value needs to be larger than minimum value.');
-     $ymax=$ymin+20;
-  }
+  my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval);
   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');
@@ -706,7 +771,8 @@ sub start_functionplotresponse {
     $result.=&Apache::edit::start_table($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)
+       .&Apache::edit::deletelist($target,$token).'&nbsp;&nbsp;&nbsp;'
+       .&Apache::edit::insertlist($target,$token)
        .'</span></td>'
        ."<td>&nbsp;"
        .&Apache::edit::end_row()
@@ -719,7 +785,7 @@ sub start_functionplotresponse {
              &Apache::edit::text_arg('Maximum x-value:','xmax',
                                      $token,'4').'&nbsp;'.
              &Apache::edit::select_arg('x-axis visible:','xaxisvisible',
-                                  ['yes','no'],$token).'&nbsp;&nbsp;'.
+                                  ['yes','no'],$token).'<br />'.
              &Apache::edit::text_arg('Label y-axis:','ylabel',
                                      $token,'6').'&nbsp;'.
              &Apache::edit::text_arg('Minimum y-value:','ymin',
@@ -727,7 +793,7 @@ sub start_functionplotresponse {
              &Apache::edit::text_arg('Maximum y-value:','ymax',
                                      $token,'4').'&nbsp;'.
              &Apache::edit::select_arg('y-axis visible:','yaxisvisible',
-                                  ['yes','no'],$token).'&nbsp;&nbsp;'.
+                                  ['yes','no'],$token).'<br />'.
              &Apache::edit::select_arg('Grid visible:','gridvisible',
                                   ['yes','no'],$token).
              &Apache::edit::end_row().&Apache::edit::start_spanning_row();
@@ -739,23 +805,39 @@ sub start_functionplotresponse {
 
   } 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
-  }
+  } elsif (($target eq 'answer') &&
+            ($env{'form.answer_output_mode'} ne 'tex') &&
+            ($Apache::lonhomework::viewgrades == 'F')) {
+      my (undef,undef,$udom,$uname)=&Apache::lonnet::whichuser();
+      my $windowopen=&Apache::lonhtmlcommon::javascript_docopen();
+      my $start_page = &Apache::loncommon::start_page('Rules Log', undef,
+                                               {'only_body' => 1,
+                                                'bgcolor'   => '#FFFFFF',
+                                                'js_ready'  => 1,});
+      my $end_page = &Apache::loncommon::end_page({'js_ready' => 1,});
+      $uname =~s/\W//g;
+      $udom  =~s/\W//g;
+      my $function_name =
+                join('_','LONCAPA_scriptvars',$uname,$udom,
+                     $env{'form.counter'},$Apache::lonxml::curdepth);
+      my $rules_var ="<script type=\"text/javascript\">
+// <![CDATA[
+    function $function_name() {newWindow=open('','new_W','width=500,height=500,scrollbars=1,resizable=yes');newWindow.$windowopen;newWindow.document.writeln('$start_page<pre>".
+    $Apache::functionplotresponse::ruleslog.
+    "<\\/pre>$end_page');newWindow.document.close();newWindow.focus()}
+// ]]>
+</script><a href=\"javascript:$function_name();void(0);\">".&mt('Rules Log')."</a><br />";
+            &Apache::lonxml::add_script_result($rules_var);
+        }
+
   return $result;
 }
 
 sub compare_rel {
    my ($relationship,$value,$realval,$tol)=@_;
-# is the real value defined?
+# is the real value undefined?
    unless (defined($realval)) {
+# the real value is not defined
       if ($relationship eq 'eq') {
          if ($value eq 'undef') {
             return 1;
@@ -773,7 +855,13 @@ sub compare_rel {
       }
    }
 
-# it is defined.
+# is the expected value undefined?
+   if ($value eq 'undef') {
+# but by now we know that the real value is defined
+      return 0;
+   }
+
+# both are defined.
    if ($relationship eq 'gt') {
       return ($realval>$value);
    } elsif ($relationship eq 'ge') {
@@ -790,12 +878,24 @@ sub compare_rel {
    return 0;
 }
 
+sub addlog {
+   my ($text)=@_;
+   $Apache::functionplotresponse::ruleslog.=$text.'<br />';
+}
+
+sub actualval {
+   my ($i,$xmin,$xmax)=@_;
+   return $xmin+$i/400.*($xmax-$xmin);
+}
+ 
 sub functionplotrulecheck {
-   my ($rule,$xmin,$xmax,$tolfunc,$toldfdx,$told2fdx2)=@_;
-   &Apache::lonnet::logthis("Rule $rule TolFunc $tolfunc TolDfDx $toldfdx TolD2fDx2 $told2fdx2");
-   my ($label,$derivative,$xinitial,$xinitiallabel,$xfinal,$xfinallabel,$relationship,$value)
-      =split(/\:/,$rule);
+   my ($rule,$xmin,$xmax,$ymin,$ymax)=@_;
 
+   my ($label,$derivative,$xinitial,$xinitiallabel,$xfinal,$xfinallabel,$minimumlength,$maximumlength,$relationship,$value,$percent)
+      =split(/\:/,$rule);
+   $percent=($percent>0?$percent:5);
+   &addlog("=================");
+   &addlog("Rule $label for ".('function itself','first derivative','second derivative')[$derivative]." $relationship $value");
    my $li=0;
    my $lh=400;
 
@@ -821,13 +921,15 @@ sub functionplotrulecheck {
    }
 # if the label is defined, use it
    if (defined($Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel})) {
+      &addlog("Using lower label $xinitiallabel");
       $li=$Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel};
    } else {
       $li=&array_index($xmin,$xmax,$xinitial);
    }
    unless ($findupper) {
       if (defined($Apache::functionplotresponse::functionplotrulelabels{$xfinallabel})) {
-         $lh=$Apache::functionplotresponse::functionplotrulelabels{$xfinallabel};
+         &addlog("Using upper label $xfinallabel");
+         $lh=$Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}-1;
       } else {
          $lh=&array_index($xmin,$xmax,$xfinal);
       }
@@ -835,16 +937,22 @@ sub functionplotrulecheck {
 # Basic sanity checks
    if ($li<0) { $li=0; }
    if ($lh>400) { $lh=400; }
-   if ($li>$lh) {
+   if (($li>$lh) || (!defined($lh))) {
        $lh=$li;
    }
 
-   &Apache::lonnet::logthis("Init $xinitial=$li Final $xfinal=$lh Findupper: $findupper");
-   my $tol=$tolfunc;
-   if ($derivative==2) {
-      $tol=$told2fdx2;
-   } elsif ($derivative==1) {
-      $tol=$toldfdx;
+   &addlog("Boundaries: x=".&actualval($li,$xmin,$xmax)." (".$Apache::functionplotresponse::actualxval[$li]."; index $li)) to x=".
+                            &actualval($lh,$xmin,$xmax)." (".$Apache::functionplotresponse::actualxval[$lh]."; index $lh))");
+   if ($findupper) {
+      &addlog("Looking for label $xfinallabel");
+   }
+   my $tol=$percent*($ymax-$ymin)/100;
+   if ($xmax>$xmin) {
+      if ($derivative==2) {
+         $tol=4.*$tol/($xmax-$xmin);
+      } elsif ($derivative==1) {
+         $tol=2.*$tol/($xmax-$xmin);
+      }
    }
    for (my $i=$li; $i<=$lh; $i++) {
         my $val;
@@ -856,74 +964,88 @@ sub functionplotrulecheck {
            $val=$Apache::functionplotresponse::func[$i];
         }
         unless (&compare_rel($relationship,$value,$val,$tol)) { 
-           &Apache::lonnet::logthis("Condition false $findupper at $i with $val");
+           &addlog("Actual value ".(defined($val)?$val:'undef').", expected $value, tolerance $tol");
+           &addlog("Condition not fulfilled at x=".&actualval($i,$xmin,$xmax)." (".$Apache::functionplotresponse::actualxval[$i]."; index $i)");
            if (($findupper) && ($i>$li)) {
+# check for minimum and maximum lengths
+              my $length=&actualval($i,$xmin,$xmax)-&actualval($li,$xmin,$xmax);
+              if ($minimumlength) {
+                 if ($length<$minimumlength) {
+                    &addlog("Rule $label failed, actual length $length, minimum length $minimumlength");
+                    return 0;
+                 }
+              }
+              if ($maximumlength) {
+                 if ($length>$maximumlength) {
+                    &addlog("Rule $label failed, actual length $length, maximum length $maximumlength");
+                    return 0;
+                 }
+              }
               $Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}=$i;
-              &Apache::lonnet::logthis("Setting $xfinallabel to $i");
+              &addlog("Rule $label passed, setting label $xfinallabel");
               return 1;
            } else {
+              &addlog("Rule $label failed.");
+              my $hintlabel=$label;
+              $hintlabel=~s/^R//;
+              push(@Apache::functionplotresponse::failedrules,$hintlabel);
+              &addlog("Set hint condition $hintlabel");
               return 0; 
            }
         }
    }
+   &addlog("Rule $label passed.");
    return 1;
 }
 
-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,$id);
+sub start_functionplotruleset {
+   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+   if ($target eq 'edit') {
+      return &Apache::edit::start_table($token).
+        '<tr><td><span class="LC_nobreak">'.&mt('Function Plot Rule Set').'</span></td>'
+       .'<td><span class="LC_nobreak">'.&mt('Delete?').' '
+       .&Apache::edit::deletelist($target,$token).'&nbsp;&nbsp;&nbsp;'.
+        &Apache::edit::insertlist($target,$token)
+       .'</span></td>'
+       ."<td>&nbsp;"
+       .&Apache::edit::end_row()
+       .&Apache::edit::start_spanning_row()
+       ."\n";
+   }
+}
 
-    } elsif ($target eq 'grade'
+sub end_functionplotruleset {
+    my ($target,$token,$tagstack,$parstack,$parser,$safeeval)=@_;
+    my $id=$Apache::inputtags::response[-1];
+    my $partid=$Apache::inputtags::part;
+    my $internalid = $partid.'_'.$id;
+
+    if ($target eq 'edit' ) {
+        return &Apache::edit::end_table();
+    }  elsif ($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 $ymin=&Apache::lonxml::get_param('ymin',$parstack,$safeeval);
-        $ymin=(defined($ymin)?$ymin:-10);
-        my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval);
-        $ymax=(defined($ymax)?$ymax:10);
-
-        my $percent=&Apache::lonxml::get_param('percenterror',$parstack,$safeeval);
-        $percent=(defined($percent)?$percent:5);
-
-        my $tolfunc=$percent*($ymax-$ymin)/100.;
-        my $toldfdx=1;
-        my $told2fdx2=1;
-        if ($xmax>$xmin) {
-           $toldfdx=$tolfunc/($xmax-$xmin);
-           $told2fdx2=$toldfdx/($xmax-$xmin);
-        }
+    my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-2);
 
         my $ad='';
         undef  %Apache::functionplotresponse::functionplotrulelabels;
+        $Apache::functionplotresponse::ruleslog='';
         $Apache::functionplotresponse::functionplotrulelabels{'start'}=400;
         $Apache::functionplotresponse::functionplotrulelabels{'end'}=0;
         if (&populate_arrays($internalid,$xmin,$xmax) eq 'no_func') {
            $ad='NOT_FUNCTION';
         } else {
+           &addlog("Start of function ".&actualval($Apache::functionplotresponse::functionplotrulelabels{'start'},$xmin,$xmax)." (index ".
+                                        $Apache::functionplotresponse::functionplotrulelabels{'start'}.")");
+           &addlog("End of function ".&actualval($Apache::functionplotresponse::functionplotrulelabels{'end'},$xmin,$xmax)." (index ".
+                                        $Apache::functionplotresponse::functionplotrulelabels{'end'}.")");
+
 # We have a function that we can actually grade, go through the spline rules.
            foreach my $rule (@Apache::functionplotresponse::functionplotrules) {
-              unless (&functionplotrulecheck($rule,$xmin,$xmax,$tolfunc,$toldfdx,$told2fdx2)) {
+              unless (&functionplotrulecheck($rule,$xmin,$xmax,$ymin,$ymax)) {
                  $ad='INCORRECT';
                  last;
               }
@@ -931,16 +1053,64 @@ sub end_functionplotresponse {
 # If it's not wrong, it's correct 
            unless ($ad) { $ad='EXACT_ANS' };
         }
+        &addlog("Set hint conditions: ".join(",",@Apache::functionplotresponse::failedrules));
+        &addlog("Assigned award detail: $ad");
+# Store for later to be assigned at end_functionplotresponse
+        $Apache::functionplotresponse::awarddetail=$ad;
+     }
+}
+
+
+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);
+#
+# Assign grade
+#
+        my $ad=$Apache::functionplotresponse::awarddetail;
 #
 # Store grading info
 #
         $Apache::lonhomework::results{"resource.$partid.$id.awarddetail"}=$ad;
         &Apache::response::handle_previous(\%previous,$ad);
    } elsif ($target eq 'web') {
+        undef @Apache::functionplotresponse::failedrules;
+   }
+   return $result;
+}
+
+sub end_functionplotelements {
+  my ($target,$token,$tagstack,$parstack,$parser,$safeeval)=@_;
+  my $result='';
+  my $id=$Apache::inputtags::response[-1];
+  my $partid=$Apache::inputtags::part;
+  my $internalid = $partid.'_'.$id;
+  if ($target eq 'edit' ) {
+     $result=&Apache::edit::end_table();
+  } elsif ($target eq 'web') {
 # Now is the time to render all of the stored splines
+     my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-2);
      foreach my $label (keys(%Apache::functionplotresponse::splineorder)) {
-        $result.=&generate_spline($internalid,$label);
+        $result.=&generate_spline($internalid,$label,$xmin,$xmax,$ymin,$ymax);
      }
 # close the init script
      $result.=&end_init_script();
@@ -964,6 +1134,64 @@ sub end_functionplotresponse {
   }
   return $result;
 }
+
+sub boundaries {
+   my ($parstack,$safeeval,$level)=@_;
+   my $xmin=&Apache::lonxml::get_param('xmin',$parstack,$safeeval,$level);
+   $xmin=(defined($xmin)?$xmin:-10);
+   my $xmax=&Apache::lonxml::get_param('xmax',$parstack,$safeeval,$level);
+   $xmax=(defined($xmax)?$xmax:10);
+   my $ymin=&Apache::lonxml::get_param('ymin',$parstack,$safeeval,$level);
+   $ymin=(defined($ymin)?$ymin:-10);
+   my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval,$level);
+   $ymax=(defined($ymax)?$ymax:10);
+   if ($xmax<=$xmin) {
+      $xmax=$xmin+20;
+   }
+   if ($ymax<=$ymin) {
+      $ymax=$ymin+20;
+   }
+   return ($xmin,$xmax,$ymin,$ymax);
+}
+
+sub start_functionplotelements {
+   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+   my $result='';
+   my $id=$Apache::inputtags::response[-1];
+   my $partid=$Apache::inputtags::part;
+   my $internalid = $partid.'_'.$id;
+
+   if ($target eq 'edit') {
+      return &Apache::edit::start_table($token).
+        '<tr><td><span class="LC_nobreak">'.&mt('Function Plot Elements').'</span></td>'
+       .'<td><span class="LC_nobreak">'.&mt('Delete?').' '
+       .&Apache::edit::deletelist($target,$token).'&nbsp;&nbsp;&nbsp;'.
+        &Apache::edit::insertlist($target,$token)
+       .'</span></td>'
+       ."<td>&nbsp;"
+       .&Apache::edit::end_row()
+       .&Apache::edit::start_spanning_row()
+       ."\n";
+   } elsif ($target eq 'web') {
+      my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-2);
+      my $xaxisvisible=(&Apache::lonxml::get_param('xaxisvisible',$parstack,$safeeval,-2)=~/on|true|yes|1/i?'true':'false');
+      my $yaxisvisible=(&Apache::lonxml::get_param('yaxisvisible',$parstack,$safeeval,-2)=~/on|true|yes|1/i?'true':'false');
+      my $gridvisible=(&Apache::lonxml::get_param('gridvisible',$parstack,$safeeval,-2)=~/on|true|yes|1/i?'true':'false');
+      my $xlabel=&Apache::lonxml::get_param('xlabel',$parstack,$safeeval,-2);
+      my $ylabel=&Apache::lonxml::get_param('ylabel',$parstack,$safeeval,-2);
+
+
+# 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;
+}
 
 1;