--- loncom/homework/functionplotresponse.pm	2011/05/27 23:00:58	1.63
+++ loncom/homework/functionplotresponse.pm	2011/11/21 19:48:52	1.81
@@ -1,7 +1,7 @@
 # LearningOnline Network with CAPA
-# option list style responses
+# Functionplot responses
 #
-# $Id: functionplotresponse.pm,v 1.63 2011/05/27 23:00:58 raeburn Exp $
+# $Id: functionplotresponse.pm,v 1.81 2011/11/21 19:48:52 www Exp $
 #
 # Copyright Michigan State University Board of Trustees
 #
@@ -31,9 +31,11 @@ use strict;
 use Apache::response();
 use Apache::lonlocal;
 use Apache::lonnet;
+use Apache::run;
  
 BEGIN {
   &Apache::lonxml::register('Apache::functionplotresponse',('functionplotresponse','backgroundplot','spline',
+                                                            'plotobject','plotvector','functionplotvectorrule','functionplotvectorsumrule',
                                                             'functionplotrule','functionplotruleset',
                                                             'functionplotelements'));
 }
@@ -75,7 +77,7 @@ sub geogebra_default_parameters {
         <param name="boxborder" value="false"  />
         <param name="centerimage" value="true"  />
 	<param name="cache_archive" value="geogebra.jar, geogebra_main.jar, geogebra_gui.jar, geogebra_cas.jar, geogebra_export.jar, geogebra_algos.jar, geogebra_javascript.jar, geogebra_properties.jar, jlatexmath.jar, jlm_cyrillic.jar, jlm_greek.jar" />
-	<param name="cache_version" value="3.9.219.0, 3.9.219.0, 3.9.219.0, 3.9.219.0, 3.9.219.0, 3.9.219.0, 3.9.219.0, 3.9.219.0, 3.9.219.0, 3.9.219.0, 3.9.219.0" />
+	<param name="cache_version" value="4.0.1.0,4.0.1.0,4.0.1.0,4.0.1.0,4.0.1.0,4.0.1.0,4.0.1.0,4.0.1.0,4.0.1.0,4.0.1.0,4.0.1.0" />
         <param name="framePossible" value="false" />
 
         <param name="showResetIcon" value="false" />
@@ -163,6 +165,14 @@ sub update_register {
 sub set_point_coordinate {
    my ($id,$variable,$x,$y,$fixed)=@_;
    my $mult=($fixed?'a*':'');
+# Get rid of wild exponents, make sure it's a number
+   $x=1.*$x;
+   $y=1.*$y;
+# GeoGebra does not understand "E"
+   $x=~s/[e|E]/\*10\^/;
+   $x=~s/\+//;
+   $y=~s/[e|E]/\*10\^/;
+   $y=~s/\+//;
    return (<<ENDSETVARIABLE);
 document.ggbApplet_$id.evalCommand("a=1");
 document.ggbApplet_$id.evalCommand("$variable=$mult($x,$y)");
@@ -370,6 +380,54 @@ sub plot_script {
 }
 
 #
+# Subroutine to produce objects
+#
+
+sub plotobject_script {
+   my ($id,$label,$x,$y)=@_;
+   unless ($label) {
+      $Apache::functionplotresponse::counter++;
+      $label='O'.$Apache::functionplotresponse::counter;
+   }
+   &generate_input_field($id,$label,$x,$y);
+   return "document.ggbApplet_$id.evalCommand('a=1');\n".
+          "document.ggbApplet_$id.setVisible('a', false);\n".
+          "document.ggbApplet_$id.setLabelVisible('a', false);\n".
+          "document.ggbApplet_$id.evalCommand('$label=a*($x,$y)');\n".
+          "document.ggbApplet_$id.setVisible('$label', true);\n".
+          "document.ggbApplet_$id.setLabelVisible('$label', true);\n";
+}
+
+#
+# Subroutine to produce vectors
+#
+
+sub plotvector_script {
+   my ($id,$label,$xs,$ys,$xe,$ye,$xmin,$xmax)=@_;
+   unless ($label) {
+      $Apache::functionplotresponse::counter++;
+      $label='V'.$Apache::functionplotresponse::counter;
+   }
+   my $startlabel=$label.'Start';
+   my $endlabel=$label.'End';
+   my $pointlabel=$label.'Point';
+   my $pointx=2.*($xmax-$xmin)+$xmax;
+   my $anglelabel=$label.'Angle';
+   return 
+       &new_point_coordinate($id,$startlabel,$xs,$ys,0).
+       &new_point_coordinate($id,$endlabel,$xe,$ye,0).
+       (<<ENDVECTOR);
+document.ggbApplet_$id.evalCommand("$label=Vector[$startlabel,$endlabel]");
+document.ggbApplet_$id.setLabelVisible("$label",true);
+document.ggbApplet_$id.setLineThickness("$label",8);
+document.ggbApplet_$id.evalCommand("$pointlabel=($pointx,y($startlabel))");
+document.ggbApplet_$id.evalCommand("$anglelabel=Angle[$pointlabel,$startlabel,$endlabel]");
+document.ggbApplet_$id.setLabelVisible("$anglelabel",true);
+document.ggbApplet_$id.setLabelStyle("$anglelabel",VALUE=2);
+ENDVECTOR
+}
+
+#
 # Answer spline display
 # 
 # points: x,y,slope_x,slope_y
@@ -422,6 +480,109 @@ sub generate_spline {
    $result.='document.ggbApplet_'.$id.'.evalCommand("Spline'.$order.'['.join(',',@coords).']");'."\n";
    return $result;
 }
+
+#
+# Object
+#
+
+sub start_plotobject {
+   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+   my $result='';
+   my $internalid = $Apache::inputtags::part.'_'.$Apache::inputtags::response[-1];
+   my $x=&Apache::lonxml::get_param('x',$parstack,$safeeval);
+   my $y=&Apache::lonxml::get_param('y',$parstack,$safeeval);
+   my $label=&Apache::lonxml::get_param('label',$parstack,$safeeval);
+   $label=~s/\W//gs;
+   $label=ucfirst($label);
+   unless ($label) { $label="NewObject"; }
+   if ($target eq 'web') {
+      my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-3);
+      unless (defined($x)) { $x=$xmin; }
+      unless (defined($y)) { $y=$ymin; }
+      $result.=&plotobject_script($internalid,$label,$x,$y);
+   } elsif ($target eq 'edit') {
+        $result=&Apache::edit::tag_start($target,$token,'Plot Object').
+             &Apache::edit::text_arg('Label on Plot:','label',
+                                     $token,'16').
+             &Apache::edit::text_arg('x:','x',
+                                     $token,'8').
+             &Apache::edit::text_arg('y:','y',
+                                     $token,'8').
+             &Apache::edit::end_row();
+  } elsif ($target eq 'modified') {
+    $env{'form.'.&Apache::edit::html_element_name('label')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('label')});
+    my $constructtag=&Apache::edit::get_new_args($token,$parstack,$safeeval,'label','x','y');
+    if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
+  }
+  return $result;
+}
+
+sub end_plotobject {
+   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+   my $result='';
+   if ($target eq 'edit') {
+       $result=&Apache::edit::end_table();
+   }
+   return $result;
+}
+
+#
+# Vector
+#
+
+sub start_plotvector {
+   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+   my $result='';
+   my $internalid = $Apache::inputtags::part.'_'.$Apache::inputtags::response[-1];
+   my $tailx=&Apache::lonxml::get_param('tailx',$parstack,$safeeval);
+   my $taily=&Apache::lonxml::get_param('taily',$parstack,$safeeval);
+   my $tipx=&Apache::lonxml::get_param('tipx',$parstack,$safeeval);
+   my $tipy=&Apache::lonxml::get_param('tipy',$parstack,$safeeval);
+
+   my $label=&Apache::lonxml::get_param('label',$parstack,$safeeval);
+   $label=~s/\W//gs;
+   $label=ucfirst($label);
+   unless ($label) { $label="NewVector"; }
+   if ($target eq 'web') {
+      my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-3);
+      unless (defined($tailx)) { $tailx=$xmin; }
+      unless (defined($taily)) { $taily=$ymin; }
+      unless (defined($tipx)) { $tipx=$xmin; }
+      unless (defined($tipy)) { $tipy=$ymin; }
+      $result.=&plotvector_script($internalid,$label,$tailx,$taily,$tipx,$tipy,$xmin,$xmax);
+   } elsif ($target eq 'edit') {
+        $result=&Apache::edit::tag_start($target,$token,'Plot Vector').
+             &Apache::edit::text_arg('Label on Plot:','label',
+                                     $token,'16').
+             &Apache::edit::text_arg('Tail x:','tailx',
+                                     $token,'8').
+             &Apache::edit::text_arg('Tail y:','taily',
+                                     $token,'8').
+             &Apache::edit::text_arg('Tip x:','tipx',
+                                     $token,'8').
+             &Apache::edit::text_arg('Tip y:','tipy',
+                                     $token,'8').
+
+             &Apache::edit::end_row();
+  } elsif ($target eq 'modified') {
+    $env{'form.'.&Apache::edit::html_element_name('label')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('label')});
+    my $constructtag=&Apache::edit::get_new_args($token,$parstack,$safeeval,'label','tailx','taily','tipx','tipy');
+    if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
+  }
+  return $result;
+}
+
+sub end_plotvector {
+   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+   my $result='';
+   if ($target eq 'edit') {
+       $result=&Apache::edit::end_table();
+   }
+   return $result;
+}
+
+
+
 #
 # <backgroundplot function="..." fixed="yes/no" />
 #
@@ -493,10 +654,6 @@ sub start_functionplotrule {
    } else {
       $label='R'.$label;
    }
-   if ($Apache::functionplotresponse::splineorder{$label}) {
-       &Apache::lonxml::error(&mt('Rule indices must be unique.'));
-   }
-
 
    if ($target eq 'grade') {
 # Simply remember - in order - for later
@@ -533,7 +690,7 @@ sub start_functionplotrule {
            &Apache::lonxml::get_param('percenterror',$parstack,$safeeval)
           )));
    } elsif ($target eq 'edit') {
-        $result=&Apache::edit::tag_start($target,$token,'Function Plot Evaluation Rule').
+        $result=&Apache::edit::tag_start($target,$token,'Function Plot Graph Rule').
              &Apache::edit::text_arg('Index/Name:','index',
                                      $token,'10').'&nbsp;'.
              &Apache::edit::select_arg(&mt('Function:'),'derivativeorder',
@@ -563,7 +720,7 @@ sub start_functionplotrule {
                                    ['lt','less than'],
                                    ['le','less than or equal']],$token).
              $result.= &Apache::edit::select_or_text_arg('Value:','value',
-                                               [['undef','not defined']],$token,'8').
+                                               [['undef','not defined']],$token,'30').
              &Apache::edit::text_arg('Percent error:','percenterror',
                                      $token,'8').
              &Apache::edit::end_row();
@@ -595,6 +752,197 @@ sub end_functionplotrule {
 
 
 #
+# <functionplotvectorrule ... />
+#
+sub start_functionplotvectorrule {
+   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('Rule indices should only contain alphanumeric characters.'));
+   }
+   $label=~s/\W//gs;
+   unless ($label) {
+      $label='R'.$Apache::functionplotresponse::counter;
+   } else {
+      $label='R'.$label;
+   }
+
+   if ($target eq 'grade') {
+# Simply remember - in order - for later
+
+      my $id=$Apache::inputtags::response[-1];
+      my $partid=$Apache::inputtags::part;
+      my $internalid = $partid.'_'.$id;
+
+      my $vector=&Apache::lonxml::get_param('vector',$parstack,$safeeval);
+      $vector=~s/\W//gs;
+      $vector=ucfirst($vector);
+
+      my $attachpoint=&Apache::lonxml::get_param('attachpoint',$parstack,$safeeval);
+      $attachpoint=~s/\W//gs;
+      $attachpoint=ucfirst($attachpoint);
+
+      my $notattachpoint=&Apache::lonxml::get_param('notattachpoint',$parstack,$safeeval);
+      $notattachpoint=~s/\W//gs;
+      $notattachpoint=ucfirst($notattachpoint);
+
+      my $tailpoint=&Apache::lonxml::get_param('tailpoint',$parstack,$safeeval);
+      $tailpoint=~s/\W//gs;
+      $tailpoint=ucfirst($tailpoint);
+      my $tippoint=&Apache::lonxml::get_param('tippoint',$parstack,$safeeval);
+      $tippoint=~s/\W//gs;
+      $tippoint=ucfirst($tippoint);
+
+      my $nottailpoint=&Apache::lonxml::get_param('nottailpoint',$parstack,$safeeval);
+      $nottailpoint=~s/\W//gs;
+      $nottailpoint=ucfirst($nottailpoint);
+      my $nottippoint=&Apache::lonxml::get_param('nottippoint',$parstack,$safeeval);
+      $nottippoint=~s/\W//gs;
+      $nottippoint=ucfirst($nottippoint);
+
+      push(@Apache::functionplotresponse::functionplotvectorrules,join(':',(
+           $label,
+           'vector',
+           $internalid,
+           $vector,
+           $attachpoint,
+           $notattachpoint,
+           $tailpoint,
+           $tippoint,
+           $nottailpoint,
+           $nottippoint,
+           &Apache::lonxml::get_param('length',$parstack,$safeeval),
+           &Apache::lonxml::get_param('angle',$parstack,$safeeval),
+           &Apache::lonxml::get_param('lengtherror',$parstack,$safeeval),
+           &Apache::lonxml::get_param('angleerror',$parstack,$safeeval),
+          )));
+   } elsif ($target eq 'edit') {
+        $result=&Apache::edit::tag_start($target,$token,'Function Plot Vector Rule').
+             &Apache::edit::text_arg('Index/Name:','index',
+                                     $token,'10').'&nbsp;'.
+             &Apache::edit::text_arg('Vector:','vector',
+                                      $token,'16').'<br />'.
+             &Apache::edit::text_arg('Attached to object:','attachpoint',
+                                      $token,'16').
+             &Apache::edit::text_arg('Not attached to object:','notattachpoint',
+                                      $token,'16').'<br />'.
+             &Apache::edit::text_arg('Tail attached to object:','tailpoint',
+                                      $token,'16').
+             &Apache::edit::text_arg('Tip attached to object:','tippoint',
+                                      $token,'16').
+             &Apache::edit::text_arg('Tail not attached to object:','nottailpoint',
+                                      $token,'16').
+             &Apache::edit::text_arg('Tip not attached to object:','nottippoint',
+                                      $token,'16').'<br />'.
+             &Apache::edit::text_arg('Length:','length',
+                                     $token,'16').
+             &Apache::edit::text_arg('Angle:','angle',
+                                     $token,'16').
+             &Apache::edit::text_arg('Absolute error length:','lengtherror',
+                                     $token,'8').
+             &Apache::edit::text_arg('Absolute error angle:','angleerror',
+                                     $token,'8').
+             &Apache::edit::end_row();
+  } elsif ($target eq 'modified') {
+    $env{'form.'.&Apache::edit::html_element_name('vector')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('vector')});
+    $env{'form.'.&Apache::edit::html_element_name('attachpoint')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('attachpoint')});
+    $env{'form.'.&Apache::edit::html_element_name('notattachpoint')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('notattachpoint')});
+    $env{'form.'.&Apache::edit::html_element_name('tailpoint')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('tailpoint')});
+    $env{'form.'.&Apache::edit::html_element_name('tippoint')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('tippoint')});
+    $env{'form.'.&Apache::edit::html_element_name('nottailpoint')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('nottailpoint')});
+    $env{'form.'.&Apache::edit::html_element_name('nottippoint')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('nottippoint')});
+    my $constructtag=&Apache::edit::get_new_args($token,$parstack,
+                                                 $safeeval,'index','vector','attachpoint','notattachpoint',
+                                                           'tailpoint','tippoint','nottailpoint','nottipoint',
+                                                           'length','angle',
+                                                           'lengtherror','angleerror');
+    if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
+   }
+   return $result;
+}
+
+sub end_functionplotvectorrule {
+   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+   my $result='';
+   if ($target eq 'edit') {
+       $result=&Apache::edit::end_table();
+   }
+   return $result;
+}
+
+#
+# <functionplotvectorsumrule ... />
+#
+sub start_functionplotvectorsumrule {
+   my ($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('Rule indices should only contain alphanumeric characters.'));
+   }
+   $label=~s/\W//gs;
+   unless ($label) {
+      $label='R'.$Apache::functionplotresponse::counter;
+   } else {
+      $label='R'.$label;
+   }
+   if ($target eq 'grade') {
+# Simply remember - in order - for later
+      my $id=$Apache::inputtags::response[-1];
+      my $partid=$Apache::inputtags::part;
+      my $internalid = $partid.'_'.$id;
+      my $object=&Apache::lonxml::get_param('object',$parstack,$safeeval);
+      $object=~s/\W//gs;
+      $object=ucfirst($object);
+      push(@Apache::functionplotresponse::functionplotvectorrules,join(':',(
+           $label,
+           'sum',
+           $internalid,
+           $object,
+           &Apache::lonxml::get_param('length',$parstack,$safeeval),
+           &Apache::lonxml::get_param('angle',$parstack,$safeeval),
+           &Apache::lonxml::get_param('lengtherror',$parstack,$safeeval),
+           &Apache::lonxml::get_param('angleerror',$parstack,$safeeval),
+          )));
+   } elsif ($target eq 'edit') {
+        $result=&Apache::edit::tag_start($target,$token,'Function Plot Vector Sum Rule').
+             &Apache::edit::text_arg('Index/Name:','index',
+                                     $token,'10').'&nbsp;'.
+             &Apache::edit::text_arg('Vectors attached to object:','object',
+                                      $token,'16').'<br />'.
+             &Apache::edit::text_arg('Sum vector length:','length',
+                                     $token,'16').
+             &Apache::edit::text_arg('Sum vector angle:','angle',
+                                     $token,'16').
+             &Apache::edit::text_arg('Error length:','lengtherror',
+                                     $token,'8').
+             &Apache::edit::text_arg('Error angle:','angleerror',
+                                     $token,'8').
+             &Apache::edit::end_row();
+  } elsif ($target eq 'modified') {
+    $env{'form.'.&Apache::edit::html_element_name('object')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('object')});
+    my $constructtag=&Apache::edit::get_new_args($token,$parstack,
+                                                 $safeeval,'index','object',
+                                                           'length','angle',
+                                                           ,'lengtherror','angleerror');
+    if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
+   }
+   return $result;
+}
+
+sub end_functionplotvectorsumrule {
+   my ($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
@@ -751,7 +1099,7 @@ sub array_index {
 #
 
 sub populate_arrays {
-    my ($id,$xmin,$xmax)=@_;
+    my ($id,$xmin,$xmax,$ymin,$ymax)=@_;
     for (my $i=0; $i<=400; $i++) {
        $Apache::functionplotresponse::actualxval[$i]=undef;
        $Apache::functionplotresponse::func[$i]=undef;
@@ -779,12 +1127,19 @@ sub populate_arrays {
                 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);
+
+# Do we already have a value for this point, and is it different from the new one?
+                   if ((defined($Apache::functionplotresponse::func[$xi])) &&
+                       (abs($Apache::functionplotresponse::func[$xi]-$funcval)>($ymax-$ymin)/100.)) { 
+                       return 'no_func'; 
+                   }
+# Okay, remember the new point
                    $Apache::functionplotresponse::func[$xi]=$funcval;
+
                    if (defined($funcval)) {
                       if ($xi<$Apache::functionplotresponse::functionplotrulelabels{'start'}) {
                          $Apache::functionplotresponse::functionplotrulelabels{'start'}=$xi;
@@ -828,6 +1183,7 @@ sub start_functionplotresponse {
   $Apache::functionplotresponse::counter=0;
 # Remember rules
   undef @Apache::functionplotresponse::functionplotrules;
+  undef @Apache::functionplotresponse::functionplotvectorrules;
 # Remember failed rules
   if ($target eq 'grade') {
      undef @Apache::functionplotresponse::failedrules;
@@ -965,6 +1321,7 @@ sub compare_rel {
 
 sub addlog {
    my ($text)=@_;
+   $text=~s/\'/\\\'/g;
    $Apache::functionplotresponse::ruleslog.=$text.'<br />';
 }
 
@@ -972,15 +1329,229 @@ sub actualval {
    my ($i,$xmin,$xmax)=@_;
    return $xmin+$i/400.*($xmax-$xmin);
 }
+
+sub fpr_val {
+   my ($arg)=@_;
+   return &actualval($Apache::functionplotresponse::functionplotrulelabels{$arg},
+                     $Apache::functionplotresponse::fpr_xmin,
+                     $Apache::functionplotresponse::fpr_xmax);
+}
+
+sub fpr_f {
+   my ($arg)=@_;
+   return $Apache::functionplotresponse::func[&array_index($Apache::functionplotresponse::fpr_xmin,
+                                                           $Apache::functionplotresponse::fpr_xmax,
+                                                           $arg)];
+}
+
+sub fpr_dfdx {
+   my ($arg)=@_;
+   return $Apache::functionplotresponse::dfuncdx[&array_index($Apache::functionplotresponse::fpr_xmin,
+                                                              $Apache::functionplotresponse::fpr_xmax,
+                                                              $arg)];
+}
+
+sub fpr_d2fdx2 {
+   my ($arg)=@_;
+   return $Apache::functionplotresponse::d2funcdx2[&array_index($Apache::functionplotresponse::fpr_xmin,
+                                                                $Apache::functionplotresponse::fpr_xmax,
+                                                                $arg)];
+}
+
+
+sub vectorcoords {
+   my ($id,$label)=@_;
+   return ($env{'form.HWVAL_'.$id.'_'.$label.'Start_x'},
+           $env{'form.HWVAL_'.$id.'_'.$label.'End_x'},
+           $env{'form.HWVAL_'.$id.'_'.$label.'Start_y'},
+           $env{'form.HWVAL_'.$id.'_'.$label.'End_y'});
+}
+
+sub objectcoords {
+   my ($id,$label)=@_;
+   return ($env{'form.HWVAL_'.$id.'_'.$label.'_x'},
+           $env{'form.HWVAL_'.$id.'_'.$label.'_y'});
+}
+
+sub attached {
+   my ($id,$vector,$object,$xmin,$xmax,$ymin,$ymax)=@_;
+   my ($xs,$xe,$ys,$ye)=&vectorcoords($id,$vector);
+   my ($xo,$yo)=&objectcoords($id,$object);
+   my $tolx=($xmax-$xmin)/100.;
+   my $toly=($ymax-$ymin)/100.;
+   my $tail=0;
+   my $tip=0;
+   &addlog("Proximity $vector ($xs,$xe,$ys,$ye) to $object ($xo,$yo)");
+   if ((abs($xs-$xo)<$tolx) && (abs($ys-$yo)<$toly)) { $tail=1; }
+   if ((abs($xe-$xo)<$tolx) && (abs($ye-$yo)<$toly)) { $tip=1; }
+   &addlog("Result tail:$tail tip:$tip");
+   return($tail,$tip);
+}
+
+ 
+sub vectorangle {
+   my ($x,$y)=@_;
+   my $angle=57.2957795*atan2($y,$x);
+   if ($angle<0) { $angle=360+$angle; }
+   return $angle;
+}
+
+sub vectorlength {
+   my ($x,$y)=@_;
+   return sqrt($x*$x+$y*$y);
+}
+
+sub relvector {
+   my ($xs,$xe,$ys,$ye)=@_;
+   return ($xe-$xs,$ye-$ys);
+}
+
+sub plotvectorlength {
+   return &vectorlength(&relvector(&vectorcoords(@_)));
+}
+
+sub plotvectorangle {
+   return &vectorangle(&relvector(&vectorcoords(@_)));
+}
+
+
+#
+# Evaluate a functionplotvectorrule
+#
+
+sub functionplotvectorrulecheck {
+   my ($rule,$xmin,$xmax,$ymin,$ymax,$safeeval)=@_;
+   &addlog("=================");
+   my ($label,$type)=split(/\:/,$rule);
+   if ($type eq 'vector') {
+      return &vectorcheck($rule,$xmin,$xmax,$ymin,$ymax,$safeeval);
+   } elsif ($type eq 'sum') {
+      return &sumcheck($rule,$xmin,$xmax,$ymin,$ymax,$safeeval);
+   }
+}
+
+sub vectorcheck {
+   my ($rule,$xmin,$xmax,$ymin,$ymax,$safeeval)=@_;
+   my ($label,$type,$id,$vector,
+       $attachpoint,$notattachpoint,
+       $tailpoint,$tippoint,$nottailpoint,$nottippoint,
+       $length,$angle,$lengtherror,$angleerror)=split(/\:/,$rule);
+   &addlog("Vector Rule $label for vector ".$vector);
+   if ($length ne '') {
+      &addlog("Checking for length $length with error $lengtherror");
+      $length=&Apache::run::run($length,$safeeval);
+      &addlog("Length evaluated to $length");
+      my $thislength=&plotvectorlength($id,$vector);
+      &addlog("Found length $thislength");
+      if (abs($thislength-$length)>$lengtherror) {
+         &setfailed($label);
+         return 0;
+      }
+   }
+   if ($angle ne '') {
+      &addlog("Checking for angle $angle with error $angleerror");
+      $angle=&Apache::run::run($angle,$safeeval);
+      &addlog("Angle evaluated to $angle");
+      my $thisangle=&plotvectorangle($id,$vector);
+      &addlog("Found angle $thisangle");
+      my $anglediff=abs($thisangle-$angle);
+      &addlog("Angle difference: $anglediff");
+      if ($anglediff>360.-$anglediff) {
+         $anglediff=360.-$anglediff;
+      }
+      &addlog("Smallest angle difference: $anglediff");
+      if ($anglediff>$angleerror) {
+         &setfailed($label);
+         return 0;
+      }
+   }
+   if ($attachpoint ne '') {
+      &addlog("Checking attached: ".$attachpoint);
+      my ($tail,$tip)=&attached($id,$vector,$attachpoint,$xmin,$xmax,$ymin,$ymax);
+      unless ($tail || $tip) {
+         &setfailed($label);
+         return 0;
+      }
+   }
+   if ($notattachpoint ne '') {
+      &addlog("Checking not attached: ".$notattachpoint);
+      my ($tail,$tip)=&attached($id,$vector,$notattachpoint,$xmin,$xmax,$ymin,$ymax);
+      if ($tail || $tip) {
+         &setfailed($label);
+         return 0;
+      }
+   }
+   if ($tailpoint ne '') {
+      &addlog("Checking tail: ".$tailpoint);
+      my ($tail,$tip)=&attached($id,$vector,$tailpoint,$xmin,$xmax,$ymin,$ymax);
+      unless ($tail) {
+         &setfailed($label);
+         return 0;
+      }
+   }
+   if ($nottailpoint ne '') {
+      &addlog("Checking not tail: ".$nottailpoint);
+      my ($tail,$tip)=&attached($id,$vector,$nottailpoint,$xmin,$xmax,$ymin,$ymax);
+      if ($tail) {
+         &setfailed($label);
+         return 0;
+      }
+   }
+   if ($tippoint ne '') {
+      &addlog("Checking tip: ".$tippoint);
+      my ($tail,$tip)=&attached($id,$vector,$tippoint,$xmin,$xmax,$ymin,$ymax);
+      unless ($tip) {
+         &setfailed($label);
+         return 0;
+      }
+   }
+   if ($nottippoint ne '') {
+      &addlog("Checking not tip: ".$nottippoint);
+      my ($tail,$tip)=&attached($id,$vector,$nottippoint,$xmin,$xmax,$ymin,$ymax);
+      if ($tip) {
+         &setfailed($label);
+         return 0;
+      }
+   }
+
+   &addlog("Rule $label passed.");
+   return 1;
+}
+
+sub sumcheck {
+   my ($rule,$xmin,$xmax,$ymin,$ymax,$safeeval)=@_;
+   my ($label,$type,$id,$object,$length,$angle,$lengtherror,$angleerror)=split(/\:/,$rule);
+   &addlog("Vector Sum Rule $label for vectors attached to ".$object);
+
+   &addlog("Rule $label passed.");
+   return 1;
+}
+
+#
+# Evaluate a functionplotrule
+#
  
 sub functionplotrulecheck {
-   my ($rule,$xmin,$xmax,$ymin,$ymax)=@_;
+   my ($rule,$xmin,$xmax,$ymin,$ymax,$safeeval)=@_;
 
    my ($label,$derivative,$xinitial,$xinitiallabel,$xfinal,$xfinallabel,$minimumlength,$maximumlength,$relationship,$value,$percent)
       =split(/\:/,$rule);
    $percent=($percent>0?$percent:5);
    &addlog("=================");
    &addlog("Rule $label for ".($derivative<0?'integral':('function itself','first derivative','second derivative')[$derivative])." $relationship $value");
+#
+# Evaluate the value
+#
+   if ($value=~/\D/) {
+      $Apache::functionplotresponse::fpr_xmin=$xmin;
+      $Apache::functionplotresponse::fpr_xmax=$xmax;
+      $value=&Apache::run::run($value,$safeeval);
+      &addlog("Value evaluated to $value");
+   }
+
+#
+# Minimum and maximum lengths of the interval
+#
    if ((defined($minimumlength)) || (defined($maximumlength))) {
       &addlog("Minimumlength $minimumlength Maximumlength $maximumlength");
    }
@@ -1055,10 +1626,7 @@ sub functionplotrulecheck {
      unless (&compare_rel($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 $hintlabel");
+        &setfailed($label);
         return 0;
      } 
    } else {
@@ -1124,8 +1692,7 @@ sub checklength {
 }
 
 sub setfailed {
-   my ($label)=@_;
-   my $hintlabel=$label;
+   my ($hintlabel)=@_;
    $hintlabel=~s/^R//;
    push(@Apache::functionplotresponse::failedrules,$hintlabel);
    &addlog("Set hint condition $hintlabel");
@@ -1169,7 +1736,7 @@ sub end_functionplotruleset {
         $Apache::functionplotresponse::ruleslog='';
         $Apache::functionplotresponse::functionplotrulelabels{'start'}=400;
         $Apache::functionplotresponse::functionplotrulelabels{'end'}=0;
-        if (&populate_arrays($internalid,$xmin,$xmax) eq 'no_func') {
+        if (&populate_arrays($internalid,$xmin,$xmax,$ymin,$ymax) eq 'no_func') {
            $ad='NOT_FUNCTION';
         } else {
            &addlog("Start of function ".&actualval($Apache::functionplotresponse::functionplotrulelabels{'start'},$xmin,$xmax)." (index ".
@@ -1179,7 +1746,14 @@ sub end_functionplotruleset {
 
 # 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,$ymin,$ymax)) {
+              unless (&functionplotrulecheck($rule,$xmin,$xmax,$ymin,$ymax,$safeeval)) {
+                 $ad='INCORRECT';
+                 last;
+              }
+           }
+# And now go through the vector rules
+           foreach my $rule (@Apache::functionplotresponse::functionplotvectorrules) {
+              unless (&functionplotvectorrulecheck($rule,$xmin,$xmax,$ymin,$ymax,$safeeval)) {
                  $ad='INCORRECT';
                  last;
               }