File:  [LON-CAPA] / loncom / homework / functionplotresponse.pm
Revision 1.85: download - view: text, annotated - select for diffs
Tue Nov 22 02:13:37 2011 UTC (12 years, 6 months ago) by www
Branches: MAIN
CVS tags: HEAD
Custom function plot rule

    1: # LearningOnline Network with CAPA
    2: # Functionplot responses
    3: #
    4: # $Id: functionplotresponse.pm,v 1.85 2011/11/22 02:13:37 www Exp $
    5: #
    6: # Copyright Michigan State University Board of Trustees
    7: #
    8: # This file is part of the LearningOnline Network with CAPA (LON-CAPA).
    9: #
   10: # LON-CAPA is free software; you can redistribute it and/or modify
   11: # it under the terms of the GNU General Public License as published by
   12: # the Free Software Foundation; either version 2 of the License, or
   13: # (at your option) any later version.
   14: #
   15: # LON-CAPA is distributed in the hope that it will be useful,
   16: # but WITHOUT ANY WARRANTY; without even the implied warranty of
   17: # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   18: # GNU General Public License for more details.
   19: #
   20: # You should have received a copy of the GNU General Public License
   21: # along with LON-CAPA; if not, write to the Free Software
   22: # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
   23: #
   24: # /home/httpd/html/adm/gpl.txt
   25: #
   26: # http://www.lon-capa.org/
   27: #
   28: 
   29: package Apache::functionplotresponse;
   30: use strict;
   31: use Apache::response();
   32: use Apache::lonlocal;
   33: use Apache::lonnet;
   34: use Apache::run;
   35: use LONCAPA;
   36:  
   37: BEGIN {
   38:   &Apache::lonxml::register('Apache::functionplotresponse',('functionplotresponse','backgroundplot','spline',
   39:                                                             'plotobject','plotvector',
   40:                                                             'functionplotvectorrule','functionplotvectorsumrule',
   41:                                                             'functionplotcustomrule',
   42:                                                             'functionplotrule','functionplotruleset',
   43:                                                             'functionplotelements'));
   44: }
   45: 
   46: #
   47: # There can be a number of applets on a page, each called ggbApplet_$id, 
   48: # where $id is the "_"-concatenated part and responseid
   49: #
   50: 
   51: sub geogebra_startcode {
   52:     my ($id)=@_;
   53:     return (<<ENDSTARTCODE);
   54: <applet name="ggbApplet_$id" code="geogebra.GeoGebraApplet" archive="geogebra.jar"
   55:          codebase="/adm/geogebra/"  width="722" height="447" MAYSCRIPT>
   56:        <param name="java_arguments" value="-Xmx512m -Djnlp.packEnabled=true"/>
   57: ENDSTARTCODE
   58: }
   59: 
   60: sub geogebra_endcode {
   61:     return &Apache::lonhtmlcommon::java_not_enabled()."</applet>\n";
   62: }
   63: 
   64: #
   65: # This is the internal GeoGebra bytecode which defines the spline functions
   66: #
   67: sub geogebra_spline_program {
   68:     return (<<ENDSPLINEPROGRAM);
   69: <param name="ggbBase64" value="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"/>
   70: ENDSPLINEPROGRAM
   71: }
   72: 
   73: #
   74: # The standard set of parameters inside <applet>
   75: #
   76: sub geogebra_default_parameters {
   77:    my ($id)=@_;
   78:    return(<<ENDDEFAULTPARAMETERS);
   79:         <param name="image" value="/adm/lonIcons/lonanim.gif"  />
   80:         <param name="boxborder" value="false"  />
   81:         <param name="centerimage" value="true"  />
   82: 	<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" />
   83: 	<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" />
   84:         <param name="framePossible" value="false" />
   85: 
   86:         <param name="showResetIcon" value="false" />
   87:         <param name="showAnimationButton" value="false" />
   88:         <param name="enableRightClick" value="false" />
   89:         <param name="errorDialogsActive" value="true" />
   90:         <param name="enableLabelDrags" value="false" />
   91:         <param name="showMenuBar" value="false" />
   92:         <param name="showToolBar" value="false" />
   93:         <param name="showToolBarHelp" value="false" />
   94:         <param name="showAlgebraInput" value="false" />
   95:         <param name="enableShiftDragZoom" value="false" />
   96:         <param name="allowRescaling" value="false" />
   97:         <param name="enableLabelDrags" value="false" />
   98:         <param name="ggbOnInitParam" value="applet_$id" />
   99: ENDDEFAULTPARAMETERS
  100: }
  101: 
  102: #
  103: # This subroutine is called by LON-CAPA at </problem>
  104: # Each applet on the page will call function ggbOnInit when it is done loading
  105: # This function in turn will call the respective function registered by start_init_script
  106: # Which one of the registered functions is called is determined by ggbOnInitParam, which GeoGebra passes to ggbOnInit
  107: #
  108: 
  109: sub init_script {
  110:    if ($#Apache::functionplotresponse::callscripts>=0) {
  111:       my $script='';
  112:       foreach my $id (@Apache::functionplotresponse::callscripts) {
  113:           $script.="if (param=='applet_$id') { loaded_$id=true; }\n";
  114:       }
  115:       $script.="if (".join(' && ',map { "loaded_$_" } (@Apache::functionplotresponse::callscripts)).
  116:                ") { setTimeout('ggbInitAll()',200) }";
  117:       my $calls=join("\n",map { "ggbInit_$_();" } (@Apache::functionplotresponse::callscripts)); 
  118:       return (<<ENDGGBINIT);
  119: <script type="text/javascript">
  120: // <![CDATA[
  121: // Function that each applet will call when loaded
  122: // It will pass "its" parameter
  123: // Set flags for when an applet is loaded, wait till all are loaded, and then some
  124: function ggbOnInit(param) {
  125: $script
  126: }
  127: function ggbInitAll() {
  128: $calls
  129: }
  130: // ]]>
  131: </script>
  132: ENDGGBINIT
  133:    }
  134: }
  135: 
  136: #
  137: # Each Geogebra applet is supposed to call this when parameters change
  138: # Changes the hidden fields on the web page
  139: #
  140: sub update_script {
  141:     my ($id)=@_;
  142:     return (<<ENDUPDATESCRIPT);
  143: <script type="text/javascript">
  144: // <![CDATA[
  145: function updatePointCoordinates_$id(coordinateName) {
  146:             var x = document.ggbApplet_$id.getXcoord(coordinateName);
  147:             var y = document.ggbApplet_$id.getYcoord(coordinateName);
  148:             document.lonhomework.elements["HWVAL_$id\_" + coordinateName + "_x"].value = x;
  149:             document.lonhomework.elements["HWVAL_$id\_" + coordinateName + "_y"].value = y;
  150:         }
  151: // ]]>
  152: </script>
  153: ENDUPDATESCRIPT
  154: }
  155: 
  156: #
  157: # Register the above update-handler for a variable
  158: #
  159: 
  160: sub update_register {
  161:    my ($id,$variable)=@_;
  162:    return "document.ggbApplet_$id.registerObjectUpdateListener('$variable','updatePointCoordinates_$id');\n";
  163: }
  164: 
  165: #
  166: # Set a point coordinate variable
  167: #
  168: sub set_point_coordinate {
  169:    my ($id,$variable,$x,$y,$fixed)=@_;
  170:    my $mult=($fixed?'a*':'');
  171: # Get rid of wild exponents, make sure it's a number
  172:    $x=1.*$x;
  173:    $y=1.*$y;
  174: # GeoGebra does not understand "E"
  175:    $x=~s/[e|E]/\*10\^/;
  176:    $x=~s/\+//;
  177:    $y=~s/[e|E]/\*10\^/;
  178:    $y=~s/\+//;
  179:    return (<<ENDSETVARIABLE);
  180: document.ggbApplet_$id.evalCommand("a=1");
  181: document.ggbApplet_$id.evalCommand("$variable=$mult($x,$y)");
  182: document.ggbApplet_$id.setLabelVisible("$variable",false);
  183: ENDSETVARIABLE
  184: }
  185: 
  186: #
  187: # Set a slope coordinate variable
  188: #
  189: sub set_slope_coordinate {
  190:    my ($id,$variable,$xrel,$yrel,$xmin,$xmax,$ymin,$ymax,$pointname,$fixed)=@_;
  191:    my $xvariable=$variable.'x';
  192:    my $yvariable=$variable.'y';
  193:    my $domain=$xmax-$xmin;
  194:    my $range=$ymax-$ymin;
  195:    my $xinterval=$domain/100.;
  196:    my $yinterval=$range/200.;
  197:    my $mult=($fixed?'a*':'');
  198:    return (<<ENDSETSVARIABLE);
  199: document.ggbApplet_$id.evalCommand("a=1");
  200: document.ggbApplet_$id.evalCommand("$xvariable=Slider[$xinterval,$domain,$xinterval]");
  201: document.ggbApplet_$id.setVisible("$xvariable", false);
  202: document.ggbApplet_$id.evalCommand("$xvariable=$xrel");
  203: document.ggbApplet_$id.evalCommand("$yvariable=Slider[-$range,$range,$yinterval]");
  204: document.ggbApplet_$id.setVisible("$yvariable", false);
  205: document.ggbApplet_$id.evalCommand("$yvariable=$yrel");
  206: document.ggbApplet_$id.evalCommand("$variable=$mult($xvariable+x($pointname),$yvariable+y($pointname))");
  207: document.ggbApplet_$id.setLabelVisible("$variable", false);
  208: ENDSETSVARIABLE
  209: }
  210: 
  211: #
  212: # Input field name for a coordinate variable
  213: #
  214: 
  215: sub field_name {
  216:     my ($id,$variable,$name)=@_;
  217:     return "HWVAL_$id\_$variable\_$name";
  218: }
  219: 
  220: #
  221: # Generate an input field for a coordinate variable
  222: #
  223: 
  224: sub generate_input_field {
  225:     my ($id,$variable,$x,$y)=@_;
  226:     $Apache::functionplotresponse::inputfields.=
  227:        "<input type='hidden' name='".&field_name($id,$variable,'x')."' value='$x' />\n".
  228:        "<input type='hidden' name='".&field_name($id,$variable,'y')."' value='$y' />\n";
  229: }
  230: 
  231: #
  232: # Initialize a new point coordinate variable at set a listener on it
  233: #
  234: sub new_point_coordinate {
  235:     my ($id,$variable,$x,$y,$fixed)=@_;
  236:     if (defined($Apache::functionplotresponse::previous{&field_name($id,$variable,'x')})) {
  237:        $x=$Apache::functionplotresponse::previous{&field_name($id,$variable,'x')};
  238:     }
  239:     if (defined($Apache::functionplotresponse::previous{&field_name($id,$variable,'y')})) {
  240:        $y=$Apache::functionplotresponse::previous{&field_name($id,$variable,'y')};
  241:     }
  242:     &generate_input_field($id,$variable,$x,$y);
  243:     return &set_point_coordinate($id,$variable,$x,$y,$fixed).&update_register($id,$variable);
  244: }
  245: 
  246: #
  247: # Initialize a new slope coordinate variable at set a listener on it
  248: #
  249: sub new_slope_coordinate {
  250:     my ($id,$variable,$x,$y,$pointname,$xp,$yp,$xmin,$xmax,$ymin,$ymax,$fixed)=@_;
  251: #
  252: # $variable: name of the slope point
  253: # $x, $y: coordinates of the slope point
  254: # $pointname: name of the associated point point
  255: # $xp $yp: coordinates of the point point
  256: #
  257:     if (defined($Apache::functionplotresponse::previous{&field_name($id,$variable,'x')})) {
  258:        $x=$Apache::functionplotresponse::previous{&field_name($id,$variable,'x')};
  259:     }
  260:     if (defined($Apache::functionplotresponse::previous{&field_name($id,$variable,'y')})) {
  261:        $y=$Apache::functionplotresponse::previous{&field_name($id,$variable,'y')};
  262:     }
  263:     if (defined($Apache::functionplotresponse::previous{&field_name($id,$pointname,'x')})) {
  264:        $xp=$Apache::functionplotresponse::previous{&field_name($id,$pointname,'x')};
  265:     }
  266:     if (defined($Apache::functionplotresponse::previous{&field_name($id,$pointname,'y')})) {
  267:        $yp=$Apache::functionplotresponse::previous{&field_name($id,$pointname,'y')};
  268:     }
  269: 
  270:     &generate_input_field($id,$variable,$x,$y);
  271:     my $xrel=$x-$xp;
  272:     my $yrel=$y-$yp;
  273:     return &set_slope_coordinate($id,$variable,$xrel,$yrel,$xmin,$xmax,$ymin,$ymax,$pointname,$fixed).&update_register($id,$variable);
  274: }
  275: 
  276: #
  277: # This registers the init-function call for ggbOnInit, which LON-CAPA will place at </problem>
  278: # It then starts the right headers
  279: #
  280: sub start_init_script {
  281:     my ($id)=@_;
  282: # Add id to the list of ggbInit_$id functions that need to be called
  283:     push(@Apache::functionplotresponse::callscripts,$id);
  284: # ... and open this function
  285:     return (<<ENDSTARTINIT);
  286: <script type="text/javascript">
  287: // <![CDATA[
  288: // variable that will eventually be passed back to the server
  289: var coordinateMap_$id = [];
  290: // flag for not loaded yet
  291: var loaded_$id=false;
  292: // Init-function for applet
  293: function ggbInit_$id() {
  294: ENDSTARTINIT
  295: }
  296: 
  297: #
  298: # This sets the axes inside ggbInit_$id
  299: #
  300: 
  301: sub axes_script {
  302:     my ($id,$xmin,$xmax,$ymin,$ymax,$xvisible,$yvisible,$gvisible)=@_;
  303:     return (<<ENDAXESSCRIPT);
  304:             // changes (xmin, xmax, ymin, ymax)
  305:             document.ggbApplet_$id.setCoordSystem($xmin,$xmax,$ymin,$ymax);
  306: 
  307:             // makes the (x,y) axis (in)visible
  308:             document.ggbApplet_$id.setAxesVisible($xvisible,$yvisible);
  309:             // makes the grid (in)visible
  310:             document.ggbApplet_$id.setGridVisible($gvisible);
  311: ENDAXESSCRIPT
  312: }
  313: 
  314: sub axes_label {
  315:     my ($id,$xmin,$xmax,$ymin,$ymax,$xlabel,$ylabel)=@_;
  316:     unless ($xlabel || $ylabel) { return ''; }
  317:     my $return='document.ggbApplet_'.$id.'.evalCommand("topRight=Corner[3]");';
  318:     if ($xlabel) {
  319:       if (($ymin<0) && ($ymax>0)) {
  320:        $return.=(<<ENDXAXISLABELSCRIPT);
  321: document.ggbApplet_$id.evalCommand("Xlabel=(x(topRight)-AxisStepX[],AxisStepY[]/6)");
  322: document.ggbApplet_$id.setVisible("Xlabel",false);
  323: document.ggbApplet_$id.evalCommand("Text[\\"$xlabel\\", Xlabel]");
  324: ENDXAXISLABELSCRIPT
  325:       } else {
  326:        $return.=(<<ENDXOFFAXISLABEL);
  327: document.ggbApplet_$id.evalCommand("LowerRight=Corner[2]");
  328: document.ggbApplet_$id.evalCommand("Text[\\"$xlabel\\", (x(LowerRight) - AxisStepX[], y(LowerRight) + AxisStepY[] / 2)]");
  329: ENDXOFFAXISLABEL
  330:       }
  331:     }
  332:     if ($ylabel) {
  333:       if (($xmin<0) && ($xmax>0)) {
  334:        $return.=(<<ENDYAXISLABELSCRIPT);
  335: document.ggbApplet_$id.evalCommand("Ylabel=(AxisStepX[]/6,y(topRight)-AxisStepY[]/3)");
  336: document.ggbApplet_$id.setVisible("Ylabel",false);
  337: document.ggbApplet_$id.evalCommand("Text[\\"$ylabel\\", Ylabel]");
  338: ENDYAXISLABELSCRIPT
  339:       } else {
  340:        $return.=(<<ENDYOFFAXISLABEL);
  341: document.ggbApplet_$id.evalCommand("UpperLeft=Corner[4]");
  342: document.ggbApplet_$id.evalCommand("Text[\\"$ylabel\\", (x(UpperLeft) + AxisStepX[] / 5, y(UpperLeft) - AxisStepY[] / 1.8)]");
  343: ENDYOFFAXISLABEL
  344:       }
  345:     }
  346:     return $return;
  347: }
  348: 
  349: #
  350: # Subroutine to produce background and answer plots
  351: #
  352: 
  353: sub plot_script {
  354:    my ($id,$function,$fixed,$label,$color,$xmin,$xmax,$thickness)=@_;
  355:    $label=~s/\W//g;
  356:    if (($label) && ($label!~/^[A-Za-z]/)) {
  357:       $label='C'.$label;
  358:    }
  359:    my $visible=0;
  360:    if ($label) {
  361:       $visible="1";
  362:    } else {
  363:       $Apache::functionplotresponse::counter++;
  364:       $label='C'.$Apache::functionplotresponse::counter;
  365:    }
  366:    my $rc=0;
  367:    my $gc=0;
  368:    my $bc=0;
  369:    if ($color) {
  370:       my ($rh,$gh,$bh)=($color=~/(..)(..)(..)/);
  371:       $rc=hex($rh);
  372:       $gc=hex($gh);
  373:       $bc=hex($bh);
  374:    }
  375:    if ($fixed) {
  376:       return "document.ggbApplet_$id.evalCommand('$label=Function[$function,$xmin,$xmax]');\n".
  377:              ($visible?'':"document.ggbApplet_$id.setLabelVisible('$label', false);\n").
  378:              ($color?"document.ggbApplet_$id.setColor('$label',$rc,$gc,$bc);\n":'').
  379:              ($thickness?"document.ggbApplet_$id.setLineThickness('$label',$thickness);\n":'');
  380:    } else {
  381:        return "document.ggbApplet_$id.evalCommand('y=$function');\n";
  382:    }
  383: }
  384: 
  385: #
  386: # Subroutine to produce objects
  387: #
  388: 
  389: sub plotobject_script {
  390:    my ($id,$label,$x,$y)=@_;
  391:    unless ($label) {
  392:       $Apache::functionplotresponse::counter++;
  393:       $label='O'.$Apache::functionplotresponse::counter;
  394:    }
  395:    &generate_input_field($id,$label,$x,$y);
  396:    return "document.ggbApplet_$id.evalCommand('a=1');\n".
  397:           "document.ggbApplet_$id.setVisible('a', false);\n".
  398:           "document.ggbApplet_$id.setLabelVisible('a', false);\n".
  399:           "document.ggbApplet_$id.evalCommand('$label=a*($x,$y)');\n".
  400:           "document.ggbApplet_$id.setVisible('$label', true);\n".
  401:           "document.ggbApplet_$id.setLabelVisible('$label', true);\n";
  402: }
  403: 
  404: #
  405: # Subroutine to produce vectors
  406: #
  407: 
  408: sub plotvector_script {
  409:    my ($id,$label,$xs,$ys,$xe,$ye,$xmin,$xmax)=@_;
  410:    unless ($label) {
  411:       $Apache::functionplotresponse::counter++;
  412:       $label='V'.$Apache::functionplotresponse::counter;
  413:    }
  414:    my $startlabel=$label.'Start';
  415:    my $endlabel=$label.'End';
  416:    my $pointlabel=$label.'Point';
  417:    my $pointx=2.*($xmax-$xmin)+$xmax;
  418:    my $anglelabel=$label.'Angle';
  419:    return 
  420:        &new_point_coordinate($id,$startlabel,$xs,$ys,0).
  421:        &new_point_coordinate($id,$endlabel,$xe,$ye,0).
  422:        (<<ENDVECTOR);
  423: document.ggbApplet_$id.evalCommand("$label=Vector[$startlabel,$endlabel]");
  424: document.ggbApplet_$id.setLabelVisible("$label",true);
  425: document.ggbApplet_$id.setLineThickness("$label",8);
  426: document.ggbApplet_$id.evalCommand("$pointlabel=($pointx,y($startlabel))");
  427: document.ggbApplet_$id.evalCommand("$anglelabel=Angle[$pointlabel,$startlabel,$endlabel]");
  428: document.ggbApplet_$id.setLabelVisible("$anglelabel",true);
  429: document.ggbApplet_$id.setLabelStyle("$anglelabel",VALUE=2);
  430: ENDVECTOR
  431: }
  432: 
  433: #
  434: # Answer spline display
  435: # 
  436: # points: x,y,slope_x,slope_y
  437: 
  438: sub answer_spline_script {
  439:    my ($id,@points)=@_;
  440:    my $order=int(($#points+1)/4);
  441:    if ($order<2) { $order=2; }
  442:    if ($order>8) { $order=8; }
  443:    $Apache::functionplotresponse::counter++;
  444:    my $label='CSpline'.$Apache::functionplotresponse::counter;
  445:    my $output='document.ggbApplet_'.$id.'.evalCommand("'.$label.'=Spline'.$order.'[';
  446:    for (my $i=0;$i<=$#points;$i+=4) {
  447:       $output.="($points[$i],$points[$i+1]),($points[$i+2],$points[$i+3]),";
  448:    }
  449:    $output=~s/\,$//;
  450:    $output.=']");'."\n";
  451:    for (my $i=2; $i<2*$order; $i+=2) {
  452:        $output.='document.ggbApplet_'.$id.'.setColor("'.$label.'_'.($i>=10?'{':'').$i.($i>=10?'}':'').'",0,170,0);'."\n";
  453:    }
  454:    for (my $i=1; $i<2*$order; $i+=2) {
  455:        $output.='document.ggbApplet_'.$id.'.setVisible("'.$label.'_'.($i>=10?'{':'').$i.($i>=10?'}':'').'",false);'."\n";
  456:    }
  457: 
  458:    return $output;
  459: }
  460: 
  461: #
  462: # Subroutine that generates code for spline $label based on stored information
  463: #
  464: 
  465: sub generate_spline {
  466:    my ($id,$label,$xmin,$xmax,$ymin,$ymax,$fixed)=@_;
  467:    my $result='';
  468:    my $order=$Apache::functionplotresponse::splineorder{$label};
  469:    my $x=$Apache::functionplotresponse::splineinitx{$label};
  470:    my $y=$Apache::functionplotresponse::splineinity{$label};
  471:    my $sx=$Apache::functionplotresponse::splinescalex{$label};
  472:    my $sy=$Apache::functionplotresponse::splinescaley{$label};
  473:    my @coords=();
  474:    foreach my $i (1..$order) {
  475:        $result.=&new_point_coordinate($id,$label.'P'.$i,$x,$y,$fixed);
  476:        my $xp=$x;
  477:        $x+=$sx/(2.*($order-1));
  478:        push(@coords,$label.'P'.$i);
  479:        $result.=&new_slope_coordinate($id,$label.'S'.$i,$x,$y+$sy,$label.'P'.$i,$xp,$y,$xmin,$xmax,$ymin,$ymax,$fixed);
  480:        $x+=$sx/(2.*($order-1));
  481:        push(@coords,$label.'S'.$i);
  482:    }
  483:    $result.='document.ggbApplet_'.$id.'.evalCommand("Spline'.$order.'['.join(',',@coords).']");'."\n";
  484:    return $result;
  485: }
  486: 
  487: #
  488: # Object
  489: #
  490: 
  491: sub start_plotobject {
  492:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  493:    my $result='';
  494:    my $internalid = $Apache::inputtags::part.'_'.$Apache::inputtags::response[-1];
  495:    my $x=&Apache::lonxml::get_param('x',$parstack,$safeeval);
  496:    my $y=&Apache::lonxml::get_param('y',$parstack,$safeeval);
  497:    my $label=&Apache::lonxml::get_param('label',$parstack,$safeeval);
  498:    $label=~s/\W//gs;
  499:    $label=ucfirst($label);
  500:    unless ($label) { $label="NewObject"; }
  501:    if ($target eq 'web') {
  502:       my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-3);
  503:       unless (defined($x)) { $x=$xmin; }
  504:       unless (defined($y)) { $y=$ymin; }
  505:       $result.=&plotobject_script($internalid,$label,$x,$y);
  506:    } elsif ($target eq 'edit') {
  507:         $result=&Apache::edit::tag_start($target,$token,'Plot Object').
  508:              &Apache::edit::text_arg('Label on Plot:','label',
  509:                                      $token,'16').
  510:              &Apache::edit::text_arg('x:','x',
  511:                                      $token,'8').
  512:              &Apache::edit::text_arg('y:','y',
  513:                                      $token,'8').
  514:              &Apache::edit::end_row();
  515:   } elsif ($target eq 'modified') {
  516:     $env{'form.'.&Apache::edit::html_element_name('label')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('label')});
  517:     my $constructtag=&Apache::edit::get_new_args($token,$parstack,$safeeval,'label','x','y');
  518:     if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
  519:   }
  520:   return $result;
  521: }
  522: 
  523: sub end_plotobject {
  524:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  525:    my $result='';
  526:    if ($target eq 'edit') {
  527:        $result=&Apache::edit::end_table();
  528:    }
  529:    return $result;
  530: }
  531: 
  532: #
  533: # Vector
  534: #
  535: 
  536: sub start_plotvector {
  537:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  538:    my $result='';
  539:    my $internalid = $Apache::inputtags::part.'_'.$Apache::inputtags::response[-1];
  540:    my $tailx=&Apache::lonxml::get_param('tailx',$parstack,$safeeval);
  541:    my $taily=&Apache::lonxml::get_param('taily',$parstack,$safeeval);
  542:    my $tipx=&Apache::lonxml::get_param('tipx',$parstack,$safeeval);
  543:    my $tipy=&Apache::lonxml::get_param('tipy',$parstack,$safeeval);
  544: 
  545:    my $label=&Apache::lonxml::get_param('label',$parstack,$safeeval);
  546:    $label=~s/\W//gs;
  547:    $label=ucfirst($label);
  548:    unless ($label) { $label="NewVector"; }
  549:    if ($target eq 'web') {
  550:       my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-3);
  551:       unless (defined($tailx)) { $tailx=$xmin; }
  552:       unless (defined($taily)) { $taily=$ymin; }
  553:       unless (defined($tipx)) { $tipx=$xmin; }
  554:       unless (defined($tipy)) { $tipy=$ymin; }
  555:       $result.=&plotvector_script($internalid,$label,$tailx,$taily,$tipx,$tipy,$xmin,$xmax);
  556:    } elsif ($target eq 'edit') {
  557:         $result=&Apache::edit::tag_start($target,$token,'Plot Vector').
  558:              &Apache::edit::text_arg('Label on Plot:','label',
  559:                                      $token,'16').
  560:              &Apache::edit::text_arg('Tail x:','tailx',
  561:                                      $token,'8').
  562:              &Apache::edit::text_arg('Tail y:','taily',
  563:                                      $token,'8').
  564:              &Apache::edit::text_arg('Tip x:','tipx',
  565:                                      $token,'8').
  566:              &Apache::edit::text_arg('Tip y:','tipy',
  567:                                      $token,'8').
  568: 
  569:              &Apache::edit::end_row();
  570:   } elsif ($target eq 'modified') {
  571:     $env{'form.'.&Apache::edit::html_element_name('label')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('label')});
  572:     my $constructtag=&Apache::edit::get_new_args($token,$parstack,$safeeval,'label','tailx','taily','tipx','tipy');
  573:     if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
  574:   }
  575:   return $result;
  576: }
  577: 
  578: sub end_plotvector {
  579:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  580:    my $result='';
  581:    if ($target eq 'edit') {
  582:        $result=&Apache::edit::end_table();
  583:    }
  584:    return $result;
  585: }
  586: 
  587: 
  588: 
  589: #
  590: # <backgroundplot function="..." fixed="yes/no" />
  591: #
  592: sub start_backgroundplot {
  593:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  594:    my $result='';
  595:    my $internalid = $Apache::inputtags::part.'_'.$Apache::inputtags::response[-1];
  596:    my $function=&Apache::lonxml::get_param('function',$parstack,$safeeval);
  597:    my $xinitial=&Apache::lonxml::get_param('xinitial',$parstack,$safeeval);
  598:    my $xfinal=&Apache::lonxml::get_param('xfinal',$parstack,$safeeval);
  599:    my $label=&Apache::lonxml::get_param('label',$parstack,$safeeval);
  600:    my $color=&Apache::lonxml::get_param('color',$parstack,$safeeval);
  601:    $color=~s/[^a-fA-F0-9]//gs;
  602:    unless (length($color)==6) { $color=''; }
  603:    my $fixed=(&Apache::lonxml::get_param('fixed',$parstack,$safeeval)=~/on|true|yes|1/i?1:0);
  604:  
  605:    unless ($function) { $function="0"; }
  606:    if ($target eq 'web') {
  607:       my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-3);
  608:       unless (defined($xinitial)) { $xinitial=$xmin; }
  609:       unless (defined($xfinal)) { $xfinal=$xmax; }
  610:       $result.=&plot_script($internalid,$function,$fixed,$label,$color,$xinitial,$xfinal);
  611:    } elsif ($target eq 'edit') {
  612:         $result=&Apache::edit::tag_start($target,$token,'Background Function Plot').
  613:              &Apache::edit::text_arg('Function:','function',
  614:                                      $token,'16').
  615:              &Apache::edit::text_arg('Initial x-value (optional):','xinitial',
  616:                                      $token,'8').
  617:              &Apache::edit::text_arg('Final x-value (optional):','xfinal',
  618:                                      $token,'8').
  619:              &Apache::edit::text_arg('Label on Plot:','label',
  620:                                      $token,'8').
  621:              &Apache::edit::text_arg('Color (hex code):','color',
  622:                                      $token,'8').
  623:              &Apache::edit::select_arg('Fixed location:','fixed',
  624:                                   ['yes','no'],$token).
  625:              &Apache::edit::end_row();
  626:   } elsif ($target eq 'modified') {
  627:     my $constructtag=&Apache::edit::get_new_args($token,$parstack,
  628:                                                  $safeeval,'function','label','xinitial','xfinal','color','fixed');
  629:     if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
  630:   }
  631:   return $result;
  632: }
  633: 
  634: sub end_backgroundplot {
  635:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  636:    my $result='';
  637:    if ($target eq 'edit') {
  638:        $result=&Apache::edit::end_table();
  639:    }
  640:    return $result;
  641: }
  642: 
  643: #
  644: # <functionplotrule ... />
  645: #
  646: sub start_functionplotrule {
  647:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  648:    my $result='';
  649:    my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval);
  650:    $Apache::functionplotresponse::counter++;
  651:    if ($label=~/\W/) {
  652:       &Apache::lonxml::warning(&mt('Rule indices should only contain alphanumeric characters.'));
  653:    }
  654:    $label=~s/\W//gs;
  655:    unless ($label) {
  656:       $label='R'.$Apache::functionplotresponse::counter;
  657:    } else {
  658:       $label='R'.$label;
  659:    }
  660: 
  661:    if ($target eq 'grade') {
  662: # Simply remember - in order - for later
  663:       my $beginninglabel=&Apache::lonxml::get_param('xinitiallabel',$parstack,$safeeval);
  664:       my $endinglabel=&Apache::lonxml::get_param('xfinallabel',$parstack,$safeeval);
  665:       if (($beginninglabel=~/\W/) || ($endinglabel=~/W/)) {
  666:           &Apache::lonxml::warning(&mt('Rule labels must be alphanumeric.'));
  667:       }
  668:       $beginninglabel=~s/\W//gs;
  669:       $endinglabel=~s/\W//gs;
  670:       my $relationship=&Apache::lonxml::get_param('relationship',$parstack,$safeeval);
  671:       $relationship=~s/\W//gs;
  672:       $relationship=lc($relationship);
  673:       unless ($relationship=~/^(eq|ge|gt|le|lt|ne)$/) {
  674:           &Apache::lonxml::warning(&mt('Rule relationship not defined.'));
  675:           $relationship='eq';
  676:       }
  677:       my $derivative=&Apache::lonxml::get_param('derivativeorder',$parstack,$safeeval);
  678:       unless (($derivative==-1) || ($derivative==0) || ($derivative==1) || ($derivative==2)) {
  679:          &Apache::lonxml::warning(&mt('Rule derivative not defined.'));
  680:          $derivative=0;
  681:       }
  682:       push(@Apache::functionplotresponse::functionplotrules,join(':',(
  683:            $label,
  684:            $derivative,
  685:            &Apache::lonxml::get_param('xinitial',$parstack,$safeeval),
  686:            $beginninglabel,
  687:            &Apache::lonxml::get_param('xfinal',$parstack,$safeeval),
  688:            $endinglabel,
  689:            &Apache::lonxml::get_param('minimumlength',$parstack,$safeeval),
  690:            &Apache::lonxml::get_param('maximumlength',$parstack,$safeeval),
  691:            $relationship,
  692:            &Apache::lonxml::get_param('value',$parstack,$safeeval),
  693:            &Apache::lonxml::get_param('percenterror',$parstack,$safeeval)
  694:           )));
  695:    } elsif ($target eq 'edit') {
  696:         $result=&Apache::edit::tag_start($target,$token,'Function Plot Graph Rule').
  697:              &Apache::edit::text_arg('Index/Name:','index',
  698:                                      $token,'10').'&nbsp;'.
  699:              &Apache::edit::select_arg(&mt('Function:'),'derivativeorder',
  700:                                   [['0','Function itself'],
  701:                                    ['1','First derivative'],
  702:                                    ['2','Second derivative'],
  703:                                    ['-1','Integral']],$token).'<br />'.
  704:              &Apache::edit::text_arg('Initial x-value:','xinitial',
  705:                                       $token,'8').
  706:              &Apache::edit::select_or_text_arg('Initial x-value label:','xinitiallabel',
  707:                                                [['start','Start of Plot'],
  708:                                                 ['end','End of Plot']],$token,'8').'<br />'.
  709: 
  710:              &Apache::edit::text_arg('Final x-value (optional):','xfinal',
  711:                                       $token,'8').
  712:              &Apache::edit::select_or_text_arg('Final x-value label (optional):','xfinallabel',
  713:                                                [['end','End of Plot']],$token,'8').'<br />'.
  714:              &Apache::edit::text_arg('Minimum length for range (optional):','minimumlength',
  715:                                      $token,'8').
  716:              &Apache::edit::text_arg('Maximum length for range (optional):','maximumlength',
  717:                                      $token,'8').'<br />'.
  718:              &Apache::edit::select_or_text_arg(&mt('Relationship:'),'relationship',
  719:                                   [['eq','equal'],
  720:                                    ['ne','not equal'],
  721:                                    ['ge','greater than or equal'],
  722:                                    ['gt','greater than'],
  723:                                    ['lt','less than'],
  724:                                    ['le','less than or equal']],$token).
  725:              $result.= &Apache::edit::select_or_text_arg('Value:','value',
  726:                                                [['undef','not defined']],$token,'30').
  727:              &Apache::edit::text_arg('Percent error:','percenterror',
  728:                                      $token,'8').
  729:              &Apache::edit::end_row();
  730:   } elsif ($target eq 'modified') {
  731:     if (($env{'form.'.&Apache::edit::html_element_name('xinitial')} ne '') && ($env{'form.'.&Apache::edit::html_element_name('xinitiallabel')} eq 'start')) {
  732:        $env{'form.'.&Apache::edit::html_element_name('xinitiallabel')}='';
  733:     }
  734:     if (($env{'form.'.&Apache::edit::html_element_name('xfinal')} ne '') && ($env{'form.'.&Apache::edit::html_element_name('xfinallabel')} eq 'end')) {
  735:        $env{'form.'.&Apache::edit::html_element_name('xfinallabel')}='';
  736:     }
  737:     my $constructtag=&Apache::edit::get_new_args($token,$parstack,
  738:                                                  $safeeval,'index','derivativeorder',
  739:                                                            'xinitial','xinitiallabel','xfinal','xfinallabel',
  740:                                                            'minimumlength','maximumlength',
  741:                                                            'relationship','value','percenterror');
  742:     if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
  743:    }
  744:    return $result;
  745: }
  746: 
  747: sub end_functionplotrule {
  748:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  749:    my $result='';
  750:    if ($target eq 'edit') {
  751:        $result=&Apache::edit::end_table();
  752:    }
  753:    return $result;
  754: }
  755: 
  756: 
  757: #
  758: # <functionplotvectorrule ... />
  759: #
  760: sub start_functionplotvectorrule {
  761:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  762:    my $result='';
  763:    my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval);
  764:    $Apache::functionplotresponse::counter++;
  765:    if ($label=~/\W/) {
  766:       &Apache::lonxml::warning(&mt('Rule indices should only contain alphanumeric characters.'));
  767:    }
  768:    $label=~s/\W//gs;
  769:    unless ($label) {
  770:       $label='R'.$Apache::functionplotresponse::counter;
  771:    } else {
  772:       $label='R'.$label;
  773:    }
  774: 
  775:    if ($target eq 'grade') {
  776: # Simply remember - in order - for later
  777: 
  778:       my $id=$Apache::inputtags::response[-1];
  779:       my $partid=$Apache::inputtags::part;
  780:       my $internalid = $partid.'_'.$id;
  781: 
  782:       my $vector=&Apache::lonxml::get_param('vector',$parstack,$safeeval);
  783:       $vector=~s/\W//gs;
  784:       $vector=ucfirst($vector);
  785: 
  786:       my $attachpoint=&Apache::lonxml::get_param('attachpoint',$parstack,$safeeval);
  787:       $attachpoint=~s/\W//gs;
  788:       $attachpoint=ucfirst($attachpoint);
  789: 
  790:       my $notattachpoint=&Apache::lonxml::get_param('notattachpoint',$parstack,$safeeval);
  791:       $notattachpoint=~s/\W//gs;
  792:       $notattachpoint=ucfirst($notattachpoint);
  793: 
  794:       my $tailpoint=&Apache::lonxml::get_param('tailpoint',$parstack,$safeeval);
  795:       $tailpoint=~s/\W//gs;
  796:       $tailpoint=ucfirst($tailpoint);
  797:       my $tippoint=&Apache::lonxml::get_param('tippoint',$parstack,$safeeval);
  798:       $tippoint=~s/\W//gs;
  799:       $tippoint=ucfirst($tippoint);
  800: 
  801:       my $nottailpoint=&Apache::lonxml::get_param('nottailpoint',$parstack,$safeeval);
  802:       $nottailpoint=~s/\W//gs;
  803:       $nottailpoint=ucfirst($nottailpoint);
  804:       my $nottippoint=&Apache::lonxml::get_param('nottippoint',$parstack,$safeeval);
  805:       $nottippoint=~s/\W//gs;
  806:       $nottippoint=ucfirst($nottippoint);
  807: 
  808:       push(@Apache::functionplotresponse::functionplotvectorrules,join(':',(
  809:            $label,
  810:            'vector',
  811:            $internalid,
  812:            $vector,
  813:            $attachpoint,
  814:            $notattachpoint,
  815:            $tailpoint,
  816:            $tippoint,
  817:            $nottailpoint,
  818:            $nottippoint,
  819:            &Apache::lonxml::get_param('length',$parstack,$safeeval),
  820:            &Apache::lonxml::get_param('angle',$parstack,$safeeval),
  821:            &Apache::lonxml::get_param('lengtherror',$parstack,$safeeval),
  822:            &Apache::lonxml::get_param('angleerror',$parstack,$safeeval),
  823:           )));
  824:    } elsif ($target eq 'edit') {
  825:         $result=&Apache::edit::tag_start($target,$token,'Function Plot Vector Rule').
  826:              &Apache::edit::text_arg('Index/Name:','index',
  827:                                      $token,'10').'&nbsp;'.
  828:              &Apache::edit::text_arg('Vector:','vector',
  829:                                       $token,'16').'<br />'.
  830:              &Apache::edit::text_arg('Attached to object:','attachpoint',
  831:                                       $token,'16').
  832:              &Apache::edit::text_arg('Not attached to object:','notattachpoint',
  833:                                       $token,'16').'<br />'.
  834:              &Apache::edit::text_arg('Tail attached to object:','tailpoint',
  835:                                       $token,'16').
  836:              &Apache::edit::text_arg('Tip attached to object:','tippoint',
  837:                                       $token,'16').
  838:              &Apache::edit::text_arg('Tail not attached to object:','nottailpoint',
  839:                                       $token,'16').
  840:              &Apache::edit::text_arg('Tip not attached to object:','nottippoint',
  841:                                       $token,'16').'<br />'.
  842:              &Apache::edit::text_arg('Length:','length',
  843:                                      $token,'30').
  844:              &Apache::edit::text_arg('Absolute error length:','lengtherror',
  845:                                      $token,'8').'<br />'.
  846:              &Apache::edit::text_arg('Angle:','angle',
  847:                                      $token,'30').
  848:              &Apache::edit::text_arg('Absolute error angle:','angleerror',
  849:                                      $token,'8').
  850:              &Apache::edit::end_row();
  851:   } elsif ($target eq 'modified') {
  852:     $env{'form.'.&Apache::edit::html_element_name('vector')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('vector')});
  853:     $env{'form.'.&Apache::edit::html_element_name('attachpoint')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('attachpoint')});
  854:     $env{'form.'.&Apache::edit::html_element_name('notattachpoint')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('notattachpoint')});
  855:     $env{'form.'.&Apache::edit::html_element_name('tailpoint')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('tailpoint')});
  856:     $env{'form.'.&Apache::edit::html_element_name('tippoint')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('tippoint')});
  857:     $env{'form.'.&Apache::edit::html_element_name('nottailpoint')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('nottailpoint')});
  858:     $env{'form.'.&Apache::edit::html_element_name('nottippoint')}=ucfirst($env{'form.'.&Apache::edit::html_element_name('nottippoint')});
  859:     my $constructtag=&Apache::edit::get_new_args($token,$parstack,
  860:                                                  $safeeval,'index','vector','attachpoint','notattachpoint',
  861:                                                            'tailpoint','tippoint','nottailpoint','nottipoint',
  862:                                                            'length','angle',
  863:                                                            'lengtherror','angleerror');
  864:     if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
  865:    }
  866:    return $result;
  867: }
  868: 
  869: sub end_functionplotvectorrule {
  870:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  871:    my $result='';
  872:    if ($target eq 'edit') {
  873:        $result=&Apache::edit::end_table();
  874:    }
  875:    return $result;
  876: }
  877: 
  878: #
  879: # <functionplotvectorsumrule ... />
  880: #
  881: sub start_functionplotvectorsumrule {
  882:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  883:    my $result='';
  884:    my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval);
  885:    $Apache::functionplotresponse::counter++;
  886:    if ($label=~/\W/) {
  887:       &Apache::lonxml::warning(&mt('Rule indices should only contain alphanumeric characters.'));
  888:    }
  889:    $label=~s/\W//gs;
  890:    unless ($label) {
  891:       $label='R'.$Apache::functionplotresponse::counter;
  892:    } else {
  893:       $label='R'.$label;
  894:    }
  895:    if ($target eq 'grade') {
  896: # Simply remember - in order - for later
  897:       my $id=$Apache::inputtags::response[-1];
  898:       my $partid=$Apache::inputtags::part;
  899:       my $internalid = $partid.'_'.$id;
  900:       my $vectors=&Apache::lonxml::get_param('vectors',$parstack,$safeeval);
  901:       push(@Apache::functionplotresponse::functionplotvectorrules,join(':',(
  902:            $label,
  903:            'sum',
  904:            $internalid,
  905:            $vectors,
  906:            &Apache::lonxml::get_param('length',$parstack,$safeeval),
  907:            &Apache::lonxml::get_param('angle',$parstack,$safeeval),
  908:            &Apache::lonxml::get_param('lengtherror',$parstack,$safeeval),
  909:            &Apache::lonxml::get_param('angleerror',$parstack,$safeeval),
  910:           )));
  911:    } elsif ($target eq 'edit') {
  912:         $result=&Apache::edit::tag_start($target,$token,'Function Plot Vector Sum Rule').
  913:              &Apache::edit::text_arg('Index/Name:','index',
  914:                                      $token,'10').'&nbsp;'.
  915:              &Apache::edit::text_arg('Comma-separated list of vectors:','vectors',
  916:                                       $token,'30').'<br />'.
  917:              &Apache::edit::text_arg('Sum vector length:','length',
  918:                                      $token,'30').
  919:              &Apache::edit::text_arg('Absolute error length:','lengtherror',
  920:                                      $token,'8').'<br />'.
  921:              &Apache::edit::text_arg('Sum vector angle:','angle',
  922:                                      $token,'30').
  923:              &Apache::edit::text_arg('Absolute error angle:','angleerror',
  924:                                      $token,'8').
  925:              &Apache::edit::end_row();
  926:    } elsif ($target eq 'modified') {
  927:       my $constructtag=&Apache::edit::get_new_args($token,$parstack,
  928:                                                    $safeeval,'index','vectors',
  929:                                                              'length','angle',
  930:                                                              'lengtherror','angleerror');
  931:       if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
  932:    }
  933:    return $result;
  934: }
  935: 
  936: sub end_functionplotvectorsumrule {
  937:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  938:    my $result='';
  939:    if ($target eq 'edit') {
  940:        $result=&Apache::edit::end_table();
  941:    }
  942:    return $result;
  943: }
  944: 
  945: #
  946: # <functionplotcustom ... />
  947: #
  948: sub start_functionplotcustomrule {
  949:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  950:    my $result='';
  951:    my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval);
  952:    $Apache::functionplotresponse::counter++;
  953:    if ($label=~/\W/) {
  954:       &Apache::lonxml::warning(&mt('Rule indices should only contain alphanumeric characters.'));
  955:    }
  956:    $label=~s/\W//gs;
  957:    unless ($label) {
  958:       $label='R'.$Apache::functionplotresponse::counter;
  959:    } else {
  960:       $label='R'.$label;
  961:    }
  962:    &Apache::lonxml::register('Apache::response',('answer'));
  963:    if ($target eq 'edit') {
  964:         $result=&Apache::edit::tag_start($target,$token,'Function Plot Custom Rule').
  965:              &Apache::edit::text_arg('Index/Name:','index',$token,'10').
  966:              &Apache::edit::end_row();
  967:   } elsif ($target eq 'modified') {
  968:       my $constructtag=&Apache::edit::get_new_args($token,$parstack,$safeeval,'index');
  969:       if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
  970:    }
  971:    return $result;
  972: }
  973: 
  974: sub end_functionplotcustomrule {
  975:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
  976:    my $result='';
  977:    if ($target eq 'edit') {
  978:       $result=&Apache::edit::end_table();
  979:    } elsif ($target eq 'grade') {
  980: # Simply remember - in order - for later
  981:       my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval);
  982:       $Apache::functionplotresponse::counter++;
  983:       if ($label=~/\W/) {
  984:          &Apache::lonxml::warning(&mt('Rule indices should only contain alphanumeric characters.'));
  985:       }
  986:       $label=~s/\W//gs;
  987:       unless ($label) {
  988:          $label='R'.$Apache::functionplotresponse::counter;
  989:       } else {
  990:          $label='R'.$label;
  991:       }
  992:       push(@Apache::functionplotresponse::functionplotvectorrules,join(':',(
  993:            $label,
  994:            'custom',
  995:            &escape($Apache::response::custom_answer[-1])
  996:           )));
  997:    }
  998:    &Apache::lonxml::deregister('Apache::response',('answer'));
  999:    return $result;
 1000: }
 1001: 
 1002: 
 1003: 
 1004: #
 1005: # <spline index="..." order="1,2,3,4" initx="..." inity="..." scalex="..." scaley="..." />
 1006: #
 1007: # Unfortunately, GeoGebra seems to want all splines after everything else, so we need to store them
 1008: #
 1009: sub start_spline {
 1010:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
 1011:    my $result='';
 1012:    if ($target eq 'web') {
 1013:       my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval);
 1014:       $Apache::functionplotresponse::counter++;
 1015:       if ($label=~/\W/) {
 1016:          &Apache::lonxml::warning(&mt('Spline indices should only contain alphanumeric characters.'));
 1017:       }
 1018:       $label=~s/\W//gs;
 1019:       unless ($label) { 
 1020:          $label='S'.$Apache::functionplotresponse::counter; 
 1021:       } else {
 1022:          $label='S'.$label;
 1023:       }
 1024:       if ($Apache::functionplotresponse::splineorder{$label}) {
 1025:          &Apache::lonxml::error(&mt('Spline indices must be unique.'));
 1026:       }
 1027: 
 1028:       my $order=&Apache::lonxml::get_param('order',$parstack,$safeeval);
 1029:       if ($order<2) { $order=2; }
 1030:       if ($order>8) { $order=8; }
 1031:       $Apache::functionplotresponse::splineorder{$label}=$order;
 1032: 
 1033:       my $x=&Apache::lonxml::get_param('initx',$parstack,$safeeval);
 1034:       unless ($x) { $x=0; }
 1035:       $Apache::functionplotresponse::splineinitx{$label}=$x;
 1036: 
 1037:       my $y=&Apache::lonxml::get_param('inity',$parstack,$safeeval);
 1038:       unless ($y) { $y=0; }
 1039:       $Apache::functionplotresponse::splineinity{$label}=$y;
 1040: 
 1041:       my $sx=&Apache::lonxml::get_param('scalex',$parstack,$safeeval);
 1042:       unless ($sx) { $sx=$order; }
 1043:       $Apache::functionplotresponse::splinescalex{$label}=$sx;
 1044: 
 1045:       my $sy=&Apache::lonxml::get_param('scaley',$parstack,$safeeval);
 1046:       unless ($sy) { $sy=2; }
 1047:       $Apache::functionplotresponse::splinescaley{$label}=$sy;
 1048:    } elsif ($target eq 'edit') {
 1049:         $result=&Apache::edit::tag_start($target,$token,'Spline').
 1050:              &Apache::edit::text_arg('Index:','index',
 1051:                                      $token,'4').'&nbsp;'.
 1052:              &Apache::edit::select_arg('Order:','order',
 1053:                                   ['2','3','4','5','6','7','8'],$token).'&nbsp;'.
 1054:              &Apache::edit::text_arg('Initial x-value:','initx',
 1055:                                      $token,'4').'&nbsp;'.
 1056:              &Apache::edit::text_arg('Initial y-value:','inity',
 1057:                                      $token,'4').'&nbsp;'.
 1058:              &Apache::edit::text_arg('Scale x:','scalex',
 1059:                                      $token,'4').'&nbsp;'.
 1060:              &Apache::edit::text_arg('Scale y:','scaley',
 1061:                                      $token,'4').
 1062:              &Apache::edit::end_row();
 1063:   } elsif ($target eq 'modified') {
 1064:     my $constructtag=&Apache::edit::get_new_args($token,$parstack,
 1065:                                                  $safeeval,'index','order','initx','inity',
 1066:                                                            'scalex','scaley');
 1067:     if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
 1068:   }
 1069:   return $result;
 1070: }
 1071: 
 1072: sub end_spline {
 1073:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
 1074:    my $result='';
 1075:    if ($target eq 'edit') {
 1076:        $result=&Apache::edit::end_table();
 1077:    }
 1078:    return $result;
 1079: }
 1080:  
 1081: sub end_init_script {
 1082:     return (<<ENDENDINIT);
 1083: }
 1084: // ]]>
 1085: </script>
 1086: ENDENDINIT
 1087: }
 1088: 
 1089: #
 1090: # Storing and restoring spline coordinates from part answers
 1091: #
 1092: sub decode_previous_answer {
 1093:    my ($answer)=@_;
 1094:    foreach my $coordinate (split(/\,/,$answer)) {
 1095:       my ($key,$value)=split(/\=/,$coordinate);
 1096:       $Apache::functionplotresponse::previous{$key}=$value;
 1097:    }
 1098: }
 1099: 
 1100: sub get_answer_from_form_fields {
 1101:    my ($id)=@_;
 1102:    my $answer='';
 1103:    my %coords=();
 1104:    foreach my $field (keys(%env)) {
 1105:       if ($field=~/^form\.HWVAL\_$id/) {
 1106:          $field=~/^form\.(.*)$/;
 1107:          $coords{$1}=$env{$field};
 1108:       }
 1109:    }
 1110:    $answer=join(',',map { $_.'='.$coords{$_} } (sort(keys(%coords))));
 1111:    return ($answer,%coords);
 1112: }
 1113: 
 1114: #
 1115: # The following functions calculate the cubic-hermite splines server-side
 1116: #
 1117: 
 1118: sub cubic_hermite {
 1119:    my ($t,$p1,$s1,$p2,$s2)=@_;
 1120:    return (2.*$t*$t*$t-3.*$t*$t+1.)*$p1 + 3.*($t*$t*$t-2.*$t*$t+$t)*($s1-$p1)+
 1121:           (-2.*$t*$t*$t+3.*$t*$t)  *$p2 + 3.*($t*$t*$t-$t*$t)      *($s2-$p2);
 1122: }
 1123: 
 1124: #
 1125: # d/dt(...)
 1126: # 
 1127: 
 1128: sub ddt_cubic_hermite {
 1129:    my ($t,$p1,$s1,$p2,$s2)=@_;
 1130:    return (6.*$t*$t-6.*$t) *$p1 + 3.*(3.*$t*$t-4.*$t+1.)*($s1-$p1)+
 1131:           (-6.*$t*$t+6.*$t)*$p2 + 3.*(3.*$t*$t-2.*$t)   *($s2-$p2);
 1132: }
 1133: 
 1134: #
 1135: # d^2/dt^2(...)
 1136: #
 1137: 
 1138: sub d2dt2_cubic_hermite {
 1139:    my ($t,$p1,$s1,$p2,$s2)=@_;
 1140:    return (12.*$t-6.) *$p1 + 3.*(6.*$t-4.)*($s1-$p1)+
 1141:           (-12.*$t+6.)*$p2 + 3.*(6.*$t-2.)*($s2-$p2);
 1142: }
 1143: 
 1144: #
 1145: # Array index calculation
 1146: #
 1147: sub array_index {
 1148:    my ($xmin,$xmax,$x)=@_;
 1149:    if ($x ne '') {
 1150:       return int(($x-$xmin)/($xmax-$xmin)*400.+0.5);
 1151:    } else {
 1152:       return undef;
 1153:    }
 1154: }
 1155: 
 1156: #
 1157: # Populate the arrays
 1158: #
 1159: 
 1160: sub populate_arrays {
 1161:     my ($id,$xmin,$xmax,$ymin,$ymax)=@_;
 1162:     for (my $i=0; $i<=400; $i++) {
 1163:        $Apache::functionplotresponse::actualxval[$i]=undef;
 1164:        $Apache::functionplotresponse::func[$i]=undef;
 1165:        $Apache::functionplotresponse::dfuncdx[$i]=undef;
 1166:        $Apache::functionplotresponse::d2funcd2x[$i]=undef;
 1167:     }
 1168:     unless ($xmax>$xmin) { return 'no_func'; }
 1169: # Run over all splines in response
 1170:     foreach my $label (split(/\,/,$env{"form.HWVAL_AllSplines_$id"})) {
 1171:         my $xiold=-1;
 1172: # Run over all points in spline
 1173:         for (my $i=1; $i<$env{"form.HWVAL_SplineOrder_".$id."_".$label}; $i++) {
 1174:             my $ni=$i+1;
 1175:             my @xparms=($env{'form.HWVAL_'.$id.'_'.$label.'P'.$i.'_x'},
 1176:                         $env{'form.HWVAL_'.$id.'_'.$label.'S'.$i.'_x'},
 1177:                         $env{'form.HWVAL_'.$id.'_'.$label.'P'.$ni.'_x'},
 1178:                         $env{'form.HWVAL_'.$id.'_'.$label.'S'.$ni.'_x'});
 1179:             my @yparms=($env{'form.HWVAL_'.$id.'_'.$label.'P'.$i.'_y'},
 1180:                         $env{'form.HWVAL_'.$id.'_'.$label.'S'.$i.'_y'},
 1181:                         $env{'form.HWVAL_'.$id.'_'.$label.'P'.$ni.'_y'},
 1182:                         $env{'form.HWVAL_'.$id.'_'.$label.'S'.$ni.'_y'});
 1183: # Run in small steps over spline parameter
 1184:             for (my $t=0; $t<=1; $t+=0.0001) {
 1185:                 my $xreal=&cubic_hermite($t,@xparms);
 1186:                 my $xi=&array_index($xmin,$xmax,$xreal);
 1187:                 if ($xi<$xiold) { return 'no_func'; }
 1188:                 if (($xi>$xiold) && ($xi>=0) && ($xi<=400)) {
 1189:                    $xiold=$xi;
 1190:                    $Apache::functionplotresponse::actualxval[$xi]=$xreal;
 1191: # Function value
 1192:                    my $funcval=&cubic_hermite($t,@yparms);
 1193: 
 1194: # Do we already have a value for this point, and is it different from the new one?
 1195:                    if ((defined($Apache::functionplotresponse::func[$xi])) &&
 1196:                        (abs($Apache::functionplotresponse::func[$xi]-$funcval)>($ymax-$ymin)/100.)) { 
 1197:                        return 'no_func'; 
 1198:                    }
 1199: # Okay, remember the new point
 1200:                    $Apache::functionplotresponse::func[$xi]=$funcval;
 1201: 
 1202:                    if (defined($funcval)) {
 1203:                       if ($xi<$Apache::functionplotresponse::functionplotrulelabels{'start'}) {
 1204:                          $Apache::functionplotresponse::functionplotrulelabels{'start'}=$xi;
 1205:                       }
 1206:                       if ($xi>$Apache::functionplotresponse::functionplotrulelabels{'end'}) {
 1207:                          $Apache::functionplotresponse::functionplotrulelabels{'end'}=$xi;
 1208:                       }
 1209:                    }
 1210: # Chain rule
 1211: # dy/dx=dy/dt/(dx/dt)
 1212:                    my $dxdt=&ddt_cubic_hermite($t,@xparms);
 1213:                    if ($dxdt) {
 1214:                       $Apache::functionplotresponse::dfuncdx[$xi]=&ddt_cubic_hermite($t,@yparms)/$dxdt;
 1215: # Second derivative
 1216:                       $Apache::functionplotresponse::d2funcdx2[$xi]=
 1217:                          ($dxdt*&d2dt2_cubic_hermite($t,@yparms)-&ddt_cubic_hermite($t,@yparms)*&d2dt2_cubic_hermite($t,@xparms))/
 1218:                          ($dxdt*$dxdt*$dxdt);
 1219:                    }
 1220:                 }
 1221:             }
 1222:         }
 1223:     }
 1224: }
 1225: 
 1226: #
 1227: # Implementation of <functionplotresponse>
 1228: #
 1229: 
 1230: sub start_functionplotresponse {
 1231:   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
 1232:   my $result='';
 1233: # To remember the splines - somehow, they need to come last
 1234:   undef %Apache::functionplotresponse::splineorder;
 1235:   undef %Apache::functionplotresponse::splineinitx;
 1236:   undef %Apache::functionplotresponse::splineinity;
 1237:   undef %Apache::functionplotresponse::splinescalex;
 1238:   undef %Apache::functionplotresponse::splinescaley;
 1239: # Remember input fields, etc
 1240:   undef %Apache::functionplotresponse::previous;
 1241:   $Apache::functionplotresponse::inputfields='';
 1242:   $Apache::functionplotresponse::counter=0;
 1243: # Remember rules
 1244:   undef @Apache::functionplotresponse::functionplotrules;
 1245:   undef @Apache::functionplotresponse::functionplotvectorrules;
 1246: # Remember failed rules
 1247:   if ($target eq 'grade') {
 1248:      undef @Apache::functionplotresponse::failedrules;
 1249:   }
 1250: # Delete previous awards
 1251:   undef $Apache::functionplotresponse::awarddetail;
 1252: # Part and ID
 1253:   my $partid=$Apache::inputtags::part;
 1254:   my $id=&Apache::response::start_response($parstack,$safeeval);
 1255: # Internal ID to mark the applet and its coordinates
 1256:   my $internalid = $partid.'_'.$id;
 1257: # Previous answer
 1258:   &decode_previous_answer($Apache::lonhomework::history{"resource.$partid.$id.submission"});
 1259: 
 1260: # Parameters of <functionplotresponse>
 1261:   my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval);
 1262:   my $xaxisvisible=(&Apache::lonxml::get_param('xaxisvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false');
 1263:   my $yaxisvisible=(&Apache::lonxml::get_param('yaxisvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false');
 1264:   my $gridvisible=(&Apache::lonxml::get_param('gridvisible',$parstack,$safeeval)=~/on|true|yes|1/i?'true':'false');
 1265:   my $xlabel=&Apache::lonxml::get_param('xlabel',$parstack,$safeeval);
 1266:   my $ylabel=&Apache::lonxml::get_param('ylabel',$parstack,$safeeval);
 1267:   if ($target eq 'edit') {
 1268:     $result.=&Apache::edit::start_table($token)
 1269:        .'<tr><td><span class="LC_nobreak">'.&mt('Function Plot Question').'</span></td>'
 1270:        .'<td><span class="LC_nobreak">'.&mt('Delete?').' '
 1271:        .&Apache::edit::deletelist($target,$token).'&nbsp;&nbsp;&nbsp;'
 1272:        .&Apache::edit::insertlist($target,$token).'&nbsp;&nbsp;&nbsp;'
 1273:        .&Apache::loncommon::help_open_topic('Function_Plot_Response_Question','Function Plot Responses')
 1274:        .'</span></td>'
 1275:        ."<td>&nbsp;"
 1276:        .&Apache::edit::end_row()
 1277:        .&Apache::edit::start_spanning_row()
 1278:        ."\n";
 1279:     $result.=&Apache::edit::text_arg('Label x-axis:','xlabel',
 1280:                                      $token,'6').'&nbsp;'.
 1281:              &Apache::edit::text_arg('Minimum x-value:','xmin',
 1282:                                      $token,'4').'&nbsp;'.
 1283:              &Apache::edit::text_arg('Maximum x-value:','xmax',
 1284:                                      $token,'4').'&nbsp;'.
 1285:              &Apache::edit::select_arg('x-axis visible:','xaxisvisible',
 1286:                                   ['yes','no'],$token).'<br />'.
 1287:              &Apache::edit::text_arg('Label y-axis:','ylabel',
 1288:                                      $token,'6').'&nbsp;'.
 1289:              &Apache::edit::text_arg('Minimum y-value:','ymin',
 1290:                                      $token,'4').'&nbsp;'.
 1291:              &Apache::edit::text_arg('Maximum y-value:','ymax',
 1292:                                      $token,'4').'&nbsp;'.
 1293:              &Apache::edit::select_arg('y-axis visible:','yaxisvisible',
 1294:                                   ['yes','no'],$token).'<br />'.
 1295:              &Apache::edit::select_arg('Grid visible:','gridvisible',
 1296:                                   ['yes','no'],$token).'<br />'.
 1297:              &Apache::edit::text_arg('Background plot(s) for answer (function(x):xmin:xmax,function(x):xmin:xmax,x1:y1:sx1:sy1:x2:y2:sx2:sy2,...):',
 1298:                                          'answerdisplay',$token,'50').
 1299:              &Apache::edit::end_row().&Apache::edit::start_spanning_row();
 1300:   } elsif ($target eq 'modified') {
 1301:     my $constructtag=&Apache::edit::get_new_args($token,$parstack,
 1302:                                                  $safeeval,'xlabel','xmin','xmax','ylabel','ymin','ymax',
 1303:                                                            'xaxisvisible','yaxisvisible','gridvisible','answerdisplay');
 1304:     if ($constructtag) { $result = &Apache::edit::rebuild_tag($token); }
 1305: 
 1306:   } elsif ($target eq 'meta') {
 1307:        $result=&Apache::response::meta_package_write('functionplotresponse');
 1308:   } elsif (($target eq 'answer') &&
 1309:             ($env{'form.answer_output_mode'} ne 'tex') &&
 1310:             ($Apache::lonhomework::viewgrades == 'F')) {
 1311:       my (undef,undef,$udom,$uname)=&Apache::lonnet::whichuser();
 1312:       my $windowopen=&Apache::lonhtmlcommon::javascript_docopen();
 1313:       my $start_page = &Apache::loncommon::start_page('Rules Log', undef,
 1314:                                                {'only_body' => 1,
 1315:                                                 'bgcolor'   => '#FFFFFF',
 1316:                                                 'js_ready'  => 1,});
 1317:       my $end_page = &Apache::loncommon::end_page({'js_ready' => 1,});
 1318:       $uname =~s/\W//g;
 1319:       $udom  =~s/\W//g;
 1320:       my $function_name =
 1321:                 join('_','LONCAPA_scriptvars',$uname,$udom,
 1322:                      $env{'form.counter'},$Apache::lonxml::curdepth);
 1323:       my $rules_var ="<script type=\"text/javascript\">
 1324: // <![CDATA[
 1325:     function $function_name() {newWindow=open('','new_W','width=500,height=500,scrollbars=1,resizable=yes');newWindow.$windowopen;newWindow.document.writeln('$start_page<pre>".
 1326:     $Apache::functionplotresponse::ruleslog.
 1327:     "<\\/pre>$end_page');newWindow.document.close();newWindow.focus()}
 1328: // ]]>
 1329: </script><a href=\"javascript:$function_name();void(0);\">".&mt('Rules Log')."</a><br />";
 1330:             &Apache::lonxml::add_script_result($rules_var);
 1331:         }
 1332: 
 1333:   return $result;
 1334: }
 1335: 
 1336: sub compare_rel {
 1337:    my ($relationship,$value,$realval,$tol)=@_;
 1338: # is the real value undefined?
 1339:    unless (defined($realval)) {
 1340: # the real value is not defined
 1341:       if ($relationship eq 'eq') {
 1342:          if ($value eq 'undef') {
 1343:             return 1;
 1344:          } else {
 1345:             return 0;
 1346:          }
 1347:       } elsif ($relationship eq 'ne') {
 1348:          if ($value eq 'undef') {
 1349:             return 0;
 1350:          } else {
 1351:             return 1;
 1352:          }
 1353:       } else {
 1354:          return 0;
 1355:       }
 1356:    }
 1357: 
 1358: # is the expected value undefined?
 1359:    if ($value eq 'undef') {
 1360: # but by now we know that the real value is defined
 1361:       return 0;
 1362:    }
 1363: 
 1364: # both are defined.
 1365:    if ($relationship eq 'gt') {
 1366:       return ($realval>$value);
 1367:    } elsif ($relationship eq 'ge') {
 1368:       return ($realval>$value-$tol);
 1369:    } elsif ($relationship eq 'lt') {
 1370:       return ($realval<$value);
 1371:    } elsif ($relationship eq 'le') {
 1372:       return ($realval<$value+$tol);
 1373:    } elsif ($relationship eq 'ne') {
 1374:       return (abs($value-$realval)>$tol);
 1375:    } else {
 1376:       return (abs($value-$realval)<$tol);
 1377:    }
 1378:    return 0;
 1379: }
 1380: 
 1381: sub addlog {
 1382:    my ($text)=@_;
 1383:    $text=~s/\'/\\\'/g;
 1384:    $Apache::functionplotresponse::ruleslog.=$text.'<br />';
 1385: }
 1386: 
 1387: sub actualval {
 1388:    my ($i,$xmin,$xmax)=@_;
 1389:    return $xmin+$i/400.*($xmax-$xmin);
 1390: }
 1391: 
 1392: sub fpr_val {
 1393:    my ($arg)=@_;
 1394:    return &actualval($Apache::functionplotresponse::functionplotrulelabels{$arg},
 1395:                      $Apache::functionplotresponse::fpr_xmin,
 1396:                      $Apache::functionplotresponse::fpr_xmax);
 1397: }
 1398: 
 1399: sub fpr_f {
 1400:    my ($arg)=@_;
 1401:    return $Apache::functionplotresponse::func[&array_index($Apache::functionplotresponse::fpr_xmin,
 1402:                                                            $Apache::functionplotresponse::fpr_xmax,
 1403:                                                            $arg)];
 1404: }
 1405: 
 1406: sub fpr_dfdx {
 1407:    my ($arg)=@_;
 1408:    return $Apache::functionplotresponse::dfuncdx[&array_index($Apache::functionplotresponse::fpr_xmin,
 1409:                                                               $Apache::functionplotresponse::fpr_xmax,
 1410:                                                               $arg)];
 1411: }
 1412: 
 1413: sub fpr_d2fdx2 {
 1414:    my ($arg)=@_;
 1415:    return $Apache::functionplotresponse::d2funcdx2[&array_index($Apache::functionplotresponse::fpr_xmin,
 1416:                                                                 $Apache::functionplotresponse::fpr_xmax,
 1417:                                                                 $arg)];
 1418: }
 1419: 
 1420: sub fpr_vectorcoords {
 1421:    my ($arg)=@_;
 1422:    $arg=~s/\W//gs;
 1423:    $arg=ucfirst($arg);
 1424:    my $id=$Apache::inputtags::response[-1];
 1425:    my $partid=$Apache::inputtags::part;
 1426:    my $internalid = $partid.'_'.$id;
 1427:    return ($env{'form.HWVAL_'.$internalid.'_'.$arg.'Start_x'},
 1428:            $env{'form.HWVAL_'.$internalid.'_'.$arg.'End_x'},
 1429:            $env{'form.HWVAL_'.$internalid.'_'.$arg.'Start_y'},
 1430:            $env{'form.HWVAL_'.$internalid.'_'.$arg.'End_y'});
 1431: }
 1432: 
 1433: sub fpr_objectcoords {
 1434:    my ($arg)=@_;
 1435:    $arg=~s/\W//gs;
 1436:    $arg=ucfirst($arg);
 1437:    my $id=$Apache::inputtags::response[-1];
 1438:    my $partid=$Apache::inputtags::part;
 1439:    my $internalid = $partid.'_'.$id;
 1440:    return ($env{'form.HWVAL_'.$internalid.'_'.$arg.'_x'},
 1441:            $env{'form.HWVAL_'.$internalid.'_'.$arg.'_y'});
 1442: }
 1443: 
 1444: sub fpr_vectorlength {
 1445:    my ($arg)=@_;
 1446:    my ($xs,$xe,$ys,$ye)=&fpr_vectorcoords($arg);
 1447:    return sqrt(($xe-$xs)*($xe-$xs)+($ye-$ys)*($ye-$ys));
 1448: }
 1449: 
 1450: sub fpr_vectorangle {
 1451:    my ($arg)=@_;
 1452:    my ($xs,$xe,$ys,$ye)=&fpr_vectorcoords($arg);
 1453:    my $angle=57.2957795*atan2(($ye-$ys),($xe-$xs));
 1454:    if ($angle<0) { $angle=360+$angle; }
 1455:    return $angle;
 1456: }
 1457: 
 1458: sub vectorcoords {
 1459:    my ($id,$label)=@_;
 1460:    return ($env{'form.HWVAL_'.$id.'_'.$label.'Start_x'},
 1461:            $env{'form.HWVAL_'.$id.'_'.$label.'End_x'},
 1462:            $env{'form.HWVAL_'.$id.'_'.$label.'Start_y'},
 1463:            $env{'form.HWVAL_'.$id.'_'.$label.'End_y'});
 1464: }
 1465: 
 1466: sub objectcoords {
 1467:    my ($id,$label)=@_;
 1468:    return ($env{'form.HWVAL_'.$id.'_'.$label.'_x'},
 1469:            $env{'form.HWVAL_'.$id.'_'.$label.'_y'});
 1470: }
 1471: 
 1472: sub attached {
 1473:    my ($id,$vector,$object,$xmin,$xmax,$ymin,$ymax)=@_;
 1474:    my ($xs,$xe,$ys,$ye)=&vectorcoords($id,$vector);
 1475:    my ($xo,$yo)=&objectcoords($id,$object);
 1476:    my $tolx=($xmax-$xmin)/100.;
 1477:    my $toly=($ymax-$ymin)/100.;
 1478:    my $tail=0;
 1479:    my $tip=0;
 1480:    &addlog("Proximity $vector ($xs,$xe,$ys,$ye) to $object ($xo,$yo)");
 1481:    if ((abs($xs-$xo)<$tolx) && (abs($ys-$yo)<$toly)) { $tail=1; }
 1482:    if ((abs($xe-$xo)<$tolx) && (abs($ye-$yo)<$toly)) { $tip=1; }
 1483:    &addlog("Result tail:$tail tip:$tip");
 1484:    return($tail,$tip);
 1485: }
 1486: 
 1487:  
 1488: sub vectorangle {
 1489:    my ($x,$y)=@_;
 1490:    my $angle=57.2957795*atan2($y,$x);
 1491:    if ($angle<0) { $angle=360+$angle; }
 1492:    return $angle;
 1493: }
 1494: 
 1495: sub vectorlength {
 1496:    my ($x,$y)=@_;
 1497:    return sqrt($x*$x+$y*$y);
 1498: }
 1499: 
 1500: sub relvector {
 1501:    my ($xs,$xe,$ys,$ye)=@_;
 1502:    return ($xe-$xs,$ye-$ys);
 1503: }
 1504: 
 1505: sub plotvectorlength {
 1506:    return &vectorlength(&relvector(&vectorcoords(@_)));
 1507: }
 1508: 
 1509: sub plotvectorangle {
 1510:    return &vectorangle(&relvector(&vectorcoords(@_)));
 1511: }
 1512: 
 1513: 
 1514: #
 1515: # Evaluate a functionplotvectorrule
 1516: #
 1517: 
 1518: sub functionplotvectorrulecheck {
 1519:    my ($rule,$xmin,$xmax,$ymin,$ymax,$safeeval)=@_;
 1520:    &addlog("=================");
 1521:    my ($label,$type)=split(/\:/,$rule);
 1522:    if ($type eq 'vector') {
 1523:       return &vectorcheck($rule,$xmin,$xmax,$ymin,$ymax,$safeeval);
 1524:    } elsif ($type eq 'sum') {
 1525:       return &sumcheck($rule,$xmin,$xmax,$ymin,$ymax,$safeeval);
 1526:    } elsif ($type eq 'custom') {
 1527:       return &customcheck($rule,$safeeval);
 1528:    }
 1529: }
 1530: 
 1531: sub vectorcheck {
 1532:    my ($rule,$xmin,$xmax,$ymin,$ymax,$safeeval)=@_;
 1533:    my ($label,$type,$id,$vector,
 1534:        $attachpoint,$notattachpoint,
 1535:        $tailpoint,$tippoint,$nottailpoint,$nottippoint,
 1536:        $length,$angle,$lengtherror,$angleerror)=split(/\:/,$rule);
 1537:    &addlog("Vector Rule $label for vector ".$vector);
 1538:    if ($length ne '') {
 1539:       &addlog("Checking for length $length with error $lengtherror");
 1540:       $length=&Apache::run::run($length,$safeeval);
 1541:       &addlog("Length evaluated to $length");
 1542:       my $thislength=&plotvectorlength($id,$vector);
 1543:       &addlog("Found length $thislength");
 1544:       if (abs($thislength-$length)>$lengtherror) {
 1545:          &setfailed($label);
 1546:          return 0;
 1547:       }
 1548:    }
 1549:    if ($angle ne '') {
 1550:       &addlog("Checking for angle $angle with error $angleerror");
 1551:       $angle=&Apache::run::run($angle,$safeeval);
 1552:       &addlog("Angle evaluated to $angle");
 1553:       my $thisangle=&plotvectorangle($id,$vector);
 1554:       &addlog("Found angle $thisangle");
 1555:       my $anglediff=abs($thisangle-$angle);
 1556:       &addlog("Angle difference: $anglediff");
 1557:       if ($anglediff>360.-$anglediff) {
 1558:          $anglediff=360.-$anglediff;
 1559:       }
 1560:       &addlog("Smallest angle difference: $anglediff");
 1561:       if ($anglediff>$angleerror) {
 1562:          &setfailed($label);
 1563:          return 0;
 1564:       }
 1565:    }
 1566:    if ($attachpoint ne '') {
 1567:       &addlog("Checking attached: ".$attachpoint);
 1568:       my ($tail,$tip)=&attached($id,$vector,$attachpoint,$xmin,$xmax,$ymin,$ymax);
 1569:       unless ($tail || $tip) {
 1570:          &setfailed($label);
 1571:          return 0;
 1572:       }
 1573:    }
 1574:    if ($notattachpoint ne '') {
 1575:       &addlog("Checking not attached: ".$notattachpoint);
 1576:       my ($tail,$tip)=&attached($id,$vector,$notattachpoint,$xmin,$xmax,$ymin,$ymax);
 1577:       if ($tail || $tip) {
 1578:          &setfailed($label);
 1579:          return 0;
 1580:       }
 1581:    }
 1582:    if ($tailpoint ne '') {
 1583:       &addlog("Checking tail: ".$tailpoint);
 1584:       my ($tail,$tip)=&attached($id,$vector,$tailpoint,$xmin,$xmax,$ymin,$ymax);
 1585:       unless ($tail) {
 1586:          &setfailed($label);
 1587:          return 0;
 1588:       }
 1589:    }
 1590:    if ($nottailpoint ne '') {
 1591:       &addlog("Checking not tail: ".$nottailpoint);
 1592:       my ($tail,$tip)=&attached($id,$vector,$nottailpoint,$xmin,$xmax,$ymin,$ymax);
 1593:       if ($tail) {
 1594:          &setfailed($label);
 1595:          return 0;
 1596:       }
 1597:    }
 1598:    if ($tippoint ne '') {
 1599:       &addlog("Checking tip: ".$tippoint);
 1600:       my ($tail,$tip)=&attached($id,$vector,$tippoint,$xmin,$xmax,$ymin,$ymax);
 1601:       unless ($tip) {
 1602:          &setfailed($label);
 1603:          return 0;
 1604:       }
 1605:    }
 1606:    if ($nottippoint ne '') {
 1607:       &addlog("Checking not tip: ".$nottippoint);
 1608:       my ($tail,$tip)=&attached($id,$vector,$nottippoint,$xmin,$xmax,$ymin,$ymax);
 1609:       if ($tip) {
 1610:          &setfailed($label);
 1611:          return 0;
 1612:       }
 1613:    }
 1614: 
 1615:    &addlog("Rule $label passed.");
 1616:    return 1;
 1617: }
 1618: 
 1619: sub sumcheck {
 1620:    my ($rule,$xmin,$xmax,$ymin,$ymax,$safeeval)=@_;
 1621:    my ($label,$type,$id,$vectors,$length,$angle,$lengtherror,$angleerror)=split(/\:/,$rule);
 1622:    &addlog("Vector Sum Rule $label for vectors ".$vectors);
 1623:    my $sumx=0;
 1624:    my $sumy=0;
 1625:    foreach my $sv (split(/\s*\,\s*/,$vectors)) {
 1626:       my ($rx,$ry)=&relvector(&vectorcoords($id,$sv));
 1627:       $sumx+=$rx;
 1628:       $sumy+=$ry;
 1629:    }
 1630:    &addlog("Sum vector ($sumx,$sumy)");
 1631:    if ($length ne '') {
 1632:       &addlog("Checking length $length with error $lengtherror");
 1633:       $length=&Apache::run::run($length,$safeeval);
 1634:       &addlog("Evaluated to $length");
 1635:       my $thislength=&vectorlength($sumx,$sumy);
 1636:       &addlog("Actual length $thislength");
 1637:       if (abs($length-$thislength)>$lengtherror) {
 1638:                   &setfailed($label);
 1639:          return 0;
 1640:       }
 1641:    }
 1642:    if ($angle ne '') {
 1643:       &addlog("Checking angle $angle with error $angleerror");
 1644:       $angle=&Apache::run::run($angle,$safeeval);
 1645:       &addlog("Evaluated to $angle");
 1646:       my $thisangle=&vectorangle($sumx,$sumy);
 1647:       &addlog("Actual angle $thisangle");
 1648:       my $anglediff=abs($thisangle-$angle);
 1649:       &addlog("Angle difference: $anglediff");
 1650:       if ($anglediff>360.-$anglediff) {
 1651:          $anglediff=360.-$anglediff;
 1652:       }
 1653:       &addlog("Smallest angle difference: $anglediff");
 1654:       if ($anglediff>$angleerror) {
 1655:          &setfailed($label);
 1656:          return 0;
 1657:       }
 1658:    }
 1659:    &addlog("Rule $label passed.");
 1660:    return 1;
 1661: }
 1662: 
 1663: sub customcheck {
 1664:    my ($rule,$safeeval)=@_;
 1665:    my ($label,$type,$prg)=split(/\:/,$rule);
 1666:    &addlog("Custom Rule ".$label);
 1667:    my $result=&Apache::run::run(&unescape($prg),$safeeval);
 1668:    &addlog("Algorithm returned $result");
 1669:    unless ($result) {
 1670:       &setfailed($label);
 1671:       return 0;
 1672:    }
 1673:    &addlog("Rule $label passed.");
 1674:    return 1;
 1675: }
 1676: 
 1677: #
 1678: # Evaluate a functionplotrule
 1679: #
 1680:  
 1681: sub functionplotrulecheck {
 1682:    my ($rule,$xmin,$xmax,$ymin,$ymax,$safeeval)=@_;
 1683: 
 1684:    my ($label,$derivative,$xinitial,$xinitiallabel,$xfinal,$xfinallabel,$minimumlength,$maximumlength,$relationship,$value,$percent)
 1685:       =split(/\:/,$rule);
 1686:    $percent=($percent>0?$percent:5);
 1687:    &addlog("=================");
 1688:    &addlog("Rule $label for ".($derivative<0?'integral':('function itself','first derivative','second derivative')[$derivative])." $relationship $value");
 1689: #
 1690: # Evaluate the value
 1691: #
 1692:    if ($value=~/\D/) {
 1693:       $Apache::functionplotresponse::fpr_xmin=$xmin;
 1694:       $Apache::functionplotresponse::fpr_xmax=$xmax;
 1695:       $value=&Apache::run::run($value,$safeeval);
 1696:       &addlog("Value evaluated to $value");
 1697:    }
 1698: 
 1699: #
 1700: # Minimum and maximum lengths of the interval
 1701: #
 1702:    if ((defined($minimumlength)) || (defined($maximumlength))) {
 1703:       &addlog("Minimumlength $minimumlength Maximumlength $maximumlength");
 1704:    }
 1705:    my $li=0;
 1706:    my $lh=400;
 1707: 
 1708: # Special case: the upper boundary was not defined
 1709: # and needs to be set to the value where
 1710: # the condition is not true anymore => set flag
 1711: 
 1712:    my $findupper=0;
 1713:    if (($xfinal eq '')
 1714:     && (!defined($Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}))
 1715:     && ($xfinallabel)) {
 1716:        $findupper=1;
 1717:    }
 1718: 
 1719: # if a hard value is set for the boundaries, it overrides the label
 1720:    if (($xinitial ne '') && ($xinitiallabel ne '') && ($xinitiallabel ne 'start')) {
 1721:       $li=&array_index($xmin,$xmax,$xinitial);
 1722:       $Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel}=$li;
 1723:    }
 1724:    if (($xfinal ne '') && ($xfinallabel ne '') && ($xfinallabel ne 'end')) {
 1725:       $lh=&array_index($xmin,$xmax,$xfinal);
 1726:       $Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}=$lh;
 1727:    }
 1728: # if the label is defined, use it
 1729:    if (defined($Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel})) {
 1730:       &addlog("Using lower label $xinitiallabel");
 1731:       $li=$Apache::functionplotresponse::functionplotrulelabels{$xinitiallabel};
 1732:    } else {
 1733:       $li=&array_index($xmin,$xmax,$xinitial);
 1734:    }
 1735:    unless ($findupper) {
 1736:       if (defined($Apache::functionplotresponse::functionplotrulelabels{$xfinallabel})) {
 1737:          &addlog("Using upper label $xfinallabel");
 1738:          $lh=$Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}-1;
 1739:       } else {
 1740:          $lh=&array_index($xmin,$xmax,$xfinal);
 1741:       }
 1742:    }
 1743: # Basic sanity checks
 1744:    if ($li<0) { $li=0; }
 1745:    if ($lh>400) { $lh=400; }
 1746:    if (($li>$lh) || (!defined($lh))) {
 1747:        $lh=$li;
 1748:    }
 1749: 
 1750:    &addlog("Boundaries: x=".&actualval($li,$xmin,$xmax)." (".$Apache::functionplotresponse::actualxval[$li]."; index $li)) to x=".
 1751:                             &actualval($lh,$xmin,$xmax)." (".$Apache::functionplotresponse::actualxval[$lh]."; index $lh))");
 1752:    if ($findupper) {
 1753:       &addlog("Looking for label $xfinallabel");
 1754:    }
 1755:    my $tol=$percent*($ymax-$ymin)/100;
 1756:    if ($xmax>$xmin) {
 1757:       if ($derivative==2) {
 1758:          $tol=4.*$tol/($xmax-$xmin);
 1759:       } elsif ($derivative==1) {
 1760:          $tol=2.*$tol/($xmax-$xmin);
 1761:       } elsif ($derivative==-1) {
 1762:          $tol=$tol*($xmax-$xmin)/2.;
 1763:       }
 1764:    }
 1765:    my $integral=0;
 1766:    my $binwidth=($xmax-$xmin)/400.;
 1767:    if (($derivative<0) && (!$findupper)) {
 1768: # definite integral, calculate over whole length
 1769:      &addlog("Calculating definite integral");
 1770:      for (my $i=$li; $i<=$lh; $i++) {
 1771:         $integral+=$Apache::functionplotresponse::func[$i]*$binwidth;
 1772:      }
 1773:      unless (&compare_rel($relationship,$value,$integral,$tol)) {
 1774:         &addlog("Actual integral ".(defined($integral)?$integral:'undef').", expected $value, tolerance $tol");
 1775:         &addlog("Rule $label failed.");
 1776:         &setfailed($label);
 1777:         return 0;
 1778:      } 
 1779:    } else {
 1780:      for (my $i=$li; $i<=$lh; $i++) {
 1781:         my $val;
 1782:         if ($derivative==2) {
 1783:            $val=$Apache::functionplotresponse::d2funcdx2[$i];
 1784:         } elsif ($derivative==1) {
 1785:            $val=$Apache::functionplotresponse::dfuncdx[$i];
 1786:         } elsif ($derivative==-1) {
 1787:            $integral+=$Apache::functionplotresponse::func[$i]*$binwidth;
 1788:            $val=$integral;      
 1789:         } else {
 1790:            $val=$Apache::functionplotresponse::func[$i];
 1791:         }
 1792:         unless (&compare_rel($relationship,$value,$val,$tol)) { 
 1793:            &addlog("Actual value ".(defined($val)?$val:'undef').", expected $value, tolerance $tol");
 1794:            &addlog("Condition not fulfilled at x=".&actualval($i,$xmin,$xmax)." (".$Apache::functionplotresponse::actualxval[$i]."; index $i)");
 1795:            if (($findupper) && ($i>$li)) {
 1796: # Check lengths
 1797:               unless (&checklength($i,$li,$minimumlength,$maximumlength,$xmin,$xmax,$label)) { return 0; }
 1798: # Successfully found a new label, set it
 1799:               $Apache::functionplotresponse::functionplotrulelabels{$xfinallabel}=$i;
 1800:               &addlog("Rule $label passed, setting label $xfinallabel");
 1801:               return 1;
 1802:            } else {
 1803:               &addlog("Rule $label failed.");
 1804:               &setfailed($label);
 1805:               return 0; 
 1806:            }
 1807:         }
 1808:      }
 1809:    }
 1810: # Corner case where this makes sense: using start or stop as defined labels
 1811:    unless (&checklength($lh,$li,$minimumlength,$maximumlength,$xmin,$xmax,$label)) { return 0; }
 1812:    &addlog("Rule $label passed.");
 1813:    return 1;
 1814: }
 1815: 
 1816: #
 1817: # check for minimum and maximum lengths
 1818: #
 1819: 
 1820: sub checklength {
 1821:     my ($i,$li,$minimumlength,$maximumlength,$xmin,$xmax,$label)=@_;
 1822:     unless (($minimumlength) || ($maximumlength)) { return 1; }
 1823:     my $length=&actualval($i,$xmin,$xmax)-&actualval($li,$xmin,$xmax);
 1824:     if ($minimumlength) {
 1825:        if ($length<$minimumlength) {
 1826:           &addlog("Rule $label failed, actual length $length, minimum length $minimumlength");
 1827:           &setfailed($label);
 1828:           return 0;
 1829:        }
 1830:     }
 1831:     if ($maximumlength) {
 1832:        if ($length>$maximumlength) {
 1833:           &addlog("Rule $label failed, actual length $length, maximum length $maximumlength");
 1834:           &setfailed($label);
 1835:           return 0;
 1836:        }
 1837:     }
 1838:     return 1;
 1839: }
 1840: 
 1841: sub setfailed {
 1842:    my ($hintlabel)=@_;
 1843:    $hintlabel=~s/^R//;
 1844:    push(@Apache::functionplotresponse::failedrules,$hintlabel);
 1845:    &addlog("Set hint condition $hintlabel");
 1846: }
 1847: 
 1848: sub start_functionplotruleset {
 1849:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
 1850:    if ($target eq 'edit') {
 1851:       return &Apache::edit::start_table($token).
 1852:         '<tr><td><span class="LC_nobreak">'.&mt('Function Plot Rule Set').'</span></td>'
 1853:        .'<td><span class="LC_nobreak">'.&mt('Delete?').' '
 1854:        .&Apache::edit::deletelist($target,$token).'&nbsp;&nbsp;&nbsp;'.
 1855:         &Apache::edit::insertlist($target,$token).'&nbsp;&nbsp;&nbsp;'
 1856:        .&Apache::loncommon::help_open_topic('Function_Plot_Response_Rule_Set','Function Plot Rules')
 1857:        .'</span></td>'
 1858:        ."<td>&nbsp;"
 1859:        .&Apache::edit::end_row()
 1860:        .&Apache::edit::start_spanning_row()
 1861:        ."\n";
 1862:    }
 1863: }
 1864: 
 1865: sub end_functionplotruleset {
 1866:     my ($target,$token,$tagstack,$parstack,$parser,$safeeval)=@_;
 1867:     my $id=$Apache::inputtags::response[-1];
 1868:     my $partid=$Apache::inputtags::part;
 1869:     my $internalid = $partid.'_'.$id;
 1870: 
 1871:     if ($target eq 'edit' ) {
 1872:         return &Apache::edit::end_table();
 1873:     }  elsif ($target eq 'grade'
 1874:          && &Apache::response::submitted()
 1875:          && $Apache::lonhomework::type ne 'exam') {
 1876: #
 1877: # Actually grade
 1878: #
 1879:     my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-2);
 1880: 
 1881:         my $ad='';
 1882:         undef  %Apache::functionplotresponse::functionplotrulelabels;
 1883:         $Apache::functionplotresponse::ruleslog='';
 1884:         $Apache::functionplotresponse::functionplotrulelabels{'start'}=400;
 1885:         $Apache::functionplotresponse::functionplotrulelabels{'end'}=0;
 1886:         if (&populate_arrays($internalid,$xmin,$xmax,$ymin,$ymax) eq 'no_func') {
 1887:            $ad='NOT_FUNCTION';
 1888:         } else {
 1889:            &addlog("Start of function ".&actualval($Apache::functionplotresponse::functionplotrulelabels{'start'},$xmin,$xmax)." (index ".
 1890:                                         $Apache::functionplotresponse::functionplotrulelabels{'start'}.")");
 1891:            &addlog("End of function ".&actualval($Apache::functionplotresponse::functionplotrulelabels{'end'},$xmin,$xmax)." (index ".
 1892:                                         $Apache::functionplotresponse::functionplotrulelabels{'end'}.")");
 1893: 
 1894: # We have a function that we can actually grade, go through the spline rules.
 1895:            foreach my $rule (@Apache::functionplotresponse::functionplotrules) {
 1896:               unless (&functionplotrulecheck($rule,$xmin,$xmax,$ymin,$ymax,$safeeval)) {
 1897:                  $ad='INCORRECT';
 1898:                  last;
 1899:               }
 1900:            }
 1901: # And now go through the vector rules
 1902:            foreach my $rule (@Apache::functionplotresponse::functionplotvectorrules) {
 1903:               unless (&functionplotvectorrulecheck($rule,$xmin,$xmax,$ymin,$ymax,$safeeval)) {
 1904:                  $ad='INCORRECT';
 1905:                  last;
 1906:               }
 1907:            }
 1908: # If it's not wrong, it's correct 
 1909:            unless ($ad) { $ad='EXACT_ANS' };
 1910:         }
 1911:         &addlog("Set hint conditions: ".join(",",@Apache::functionplotresponse::failedrules));
 1912:         &addlog("Assigned award detail: $ad");
 1913: # Store for later to be assigned at end_functionplotresponse
 1914:         $Apache::functionplotresponse::awarddetail=$ad;
 1915:      }
 1916: }
 1917: 
 1918: 
 1919: sub end_functionplotresponse {
 1920:   my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
 1921:   &Apache::response::end_response;
 1922: 
 1923:   my $result;
 1924:   my $id=$Apache::inputtags::response[-1];
 1925:   my $partid=$Apache::inputtags::part;
 1926:   my $internalid = $partid.'_'.$id;
 1927: 
 1928:     if ($target eq 'edit') { $result=&Apache::edit::end_table(); }
 1929:     if ($target eq 'grade'
 1930:          && &Apache::response::submitted()
 1931:          && $Apache::lonhomework::type eq 'exam') {
 1932: 
 1933:         &Apache::response::scored_response($partid,$id);
 1934: 
 1935:     } elsif ($target eq 'grade'
 1936:          && &Apache::response::submitted()
 1937:          && $Apache::lonhomework::type ne 'exam') {
 1938:         my ($response,%coords)=&get_answer_from_form_fields($internalid);
 1939:         $Apache::lonhomework::results{"resource.$partid.$id.submission"}=$response;
 1940:         my %previous=&Apache::response::check_for_previous($response,$partid,$id);
 1941: #
 1942: # Assign grade
 1943: #
 1944:         my $ad=$Apache::functionplotresponse::awarddetail;
 1945: #
 1946: # Store grading info
 1947: #
 1948:         $Apache::lonhomework::results{"resource.$partid.$id.awarddetail"}=$ad;
 1949:         &Apache::response::handle_previous(\%previous,$ad);
 1950:    } elsif ($target eq 'web') {
 1951:         undef @Apache::functionplotresponse::failedrules;
 1952:    }
 1953:    return $result;
 1954: }
 1955: 
 1956: sub end_functionplotelements {
 1957:   my ($target,$token,$tagstack,$parstack,$parser,$safeeval)=@_;
 1958:   my $result='';
 1959:   my $id=$Apache::inputtags::response[-1];
 1960:   my $partid=$Apache::inputtags::part;
 1961:   my $internalid = $partid.'_'.$id;
 1962:   if ($target eq 'edit' ) {
 1963:      $result=&Apache::edit::end_table();
 1964:   } elsif ($target eq 'web') {
 1965:      my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-2);
 1966: 
 1967: # Are we in show answer mode?
 1968:      my $showanswer=&Apache::response::show_answer();
 1969:      if ($showanswer) {
 1970: # Render answerdisplay
 1971:         my $answerdisplay=&Apache::lonxml::get_param('answerdisplay',$parstack,$safeeval,-2);
 1972:         if ($answerdisplay=~/\S/s) {
 1973:            foreach my $plot (split(/\s*\,\s*/,$answerdisplay)) {
 1974:               my @components=split(/\s*\:\s*/,$plot);
 1975:               if ($#components<3) {
 1976: # Just a simple plot
 1977:                  my ($func,$xl,$xh)=@components;
 1978:                  if ((!defined($xl)) || ($xl eq '')) { $xl=$xmin; }
 1979:                  if ((!defined($xh)) || ($xh eq '')) { $xh=$xmax; }
 1980:                  $result.=&plot_script($internalid,$func,1,'','00aa00',$xl,$xh,6);
 1981:               } else {
 1982: # This is a spline
 1983:                  $result.=&answer_spline_script($internalid,@components);
 1984:               }
 1985:            }
 1986:         }
 1987:      }
 1988:      my $fixed=0;
 1989:      if (($showanswer) || (&Apache::response::check_status()>=2)) { $fixed=1; }
 1990: # Now is the time to render all of the stored splines
 1991:      foreach my $label (keys(%Apache::functionplotresponse::splineorder)) {
 1992:         $result.=&generate_spline($internalid,$label,$xmin,$xmax,$ymin,$ymax,$fixed);
 1993:      }
 1994: # close the init script
 1995:      $result.=&end_init_script();
 1996: # register all splines in this response 
 1997:      $result.='<input type="hidden" name="HWVAL_AllSplines_'.$internalid.'" value="'.
 1998:                  join(',',keys(%Apache::functionplotresponse::splineorder)).'" />'."\n";
 1999:      foreach my $label (keys(%Apache::functionplotresponse::splineorder)) {
 2000:         $result.='<input type="hidden" name="HWVAL_SplineOrder_'.$internalid.'_'.$label.'" value="'.
 2001:                  $Apache::functionplotresponse::splineorder{$label}.'" />'."\n";
 2002:      }
 2003: # generate the input fields
 2004:      $result.=$Apache::functionplotresponse::inputfields;
 2005: # actually start the <applet>-tag
 2006:      $result.=&geogebra_startcode($internalid);
 2007: # load the spline bytecode
 2008:      $result.=&geogebra_spline_program();
 2009: # set default parameters
 2010:      $result.=&geogebra_default_parameters($internalid);
 2011: # close the <applet>-tag
 2012:      $result.=&geogebra_endcode();
 2013:   }
 2014:   return $result;
 2015: }
 2016: 
 2017: sub boundaries {
 2018:    my ($parstack,$safeeval,$level)=@_;
 2019:    my $xmin=&Apache::lonxml::get_param('xmin',$parstack,$safeeval,$level);
 2020:    $xmin=(defined($xmin)?$xmin:-10);
 2021:    my $xmax=&Apache::lonxml::get_param('xmax',$parstack,$safeeval,$level);
 2022:    $xmax=(defined($xmax)?$xmax:10);
 2023:    my $ymin=&Apache::lonxml::get_param('ymin',$parstack,$safeeval,$level);
 2024:    $ymin=(defined($ymin)?$ymin:-10);
 2025:    my $ymax=&Apache::lonxml::get_param('ymax',$parstack,$safeeval,$level);
 2026:    $ymax=(defined($ymax)?$ymax:10);
 2027:    if ($xmax<=$xmin) {
 2028:       $xmax=$xmin+20;
 2029:    }
 2030:    if ($ymax<=$ymin) {
 2031:       $ymax=$ymin+20;
 2032:    }
 2033:    return ($xmin,$xmax,$ymin,$ymax);
 2034: }
 2035: 
 2036: sub start_functionplotelements {
 2037:    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
 2038:    my $result='';
 2039:    my $id=$Apache::inputtags::response[-1];
 2040:    my $partid=$Apache::inputtags::part;
 2041:    my $internalid = $partid.'_'.$id;
 2042: 
 2043:    if ($target eq 'edit') {
 2044:       return &Apache::edit::start_table($token).
 2045:         '<tr><td><span class="LC_nobreak">'.&mt('Function Plot Elements').'</span></td>'
 2046:        .'<td><span class="LC_nobreak">'.&mt('Delete?').' '
 2047:        .&Apache::edit::deletelist($target,$token).'&nbsp;&nbsp;&nbsp;'.
 2048:         &Apache::edit::insertlist($target,$token).'&nbsp;&nbsp;&nbsp;'
 2049:        .&Apache::loncommon::help_open_topic('Function_Plot_Response_Elements','Function Plot Elements')
 2050:        .'</span></td>'
 2051:        ."<td>&nbsp;"
 2052:        .&Apache::edit::end_row()
 2053:        .&Apache::edit::start_spanning_row()
 2054:        ."\n";
 2055:    } elsif ($target eq 'web') {
 2056:       my ($xmin,$xmax,$ymin,$ymax)=&boundaries($parstack,$safeeval,-2);
 2057:       my $xaxisvisible=(&Apache::lonxml::get_param('xaxisvisible',$parstack,$safeeval,-2)=~/on|true|yes|1/i?'true':'false');
 2058:       my $yaxisvisible=(&Apache::lonxml::get_param('yaxisvisible',$parstack,$safeeval,-2)=~/on|true|yes|1/i?'true':'false');
 2059:       my $gridvisible=(&Apache::lonxml::get_param('gridvisible',$parstack,$safeeval,-2)=~/on|true|yes|1/i?'true':'false');
 2060:       my $xlabel=&Apache::lonxml::get_param('xlabel',$parstack,$safeeval,-2);
 2061:       my $ylabel=&Apache::lonxml::get_param('ylabel',$parstack,$safeeval,-2);
 2062: 
 2063: 
 2064: # paste in the update routine to receive stuff back from the applet
 2065:      $result.=&update_script($internalid);
 2066: # start the initscript for this applet
 2067:      $result.=&start_init_script($internalid);
 2068: # put the axis commands inside
 2069:      $result.=&axes_script($internalid,$xmin,$xmax,$ymin,$ymax,$xaxisvisible,$yaxisvisible,$gridvisible);
 2070:      $result.=&axes_label($internalid,$xmin,$xmax,$ymin,$ymax,$xlabel,$ylabel);
 2071: # init script is left open
 2072:   }
 2073:   return $result;
 2074: }
 2075: 
 2076: 1;
 2077: 
 2078: __END__
 2079:  
 2080: =head1 NAME
 2081: 
 2082: Apache::functionplotresponse.pm;
 2083: 
 2084: =head1 SYNOPSIS
 2085: 
 2086: Handles tags associated with accepting function plots.
 2087: 
 2088: This is part of the LearningOnline Network with CAPA project
 2089: described at http://www.lon-capa.org.
 2090: 
 2091: =head1 HANDLER SUBROUTINE
 2092: 
 2093: start_functionplotresponse()
 2094: 
 2095: =head1 OTHER SUBROUTINES
 2096: 
 2097: =over
 2098: 
 2099: =item end_functionplotresponse()
 2100: 
 2101: =back
 2102: 
 2103: =cut

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