--- loncom/homework/functionplotresponse.pm	2010/10/05 00:10:07	1.6
+++ loncom/homework/functionplotresponse.pm	2010/11/11 03:52:35	1.33
@@ -1,7 +1,7 @@
 # LearningOnline Network with CAPA
 # option list style responses
 #
-# $Id: functionplotresponse.pm,v 1.6 2010/10/05 00:10:07 www Exp $
+# $Id: functionplotresponse.pm,v 1.33 2010/11/11 03:52:35 www Exp $
 #
 # Copyright Michigan State University Board of Trustees
 #
@@ -33,7 +33,7 @@ use Apache::lonlocal;
 use Apache::lonnet;
 
 BEGIN {
-  &Apache::lonxml::register('Apache::functionplotresponse',('functionplotresponse','backgroundplot','spline'));
+  &Apache::lonxml::register('Apache::functionplotresponse',('functionplotresponse','backgroundplot','spline','functionplotrule'));
 }
 
 #
@@ -101,12 +101,25 @@ ENDDEFAULTPARAMETERS
 #
 
 sub init_script {
-   if ($Apache::functionplotresponse::callscripts) {
+   if ($#Apache::functionplotresponse::callscripts>=0) {
+      my $script='';
+      foreach my $id (@Apache::functionplotresponse::callscripts) {
+          $script.="if (param=='applet_$id') { loaded_$id=true; }\n";
+      }
+      $script.="if (".join(' && ',map { "loaded_$_" } (@Apache::functionplotresponse::callscripts)).
+               ") { setTimeout('ggbInitAll()',20) }";
+      my $calls=join("\n",map { "ggbInit_$_();" } (@Apache::functionplotresponse::callscripts)); 
       return (<<ENDGGBINIT);
 <script type="text/javascript">
 // <![CDATA[
+// Function that each applet will call when loaded
+// It will pass "its" parameter
+// Set flags for when an applet is loaded, wait till all are loaded, and then some
 function ggbOnInit(param) {
-$Apache::functionplotresponse::callscripts
+$script
+}
+function ggbInitAll() {
+$calls
 }
 // ]]>
 </script>
@@ -116,6 +129,7 @@ ENDGGBINIT
 
 #
 # Each Geogebra applet is supposed to call this when parameters change
+# Changes the hidden fields on the web page
 #
 sub update_script {
     my ($id)=@_;
@@ -125,8 +139,8 @@ sub update_script {
 function updatePointCoordinates_$id(coordinateName) {
             var x = document.ggbApplet_$id.getXcoord(coordinateName);
             var y = document.ggbApplet_$id.getYcoord(coordinateName);
-            coordinateMap_$id\[coordinateName + ".x"] = x;
-            coordinateMap_$id\[coordinateName + ".y"] = y;
+            document.lonhomework.elements["HWVAL_$id\_" + coordinateName + "_x"].value = x;
+            document.lonhomework.elements["HWVAL_$id\_" + coordinateName + "_y"].value = y;
         }
 // ]]>
 </script>
@@ -148,17 +162,42 @@ sub update_register {
 sub set_coordinate {
    my ($id,$variable,$x,$y)=@_;
    return (<<ENDSETVARIABLE);
-coordinateMap_$id\['$variable.x'] = $x;
-coordinateMap_$id\['$variable.y'] = $y;
-document.ggbApplet_$id.evalCommand("$variable=("+coordinateMap_$id\["$variable.x"]+","+coordinateMap_$id\["$variable.y"]+")");
+document.ggbApplet_$id.evalCommand("$variable=($x,$y)");
 ENDSETVARIABLE
 }
 
 #
+# Input field name for a coordinate variable
+#
+
+sub field_name {
+    my ($id,$variable,$name)=@_;
+    return "HWVAL_$id\_$variable\_$name";
+}
+
+#
+# Generate an input field for a coordinate variable
+#
+
+sub generate_input_field {
+    my ($id,$variable,$x,$y)=@_;
+    $Apache::functionplotresponse::inputfields.=
+       "<input type='hidden' name='".&field_name($id,$variable,'x')."' value='$x' />\n".
+       "<input type='hidden' name='".&field_name($id,$variable,'y')."' value='$y' />\n";
+}
+
+#
 # Initialize a new coordinate variable at set a listener on it
 #
 sub new_coordinate {
     my ($id,$variable,$x,$y)=@_;
+    if (defined($Apache::functionplotresponse::previous{&field_name($id,$variable,'x')})) {
+       $x=$Apache::functionplotresponse::previous{&field_name($id,$variable,'x')};
+    }
+    if (defined($Apache::functionplotresponse::previous{&field_name($id,$variable,'y')})) {
+       $y=$Apache::functionplotresponse::previous{&field_name($id,$variable,'y')};
+    }
+    &generate_input_field($id,$variable,$x,$y);
     return &set_coordinate($id,$variable,$x,$y).&update_register($id,$variable);
 }
 
@@ -168,14 +207,16 @@ sub new_coordinate {
 #
 sub start_init_script {
     my ($id)=@_;
-# Add a line to ggbOnInit-function which calls the right function based on parameter passed from GeoGebra
-    $Apache::functionplotresponse::callscripts.="if (param=='applet_$id') { ggbInit_$id(); }\n";
+# Add id to the list of ggbInit_$id functions that need to be called
+    push(@Apache::functionplotresponse::callscripts,$id);
 # ... and open this function
     return (<<ENDSTARTINIT);
 <script type="text/javascript">
 // <![CDATA[
 // variable that will eventually be passed back to the server
 var coordinateMap_$id = [];
+// flag for not loaded yet
+var loaded_$id=false;
 // Init-function for applet
 function ggbInit_$id() {
 ENDSTARTINIT
@@ -198,10 +239,33 @@ sub axes_script {
 ENDAXESSCRIPT
 }
 
+sub axes_label {
+    my ($id,$xlabel,$ylabel)=@_;
+    unless ($xlabel || $ylabel) { return ''; }
+    my $return='document.ggbApplet_'.$id.'.evalCommand("topRight=Corner[3]");';
+    if ($xlabel) {
+       $return.=(<<ENDXAXISLABELSCRIPT);
+document.ggbApplet_$id.evalCommand("Xlabel=(x(topRight)-AxisStepX[],AxisStepY[]/6)");
+document.ggbApplet_$id.setVisible("Xlabel",false);
+document.ggbApplet_$id.evalCommand("Text[\\"$xlabel\\", Xlabel]");
+ENDXAXISLABELSCRIPT
+    }
+    if ($ylabel) {
+       $return.=(<<ENDYAXISLABELSCRIPT);
+document.ggbApplet_$id.evalCommand("Ylabel=(AxisStepX[]/6,y(topRight)-AxisStepY[]/3)");
+document.ggbApplet_$id.setVisible("Ylabel",false);
+document.ggbApplet_$id.evalCommand("Text[\\"$ylabel\\", Ylabel]");
+ENDYAXISLABELSCRIPT
+    }
+    return $return;
+}
+
 sub plot_script {
    my ($id,$function,$fixed)=@_;
    if ($fixed) {
 # Use stupid trick to nail this to a location
+# Oddly, it seems like only one plot cannot be nailed to a location
+# Non-nailed-down plots apparently get overwritten
       return (<<ENDPLOTSCRIPT);
             document.ggbApplet_$id.evalCommand("a=1");
             document.ggbApplet_$id.setVisible("a",false);
@@ -214,12 +278,27 @@ ENDPLOTSCRIPT
 }
 
 #
-# Subroutine that generates spline $label based on stored information
+# Subroutine that generates code for spline $label based on stored information
 #
 
 sub generate_spline {
    my ($id,$label)=@_;
    my $result='';
+   my $order=$Apache::functionplotresponse::splineorder{$label};
+   my $x=$Apache::functionplotresponse::splineinitx{$label};
+   my $y=$Apache::functionplotresponse::splineinity{$label};
+   my $sx=$Apache::functionplotresponse::splinescalex{$label};
+   my $sy=$Apache::functionplotresponse::splinescaley{$label};
+   my @coords=();
+   foreach my $i (1..$order) {
+       $result.=&new_coordinate($id,$label.'P'.$i,$x,$y);
+       $x+=$sx/(2.*($order-1));
+       push(@coords,$label.'P'.$i);
+       $result.=&new_coordinate($id,$label.'S'.$i,$x,$y+$sy);
+       $x+=$sx/(2.*($order-1));
+       push(@coords,$label.'S'.$i);
+   }
+   $result.='document.ggbApplet_'.$id.'.evalCommand("Spline'.$order.'['.join(',',@coords).']");'."\n";
    return $result;
 }
 #
@@ -235,48 +314,209 @@ sub start_backgroundplot {
    unless ($function) { $function="0"; }
    if ($target eq 'web') {
       $result.=&plot_script($internalid,$function,$fixed);
+   } elsif ($target eq 'edit') {
+        $result=&Apache::edit::tag_start($target,$token,'Background Function Plot').
+             &Apache::edit::text_arg('Function:','function',
+                                     $token,'16').
+             &Apache::edit::select_arg('Fixed location:','fixed',
+                                  ['yes','no'],$token).
+             &Apache::edit::end_row();
+  } elsif ($target eq 'modified') {
+    my $constructtag=&Apache::edit::get_new_args($token,$parstack,
+                                                 $safeeval,'function','fixed');
+    if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
+  }
+  return $result;
+}
+
+sub end_backgroundplot {
+   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+   my $result='';
+   if ($target eq 'edit') {
+       $result=&Apache::edit::end_table();
    }
    return $result;
 }
 
-sub end_backgroundplot {
-   return '';
+#
+# <functionplotrule ... />
+#
+sub start_functionplotrule {
+   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 ($Apache::functionplotresponse::splineorder{$label}) {
+       &Apache::lonxml::error(&mt('Rule indices must be unique.'));
+   }
+
+
+   if ($target eq 'grade') {
+# Simply remember - in order - for later
+      my $beginninglabel=&Apache::lonxml::get_param('xinitiallabel',$parstack,$safeeval);
+      my $endinglabel=&Apache::lonxml::get_param('xfinallabel',$parstack,$safeeval);
+      if (($beginninglabel=~/\W/) || ($endinglabel=~/W/)) {
+          &Apache::lonxml::warning(&mt('Rule labels must be alphanumeric.'));
+      }
+      $beginninglabel=~s/\W//gs;
+      $endinglabel=~s/\W//gs;
+      my $relationship=&Apache::lonxml::get_param('relationship',$parstack,$safeeval);
+      $relationship=~s/\W//gs;
+      $relationship=lc($relationship);
+      unless ($relationship=~/^(eq|ge|gt|le|lt|ne)$/) {
+          &Apache::lonxml::warning(&mt('Rule relationship not defined.'));
+          $relationship='eq';
+      }
+      my $derivative=&Apache::lonxml::get_param('derivative',$parstack,$safeeval);
+      unless (($derivative==0) || ($derivative==1) || ($derivative==2)) {
+         &Apache::lonxml::warning(&mt('Rule derivative not defined.'));
+         $derivative=0;
+      }
+      push(@Apache::functionplotresponse::functionplotrules,join(':',(
+           $label,
+           $derivative,
+           &Apache::lonxml::get_param('xinitial',$parstack,$safeeval),
+           $beginninglabel,
+           &Apache::lonxml::get_param('xfinal',$parstack,$safeeval),
+           $endinglabel,
+           $relationship,
+           &Apache::lonxml::get_param('value',$parstack,$safeeval),
+           &Apache::lonxml::get_param('percenterror',$parstack,$safeeval)
+          )));
+   } elsif ($target eq 'edit') {
+        $result=&Apache::edit::tag_start($target,$token,'Function Plot Evaluation Rule').
+             &Apache::edit::text_arg('Index:','index',
+                                     $token,'4').'&nbsp;'.
+             &Apache::edit::select_arg(&mt('Function:'),'derivative',
+                                  [['0','Function itself'],
+                                   ['1','First derivative'],
+                                   ['2','Second derivative']],$token).'<br />'.
+
+             &Apache::edit::text_arg('(Initial) x-value:','xinitial',
+                                      $token,'4').
+             &Apache::edit::select_or_text_arg('(Initial) x-value label:','xinitiallabel',
+                                               [['start','Start of Plot']],$token,'8').'<br />'.
+
+             &Apache::edit::text_arg('Optional final x-value for ranges:','xfinal',
+                                      $token,'4').
+             &Apache::edit::select_or_text_arg('Optional final x-value label:','xfinallabel',
+                                               [['end','End of Plot']],$token,'8').'<br />'.
+
+             &Apache::edit::select_arg(&mt('Relationship:'),'relationship',
+                                  [['eq','equal'],
+                                   ['ne','not equal'],
+                                   ['ge','greater than or equal'],
+                                   ['gt','greater than'],
+                                   ['lt','less than'],
+                                   ['le','less than or equal']],$token).
+             $result.= &Apache::edit::select_or_text_arg('Value:','value',
+                                               [['undef','not defined']],$token,'4').
+             &Apache::edit::text_arg('Percent error:','percenterror',
+                                     $token,'4').
+             &Apache::edit::end_row();
+  } elsif ($target eq 'modified') {
+    my $constructtag=&Apache::edit::get_new_args($token,$parstack,
+                                                 $safeeval,'index','derivative','xinitial','xinitiallabel','xfinal','xfinallabel','relationship',
+                                                           'value','percenterror');
+    if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
+   }
+   return $result;
+}
+
+sub end_functionplotrule {
+   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+   my $result='';
+   if ($target eq 'edit') {
+       $result=&Apache::edit::end_table();
+   }
+   return $result;
 }
 
+
 #
-# <spline label="..." order="1,2,3,4" initx="..." inity="..." scalex="..." scaley="..." />
+# <spline index="..." order="1,2,3,4" initx="..." inity="..." scalex="..." scaley="..." />
 #
 # Unfortunately, GeoGebra seems to want all splines after everything else, so we need to store them
 #
 sub start_spline {
    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
-   my $label=&Apache::lonxml::get_param('label',$parstack,$safeeval);
-   $Apache::functionplotresponse::counter++;
-   unless ($label) { $label='S'.$Apache::functionplotresponse::counter; }
-
-   my $order=&Apache::lonxml::get_param('order',$parstack,$safeeval);
-   if (($order<2) || ($order>4)) { $order=2; }
-   $Apache::functionplotresponse::splineorder{$label}=$order;
-
-   my $x=&Apache::lonxml::get_param('initx',$parstack,$safeeval);
-   unless ($x) { $x=0; }
-   $Apache::functionplotresponse::splineinitx{$label}=$x;
-
-   my $y=&Apache::lonxml::get_param('inity',$parstack,$safeeval);
-   unless ($y) { $y=0; }
-   $Apache::functionplotresponse::splineinity{$label}=$y;
-
-   my $sx=&Apache::lonxml::get_param('scalex',$parstack,$safeeval);
-   unless ($sx) { $sx=$order; }
-   $Apache::functionplotresponse::splinescalex{$label}=$sx;
-
-   my $sy=&Apache::lonxml::get_param('scaley',$parstack,$safeeval);
-   unless ($sy) { $sy=2; }
-   $Apache::functionplotresponse::splinescaley{$label}=$sy;
+   my $result='';
+   if ($target eq 'web') {
+      my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval);
+      $Apache::functionplotresponse::counter++;
+      if ($label=~/\W/) {
+         &Apache::lonxml::warning(&mt('Spline indices should only contain alphanumeric characters.'));
+      }
+      $label=~s/\W//gs;
+      unless ($label) { 
+         $label='S'.$Apache::functionplotresponse::counter; 
+      } else {
+         $label='S'.$label;
+      }
+      if ($Apache::functionplotresponse::splineorder{$label}) {
+         &Apache::lonxml::error(&mt('Spline indices must be unique.'));
+      }
+
+      my $order=&Apache::lonxml::get_param('order',$parstack,$safeeval);
+      if ($order<2) { $order=2; }
+      if ($order>8) { $order=8; }
+      $Apache::functionplotresponse::splineorder{$label}=$order;
+
+      my $x=&Apache::lonxml::get_param('initx',$parstack,$safeeval);
+      unless ($x) { $x=0; }
+      $Apache::functionplotresponse::splineinitx{$label}=$x;
+
+      my $y=&Apache::lonxml::get_param('inity',$parstack,$safeeval);
+      unless ($y) { $y=0; }
+      $Apache::functionplotresponse::splineinity{$label}=$y;
+
+      my $sx=&Apache::lonxml::get_param('scalex',$parstack,$safeeval);
+      unless ($sx) { $sx=$order; }
+      $Apache::functionplotresponse::splinescalex{$label}=$sx;
+
+      my $sy=&Apache::lonxml::get_param('scaley',$parstack,$safeeval);
+      unless ($sy) { $sy=2; }
+      $Apache::functionplotresponse::splinescaley{$label}=$sy;
+   } elsif ($target eq 'edit') {
+        $result=&Apache::edit::tag_start($target,$token,'Spline').
+             &Apache::edit::text_arg('Index:','index',
+                                     $token,'4').'&nbsp;'.
+             &Apache::edit::select_arg('Order:','order',
+                                  ['2','3','4','5','6','7','8','9'],$token).'&nbsp;'.
+             &Apache::edit::text_arg('Initial x-value:','initx',
+                                     $token,'4').'&nbsp;'.
+             &Apache::edit::text_arg('Initial y-value:','inity',
+                                     $token,'4').'&nbsp;'.
+             &Apache::edit::text_arg('Scale x:','scalex',
+                                     $token,'4').'&nbsp;'.
+             &Apache::edit::text_arg('Scale y:','scaley',
+                                     $token,'4').
+             &Apache::edit::end_row();
+  } elsif ($target eq 'modified') {
+    my $constructtag=&Apache::edit::get_new_args($token,$parstack,
+                                                 $safeeval,'index','order','initx','inity',
+                                                           'scalex','scaley');
+    if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
+  }
+  return $result;
 }
 
 sub end_spline {
-   return '';
+   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+   my $result='';
+   if ($target eq 'edit') {
+       $result=&Apache::edit::end_table();
+   }
+   return $result;
 }
  
 sub end_init_script {
@@ -287,6 +527,137 @@ sub end_init_script {
 ENDENDINIT
 }
 
+#
+# Storing and restoring spline coordinates from part answers
+#
+sub decode_previous_answer {
+   my ($answer)=@_;
+   foreach my $coordinate (split(/\,/,$answer)) {
+      my ($key,$value)=split(/\=/,$coordinate);
+      $Apache::functionplotresponse::previous{$key}=$value;
+   }
+}
+
+sub get_answer_from_form_fields {
+   my ($id)=@_;
+   my $answer='';
+   my %coords=();
+   foreach my $field (keys(%env)) {
+      if ($field=~/^form\.HWVAL\_$id/) {
+         $field=~/^form\.(.*)$/;
+         $coords{$1}=$env{$field};
+      }
+   }
+   $answer=join(',',map { $_.'='.$coords{$_} } (sort(keys(%coords))));
+   return ($answer,%coords);
+}
+
+#
+# The following functions calculate the cubic-hermite splines server-side
+#
+
+sub cubic_hermite {
+   my ($t,$p1,$s1,$p2,$s2)=@_;
+   return (2.*$t*$t*$t-3.*$t*$t+1.)*$p1 + 5.*($t*$t*$t-2.*$t*$t+$t)*($s1-$p1)+
+          (-2.*$t*$t*$t+3.*$t*$t)  *$p2 + 5.*($t*$t*$t-$t*$t)      *($s2-$p2);
+}
+
+#
+# d/dt(...)
+# 
+
+sub ddt_cubic_hermite {
+   my ($t,$p1,$s1,$p2,$s2)=@_;
+   return (6.*$t*$t-6.*$t) *$p1 + 5.*(3.*$t*$t-4.*$t+1.)*($s1-$p1)+
+          (-6.*$t*$t+6.*$t)*$p2 + 5.*(3.*$t*$t-2.*$t)   *($s2-$p2);
+}
+
+#
+# d^2/dt^2(...)
+#
+
+sub d2dt2_cubic_hermite {
+   my ($t,$p1,$s1,$p2,$s2)=@_;
+   return (12.*$t-6.) *$p1 + 5.*(6.*$t-4.)*($s1-$p1)+
+          (-12.*$t+6.)*$p2 + 5.*(6.*$t-2.)*($s2-$p2);
+}
+
+#
+# Array index calculation
+#
+sub array_index {
+   my ($xmin,$xmax,$x)=@_;
+   return int(($x-$xmin)/($xmax-$xmin)*400.+0.5);
+}
+
+#
+# Populate the arrays
+#
+
+sub populate_arrays {
+    my ($id,$xmin,$xmax)=@_;
+    for (my $i=0; $i<=400; $i++) {
+       $Apache::functionplotresponse::func[$i]=undef;
+       $Apache::functionplotresponse::dfuncdx[$i]=undef;
+       $Apache::functionplotresponse::d2funcd2x[$i]=undef;
+    }
+    unless ($xmax>$xmin) { return 'no_func'; }
+# Run over all splines in response
+    foreach my $label (split(/\,/,$env{"form.HWVAL_AllSplines_$id"})) {
+        my $xiold=-1;
+# Run over all points in spline
+        for (my $i=1; $i<$env{"form.HWVAL_SplineOrder_".$id."_".$label}; $i++) {
+            my $ni=$i+1;
+            my @xparms=($env{'form.HWVAL_'.$id.'_'.$label.'P'.$i.'_x'},
+                        $env{'form.HWVAL_'.$id.'_'.$label.'S'.$i.'_x'},
+                        $env{'form.HWVAL_'.$id.'_'.$label.'P'.$ni.'_x'},
+                        $env{'form.HWVAL_'.$id.'_'.$label.'S'.$ni.'_x'});
+            my @yparms=($env{'form.HWVAL_'.$id.'_'.$label.'P'.$i.'_y'},
+                        $env{'form.HWVAL_'.$id.'_'.$label.'S'.$i.'_y'},
+                        $env{'form.HWVAL_'.$id.'_'.$label.'P'.$ni.'_y'},
+                        $env{'form.HWVAL_'.$id.'_'.$label.'S'.$ni.'_y'});
+# Run in small steps over spline parameter
+            for (my $t=0; $t<=1; $t+=0.0001) {
+                my $xi=&array_index($xmin,$xmax,&cubic_hermite($t,@xparms));
+                if ($xi<$xiold) { return 'no_func'; }
+                if (($xi>$xiold) && ($xi>=0) && ($xi<=400)) {
+                   if (defined($Apache::functionplotresponse::func[$xi])) { return 'no_func'; }
+                   $xiold=$xi;
+# Function value
+                   my $funcval=&cubic_hermite($t,@yparms);
+                   $Apache::functionplotresponse::func[$xi]=$funcval;
+                   if (defined($funcval)) {
+                      if ($xi<$Apache::functionplotresponse::functionplotrulelabels{'start'}) {
+                         $Apache::functionplotresponse::functionplotrulelabels{'start'}=$xi;
+                      }
+                      if ($xi>$Apache::functionplotresponse::functionplotrulelabels{'end'}) {
+                         $Apache::functionplotresponse::functionplotrulelabels{'end'}=$xi;
+                      }
+                   }
+# Chain rule
+# dy/dx=dy/dt/(dx/dt)
+                   my $dxdt=&ddt_cubic_hermite($t,@xparms);
+                   if ($dxdt) {
+                      $Apache::functionplotresponse::dfuncdx[$xi]=&ddt_cubic_hermite($t,@yparms)/$dxdt;
+                   }
+# Faa di Bruno
+# d^2y/dx^2=(d^2y/dt^2)/(dx/dt)^2+(dy/dt)/(d^2x/dt^2)
+                   my $d2xdt2=&d2dt2_cubic_hermite($t,@xparms);
+                   if (($dxdt) && ($d2xdt2)) {
+                      $Apache::functionplotresponse::d2funcdx2[$xi]=
+                         &d2dt2_cubic_hermite($t,@yparms)/($dxdt*$dxdt)
+                        +&ddt_cubic_hermite($t,@yparms)/$d2xdt2;
+                   }
+                }
+            }
+        }
+    }
+}
+
+#
+# Implentation of <functionplotresponse>
+#
+
 sub start_functionplotresponse {
   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
   my $result='';
@@ -296,49 +667,287 @@ sub start_functionplotresponse {
   undef %Apache::functionplotresponse::splineinity;
   undef %Apache::functionplotresponse::splinescalex;
   undef %Apache::functionplotresponse::splinescaley;
+# Remember input fields, etc
+  undef %Apache::functionplotresponse::previous;
+  $Apache::functionplotresponse::inputfields='';
   $Apache::functionplotresponse::counter=0;
+# Remember rules
+  undef @Apache::functionplotresponse::functionplotrules;
+# Part and ID
+  my $partid=$Apache::inputtags::part;
+  my $id=&Apache::response::start_response($parstack,$safeeval);
 # Internal ID to mark the applet and its coordinates
-  my $internalid = $Apache::inputtags::part.'_'.&Apache::response::start_response($parstack,$safeeval);
+  my $internalid = $partid.'_'.$id;
+# Previous answer
+  &decode_previous_answer($Apache::lonhomework::history{"resource.$partid.$id.submission"});
+
 # Parameters of <functionplotresponse>
   my $xmin=&Apache::lonxml::get_param('xmin',$parstack,$safeeval);
-  $xmin=($xmin?$xmin:-10);
+  $xmin=(defined($xmin)?$xmin:-10);
   my $xmax=&Apache::lonxml::get_param('xmax',$parstack,$safeeval);
-  $xmax=($xmax?$xmax:10);
+  $xmax=(defined($xmax)?$xmax:10);
   my $ymin=&Apache::lonxml::get_param('ymin',$parstack,$safeeval);
-  $ymin=($ymin?$ymin:-10);
+  $ymin=(defined($ymin)?$ymin:-10);
   my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval);
-  $ymax=($ymax?$ymax:10);
+  $ymax=(defined($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 $xaxisvisible=(&Apache::lonxml::get_param('xaxisvisible',$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,$safeeval)=~/on|true|yes|1/i?'true':'false');
-
-  if ($target eq 'web') {
+  my $xlabel=&Apache::lonxml::get_param('xlabel',$parstack,$safeeval);
+  my $ylabel=&Apache::lonxml::get_param('ylabel',$parstack,$safeeval);
+  if ($target eq 'edit') {
+    $result.=&Apache::edit::start_table($token)
+       .'<tr><td><span class="LC_nobreak">'.&mt('Function Plot Question').'</span></td>'
+       .'<td><span class="LC_nobreak">'.&mt('Delete?').' '
+       .&Apache::edit::deletelist($target,$token)
+       .'</span></td>'
+       ."<td>&nbsp;"
+       .&Apache::edit::end_row()
+       .&Apache::edit::start_spanning_row()
+       ."\n";
+    $result.=&Apache::edit::text_arg('Label x-axis:','xlabel',
+                                     $token,'6').'&nbsp;'.
+             &Apache::edit::text_arg('Minimum x-value:','xmin',
+                                     $token,'4').'&nbsp;'.
+             &Apache::edit::text_arg('Maximum x-value:','xmax',
+                                     $token,'4').'&nbsp;'.
+             &Apache::edit::select_arg('x-axis visible:','xaxisvisible',
+                                  ['yes','no'],$token).'<br />'.
+             &Apache::edit::text_arg('Label y-axis:','ylabel',
+                                     $token,'6').'&nbsp;'.
+             &Apache::edit::text_arg('Minimum y-value:','ymin',
+                                     $token,'4').'&nbsp;'.
+             &Apache::edit::text_arg('Maximum y-value:','ymax',
+                                     $token,'4').'&nbsp;'.
+             &Apache::edit::select_arg('y-axis visible:','yaxisvisible',
+                                  ['yes','no'],$token).'<br />'.
+             &Apache::edit::select_arg('Grid visible:','gridvisible',
+                                  ['yes','no'],$token).
+             &Apache::edit::end_row().&Apache::edit::start_spanning_row();
+  } elsif ($target eq 'modified') {
+    my $constructtag=&Apache::edit::get_new_args($token,$parstack,
+                                                 $safeeval,'xlabel','xmin','xmax','ylabel','ymin','ymax',
+                                                           'xaxisvisible','yaxisvisible','gridvisible');
+    if ($constructtag) { $result = &Apache::edit::rebuild_tag($token); }
+
+  } elsif ($target eq 'meta') {
+       $result=&Apache::response::meta_package_write('functionplotresponse');
+  } elsif ($target eq 'web') {
 # paste in the update routine to receive stuff back from the applet
      $result.=&update_script($internalid);
 # start the initscript for this applet
      $result.=&start_init_script($internalid);
 # put the axis commands inside
      $result.=&axes_script($internalid,$xmin,$xmax,$ymin,$ymax,$xaxisvisible,$yaxisvisible,$gridvisible);
+     $result.=&axes_label($internalid,$xlabel,$ylabel);
 # init script is left open
   }
   return $result;
 }
 
+sub compare_rel {
+   my ($relationship,$value,$realval,$tol)=@_;
+# is the real value defined?
+   unless (defined($realval)) {
+      if ($relationship eq 'eq') {
+         if ($value eq 'undef') {
+            return 1;
+         } else {
+            return 0;
+         }
+      } elsif ($relationship eq 'ne') {
+         if ($value eq 'undef') {
+            return 0;
+         } else {
+            return 1;
+         }
+      } else {
+         return 0;
+      }
+   }
+
+# it is defined.
+   if ($relationship eq 'gt') {
+      return ($realval>$value);
+   } elsif ($relationship eq 'ge') {
+      return ($realval>$value-$tol);
+   } elsif ($relationship eq 'lt') {
+      return ($realval<$value);
+   } elsif ($relationship eq 'le') {
+      return ($realval<$value+$tol);
+   } elsif ($relationship eq 'ne') {
+      return (abs($value-$realval)>$tol);
+   } else {
+      return (abs($value-$realval)<$tol);
+   }
+   return 0;
+}
+
+sub functionplotrulecheck {
+   my ($rule,$xmin,$xmax,$ymin,$ymax)=@_;
+
+#   &Apache::lonnet::logthis("Rule $rule $xmin $xmax $ymin $ymax");
+
+   my ($label,$derivative,$xinitial,$xinitiallabel,$xfinal,$xfinallabel,$relationship,$value,$percent)
+      =split(/\:/,$rule);
+   $percent=($percent>0?$percent:5);
+
+   my $li=0;
+   my $lh=400;
+
+# Special case: the upper boundary was not defined
+# and needs to be set to the value where
+# the condition is not true anymore => set flag
+
+   my $findupper=0;
+   if (($xfinal eq '')
+    && (!defined($Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}))
+    && ($xfinallabel)) {
+       $findupper=1;
+   }
+
+# if a hard value is set for the boundaries, it overrides the label
+   if (($xinitial ne '') && ($xinitiallabel ne '') && ($xinitiallabel ne 'start')) {
+      $li=&array_index($xmin,$xmax,$xinitial);
+      $Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel}=$li;
+   }
+   if (($xfinal ne '') && ($xfinallabel ne '') && ($xfinallabel ne 'end')) {
+      $lh=&array_index($xmin,$xmax,$xfinal);
+      $Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}=$lh;
+   }
+# if the label is defined, use it
+   if (defined($Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel})) {
+      $li=$Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel};
+   } else {
+      $li=&array_index($xmin,$xmax,$xinitial);
+   }
+   unless ($findupper) {
+      if (defined($Apache::functionplotresponse::functionplotrulelabels{$xfinallabel})) {
+         $lh=$Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}-1;
+      } else {
+         $lh=&array_index($xmin,$xmax,$xfinal);
+      }
+   }
+# Basic sanity checks
+   if ($li<0) { $li=0; }
+   if ($lh>400) { $lh=400; }
+   if ($li>$lh) {
+       $lh=$li;
+   }
+
+#   &Apache::lonnet::logthis("Init $xinitial=$li Final $xfinal=$lh Findupper: $findupper");
+   my $tol=$percent*($ymax-$ymin)/100;
+   if ($xmax>$xmin) {
+      if ($derivative==2) {
+         $tol=4.*$tol/($xmax-$xmin);
+      } elsif ($derivative==1) {
+         $tol=2.*$tol/($xmax-$xmin);
+      }
+   }
+   for (my $i=$li; $i<=$lh; $i++) {
+        my $val;
+        if ($derivative==2) {
+           $val=$Apache::functionplotresponse::d2funcdx2[$i];
+        } elsif ($derivative==1) {
+           $val=$Apache::functionplotresponse::dfuncdx[$i];
+        } else {
+           $val=$Apache::functionplotresponse::func[$i];
+        }
+        unless (&compare_rel($relationship,$value,$val,$tol)) { 
+#           &Apache::lonnet::logthis("Condition false $findupper at $i with $val tol:$tol from $value");
+           if (($findupper) && ($i>$li)) {
+              $Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}=$i;
+#              &Apache::lonnet::logthis("Setting $xfinallabel to $i");
+              return 1;
+           } else {
+              return 0; 
+           }
+        }
+   }
+   return 1;
+}
+
 sub end_functionplotresponse {
   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
   &Apache::response::end_response;
 
   my $result;
-  my $internalid = $Apache::inputtags::part.'_'.$Apache::inputtags::response[-1];
+  my $id=$Apache::inputtags::response[-1];
+  my $partid=$Apache::inputtags::part;
+  my $internalid = $partid.'_'.$id;
+
+    if ($target eq 'edit') { $result=&Apache::edit::end_table(); }
+    if ($target eq 'grade'
+         && &Apache::response::submitted()
+         && $Apache::lonhomework::type eq 'exam') {
+
+        &Apache::response::scored_response($partid,$id);
+
+    } elsif ($target eq 'grade'
+         && &Apache::response::submitted()
+         && $Apache::lonhomework::type ne 'exam') {
+        my ($response,%coords)=&get_answer_from_form_fields($internalid);
+        $Apache::lonhomework::results{"resource.$partid.$id.submission"}=$response;
+        my %previous=&Apache::response::check_for_previous($response,$partid,$id);
+#
+# Actually grade
+#
+        my $xmin=&Apache::lonxml::get_param('xmin',$parstack,$safeeval);
+        $xmin=(defined($xmin)?$xmin:-10);
+        my $xmax=&Apache::lonxml::get_param('xmax',$parstack,$safeeval);
+        $xmax=(defined($xmax)?$xmax:10);
+        my $ymin=&Apache::lonxml::get_param('ymin',$parstack,$safeeval);
+        $ymin=(defined($ymin)?$ymin:-10);
+        my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval);
+        $ymax=(defined($ymax)?$ymax:10);
+
+        my $ad='';
+        undef  %Apache::functionplotresponse::functionplotrulelabels;
+        $Apache::functionplotresponse::functionplotrulelabels{'start'}=400;
+        $Apache::functionplotresponse::functionplotrulelabels{'end'}=0;
+        if (&populate_arrays($internalid,$xmin,$xmax) eq 'no_func') {
+           $ad='NOT_FUNCTION';
+        } else {
+# We have a function that we can actually grade, go through the spline rules.
+           foreach my $rule (@Apache::functionplotresponse::functionplotrules) {
+              unless (&functionplotrulecheck($rule,$xmin,$xmax,$ymin,$ymax)) {
+                 $ad='INCORRECT';
+                 last;
+              }
+           }
+# If it's not wrong, it's correct 
+           unless ($ad) { $ad='EXACT_ANS' };
+        }
 
-#  if ($target eq 'edit') { $result=&Apache::edit::end_table(); }
-  if ($target eq 'web') {
+#
+# Store grading info
+#
+        $Apache::lonhomework::results{"resource.$partid.$id.awarddetail"}=$ad;
+        &Apache::response::handle_previous(\%previous,$ad);
+   } elsif ($target eq 'web') {
 # Now is the time to render all of the stored splines
      foreach my $label (keys(%Apache::functionplotresponse::splineorder)) {
         $result.=&generate_spline($internalid,$label);
      }
 # close the init script
      $result.=&end_init_script();
+# register all splines in this response 
+     $result.='<input type="hidden" name="HWVAL_AllSplines_'.$internalid.'" value="'.
+                 join(',',keys(%Apache::functionplotresponse::splineorder)).'" />'."\n";
+     foreach my $label (keys(%Apache::functionplotresponse::splineorder)) {
+        $result.='<input type="hidden" name="HWVAL_SplineOrder_'.$internalid.'_'.$label.'" value="'.
+                 $Apache::functionplotresponse::splineorder{$label}.'" />'."\n";
+     }
+# generate the input fields
+     $result.=$Apache::functionplotresponse::inputfields;
 # actually start the <applet>-tag
      $result.=&geogebra_startcode($internalid);
 # load the spline bytecode