--- loncom/homework/functionplotresponse.pm	2010/11/19 15:41:28	1.39
+++ loncom/homework/functionplotresponse.pm	2010/12/03 00:52:59	1.49
@@ -1,7 +1,7 @@
 # LearningOnline Network with CAPA
 # option list style responses
 #
-# $Id: functionplotresponse.pm,v 1.39 2010/11/19 15:41:28 www Exp $
+# $Id: functionplotresponse.pm,v 1.49 2010/12/03 00:52:59 www Exp $
 #
 # Copyright Michigan State University Board of Trustees
 #
@@ -47,7 +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
 }
@@ -61,7 +61,7 @@ sub geogebra_endcode {
 #
 sub geogebra_spline_program {
     return (<<ENDSPLINEPROGRAM);
-<param name="ggbBase64" value="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"/>
+<param name="ggbBase64" value="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" />
 ENDSPLINEPROGRAM
 }
 
@@ -74,7 +74,6 @@ 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 -Djnlp.packEnabled=true" />
 	<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" />
@@ -159,16 +158,44 @@ sub update_register {
 }
 
 #
-# Set a coordinate variable
+# Set a point coordinate variable
 #
-sub set_coordinate {
-   my ($id,$variable,$x,$y)=@_;
+sub set_point_coordinate {
+   my ($id,$variable,$x,$y,$fixed)=@_;
+   my $mult=($fixed?'a*':'');
    return (<<ENDSETVARIABLE);
-document.ggbApplet_$id.evalCommand("$variable=($x,$y)");
+document.ggbApplet_$id.evalCommand("a=1");
+document.ggbApplet_$id.evalCommand("$variable=$mult($x,$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,$pointname,$fixed)=@_;
+   my $xvariable=$variable.'x';
+   my $yvariable=$variable.'y';
+   my $domain=$xmax-$xmin;
+   my $range=$ymax-$ymin;
+   my $xinterval=$domain/100.;
+   my $yinterval=$range/200.;
+   my $mult=($fixed?'a*':'');
+   return (<<ENDSETSVARIABLE);
+document.ggbApplet_$id.evalCommand("a=1");
+document.ggbApplet_$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=$mult($xvariable+x($pointname),$yvariable+y($pointname))");
+document.ggbApplet_$id.setLabelVisible("$variable", false);
+ENDSETSVARIABLE
+}
+
+#
 # Input field name for a coordinate variable
 #
 
@@ -189,10 +216,10 @@ 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 {
-    my ($id,$variable,$x,$y)=@_;
+sub new_point_coordinate {
+    my ($id,$variable,$x,$y,$fixed)=@_;
     if (defined($Apache::functionplotresponse::previous{&field_name($id,$variable,'x')})) {
        $x=$Apache::functionplotresponse::previous{&field_name($id,$variable,'x')};
     }
@@ -200,7 +227,37 @@ 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,$fixed).&update_register($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,$fixed)=@_;
+#
+# $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,$fixed).&update_register($id,$variable);
 }
 
 #
@@ -242,40 +299,69 @@ ENDAXESSCRIPT
 }
 
 sub axes_label {
-    my ($id,$xlabel,$ylabel)=@_;
+    my ($id,$xmin,$xmax,$ymin,$ymax,$xlabel,$ylabel)=@_;
     unless ($xlabel || $ylabel) { return ''; }
     my $return='document.ggbApplet_'.$id.'.evalCommand("topRight=Corner[3]");';
     if ($xlabel) {
+      if (($ymin<0) && ($ymax>0)) {
        $return.=(<<ENDXAXISLABELSCRIPT);
 document.ggbApplet_$id.evalCommand("Xlabel=(x(topRight)-AxisStepX[],AxisStepY[]/6)");
 document.ggbApplet_$id.setVisible("Xlabel",false);
 document.ggbApplet_$id.evalCommand("Text[\\"$xlabel\\", Xlabel]");
 ENDXAXISLABELSCRIPT
+      } else {
+       $return.=(<<ENDXOFFAXISLABEL);
+document.ggbApplet_$id.evalCommand("LowerRight=Corner[2]");
+document.ggbApplet_$id.evalCommand("Text[\\"$xlabel\\", (x(LowerRight) - AxisStepX[], y(LowerRight) + AxisStepY[] / 2)]");
+ENDXOFFAXISLABEL
+      }
     }
     if ($ylabel) {
+      if (($xmin<0) && ($xmax>0)) {
        $return.=(<<ENDYAXISLABELSCRIPT);
 document.ggbApplet_$id.evalCommand("Ylabel=(AxisStepX[]/6,y(topRight)-AxisStepY[]/3)");
 document.ggbApplet_$id.setVisible("Ylabel",false);
 document.ggbApplet_$id.evalCommand("Text[\\"$ylabel\\", Ylabel]");
 ENDYAXISLABELSCRIPT
+      } else {
+       $return.=(<<ENDYOFFAXISLABEL);
+document.ggbApplet_$id.evalCommand("UpperLeft=Corner[4]");
+document.ggbApplet_$id.evalCommand("Text[\\"$ylabel\\", (x(UpperLeft) + AxisStepX[] / 5, y(UpperLeft) - AxisStepY[] / 1.8)]");
+ENDYOFFAXISLABEL
+      }
     }
     return $return;
 }
 
 sub plot_script {
-   my ($id,$function,$fixed)=@_;
+   my ($id,$function,$fixed,$label,$color,$xmin,$xmax,$thickness)=@_;
+   $label=~s/\W//g;
+   if (($label) && ($label!~/^[A-Za-z]/)) {
+      $label='C'.$label;
+   }
+   my $visible=0;
+   if ($label) {
+      $visible="1";
+   } else {
+      $Apache::functionplotresponse::counter++;
+      $label='C'.$Apache::functionplotresponse::counter;
+   }
+   my $rc=0;
+   my $gc=0;
+   my $bc=0;
+   if ($color) {
+      my ($rh,$gh,$bh)=($color=~/(..)(..)(..)/);
+      $rc=hex($rh);
+      $gc=hex($gh);
+      $bc=hex($bh);
+   }
    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]');\n".
+             ($visible?'':"document.ggbApplet_$id.setLabelVisible('$label', false);\n").
+             ($color?"document.ggbApplet_$id.setColor('$label',$rc,$gc,$bc);\n":'').
+             ($thickness?"document.ggbApplet_$id.setLineThickness('$label',$thickness);\n":'');
    } else {
-       return "document.ggbApplet_$id.evalCommand('y=$function')";
+       return "document.ggbApplet_$id.evalCommand('y=$function');\n";
    }
 }
 
@@ -284,7 +370,7 @@ ENDPLOTSCRIPT
 #
 
 sub generate_spline {
-   my ($id,$label)=@_;
+   my ($id,$label,$xmin,$xmax,$ymin,$ymax,$fixed)=@_;
    my $result='';
    my $order=$Apache::functionplotresponse::splineorder{$label};
    my $x=$Apache::functionplotresponse::splineinitx{$label};
@@ -293,10 +379,11 @@ 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,$fixed);
+       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,$ymax,$fixed);
        $x+=$sx/(2.*($order-1));
        push(@coords,$label.'S'.$i);
    }
@@ -311,21 +398,38 @@ sub start_backgroundplot {
    my $result='';
    my $internalid = $Apache::inputtags::part.'_'.$Apache::inputtags::response[-1];
    my $function=&Apache::lonxml::get_param('function',$parstack,$safeeval);
+   my $xinitial=&Apache::lonxml::get_param('xinitial',$parstack,$safeeval);
+   my $xfinal=&Apache::lonxml::get_param('xfinal',$parstack,$safeeval);
+   my $label=&Apache::lonxml::get_param('label',$parstack,$safeeval);
+   my $color=&Apache::lonxml::get_param('color',$parstack,$safeeval);
+   $color=~s/[^a-fA-F0-9]//gs;
+   unless (length($color)==6) { $color=''; }
    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);
+      unless (defined($xinitial)) { $xinitial=$xmin; }
+      unless (defined($xfinal)) { $xfinal=$xmax; }
+      $result.=&plot_script($internalid,$function,$fixed,$label,$color,$xinitial,$xfinal);
    } 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('Initial x-value (optional):','xinitial',
+                                     $token,'8').
+             &Apache::edit::text_arg('Final x-value (optional):','xfinal',
+                                     $token,'8').
+             &Apache::edit::text_arg('Label on Plot:','label',
+                                     $token,'8').
+             &Apache::edit::text_arg('Color (hex code):','color',
+                                     $token,'8').
              &Apache::edit::select_arg('Fixed location:','fixed',
                                   ['yes','no'],$token).
              &Apache::edit::end_row();
   } elsif ($target eq 'modified') {
     my $constructtag=&Apache::edit::get_new_args($token,$parstack,
-                                                 $safeeval,'function','fixed');
+                                                 $safeeval,'function','label','xinitial','xfinal','color','fixed');
     if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
   }
   return $result;
@@ -379,7 +483,7 @@ sub start_functionplotrule {
           $relationship='eq';
       }
       my $derivative=&Apache::lonxml::get_param('derivativeorder',$parstack,$safeeval);
-      unless (($derivative==0) || ($derivative==1) || ($derivative==2)) {
+      unless (($derivative==-1) || ($derivative==0) || ($derivative==1) || ($derivative==2)) {
          &Apache::lonxml::warning(&mt('Rule derivative not defined.'));
          $derivative=0;
       }
@@ -403,19 +507,21 @@ sub start_functionplotrule {
              &Apache::edit::select_arg(&mt('Function:'),'derivativeorder',
                                   [['0','Function itself'],
                                    ['1','First derivative'],
-                                   ['2','Second derivative']],$token).'<br />'.
-             &Apache::edit::text_arg('(Initial) x-value:','xinitial',
+                                   ['2','Second derivative'],
+                                   ['-1','Integral']],$token).'<br />'.
+             &Apache::edit::text_arg('Initial x-value:','xinitial',
                                       $token,'8').
-             &Apache::edit::select_or_text_arg('(Initial) x-value label:','xinitiallabel',
-                                               [['start','Start of Plot']],$token,'8').'<br />'.
+             &Apache::edit::select_or_text_arg('Initial x-value label:','xinitiallabel',
+                                               [['start','Start of Plot'],
+                                                ['end','End of Plot']],$token,'8').'<br />'.
 
-             &Apache::edit::text_arg('Optional final x-value for ranges:','xfinal',
+             &Apache::edit::text_arg('Final x-value (optional):','xfinal',
                                       $token,'8').
-             &Apache::edit::select_or_text_arg('Optional final x-value label:','xfinallabel',
+             &Apache::edit::select_or_text_arg('Final x-value label (optional):','xfinallabel',
                                                [['end','End of Plot']],$token,'8').'<br />'.
-             &Apache::edit::text_arg('Optional minimum length for range:','minimumlength',
+             &Apache::edit::text_arg('Minimum length for range (optional):','minimumlength',
                                      $token,'8').
-             &Apache::edit::text_arg('Optional maximum length for range:','maximumlength',
+             &Apache::edit::text_arg('Maximum length for range (optional):','maximumlength',
                                      $token,'8').'<br />'.
              &Apache::edit::select_or_text_arg(&mt('Relationship:'),'relationship',
                                   [['eq','equal'],
@@ -499,7 +605,7 @@ sub start_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;'.
+                                  ['2','3','4','5','6','7','8'],$token).'&nbsp;'.
              &Apache::edit::text_arg('Initial x-value:','initx',
                                      $token,'4').'&nbsp;'.
              &Apache::edit::text_arg('Initial y-value:','inity',
@@ -566,8 +672,8 @@ sub get_answer_from_form_fields {
 
 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);
+   return (2.*$t*$t*$t-3.*$t*$t+1.)*$p1 + 3.*($t*$t*$t-2.*$t*$t+$t)*($s1-$p1)+
+          (-2.*$t*$t*$t+3.*$t*$t)  *$p2 + 3.*($t*$t*$t-$t*$t)      *($s2-$p2);
 }
 
 #
@@ -576,8 +682,8 @@ sub cubic_hermite {
 
 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-$p2);
+   return (6.*$t*$t-6.*$t) *$p1 + 3.*(3.*$t*$t-4.*$t+1.)*($s1-$p1)+
+          (-6.*$t*$t+6.*$t)*$p2 + 3.*(3.*$t*$t-2.*$t)   *($s2-$p2);
 }
 
 #
@@ -586,8 +692,8 @@ sub ddt_cubic_hermite {
 
 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-$p2);
+   return (12.*$t-6.) *$p1 + 3.*(6.*$t-4.)*($s1-$p1)+
+          (-12.*$t+6.)*$p2 + 3.*(6.*$t-2.)*($s2-$p2);
 }
 
 #
@@ -699,22 +805,7 @@ 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,$safeeval)=~/on|true|yes|1/i?'true':'false');
@@ -748,12 +839,15 @@ sub start_functionplotresponse {
              &Apache::edit::select_arg('y-axis visible:','yaxisvisible',
                                   ['yes','no'],$token).'<br />'.
              &Apache::edit::select_arg('Grid visible:','gridvisible',
-                                  ['yes','no'],$token).
+                                  ['yes','no'],$token).'<br />'.
+             &Apache::edit::text_arg('Background plot(s) for answer (function:xmin:xmax,function:xmin:xmax,...):',
+                                         'answerdisplay',$token,'50');
+
              &Apache::edit::end_row().&Apache::edit::start_spanning_row();
   } elsif ($target eq 'modified') {
     my $constructtag=&Apache::edit::get_new_args($token,$parstack,
                                                  $safeeval,'xlabel','xmin','xmax','ylabel','ymin','ymax',
-                                                           'xaxisvisible','yaxisvisible','gridvisible');
+                                                           'xaxisvisible','yaxisvisible','gridvisible','answerdisplay');
     if ($constructtag) { $result = &Apache::edit::rebuild_tag($token); }
 
   } elsif ($target eq 'meta') {
@@ -848,7 +942,10 @@ sub functionplotrulecheck {
       =split(/\:/,$rule);
    $percent=($percent>0?$percent:5);
    &addlog("=================");
-   &addlog("Rule $label for ".('function itself','first derivative','second derivative')[$derivative]." $relationship $value");
+   &addlog("Rule $label for ".($derivative<0?'integral':('function itself','first derivative','second derivative')[$derivative])." $relationship $value");
+   if ((defined($minimumlength)) || (defined($maximumlength))) {
+      &addlog("Minimumlength $minimumlength Maximumlength $maximumlength");
+   }
    my $li=0;
    my $lh=400;
 
@@ -905,14 +1002,37 @@ sub functionplotrulecheck {
          $tol=4.*$tol/($xmax-$xmin);
       } elsif ($derivative==1) {
          $tol=2.*$tol/($xmax-$xmin);
+      } elsif ($derivative==-1) {
+         $tol=$tol*($xmax-$xmin)/2.;
       }
    }
-   for (my $i=$li; $i<=$lh; $i++) {
+   my $integral=0;
+   my $binwidth=($xmax-$xmin)/400.;
+   if (($derivative<0) && (!$findupper)) {
+# definite integral, calculate over whole length
+     &addlog("Calculating definite integral");
+     for (my $i=$li; $i<=$lh; $i++) {
+        $integral+=$Apache::functionplotresponse::func[$i]*$binwidth;
+     }
+     unless (&compare_rel($relationship,$value,$integral,$tol)) {
+        &addlog("Actual integral ".(defined($integral)?$integral:'undef').", expected $value, tolerance $tol");
+        &addlog("Rule $label failed.");
+        my $hintlabel=$label;
+        $hintlabel=~s/^R//;
+        push(@Apache::functionplotresponse::failedrules,$hintlabel);
+        &addlog("Set hint condition $hintlabel");
+        return 0;
+     } 
+   } else {
+     for (my $i=$li; $i<=$lh; $i++) {
         my $val;
         if ($derivative==2) {
            $val=$Apache::functionplotresponse::d2funcdx2[$i];
         } elsif ($derivative==1) {
            $val=$Apache::functionplotresponse::dfuncdx[$i];
+        } elsif ($derivative==-1) {
+           $integral+=$Apache::functionplotresponse::func[$i]*$binwidth;
+           $val=$integral;      
         } else {
            $val=$Apache::functionplotresponse::func[$i];
         }
@@ -920,37 +1040,59 @@ sub functionplotrulecheck {
            &addlog("Actual value ".(defined($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 $maximumlength");
-                    return 0;
-                 }
-              }
+# Check lengths
+              unless (&checklength($i,$li,$minimumlength,$maximumlength,$xmin,$xmax,$label)) { return 0; }
+# Successfully found a new label, set it
               $Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}=$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 $hintlabel");
+              &setfailed($label);
               return 0; 
            }
         }
+     }
    }
+# Corner case where this makes sense: using start or stop as defined labels
+   unless (&checklength($lh,$li,$minimumlength,$maximumlength,$xmin,$xmax,$label)) { return 0; }
    &addlog("Rule $label passed.");
    return 1;
 }
 
+#
+# check for minimum and maximum lengths
+#
+
+sub checklength {
+    my ($i,$li,$minimumlength,$maximumlength,$xmin,$xmax,$label)=@_;
+    unless (($minimumlength) || ($maximumlength)) { return 1; }
+    my $length=&actualval($i,$xmin,$xmax)-&actualval($li,$xmin,$xmax);
+    if ($minimumlength) {
+       if ($length<$minimumlength) {
+          &addlog("Rule $label failed, actual length $length, minimum length $minimumlength");
+          &setfailed($label);
+          return 0;
+       }
+    }
+    if ($maximumlength) {
+       if ($length>$maximumlength) {
+          &addlog("Rule $label failed, actual length $length, maximum length $maximumlength");
+          &setfailed($label);
+          return 0;
+       }
+    }
+    return 1;
+}
+
+sub setfailed {
+   my ($label)=@_;
+   my $hintlabel=$label;
+   $hintlabel=~s/^R//;
+   push(@Apache::functionplotresponse::failedrules,$hintlabel);
+   &addlog("Set hint condition $hintlabel");
+}
+
 sub start_functionplotruleset {
    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
    if ($target eq 'edit') {
@@ -981,14 +1123,7 @@ sub end_functionplotruleset {
 #
 # Actually grade
 #
-        my $xmin=&Apache::lonxml::get_param('xmin',$parstack,$safeeval,-2);
-        $xmin=(defined($xmin)?$xmin:-10);
-        my $xmax=&Apache::lonxml::get_param('xmax',$parstack,$safeeval,-2);
-        $xmax=(defined($xmax)?$xmax:10);
-        my $ymin=&Apache::lonxml::get_param('ymin',$parstack,$safeeval,-2);
-        $ymin=(defined($ymin)?$ymin:-10);
-        my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval,-2);
-        $ymax=(defined($ymax)?$ymax:10);
+    my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-2);
 
         my $ad='';
         undef  %Apache::functionplotresponse::functionplotrulelabels;
@@ -1067,9 +1202,27 @@ sub end_functionplotelements {
   if ($target eq 'edit' ) {
      $result=&Apache::edit::end_table();
   } elsif ($target eq 'web') {
+     my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-2);
+
+# Are we in show answer mode?
+     my $showanswer=&Apache::response::show_answer();
+     if ($showanswer) {
+# Render answerdisplay
+        my $answerdisplay=&Apache::lonxml::get_param('answerdisplay',$parstack,$safeeval,-2);
+        if ($answerdisplay=~/\S/s) {
+           foreach my $plot (split(/\s*\,\s*/,$answerdisplay)) {
+              my ($func,$xl,$xh)=split(/\s*\:\s*/,$plot);
+              if ((!defined($xl)) || ($xl eq '')) { $xl=$xmin; }
+              if ((!defined($xh)) || ($xh eq '')) { $xh=$xmax; }
+              $result.=&plot_script($internalid,$func,1,'','00aa00',$xl,$xh,6);
+           }
+        }
+     }
+     my $fixed=0;
+     if (($showanswer) || (&Apache::response::check_status()>=2)) { $fixed=1; }
 # Now is the time to render all of the stored splines
      foreach my $label (keys(%Apache::functionplotresponse::splineorder)) {
-        $result.=&generate_spline($internalid,$label);
+        $result.=&generate_spline($internalid,$label,$xmin,$xmax,$ymin,$ymax,$fixed);
      }
 # close the init script
      $result.=&end_init_script();
@@ -1094,6 +1247,25 @@ sub end_functionplotelements {
   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 $result='';
@@ -1113,20 +1285,7 @@ sub start_functionplotelements {
        .&Apache::edit::start_spanning_row()
        ."\n";
    } elsif ($target eq 'web') {
-      my $xmin=&Apache::lonxml::get_param('xmin',$parstack,$safeeval,-2);
-      $xmin=(defined($xmin)?$xmin:-10);
-      my $xmax=&Apache::lonxml::get_param('xmax',$parstack,$safeeval,-2);
-      $xmax=(defined($xmax)?$xmax:10);
-      my $ymin=&Apache::lonxml::get_param('ymin',$parstack,$safeeval,-2);
-      $ymin=(defined($ymin)?$ymin:-10);
-      my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval,-2);
-      $ymax=(defined($ymax)?$ymax:10);
-      if ($xmax<=$xmin) {
-        $xmax=$xmin+20;
-      }
-      if ($ymax<=$ymin) {
-         $ymax=$ymin+20;
-      }
+      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');
@@ -1140,7 +1299,7 @@ sub start_functionplotelements {
      $result.=&start_init_script($internalid);
 # put the axis commands inside
      $result.=&axes_script($internalid,$xmin,$xmax,$ymin,$ymax,$xaxisvisible,$yaxisvisible,$gridvisible);
-     $result.=&axes_label($internalid,$xlabel,$ylabel);
+     $result.=&axes_label($internalid,$xmin,$xmax,$ymin,$ymax,$xlabel,$ylabel);
 # init script is left open
   }
   return $result;