--- loncom/homework/functionplotresponse.pm	2010/11/19 15:41:28	1.39
+++ loncom/homework/functionplotresponse.pm	2012/08/17 22:51:59	1.100
@@ -1,7 +1,7 @@
 # LearningOnline Network with CAPA
-# option list style responses
+# Functionplot responses
 #
-# $Id: functionplotresponse.pm,v 1.39 2010/11/19 15:41:28 www Exp $
+# $Id: functionplotresponse.pm,v 1.100 2012/08/17 22:51:59 www Exp $
 #
 # Copyright Michigan State University Board of Trustees
 #
@@ -31,52 +31,134 @@ use strict;
 use Apache::response();
 use Apache::lonlocal;
 use Apache::lonnet;
+use Apache::run;
+use LONCAPA;
  
 BEGIN {
   &Apache::lonxml::register('Apache::functionplotresponse',('functionplotresponse','backgroundplot','spline',
+                                                            'plotobject','plotvector',
+                                                            'functionplotvectorrule','functionplotvectorsumrule',
+                                                            'drawvectorsum',
+                                                            'functionplotcustomrule',
                                                             'functionplotrule','functionplotruleset',
                                                             'functionplotelements'));
 }
 
 #
+# Use old Java or HTML5/Javascript for GeoGebra? Depends on browser!
+# Return a true value if HTML5 should be used.
+
+sub useHTML5 {
+    if  ($env{'browser.type'} eq 'chrome') { return 1; }
+    if (($env{'browser.type'} eq 'safari') &&
+        ($env{'browser.os'} eq 'mac')) { return 1; }
+    return 0;
+}
+
+#
+# HTML5 version does not understand "_" in IDs
+#
+sub appid {
+    my ($id)=@_;
+    $id=~s/\_/rid/gs;
+    $id=~s/\W//gs;
+    return $id;
+}
+
+#
+# Routines to start the applet (Java) or the HTML5/JavaScript
+#
 # There can be a number of applets on a page, each called ggbApplet_$id, 
 # where $id is the "_"-concatenated part and responseid
 #
 
 sub geogebra_startcode {
+    my ($id,$width,$height)=@_;
+    if (&useHTML5()) {
+        return &html5_geogebra_startcode(@_);
+    } else {
+        return &java_geogebra_startcode(@_).
+               &java_geogebra_code_param();
+    }
+}
+
+sub geogebra_endcode {
+    if (&useHTML5()) {
+        return '';
+    } else {
+        return &java_geogebra_endcode();
+    }
+}
+
+sub geogebra_default_parameters {
     my ($id)=@_;
+    if (&useHTML5()) {
+        return '';
+    } else {
+        return &java_geogebra_default_parameters($id);
+    }
+}
+# === Java code
+
+sub java_geogebra_startcode {
+    my ($id,$width,$height)=@_;
+    my $appid=&appid($id);
+    $width=int(1.*$width);
+    $height=int(1.*$height);
+    unless ($width) { $width=700; }
+    unless ($height) { $height=400; }
     return (<<ENDSTARTCODE);
-<applet name="ggbApplet_$id" code="geogebra.GeoGebraApplet" archive="geogebra.jar"
-         codebase="/adm/geogebra/"  width="714" height="447" MAYSCRIPT>
+<applet name="ggbApplet$appid" code="geogebra.GeoGebraApplet" archive="geogebra.jar"
+         codebase="/adm/geogebra/"  width="$width" height="$height" MAYSCRIPT>
        <param name="java_arguments" value="-Xmx512m -Djnlp.packEnabled=true"/>
 ENDSTARTCODE
 }
 
-sub geogebra_endcode {
+sub java_geogebra_endcode {
     return &Apache::lonhtmlcommon::java_not_enabled()."</applet>\n";
 }
 
+sub java_geogebra_code_param {
+    return '<param name="ggbBase64" value="'.&geogebra_internal_program().'" />';
+}
+
+# === HTML5 code
+
+sub html5_geogebra_startcode {
+    my ($id,$width,$height)=@_;
+    my $appid=&appid($id);
+    $width=int(1.*$width);
+    $height=int(1.*$height);
+    unless ($width) { $width=700; }
+    unless ($height) { $height=400; }
+    my $code=&geogebra_internal_program();
+    return (<<ENDSTARTCODE);
+<article class="geogebraweb" data-param-enableLabelDrags="false" data-param-enableShiftDragZoom="false" 
+data-param-width="$width" data-param-height="$height" data-param-id="ggbApplet$appid" 
+data-param-ggbbase64="$code"></article>
+ENDSTARTCODE
+}
+
 #
 # This is the internal GeoGebra bytecode which defines the spline functions
 #
-sub geogebra_spline_program {
-    return (<<ENDSPLINEPROGRAM);
-<param name="ggbBase64" value="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"/>
-ENDSPLINEPROGRAM
+sub geogebra_internal_program {
+    return
+'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';
 }
 
 #
 # The standard set of parameters inside <applet>
 #
-sub geogebra_default_parameters {
+sub java_geogebra_default_parameters {
    my ($id)=@_;
+   my $appid=&appid($id);
    return(<<ENDDEFAULTPARAMETERS);
         <param name="image" value="/adm/lonIcons/lonanim.gif"  />
         <param name="boxborder" value="false"  />
         <param name="centerimage" value="true"  />
-        <param name="java_arguments" value="-Xmx512m -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="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="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" />
@@ -91,7 +173,7 @@ sub geogebra_default_parameters {
         <param name="enableShiftDragZoom" value="false" />
         <param name="allowRescaling" value="false" />
         <param name="enableLabelDrags" value="false" />
-        <param name="ggbOnInitParam" value="applet_$id" />
+        <param name="ggbOnInitParam" value="ggbApplet$appid" />
 ENDDEFAULTPARAMETERS
 }
 
@@ -106,12 +188,18 @@ sub init_script {
    if ($#Apache::functionplotresponse::callscripts>=0) {
       my $script='';
       foreach my $id (@Apache::functionplotresponse::callscripts) {
-          $script.="if (param=='applet_$id') { loaded_$id=true; }\n";
+          $script.="if (param=='ggbApplet".&appid($id)."') { loaded_$id=true; }\n";
       }
       $script.="if (".join(' && ',map { "loaded_$_" } (@Apache::functionplotresponse::callscripts)).
-               ") { setTimeout('ggbInitAll()',20) }";
+               ") { setTimeout('ggbInitAll()',200) }";
       my $calls=join("\n",map { "ggbInit_$_();" } (@Apache::functionplotresponse::callscripts)); 
+      my $html5init='';
+      if (&useHTML5()) {
+          $html5init=
+           '<script type="text/javascript" language="javascript" src="/adm/geogebra/web/web.nocache.js"></script>';
+      }
       return (<<ENDGGBINIT);
+$html5init
 <script type="text/javascript">
 // <![CDATA[
 // Function that each applet will call when loaded
@@ -135,12 +223,13 @@ ENDGGBINIT
 #
 sub update_script {
     my ($id)=@_;
+    my $appid=&appid($id);
     return (<<ENDUPDATESCRIPT);
 <script type="text/javascript">
 // <![CDATA[
 function updatePointCoordinates_$id(coordinateName) {
-            var x = document.ggbApplet_$id.getXcoord(coordinateName);
-            var y = document.ggbApplet_$id.getYcoord(coordinateName);
+            var x = document.ggbApplet$appid.getXcoord(coordinateName);
+            var y = document.ggbApplet$appid.getYcoord(coordinateName);
             document.lonhomework.elements["HWVAL_$id\_" + coordinateName + "_x"].value = x;
             document.lonhomework.elements["HWVAL_$id\_" + coordinateName + "_y"].value = y;
         }
@@ -155,20 +244,59 @@ ENDUPDATESCRIPT
 
 sub update_register {
    my ($id,$variable)=@_;
-   return "document.ggbApplet_$id.registerObjectUpdateListener('$variable','updatePointCoordinates_$id');\n";
+   my $appid=&appid($id);
+   return "document.ggbApplet$appid.registerObjectUpdateListener('$variable','updatePointCoordinates_$id');\n";
 }
 
 #
-# 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 $appid=&appid($id);
+   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("$variable=($x,$y)");
+document.ggbApplet$appid.evalCommand("a=1");
+document.ggbApplet$appid.evalCommand("$variable=$mult($x,$y)");
+document.ggbApplet$appid.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 $appid=&appid($id);
+   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$appid.evalCommand("a=1");
+document.ggbApplet$appid.evalCommand("$xvariable=Slider[$xinterval,$domain,$xinterval]");
+document.ggbApplet$appid.setVisible("$xvariable", false);
+document.ggbApplet$appid.evalCommand("$xvariable=$xrel");
+document.ggbApplet$appid.evalCommand("$yvariable=Slider[-$range,$range,$yinterval]");
+document.ggbApplet$appid.setVisible("$yvariable", false);
+document.ggbApplet$appid.evalCommand("$yvariable=$yrel");
+document.ggbApplet$appid.evalCommand("$variable=$mult($xvariable+x($pointname),$yvariable+y($pointname))");
+document.ggbApplet$appid.setLabelVisible("$variable", false);
+ENDSETSVARIABLE
+}
+
+#
 # Input field name for a coordinate variable
 #
 
@@ -189,18 +317,48 @@ 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_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')};
+    }
+    if (defined($Apache::functionplotresponse::previous{&field_name($id,$variable,'y')})) {
+       $y=$Apache::functionplotresponse::previous{&field_name($id,$variable,'y')};
+    }
+    &generate_input_field($id,$variable,$x,$y);
+    return &set_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 $yp: coordinates of the point point
 #
-sub new_coordinate {
-    my ($id,$variable,$x,$y)=@_;
     if (defined($Apache::functionplotresponse::previous{&field_name($id,$variable,'x')})) {
        $x=$Apache::functionplotresponse::previous{&field_name($id,$variable,'x')};
     }
     if (defined($Apache::functionplotresponse::previous{&field_name($id,$variable,'y')})) {
        $y=$Apache::functionplotresponse::previous{&field_name($id,$variable,'y')};
     }
+    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);
-    return &set_coordinate($id,$variable,$x,$y).&update_register($id,$variable);
+    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);
 }
 
 #
@@ -230,53 +388,168 @@ ENDSTARTINIT
 
 sub axes_script {
     my ($id,$xmin,$xmax,$ymin,$ymax,$xvisible,$yvisible,$gvisible)=@_;
+    my $appid=&appid($id);
     return (<<ENDAXESSCRIPT);
             // changes (xmin, xmax, ymin, ymax)
-            document.ggbApplet_$id.setCoordSystem($xmin,$xmax,$ymin,$ymax);
+            document.ggbApplet$appid.setCoordSystem($xmin,$xmax,$ymin,$ymax);
 
             // makes the (x,y) axis (in)visible
-            document.ggbApplet_$id.setAxesVisible($xvisible,$yvisible);
+            document.ggbApplet$appid.setAxesVisible($xvisible,$yvisible);
             // makes the grid (in)visible
-            document.ggbApplet_$id.setGridVisible($gvisible);
+            document.ggbApplet$appid.setGridVisible($gvisible);
 ENDAXESSCRIPT
 }
 
 sub axes_label {
-    my ($id,$xlabel,$ylabel)=@_;
+    my ($id,$xmin,$xmax,$ymin,$ymax,$xlabel,$ylabel)=@_;
+    my $appid=&appid($id);
     unless ($xlabel || $ylabel) { return ''; }
-    my $return='document.ggbApplet_'.$id.'.evalCommand("topRight=Corner[3]");';
+    my $return='document.ggbApplet'.$appid.'.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[\\"$xlabel\\", Xlabel]");
+document.ggbApplet$appid.evalCommand("Xlabel=(x(topRight)-AxisStepX[],AxisStepY[]/6)");
+document.ggbApplet$appid.setVisible("Xlabel",false);
+document.ggbApplet$appid.evalCommand("Text[\\"$xlabel\\", Xlabel]");
 ENDXAXISLABELSCRIPT
+      } else {
+       $return.=(<<ENDXOFFAXISLABEL);
+document.ggbApplet$appid.evalCommand("LowerRight=Corner[2]");
+document.ggbApplet$appid.evalCommand("Text[\\"$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[\\"$ylabel\\", Ylabel]");
+document.ggbApplet$appid.evalCommand("Ylabel=(AxisStepX[]/6,y(topRight)-AxisStepY[]/3)");
+document.ggbApplet$appid.setVisible("Ylabel",false);
+document.ggbApplet$appid.evalCommand("Text[\\"$ylabel\\", Ylabel]");
 ENDYAXISLABELSCRIPT
+      } else {
+       $return.=(<<ENDYOFFAXISLABEL);
+document.ggbApplet$appid.evalCommand("UpperLeft=Corner[4]");
+document.ggbApplet$appid.evalCommand("Text[\\"$ylabel\\", (x(UpperLeft) + AxisStepX[] / 5, y(UpperLeft) - AxisStepY[] / 1.8)]");
+ENDYOFFAXISLABEL
+      }
     }
     return $return;
 }
 
+#
+# Subroutine to produce background and answer plots
+#
+
 sub plot_script {
-   my ($id,$function,$fixed)=@_;
+   my ($id,$function,$fixed,$label,$color,$xmin,$xmax,$thickness)=@_;
+   my $appid=&appid($id);
+   $label=~s/\W//g;
+   if (($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*($function)");
-ENDPLOTSCRIPT
+      return "document.ggbApplet$appid.evalCommand('$label=Function[$function,$xmin,$xmax]');\n".
+             ($visible?'':"document.ggbApplet$appid.setLabelVisible('$label', false);\n").
+             ($color?"document.ggbApplet$appid.setColor('$label',$rc,$gc,$bc);\n":'').
+             ($thickness?"document.ggbApplet$appid.setLineThickness('$label',$thickness);\n":'');
    } else {
-       return "document.ggbApplet_$id.evalCommand('y=$function')";
+       return "document.ggbApplet$appid.evalCommand('y=$function');\n";
+   }
+}
+
+#
+# Subroutine to produce objects
+#
+
+sub plotobject_script {
+   my ($id,$label,$x,$y)=@_;
+   my $appid=&appid($id);
+   unless ($label) {
+      $Apache::functionplotresponse::counter++;
+      $label='O'.$Apache::functionplotresponse::counter;
+   }
+   &generate_input_field($id,$label,$x,$y);
+   return "document.ggbApplet$appid.evalCommand('a=1');\n".
+          "document.ggbApplet$appid.setVisible('a', false);\n".
+          "document.ggbApplet$appid.setLabelVisible('a', false);\n".
+          "document.ggbApplet$appid.evalCommand('$label=a*($x,$y)');\n".
+          "document.ggbApplet$appid.setVisible('$label', true);\n".
+          "document.ggbApplet$appid.setLabelVisible('$label', true);\n";
+}
+
+#
+# Subroutine to produce vectors
+#
+
+sub plotvector_script {
+   my ($id,$label,$xs,$ys,$xe,$ye,$xmin,$xmax,$fixed)=@_;
+   my $appid=&appid($id);
+   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,$fixed).
+       &new_point_coordinate($id,$endlabel,$xe,$ye,$fixed).
+       (<<ENDVECTOR);
+document.ggbApplet$appid.evalCommand("$label=Vector[$startlabel,$endlabel]");
+document.ggbApplet$appid.setLabelVisible("$label",true);
+document.ggbApplet$appid.setLineThickness("$label",8);
+document.ggbApplet$appid.evalCommand("$pointlabel=($pointx,y($startlabel))");
+document.ggbApplet$appid.evalCommand("$anglelabel=Angle[$pointlabel,$startlabel,$endlabel]");
+document.ggbApplet$appid.setLabelVisible("$anglelabel",true);
+document.ggbApplet$appid.setLabelStyle("$anglelabel",VALUE=2);
+ENDVECTOR
+}
+
+#
+# Answer spline display
+# 
+# points: x,y,slope_x,slope_y
+
+sub answer_spline_script {
+   my ($id,@points)=@_;
+   my $appid=&appid($id);
+   my $order=int(($#points+1)/4);
+   if ($order<2) { $order=2; }
+   if ($order>8) { $order=8; }
+   $Apache::functionplotresponse::counter++;
+   my $label='CSpline'.$Apache::functionplotresponse::counter;
+   my $output='document.ggbApplet'.$appid.'.evalCommand("'.$label.'=Spline'.$order.'[';
+   for (my $i=0;$i<=$#points;$i+=4) {
+      $output.="($points[$i],$points[$i+1]),($points[$i+2],$points[$i+3]),";
+   }
+   $output=~s/\,$//;
+   $output.=']");'."\n";
+   for (my $i=2; $i<2*$order; $i+=2) {
+       $output.='document.ggbApplet'.$appid.'.setColor("'.$label.'_'.($i>=10?'{':'').$i.($i>=10?'}':'').'",0,170,0);'."\n";
+   }
+   for (my $i=1; $i<2*$order; $i+=2) {
+       $output.='document.ggbApplet'.$appid.'.setVisible("'.$label.'_'.($i>=10?'{':'').$i.($i>=10?'}':'').'",false);'."\n";
    }
+
+   return $output;
 }
 
 #
@@ -284,7 +557,8 @@ ENDPLOTSCRIPT
 #
 
 sub generate_spline {
-   my ($id,$label)=@_;
+   my ($id,$label,$xmin,$xmax,$ymin,$ymax,$fixed)=@_;
+   my $appid=&appid($id);
    my $result='';
    my $order=$Apache::functionplotresponse::splineorder{$label};
    my $x=$Apache::functionplotresponse::splineinitx{$label};
@@ -293,16 +567,216 @@ 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);
    }
-   $result.='document.ggbApplet_'.$id.'.evalCommand("Spline'.$order.'['.join(',',@coords).']");'."\n";
+   $result.='document.ggbApplet'.$appid.'.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) { $label="NewVector"; }
+   if ($Apache::functionplotresponse::vectorlabels{$label}) {
+       &Apache::lonxml::warning(&mt('Vector labels must be unique: [_1]',$label));
+   }
+   $Apache::functionplotresponse::vectorlabels{$label}=1;
+   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; }
+      my $fixed=0;
+      if ((&Apache::response::show_answer()) || (&Apache::response::check_status()>=2)) { $fixed=1; }
+      $result.=&plotvector_script($internalid,$label,$tailx,$taily,$tipx,$tipy,$xmin,$xmax,$fixed);
+   } 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 $result;
+}
+
+
+#
+# Vector sum - have GeoGebra draw a sum of specified vectors to help students draw
+#
+
+sub start_drawvectorsum {
+    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+    my $result='';
+    my $internalid = $Apache::inputtags::part.'_'.$Apache::inputtags::response[-1];
+    my $internalappid=&appid($internalid);
+    my $tailx=&Apache::lonxml::get_param('tailx',$parstack,$safeeval);
+    my $taily=&Apache::lonxml::get_param('taily',$parstack,$safeeval);
+    my $showvalue=&Apache::lonxml::get_param('showvalue',$parstack,$safeeval);
+    my $vectorlist=&Apache::lonxml::get_param('vectorlist',$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($vectorlist)) { $vectorlist=''; }
+        my @vectors=split(/\,/,$vectorlist);
+        if ($#vectors>0) {
+            my @sumx=();
+            my @sumy=();
+            foreach my $thisvector (@vectors) {
+                $thisvector=~s/\W//gs;
+                $thisvector=ucfirst($thisvector);
+                unless ($thisvector) { next; }
+                unless ($Apache::functionplotresponse::vectorlabels{$thisvector}) {
+                    &Apache::lonxml::warning(&mt('Vectors must be defined before using them for drawing vector sums: [_1]',$thisvector));
+                    next;
+                }
+                my $vectorx=$thisvector.'X';
+                my $vectory=$thisvector.'Y';
+                $result.=(<<ENDADDVEC);
+document.ggbApplet$internalappid.evalCommand("$vectorx=x($thisvector)");
+document.ggbApplet$internalappid.evalCommand("$vectory=y($thisvector)");
+document.ggbApplet$internalappid.evalCommand("Include$thisvector$label=Checkbox[]");
+ENDADDVEC
+                push(@sumx,"If[Include$thisvector$label,$vectorx,0]");
+                push(@sumy,"If[Include$thisvector$label,$vectory,0]");
+            }
+            $result.="document.ggbApplet$internalappid.evalCommand(".'"'."xTot$label=".join('+',@sumx).'");'."\n";
+            $result.="document.ggbApplet$internalappid.evalCommand(".'"'."yTot$label=".join('+',@sumy).'");'."\n";
+            my $show=0;
+            if ($showvalue=~/yes/i) {
+                $show=1;
+            }
+            $result.=(<<ENDMAKEVECTOR);
+document.ggbApplet$internalappid.evalCommand("$label=Vector[($tailx,$taily),($tailx+xTot$label,$taily+yTot$label)]");
+document.ggbApplet$internalappid.setLabelVisible("$label",true);
+document.ggbApplet$internalappid.setLineThickness("$label",8);
+document.ggbApplet$internalappid.setColor("$label",255,0,0);
+document.ggbApplet$internalappid.setLabelStyle("$label",VALUE=$show);
+ENDMAKEVECTOR
+        }
+    } elsif ($target eq 'edit') {
+        $result=&Apache::edit::tag_start($target,$token,'Draw Vector Sum').
+             &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',
+                                     $token,'8').
+             &Apache::edit::select_arg('Show Value:','showvalue',
+                                  ['yes','no'],$token).'<br />'.
+             &Apache::edit::text_arg('Vector List:','vectorlist',
+                                     $token,'40').
+             &Apache::edit::end_row();
+    } elsif ($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','showvalue','vectorlist');
+        if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
+    }
+    return $result;
+}
+
+
+sub end_drawvectorsum {
+    my ($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" />
 #
@@ -311,21 +785,38 @@ 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;
@@ -357,10 +848,6 @@ 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
@@ -379,7 +866,7 @@ 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.'));
          $derivative=0;
       }
@@ -397,25 +884,27 @@ sub start_functionplotrule {
            &Apache::lonxml::get_param('percenterror',$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',
                                      $token,'10').'&nbsp;'.
              &Apache::edit::select_arg(&mt('Function:'),'derivativeorder',
                                   [['0','Function itself'],
                                    ['1','First derivative'],
-                                   ['2','Second derivative']],$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',
                                      $token,'8').'<br />'.
              &Apache::edit::select_or_text_arg(&mt('Relationship:'),'relationship',
                                   [['eq','equal'],
@@ -425,11 +914,17 @@ sub start_functionplotrule {
                                    ['lt','less than'],
                                    ['le','less than or equal']],$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',
                                      $token,'8').
              &Apache::edit::end_row();
   } elsif ($target eq 'modified') {
+    if (($env{'form.'.&Apache::edit::html_element_name('xinitial')} ne '') && ($env{'form.'.&Apache::edit::html_element_name('xinitiallabel')} eq 'start')) {
+       $env{'form.'.&Apache::edit::html_element_name('xinitiallabel')}='';
+    }
+    if (($env{'form.'.&Apache::edit::html_element_name('xfinal')} ne '') && ($env{'form.'.&Apache::edit::html_element_name('xfinallabel')} eq 'end')) {
+       $env{'form.'.&Apache::edit::html_element_name('xfinallabel')}='';
+    }
     my $constructtag=&Apache::edit::get_new_args($token,$parstack,
                                                  $safeeval,'index','derivativeorder',
                                                            'xinitial','xinitiallabel','xfinal','xfinallabel',
@@ -451,6 +946,225 @@ 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);
+
+      push(@Apache::functionplotresponse::functionplotvectorrules,join(':',(
+           $label,
+           'vector',
+           $internalid,
+           $vector,
+           &Apache::lonxml::get_param('attachpoint',$parstack,$safeeval),
+           &Apache::lonxml::get_param('notattachpoint',$parstack,$safeeval),
+           &Apache::lonxml::get_param('tailpoint',$parstack,$safeeval),
+           &Apache::lonxml::get_param('tippoint',$parstack,$safeeval),
+           &Apache::lonxml::get_param('nottailpoint',$parstack,$safeeval),
+           &Apache::lonxml::get_param('nottippoint',$parstack,$safeeval),
+           &Apache::lonxml::get_param('length',$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,'30').
+             &Apache::edit::text_arg('Absolute error length:','lengtherror',
+                                     $token,'8').'<br />'.
+             &Apache::edit::text_arg('Angle:','angle',
+                                     $token,'30').
+             &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')});
+    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 $vectors=&Apache::lonxml::get_param('vectors',$parstack,$safeeval);
+      push(@Apache::functionplotresponse::functionplotvectorrules,join(':',(
+           $label,
+           'sum',
+           $internalid,
+           $vectors,
+           &Apache::lonxml::get_param('length',$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('Comma-separated list of vectors:','vectors',
+                                      $token,'30').'<br />'.
+             &Apache::edit::text_arg('Sum vector length:','length',
+                                     $token,'30').
+             &Apache::edit::text_arg('Absolute error length:','lengtherror',
+                                     $token,'8').'<br />'.
+             &Apache::edit::text_arg('Sum vector angle:','angle',
+                                     $token,'30').
+             &Apache::edit::text_arg('Absolute error angle:','angleerror',
+                                     $token,'8').
+             &Apache::edit::end_row();
+   } elsif ($target eq 'modified') {
+      my $constructtag=&Apache::edit::get_new_args($token,$parstack,
+                                                   $safeeval,'index','vectors',
+                                                             'length','angle',
+                                                             'lengtherror','angleerror');
+      if ($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 $result;
+}
+
+#
+# <functionplotcustom ... />
+#
+sub start_functionplotcustomrule {
+   my ($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;
+   }
+   &Apache::lonxml::register('Apache::response',('answer'));
+   if ($target eq 'edit') {
+        $result=&Apache::edit::tag_start($target,$token,'Function Plot Custom Rule').
+             &Apache::edit::text_arg('Index/Name:','index',$token,'10').
+             &Apache::edit::end_row();
+  } elsif ($target eq 'modified') {
+      my $constructtag=&Apache::edit::get_new_args($token,$parstack,$safeeval,'index');
+      if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
+   }
+   return $result;
+}
+
+sub end_functionplotcustomrule {
+   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+   my $result='';
+   if ($target eq 'edit') {
+      $result=&Apache::edit::end_table();
+   } elsif ($target eq 'grade') {
+# Simply remember - in order - for later
+      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;
+      }
+      push(@Apache::functionplotresponse::functionplotvectorrules,join(':',(
+           $label,
+           'custom',
+           &escape($Apache::response::custom_answer[-1])
+          )));
+   }
+   &Apache::lonxml::deregister('Apache::response',('answer'));
+   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
@@ -499,7 +1213,7 @@ 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 +1280,8 @@ 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 +1290,8 @@ 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 +1300,8 @@ 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);
 }
 
 #
@@ -607,7 +1321,7 @@ 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;
@@ -635,12 +1349,19 @@ 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;
@@ -682,8 +1403,11 @@ sub start_functionplotresponse {
   undef %Apache::functionplotresponse::previous;
   $Apache::functionplotresponse::inputfields='';
   $Apache::functionplotresponse::counter=0;
+# Remember vectors
+  undef %Apache::functionplotresponse::vectorlabels;
 # Remember rules
   undef @Apache::functionplotresponse::functionplotrules;
+  undef @Apache::functionplotresponse::functionplotvectorrules;
 # Remember failed rules
   if ($target eq 'grade') {
      undef @Apache::functionplotresponse::failedrules;
@@ -699,22 +1423,7 @@ 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,$safeeval)=~/on|true|yes|1/i?'true':'false');
@@ -725,13 +1434,18 @@ sub start_functionplotresponse {
        .'<tr><td><span class="LC_nobreak">'.&mt('Function Plot Question').'</span></td>'
        .'<td><span class="LC_nobreak">'.&mt('Delete?').' '
        .&Apache::edit::deletelist($target,$token).'&nbsp;&nbsp;&nbsp;'
-       .&Apache::edit::insertlist($target,$token)
+       .&Apache::edit::insertlist($target,$token).'&nbsp;&nbsp;&nbsp;'
+       .&Apache::loncommon::help_open_topic('Function_Plot_Response_Question','Function Plot Responses')
        .'</span></td>'
        ."<td>&nbsp;"
        .&Apache::edit::end_row()
        .&Apache::edit::start_spanning_row()
        ."\n";
-    $result.=&Apache::edit::text_arg('Label x-axis:','xlabel',
+    $result.=&Apache::edit::text_arg('Width (pixels):','width',
+                                     $token,'6').'&nbsp;'.
+             &Apache::edit::text_arg('Height (pixels):','height',
+                                     $token,'6').'<br />'.
+             &Apache::edit::text_arg('Label x-axis:','xlabel',
                                      $token,'6').'&nbsp;'.
              &Apache::edit::text_arg('Minimum x-value:','xmin',
                                      $token,'4').'&nbsp;'.
@@ -748,12 +1462,14 @@ sub start_functionplotresponse {
              &Apache::edit::select_arg('y-axis visible:','yaxisvisible',
                                   ['yes','no'],$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(x):xmin:xmax,function(x):xmin:xmax,x1:y1:sx1:sy1:x2:y2:sx2:sy2,...):',
+                                         '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');
+                                                 $safeeval,'width','height','xlabel','xmin','xmax','ylabel','ymin','ymax',
+                                                           'xaxisvisible','yaxisvisible','gridvisible','answerdisplay');
     if ($constructtag) { $result = &Apache::edit::rebuild_tag($token); }
 
   } elsif ($target eq 'meta') {
@@ -762,27 +1478,16 @@ sub start_functionplotresponse {
             ($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);
-        }
-
+      &Apache::lonxml::add_script_result(
+          &Apache::loncommon::modal_adhoc_window($function_name,700,500,
+             '<pre>'.$Apache::functionplotresponse::ruleslog.'</pre>',
+              &mt('Rules Log'))."<br />");
+  }
   return $result;
 }
 
@@ -833,6 +1538,7 @@ sub compare_rel {
 
 sub addlog {
    my ($text)=@_;
+   $text=~s/\'/\\\'/g;
    $Apache::functionplotresponse::ruleslog.=$text.'<br />';
 }
 
@@ -840,15 +1546,331 @@ 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,
+                                                                $arg)];
+}
+
+sub fpr_vectorcoords {
+   my ($arg)=@_;
+   $arg=~s/\W//gs;
+   $arg=ucfirst($arg);
+   my $id=$Apache::inputtags::response[-1];
+   my $partid=$Apache::inputtags::part;
+   my $internalid = $partid.'_'.$id;
+   return ($env{'form.HWVAL_'.$internalid.'_'.$arg.'Start_x'},
+           $env{'form.HWVAL_'.$internalid.'_'.$arg.'End_x'},
+           $env{'form.HWVAL_'.$internalid.'_'.$arg.'Start_y'},
+           $env{'form.HWVAL_'.$internalid.'_'.$arg.'End_y'});
+}
+
+sub fpr_objectcoords {
+   my ($arg)=@_;
+   $arg=~s/\W//gs;
+   $arg=ucfirst($arg);
+   my $id=$Apache::inputtags::response[-1];
+   my $partid=$Apache::inputtags::part;
+   my $internalid = $partid.'_'.$id;
+   return ($env{'form.HWVAL_'.$internalid.'_'.$arg.'_x'},
+           $env{'form.HWVAL_'.$internalid.'_'.$arg.'_y'});
+}
+
+sub fpr_vectorlength {
+   my ($arg)=@_;
+   my ($xs,$xe,$ys,$ye)=&fpr_vectorcoords($arg);
+   return sqrt(($xe-$xs)*($xe-$xs)+($ye-$ys)*($ye-$ys));
+}
+
+sub fpr_vectorangle {
+   my ($arg)=@_;
+   my ($xs,$xe,$ys,$ye)=&fpr_vectorcoords($arg);
+   my $angle=57.2957795*atan2(($ye-$ys),($xe-$xs));
+   if ($angle<0) { $angle=360+$angle; }
+   return $angle;
+}
+
+sub vectorcoords {
+   my ($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,$vector,$objects,$xmin,$xmax,$ymin,$ymax)=@_;
+   my ($xs,$xe,$ys,$ye)=&vectorcoords($id,$vector);
+   my $tolx=($xmax-$xmin)/100.;
+   my $toly=($ymax-$ymin)/100.;
+   my $tail=0;
+   my $tip=0;
+   foreach my $obj (split(/\s*\,\s*/,$objects)) {
+      $obj=~s/\W//g;
+      unless ($obj) { next; }
+      $obj=ucfirst($obj);
+      my ($xo,$yo)=&objectcoords($id,$obj);
+      &addlog("Proximity $vector ($xs,$ys)-($xe,$ye) to $obj ($xo,$yo)");
+      if ((abs($xs-$xo)<$tolx) && (abs($ys-$yo)<$toly)) {
+         $tail=1;
+         &addlog("Attached tail: $obj"); 
+      }
+      if ((abs($xe-$xo)<$tolx) && (abs($ye-$yo)<$toly)) { 
+         $tip=1;
+         &addlog("Attached tip: $obj"); 
+      }
+   }
+   &addlog("Result tail:$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);
+   } elsif ($type eq 'custom') {
+      return &customcheck($rule,$safeeval);
+   }
+}
+
+sub vectorcheck {
+   my ($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,$vectors,$length,$angle,$lengtherror,$angleerror)=split(/\:/,$rule);
+   &addlog("Vector Sum Rule $label for vectors ".$vectors);
+   my $sumx=0;
+   my $sumy=0;
+   foreach my $sv (split(/\s*\,\s*/,$vectors)) {
+      my ($rx,$ry)=&relvector(&vectorcoords($id,$sv));
+      $sumx+=$rx;
+      $sumy+=$ry;
+   }
+   &addlog("Sum vector ($sumx,$sumy)");
+   if ($length ne '') {
+      &addlog("Checking length $length with error $lengtherror");
+      $length=&Apache::run::run($length,$safeeval);
+      &addlog("Evaluated to $length");
+      my $thislength=&vectorlength($sumx,$sumy);
+      &addlog("Actual length $thislength");
+      if (abs($length-$thislength)>$lengtherror) {
+                  &setfailed($label);
+         return 0;
+      }
+   }
+   if ($angle ne '') {
+      &addlog("Checking angle $angle with error $angleerror");
+      $angle=&Apache::run::run($angle,$safeeval);
+      &addlog("Evaluated to $angle");
+      my $thisangle=&vectorangle($sumx,$sumy);
+      &addlog("Actual 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;
+      }
+   }
+   &addlog("Rule $label passed.");
+   return 1;
+}
+
+sub customcheck {
+   my ($rule,$safeeval)=@_;
+   my ($label,$type,$prg)=split(/\:/,$rule);
+   &addlog("Custom Rule ".$label);
+   my $result=&Apache::run::run(&unescape($prg),$safeeval);
+   &addlog("Algorithm returned $result");
+   unless ($result) {
+      &setfailed($label);
+      return 0;
+   }
+   &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 $label for ".('function itself','first derivative','second derivative')[$derivative]." $relationship $value");
+   &addlog("Rule $label for ".($derivative<0?'integral':('function itself','first derivative','second derivative')[$derivative])." $relationship $value");
+#
+# Evaluate the value
+#
+   if (($value=~/\D/) && ($value ne 'undef')) {
+      $Apache::functionplotresponse::fpr_xmin=$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");
+   }
    my $li=0;
    my $lh=400;
 
@@ -905,14 +1927,34 @@ 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 $label failed.");
+        &setfailed($label);
+        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[$i];
         }
@@ -920,37 +1962,58 @@ sub functionplotrulecheck {
            &addlog("Actual value ".(defined($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 ($hintlabel)=@_;
+   $hintlabel=~s/^R//;
+   push(@Apache::functionplotresponse::failedrules,$hintlabel);
+   &addlog("Set hint condition $hintlabel");
+}
+
 sub start_functionplotruleset {
    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
    if ($target eq 'edit') {
@@ -958,7 +2021,8 @@ sub start_functionplotruleset {
         '<tr><td><span class="LC_nobreak">'.&mt('Function Plot Rule Set').'</span></td>'
        .'<td><span class="LC_nobreak">'.&mt('Delete?').' '
        .&Apache::edit::deletelist($target,$token).'&nbsp;&nbsp;&nbsp;'.
-        &Apache::edit::insertlist($target,$token)
+        &Apache::edit::insertlist($target,$token).'&nbsp;&nbsp;&nbsp;'
+       .&Apache::loncommon::help_open_topic('Function_Plot_Response_Rule_Set','Function Plot Rules')
        .'</span></td>'
        ."<td>&nbsp;"
        .&Apache::edit::end_row()
@@ -981,21 +2045,14 @@ 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;
         $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 ".
@@ -1005,7 +2062,14 @@ 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)) {
                  $ad='INCORRECT';
                  last;
               }
@@ -1067,9 +2131,34 @@ sub end_functionplotelements {
   if ($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 @components=split(/\s*\:\s*/,$plot);
+              if ($#components<3) {
+# Just a simple plot
+                 my ($func,$xl,$xh)=@components;
+                 if ((!defined($xl)) || ($xl eq '')) { $xl=$xmin; }
+                 if ((!defined($xh)) || ($xh eq '')) { $xh=$xmax; }
+                 $result.=&plot_script($internalid,$func,1,'','00aa00',$xl,$xh,6);
+              } else {
+# This is a spline
+                 $result.=&answer_spline_script($internalid,@components);
+              }
+           }
+        }
+     }
+     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();
@@ -1083,9 +2172,9 @@ sub end_functionplotelements {
 # generate the input fields
      $result.=$Apache::functionplotresponse::inputfields;
 # actually start the <applet>-tag
-     $result.=&geogebra_startcode($internalid);
-# load the spline bytecode
-     $result.=&geogebra_spline_program();
+     $result.=&geogebra_startcode($internalid,
+                                  &Apache::lonxml::get_param('width',$parstack,$safeeval,-2),
+                                  &Apache::lonxml::get_param('height',$parstack,$safeeval,-2));
 # set default parameters
      $result.=&geogebra_default_parameters($internalid);
 # close the <applet>-tag
@@ -1094,6 +2183,25 @@ 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 $result='';
@@ -1106,27 +2214,15 @@ sub start_functionplotelements {
         '<tr><td><span class="LC_nobreak">'.&mt('Function Plot Elements').'</span></td>'
        .'<td><span class="LC_nobreak">'.&mt('Delete?').' '
        .&Apache::edit::deletelist($target,$token).'&nbsp;&nbsp;&nbsp;'.
-        &Apache::edit::insertlist($target,$token)
+        &Apache::edit::insertlist($target,$token).'&nbsp;&nbsp;&nbsp;'
+       .&Apache::loncommon::help_open_topic('Function_Plot_Response_Elements','Function Plot Elements')
        .'</span></td>'
        ."<td>&nbsp;"
        .&Apache::edit::end_row()
        .&Apache::edit::start_spanning_row()
        ."\n";
    } elsif ($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 +2236,7 @@ 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;