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Diff for /loncom/homework/functionplotresponse.pm between versions 1.12 and 1.102

-version 1.12, 2010/10/09 22:31:49
+version 1.102, 2013/07/12 21:19:17
  Line 1
  # LearningOnline Network with CAPA
- # option list style responses
+ # Functionplot responses
  #
  # $Id$
  #
  Line 31  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','splinerule'));
+   &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"
+ <applet name="ggbApplet$appid" code="geogebra.GeoGebraApplet" archive="geogebra.jar"
-          codebase="/adm/geogebra/"  width="714" height="447" MAYSCRIPT>
+          codebase="/adm/geogebra/"  width="$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="$code"></article>
+ ENDSTARTCODE
+ }
  #
  # This is the internal GeoGebra bytecode which defines the spline functions
  #
- sub geogebra_spline_program {
+ sub geogebra_internal_program {
-     return (<<ENDSPLINEPROGRAM);
+     return
- <param name="ggbBase64" value="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"/>
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- ENDSPLINEPROGRAM
  }
  #
  # The standard set of parameters inside <applet>
  #
- sub geogebra_default_parameters {
+ sub java_geogebra_default_parameters {
     my ($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" />
+ 	<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_archive" value="geogebra.jar, geogebra_main.jar, geogebra_gui.jar, geogebra_cas.jar, geogebra_export.jar, geogebra_properties.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="cache_version" value="3.2.44.0, 3.2.44.0, 3.2.44.0, 3.2.44.0, 3.2.44.0, 3.2.44.0" />
          <param name="framePossible" value="false" />
          <param name="showResetIcon" value="false" />
- Line 89  sub geogebra_default_parameters {
+ Line 173  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
  }
- Line 101  ENDDEFAULTPARAMETERS
+ Line 185  ENDDEFAULTPARAMETERS
  #
  sub init_script {
-    if ($Apache::functionplotresponse::callscripts) {
+    if ($#Apache::functionplotresponse::callscripts>=0) {
+       my $script='';
+       foreach my $id (@Apache::functionplotresponse::callscripts) {
+           $script.="if (param=='ggbApplet".&appid($id)."') { loaded_$id=true; }\n";
+       }
+       $script.="if (".join(' && ',map { "loaded_$_" } (@Apache::functionplotresponse::callscripts)).
+                ") { 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
+ // 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() {
+ $calls
  }
  // ]]>
  </script>
- Line 120  ENDGGBINIT
+ Line 223  ENDGGBINIT
  #
  sub update_script {
      my ($id)=@_;
+     my $appid=&appid($id);
      return (<<ENDUPDATESCRIPT);
  <script type="text/javascript">
  // <![CDATA[
  function updatePointCoordinates_$id(coordinateName) {
-             var x = document.ggbApplet_$id.getXcoord(coordinateName);
+             var x = document.ggbApplet$appid.getXcoord(coordinateName);
-             var y = document.ggbApplet_$id.getYcoord(coordinateName);
+             var y = document.ggbApplet$appid.getYcoord(coordinateName);
              document.lonhomework.elements["HWVAL_$id\_" + coordinateName + "_x"].value = x;
              document.lonhomework.elements["HWVAL_$id\_" + coordinateName + "_y"].value = y;
          }
- Line 140  ENDUPDATESCRIPT
+ Line 244  ENDUPDATESCRIPT
  sub update_register {
     my ($id,$variable)=@_;
-    return "document.ggbApplet_$id.registerObjectUpdateListener('$variable','updatePointCoordinates_$id');\n";
+    my $appid=&appid($id);
+    return "document.ggbApplet$appid.registerObjectUpdateListener('$variable','updatePointCoordinates_$id');\n";
  }
  #
- # Set a coordinate variable
+ # Set a point coordinate variable
  #
- sub set_coordinate {
+ sub set_point_coordinate {
-    my ($id,$variable,$x,$y)=@_;
+    my ($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
  #
- Line 174  sub generate_input_field {
+ Line 317  sub generate_input_field {
  }
  #
- # Initialize a new coordinate variable at set a listener on it
+ # Initialize a new point coordinate variable at set a listener on it
  #
- sub new_coordinate {
+ sub new_point_coordinate {
-     my ($id,$variable,$x,$y)=@_;
+     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')};
      }
- Line 185  sub new_coordinate {
+ Line 328  sub new_coordinate {
         $y=$Apache::functionplotresponse::previous{&field_name($id,$variable,'y')};
      }
      &generate_input_field($id,$variable,$x,$y);
-     return &set_coordinate($id,$variable,$x,$y).&update_register($id,$variable);
+     return &set_point_coordinate($id,$variable,$x,$y,$fixed).&update_register($id,$variable);
+ }
+ #
+ # Initialize a new slope coordinate variable at set a listener on it
+ #
+ sub new_slope_coordinate {
+     my ($id,$variable,$x,$y,$pointname,$xp,$yp,$xmin,$xmax,$ymin,$ymax,$fixed)=@_;
+ #
+ # $variable: name of the slope point
+ # $x, $y: coordinates of the slope point
+ # $pointname: name of the associated point point
+ # $xp $yp: coordinates of the point point
+ #
+     if (defined($Apache::functionplotresponse::previous{&field_name($id,$variable,'x')})) {
+        $x=$Apache::functionplotresponse::previous{&field_name($id,$variable,'x')};
+     }
+     if (defined($Apache::functionplotresponse::previous{&field_name($id,$variable,'y')})) {
+        $y=$Apache::functionplotresponse::previous{&field_name($id,$variable,'y')};
+     }
+     if (defined($Apache::functionplotresponse::previous{&field_name($id,$pointname,'x')})) {
+        $xp=$Apache::functionplotresponse::previous{&field_name($id,$pointname,'x')};
+     }
+     if (defined($Apache::functionplotresponse::previous{&field_name($id,$pointname,'y')})) {
+        $yp=$Apache::functionplotresponse::previous{&field_name($id,$pointname,'y')};
+     }
+     &generate_input_field($id,$variable,$x,$y);
+     my $xrel=$x-$xp;
+     my $yrel=$y-$yp;
+     return &set_slope_coordinate($id,$variable,$xrel,$yrel,$xmin,$xmax,$ymin,$ymax,$pointname,$fixed).&update_register($id,$variable);
  }
  #
- Line 194  sub new_coordinate {
+ Line 367  sub new_coordinate {
  #
  sub start_init_script {
      my ($id)=@_;
- # Add a line to ggbOnInit-function which calls the right function based on parameter passed from GeoGebra
+ # Add id to the list of ggbInit_$id functions that need to be called
-     $Apache::functionplotresponse::callscripts.="if (param=='applet_$id') { ggbInit_$id(); }\n";
+     push(@Apache::functionplotresponse::callscripts,$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_$id() {
  ENDSTARTINIT
- Line 213  ENDSTARTINIT
+ Line 388  ENDSTARTINIT
  sub axes_script {
      my ($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 ($id,$xmin,$xmax,$ymin,$ymax,$xlabel,$ylabel)=@_;
+     my $appid=&appid($id);
+     unless ($xlabel || $ylabel) { return ''; }
+     my $return='document.ggbApplet'.$appid.'.evalCommand("topRight=Corner[3]");';
+     if ($xlabel) {
+       if (($ymin<0) && ($ymax>0)) {
+        $return.=(<<ENDXAXISLABELSCRIPT);
+ document.ggbApplet$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)) {
+        $return.=(<<ENDYAXISLABELSCRIPT);
+ document.ggbApplet$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 ($fixed) {
- # Use stupid trick to nail this to a location
+       return "document.ggbApplet$appid.evalCommand('$label=Function[$function,$xmin,$xmax]');\n".
-       return (<<ENDPLOTSCRIPT);
+              ($visible?'':"document.ggbApplet$appid.setLabelVisible('$label', false);\n").
-             document.ggbApplet_$id.evalCommand("a=1");
+              ($color?"document.ggbApplet$appid.setColor('$label',$rc,$gc,$bc);\n":'').
-             document.ggbApplet_$id.setVisible("a",false);
+              ($thickness?"document.ggbApplet$appid.setLineThickness('$label',$thickness);\n":'');
-             // This MUST be a DEPENDENT OBJECT in order to be locked down:
-             document.ggbApplet_$id.evalCommand("y=a*($function)");
- ENDPLOTSCRIPT
     } else {
-        return "document.ggbApplet_$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 $output;
  }
  #
- Line 244  ENDPLOTSCRIPT
+ Line 557  ENDPLOTSCRIPT
  #
  sub generate_spline {
-    my ($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};
- Line 253  sub generate_spline {
+ Line 567  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" />
  #
- Line 271  sub start_backgroundplot {
+ Line 785  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; }
-    return $result;
+       unless (defined($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',
+                                      $token,'8', 'colorchooser').
+              &Apache::edit::select_arg('Fixed location:','fixed',
+                                   ['yes','no'],$token).
+              &Apache::edit::end_row();
+   } elsif ($target eq 'modified') {
+     my $constructtag=&Apache::edit::get_new_args($token,$parstack,
+                                                  $safeeval,'function','label','xinitial','xfinal','color','fixed');
+     if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
+   }
+   return $result;
  }
  sub end_backgroundplot {
-    return '';
+    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+    my $result='';
+    if ($target eq 'edit') {
+        $result=&Apache::edit::end_table();
+    }
+    return $result;
  }
  #
- # <splinerule ... />
+ # <functionplotrule ... />
  #
- sub start_splinerule {
+ sub start_functionplotrule {
     my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
     my $result='';
-    my $internalid = $Apache::inputtags::part.'_'.$Apache::inputtags::response[-1];
+    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 $beginninglabel=&Apache::lonxml::get_param('xinitiallabel',$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 $derivative=&Apache::lonxml::get_param('derivativeorder',$parstack,$safeeval);
+       unless (($derivative==-1) || ($derivative==0) || ($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),
+            $endinglabel,
+            &Apache::lonxml::get_param('minimumlength',$parstack,$safeeval),
+            &Apache::lonxml::get_param('maximumlength',$parstack,$safeeval),
+            $relationship,
+            &Apache::lonxml::get_param('value',$parstack,$safeeval),
+            &Apache::lonxml::get_param('percenterror',$parstack,$safeeval)
+           )));
+    } elsif ($target eq 'edit') {
+         $result=&Apache::edit::tag_start($target,$token,'Function Plot Graph Rule').
+              &Apache::edit::text_arg('Index/Name:','index',
+                                      $token,'10').'&nbsp;'.
+              &Apache::edit::select_arg(&mt('Function:'),'derivativeorder',
+                                   [['0','Function itself'],
+                                    ['1','First derivative'],
+                                    ['2','Second derivative'],
+                                    ['-1','Integral']],$token).'<br />'.
+              &Apache::edit::text_arg('Initial x-value:','xinitial',
+                                       $token,'8').
+              &Apache::edit::select_or_text_arg('Initial x-value label:','xinitiallabel',
+                                                [['start','Start of Plot'],
+                                                 ['end','End of Plot']],$token,'8').'<br />'.
+              &Apache::edit::text_arg('Final x-value (optional):','xfinal',
+                                       $token,'8').
+              &Apache::edit::select_or_text_arg('Final x-value label (optional):','xfinallabel',
+                                                [['end','End of Plot']],$token,'8').'<br />'.
+              &Apache::edit::text_arg('Minimum length for range (optional):','minimumlength',
+                                      $token,'8').
+              &Apache::edit::text_arg('Maximum length for range (optional):','maximumlength',
+                                      $token,'8').'<br />'.
+              &Apache::edit::select_or_text_arg(&mt('Relationship:'),'relationship',
+                                   [['eq','equal'],
+                                    ['ne','not equal'],
+                                    ['ge','greater than or equal'],
+                                    ['gt','greater than'],
+                                    ['lt','less than'],
+                                    ['le','less than or equal']],$token).
+              $result.= &Apache::edit::select_or_text_arg('Value:','value',
+                                                [['undef','not defined']],$token,'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,
+                                                  $safeeval,'index','derivativeorder',
+                                                            'xinitial','xinitiallabel','xfinal','xfinallabel',
+                                                            'minimumlength','maximumlength',
+                                                            'relationship','value','percenterror');
+     if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
+    }
     return $result;
  }
- sub end_splinerule {
+ sub end_functionplotrule {
-    return '';
+    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+    my $result='';
+    if ($target eq 'edit') {
+        $result=&Apache::edit::end_table();
+    }
+    return $result;
  }
  #
- # <spline label="..." order="1,2,3,4" initx="..." inity="..." scalex="..." scaley="..." />
+ # <functionplotvectorrule ... />
  #
- # Unfortunately, GeoGebra seems to want all splines after everything else, so we need to store them
+ sub start_functionplotvectorrule {
+    my ($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 $result;
+ }
  #
- sub start_spline {
+ # <functionplotvectorsumrule ... />
+ #
+ sub start_functionplotvectorsumrule {
     my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
-    my $label=&Apache::lonxml::get_param('label',$parstack,$safeeval);
+    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) { $label='S'.$Apache::functionplotresponse::counter; }
+    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;
+ }
-    my $order=&Apache::lonxml::get_param('order',$parstack,$safeeval);
+ sub end_functionplotvectorsumrule {
-    if ($order<2) { $order=2; }
+    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
-    if ($order>8) { $order=8; }
+    my $result='';
-    $Apache::functionplotresponse::splineorder{$label}=$order;
+    if ($target eq 'edit') {
+        $result=&Apache::edit::end_table();
+    }
+    return $result;
+ }
-    my $x=&Apache::lonxml::get_param('initx',$parstack,$safeeval);
+ #
-    unless ($x) { $x=0; }
+ # <functionplotcustom ... />
-    $Apache::functionplotresponse::splineinitx{$label}=$x;
+ #
+ sub start_functionplotcustomrule {
-    my $y=&Apache::lonxml::get_param('inity',$parstack,$safeeval);
+    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
-    unless ($y) { $y=0; }
+    my $result='';
-    $Apache::functionplotresponse::splineinity{$label}=$y;
+    my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval);
+    $Apache::functionplotresponse::counter++;
-    my $sx=&Apache::lonxml::get_param('scalex',$parstack,$safeeval);
+    if ($label=~/\W/) {
-    unless ($sx) { $sx=$order; }
+       &Apache::lonxml::warning(&mt('Rule indices should only contain alphanumeric characters.'));
-    $Apache::functionplotresponse::splinescalex{$label}=$sx;
+    }
+    $label=~s/\W//gs;
-    my $sy=&Apache::lonxml::get_param('scaley',$parstack,$safeeval);
+    unless ($label) {
-    unless ($sy) { $sy=2; }
+       $label='R'.$Apache::functionplotresponse::counter;
-    $Apache::functionplotresponse::splinescaley{$label}=$sy;
+    } else {
-    return '';
+       $label='R'.$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 $result;
+ }
+ #
+ # <spline index="..." order="1,2,3,4" initx="..." inity="..." scalex="..." scaley="..." />
+ #
+ # Unfortunately, GeoGebra seems to want all splines after everything else, so we need to store them
+ #
+ sub start_spline {
+    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+    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',
+                                      $token,'4').'&nbsp;'.
+              &Apache::edit::select_arg('Order:','order',
+                                   ['2','3','4','5','6','7','8'],$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 $result;
  }
  sub end_init_script {
- Line 371  sub get_answer_from_form_fields {
+ Line 1274  sub get_answer_from_form_fields {
     return ($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.)*$p1 + 3.*($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);
+ }
+ #
+ # d/dt(...)
+ #
+ sub ddt_cubic_hermite {
+    my ($t,$p1,$s1,$p2,$s2)=@_;
+    return (6.*$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-$p2);
+ }
+ #
+ # d^2/dt^2(...)
+ #
+ sub d2dt2_cubic_hermite {
+    my ($t,$p1,$s1,$p2,$s2)=@_;
+    return (12.*$t-6.) *$p1 + 3.*(6.*$t-4.)*($s1-$p1)+
+           (-12.*$t+6.)*$p2 + 3.*(6.*$t-2.)*($s2-$p2);
+ }
+ #
+ # Array index calculation
+ #
+ sub array_index {
+    my ($xmin,$xmax,$x)=@_;
+    if ($x ne '') {
+       return int(($x-$xmin)/($xmax-$xmin)*400.+0.5);
+    } else {
+       return undef;
+    }
+ }
+ #
+ # Populate the arrays
+ #
+ sub populate_arrays {
+     my ($id,$xmin,$xmax,$ymin,$ymax)=@_;
+     for (my $i=0; $i<=400; $i++) {
+        $Apache::functionplotresponse::actualxval[$i]=undef;
+        $Apache::functionplotresponse::func[$i]=undef;
+        $Apache::functionplotresponse::dfuncdx[$i]=undef;
+        $Apache::functionplotresponse::d2funcd2x[$i]=undef;
+     }
+     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 $xreal=&cubic_hermite($t,@xparms);
+                 my $xi=&array_index($xmin,$xmax,$xreal);
+                 if ($xi<$xiold) { return 'no_func'; }
+                 if (($xi>$xiold) && ($xi>=0) && ($xi<=400)) {
+                    $xiold=$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;
+                       }
+                       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;
+ # Second derivative
+                       $Apache::functionplotresponse::d2funcdx2[$xi]=
+                          ($dxdt*&d2dt2_cubic_hermite($t,@yparms)-&ddt_cubic_hermite($t,@yparms)*&d2dt2_cubic_hermite($t,@xparms))/
+                          ($dxdt*$dxdt*$dxdt);
+                    }
+                 }
+             }
+         }
+     }
+ }
+ #
+ # Implementation of <functionplotresponse>
+ #
  sub start_functionplotresponse {
    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
    my $result='';
- Line 384  sub start_functionplotresponse {
+ Line 1403  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;
+   }
+ # Delete previous awards
+   undef $Apache::functionplotresponse::awarddetail;
  # Part and ID
    my $partid=$Apache::inputtags::part;
    my $id=&Apache::response::start_response($parstack,$safeeval);
- Line 393  sub start_functionplotresponse {
+ Line 1423  sub start_functionplotresponse {
    &decode_previous_answer($Apache::lonhomework::history{"resource.$partid.$id.submission"});
  # Parameters of <functionplotresponse>
-   my $xmin=&Apache::lonxml::get_param('xmin',$parstack,$safeeval);
+   my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval);
-   $xmin=($xmin?$xmin:-10);
-   my $xmax=&Apache::lonxml::get_param('xmax',$parstack,$safeeval);
-   $xmax=($xmax?$xmax:10);
-   my $ymin=&Apache::lonxml::get_param('ymin',$parstack,$safeeval);
-   $ymin=($ymin?$ymin:-10);
-   my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval);
-   $ymax=($ymax?$ymax:10);
    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');
+   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)
+        .&Apache::edit::deletelist($target,$token).'&nbsp;&nbsp;&nbsp;'
+        .&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('Minimum x-value:','xmin',
+     $result.=&Apache::edit::text_arg('Width (pixels):','width',
-                                      $token,'4').
+                                      $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;'.
               &Apache::edit::text_arg('Maximum x-value:','xmax',
-                                      $token,'4').
+                                      $token,'4').'&nbsp;'.
               &Apache::edit::select_arg('x-axis visible:','xaxisvisible',
-                                   ['yes','no'],$token).
+                                   ['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').
+                                      $token,'4').'&nbsp;'.
               &Apache::edit::text_arg('Maximum y-value:','ymax',
-                                      $token,'4').
+                                      $token,'4').'&nbsp;'.
               &Apache::edit::select_arg('y-axis visible:','yaxisvisible',
-                                   ['yes','no'],$token).
+                                   ['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,'xmin','xmax','ymin','ymax',
+                                                  $safeeval,'width','height','xlabel','xmin','xmax','ylabel','ymin','ymax',
-                                                            'xaxisvisible','yaxisvisible','gridvisible');
+                                                            'xaxisvisible','yaxisvisible','gridvisible','answerdisplay');
      if ($constructtag) { $result = &Apache::edit::rebuild_tag($token); }
    } elsif ($target eq 'meta') {
         $result=&Apache::response::meta_package_write('functionplotresponse');
-   } elsif ($target eq 'web') {
+   } elsif (($target eq 'answer') &&
- # paste in the update routine to receive stuff back from the applet
+             ($env{'form.answer_output_mode'} ne 'tex') &&
-      $result.=&update_script($internalid);
+             ($Apache::lonhomework::viewgrades == 'F')) {
- # start the initscript for this applet
+       my (undef,undef,$udom,$uname)=&Apache::lonnet::whichuser();
-      $result.=&start_init_script($internalid);
+       $uname =~s/\W//g;
- # put the axis commands inside
+       $udom  =~s/\W//g;
-      $result.=&axes_script($internalid,$xmin,$xmax,$ymin,$ymax,$xaxisvisible,$yaxisvisible,$gridvisible);
+       my $function_name =
- # init script is left open
+                 join('_','LONCAPA_scriptvars',$uname,$udom,
+                      $env{'form.counter'},$Apache::lonxml::curdepth);
+       &Apache::lonxml::add_script_result(
+           &Apache::loncommon::modal_adhoc_window($function_name,700,500,
+              '<pre style="background-color:#ffffff;">'.$Apache::functionplotresponse::ruleslog.'</pre>',
+               &mt('Rules Log'))."<br />");
    }
    return $result;
  }
+ sub compare_rel {
+    my ($relationship,$value,$realval,$tol)=@_;
+ # is the real value undefined?
+    unless (defined($realval)) {
+ # the real value is not defined
+       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;
+       }
+    }
+ # is the expected value undefined?
+    if ($value eq 'undef') {
+ # but by now we know that the real value is defined
+       return 0;
+    }
+ # both are defined.
+    if ($relationship eq 'gt') {
+       return ($realval>$value);
+    } elsif ($relationship eq 'ge') {
+       return ($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 addlog {
+    my ($text)=@_;
+    $text=~s/\'/\\\'/g;
+    $Apache::functionplotresponse::ruleslog.=$text.'<br />';
+ }
+ 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,$safeeval)=@_;
+    my ($label,$derivative,$xinitial,$xinitiallabel,$xfinal,$xfinallabel,$minimumlength,$maximumlength,$relationship,$value,$percent)
+       =split(/\:/,$rule);
+    $percent=($percent>0?$percent:5);
+    &addlog("=================");
+    &addlog("Rule $label for ".($derivative<0?'integral':('function itself','first derivative','second derivative')[$derivative])." $relationship $value");
+ #
+ # Evaluate the value
+ #
+    if (($value=~/\D/) && ($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;
+ # 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})) {
+       &addlog("Using lower label $xinitiallabel");
+       $li=$Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel};
+    } else {
+       $li=&array_index($xmin,$xmax,$xinitial);
+    }
+    unless ($findupper) {
+       if (defined($Apache::functionplotresponse::functionplotrulelabels{$xfinallabel})) {
+          &addlog("Using upper label $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>$lh) || (!defined($lh))) {
+        $lh=$li;
+    }
+    &addlog("Boundaries: x=".&actualval($li,$xmin,$xmax)." (".$Apache::functionplotresponse::actualxval[$li]."; index $li)) to x=".
+                             &actualval($lh,$xmin,$xmax)." (".$Apache::functionplotresponse::actualxval[$lh]."; index $lh))");
+    if ($findupper) {
+       &addlog("Looking for label $xfinallabel");
+    }
+    my $tol=$percent*($ymax-$ymin)/100;
+    if ($xmax>$xmin) {
+       if ($derivative==2) {
+          $tol=4.*$tol/($xmax-$xmin);
+       } elsif ($derivative==1) {
+          $tol=2.*$tol/($xmax-$xmin);
+       } elsif ($derivative==-1) {
+          $tol=$tol*($xmax-$xmin)/2.;
+       }
+    }
+    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[$i];
+         }
+         unless (&compare_rel($relationship,$value,$val,$tol)) {
+            &addlog("Actual value ".(defined($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 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 $label failed.");
+               &setfailed($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 ($target eq 'edit') {
+       return &Apache::edit::start_table($token).
+         '<tr><td><span class="LC_nobreak">'.&mt('Function Plot Rule Set').'</span></td>'
+        .'<td><span class="LC_nobreak">'.&mt('Delete?').' '
+        .&Apache::edit::deletelist($target,$token).'&nbsp;&nbsp;&nbsp;'.
+         &Apache::edit::insertlist($target,$token).'&nbsp;&nbsp;&nbsp;'
+        .&Apache::loncommon::help_open_topic('Function_Plot_Response_Rule_Set','Function Plot Rules')
+        .'</span></td>'
+        ."<td>&nbsp;"
+        .&Apache::edit::end_row()
+        .&Apache::edit::start_spanning_row()
+        ."\n";
+    }
+ }
+ sub end_functionplotruleset {
+     my ($target,$token,$tagstack,$parstack,$parser,$safeeval)=@_;
+     my $id=$Apache::inputtags::response[-1];
+     my $partid=$Apache::inputtags::part;
+     my $internalid = $partid.'_'.$id;
+     if ($target eq 'edit' ) {
+         return &Apache::edit::end_table();
+     }  elsif ($target eq 'grade'
+          && &Apache::response::submitted()
+          && $Apache::lonhomework::type ne 'exam') {
+ #
+ # Actually grade
+ #
+     my ($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,$ymin,$ymax) eq 'no_func') {
+            $ad='NOT_FUNCTION';
+         } else {
+            &addlog("Start of function ".&actualval($Apache::functionplotresponse::functionplotrulelabels{'start'},$xmin,$xmax)." (index ".
+                                         $Apache::functionplotresponse::functionplotrulelabels{'start'}.")");
+            &addlog("End of function ".&actualval($Apache::functionplotresponse::functionplotrulelabels{'end'},$xmin,$xmax)." (index ".
+                                         $Apache::functionplotresponse::functionplotrulelabels{'end'}.")");
+ # We have a function that we can actually grade, go through the spline rules.
+            foreach my $rule (@Apache::functionplotresponse::functionplotrules) {
+               unless (&functionplotrulecheck($rule,$xmin,$xmax,$ymin,$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)) {
+                  $ad='INCORRECT';
+                  last;
+               }
+            }
+ # If it's not wrong, it's correct
+            unless ($ad) { $ad='EXACT_ANS' };
+         }
+         &addlog("Set hint conditions: ".join(",",@Apache::functionplotresponse::failedrules));
+         &addlog("Assigned award detail: $ad");
+ # Store for later to be assigned at end_functionplotresponse
+         $Apache::functionplotresponse::awarddetail=$ad;
+      }
+ }
  sub end_functionplotresponse {
    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
    &Apache::response::end_response;
- Line 463  sub end_functionplotresponse {
+ Line 2099  sub end_functionplotresponse {
           && &Apache::response::submitted()
           && $Apache::lonhomework::type eq 'exam') {
-         #&Apache::response::scored_response($partid,$id);
+         &Apache::response::scored_response($partid,$id);
      } elsif ($target eq 'grade'
           && &Apache::response::submitted()
- Line 472  sub end_functionplotresponse {
+ Line 2108  sub end_functionplotresponse {
          $Apache::lonhomework::results{"resource.$partid.$id.submission"}=$response;
          my %previous=&Apache::response::check_for_previous($response,$partid,$id);
  #
- # Actually grade
+ # Assign grade
  #
-         my $ad='INCORRECT';
+         my $ad=$Apache::functionplotresponse::awarddetail;
  #
  # Store grading info
  #
          $Apache::lonhomework::results{"resource.$partid.$id.awarddetail"}=$ad;
          &Apache::response::handle_previous(\%previous,$ad);
     } elsif ($target eq 'web') {
+         undef @Apache::functionplotresponse::failedrules;
+    }
+    return $result;
+ }
+ sub end_functionplotelements {
+   my ($target,$token,$tagstack,$parstack,$parser,$safeeval)=@_;
+   my $result='';
+   my $id=$Apache::inputtags::response[-1];
+   my $partid=$Apache::inputtags::part;
+   my $internalid = $partid.'_'.$id;
+   if ($target eq 'edit' ) {
+      $result=&Apache::edit::end_table();
+   } elsif ($target eq 'web') {
+      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();
+ # 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);
+      $result.=&geogebra_startcode($internalid,
- # load the spline bytecode
+                                   &Apache::lonxml::get_param('width',$parstack,$safeeval,-2),
-      $result.=&geogebra_spline_program();
+                                   &Apache::lonxml::get_param('height',$parstack,$safeeval,-2));
  # set default parameters
       $result.=&geogebra_default_parameters($internalid);
  # close the <applet>-tag
- Line 500  sub end_functionplotresponse {
+ Line 2182  sub end_functionplotresponse {
    }
    return $result;
  }
+ sub boundaries {
+    my ($parstack,$safeeval,$level)=@_;
+    my $xmin=&Apache::lonxml::get_param('xmin',$parstack,$safeeval,$level);
+    $xmin=(defined($xmin)?$xmin:-10);
+    my $xmax=&Apache::lonxml::get_param('xmax',$parstack,$safeeval,$level);
+    $xmax=(defined($xmax)?$xmax:10);
+    my $ymin=&Apache::lonxml::get_param('ymin',$parstack,$safeeval,$level);
+    $ymin=(defined($ymin)?$ymin:-10);
+    my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval,$level);
+    $ymax=(defined($ymax)?$ymax:10);
+    if ($xmax<=$xmin) {
+       $xmax=$xmin+20;
+    }
+    if ($ymax<=$ymin) {
+       $ymax=$ymin+20;
+    }
+    return ($xmin,$xmax,$ymin,$ymax);
+ }
+ sub start_functionplotelements {
+    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
+    my $result='';
+    my $id=$Apache::inputtags::response[-1];
+    my $partid=$Apache::inputtags::part;
+    my $internalid = $partid.'_'.$id;
+    if ($target eq 'edit') {
+       return &Apache::edit::start_table($token).
+         '<tr><td><span class="LC_nobreak">'.&mt('Function Plot Elements').'</span></td>'
+        .'<td><span class="LC_nobreak">'.&mt('Delete?').' '
+        .&Apache::edit::deletelist($target,$token).'&nbsp;&nbsp;&nbsp;'.
+         &Apache::edit::insertlist($target,$token).'&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,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-2);
+       my $xaxisvisible=(&Apache::lonxml::get_param('xaxisvisible',$parstack,$safeeval,-2)=~/on|true|yes|1/i?'true':'false');
+       my $yaxisvisible=(&Apache::lonxml::get_param('yaxisvisible',$parstack,$safeeval,-2)=~/on|true|yes|1/i?'true':'false');
+       my $gridvisible=(&Apache::lonxml::get_param('gridvisible',$parstack,$safeeval,-2)=~/on|true|yes|1/i?'true':'false');
+       my $xlabel=&Apache::lonxml::get_param('xlabel',$parstack,$safeeval,-2);
+       my $ylabel=&Apache::lonxml::get_param('ylabel',$parstack,$safeeval,-2);
+ # paste in the update routine to receive stuff back from the applet
+      $result.=&update_script($internalid);
+ # start the initscript for this applet
+      $result.=&start_init_script($internalid);
+ # put the axis commands inside
+      $result.=&axes_script($internalid,$xmin,$xmax,$ymin,$ymax,$xaxisvisible,$yaxisvisible,$gridvisible);
+      $result.=&axes_label($internalid,$xmin,$xmax,$ymin,$ymax,$xlabel,$ylabel);
+ # init script is left open
+   }
+   return $result;
+ }
 ;

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