--- loncom/homework/functionplotresponse.pm	2010/10/31 12:33:02	1.21
+++ loncom/homework/functionplotresponse.pm	2010/11/06 14:37:24	1.23
@@ -1,7 +1,7 @@
 # LearningOnline Network with CAPA
 # option list style responses
 #
-# $Id: functionplotresponse.pm,v 1.21 2010/10/31 12:33:02 www Exp $
+# $Id: functionplotresponse.pm,v 1.23 2010/11/06 14:37:24 www Exp $
 #
 # Copyright Michigan State University Board of Trustees
 #
@@ -363,7 +363,7 @@ sub end_splinerule {
 
 
 #
-# <spline label="..." order="1,2,3,4" initx="..." inity="..." scalex="..." scaley="..." />
+# <spline index="..." order="1,2,3,4" initx="..." inity="..." scalex="..." scaley="..." />
 #
 # Unfortunately, GeoGebra seems to want all splines after everything else, so we need to store them
 #
@@ -371,15 +371,19 @@ sub start_spline {
    my ($target,$token,$tagstack,$parstack,$parser,$safeeval,$style)=@_;
    my $result='';
    if ($target eq 'web') {
-      my $label=&Apache::lonxml::get_param('label',$parstack,$safeeval);
+      my $label=&Apache::lonxml::get_param('index',$parstack,$safeeval);
       $Apache::functionplotresponse::counter++;
       if ($label=~/\W/) {
-         &Apache::lonxml::warning(&mt('Spline labels should only contain alphanumeric characters.'));
+         &Apache::lonxml::warning(&mt('Spline indices should only contain alphanumeric characters.'));
       }
       $label=~s/\W//gs;
-      unless ($label) { $label='S'.$Apache::functionplotresponse::counter; }
+      unless ($label) { 
+         $label='S'.$Apache::functionplotresponse::counter; 
+      } else {
+         $label='S'.$label;
+      }
       if ($Apache::functionplotresponse::splineorder{$label}) {
-         &Apache::lonxml::error(&mt('Spline labels must be unique.'));
+         &Apache::lonxml::error(&mt('Spline indices must be unique.'));
       }
 
       my $order=&Apache::lonxml::get_param('order',$parstack,$safeeval);
@@ -404,7 +408,7 @@ sub start_spline {
       $Apache::functionplotresponse::splinescaley{$label}=$sy;
    } elsif ($target eq 'edit') {
         $result=&Apache::edit::tag_start($target,$token,'Spline').
-             &Apache::edit::text_arg('Label:','label',
+             &Apache::edit::text_arg('Index:','index',
                                      $token,'4').'&nbsp;'.
              &Apache::edit::select_arg('Order:','order',
                                   ['2','3','4','5','6','7','8','9'],$token).'&nbsp;'.
@@ -419,7 +423,7 @@ sub start_spline {
              &Apache::edit::end_row();
   } elsif ($target eq 'modified') {
     my $constructtag=&Apache::edit::get_new_args($token,$parstack,
-                                                 $safeeval,'label','order','initx','inity',
+                                                 $safeeval,'index','order','initx','inity',
                                                            'scalex','scaley');
     if ($constructtag) { $result=&Apache::edit::rebuild_tag($token); }
   }
@@ -524,7 +528,6 @@ sub indices_scale {
    my ($xmin,$xmax,$x)=@_;
    my $i=&array_index($xmin,$xmax,$x);
    my $xr=&index_x($xmin,$xmax,$i);
-   &Apache::lonnet::logthis("x:$x i:$i xr:$xr");
    if ($xr<$x) {
 # Desired x is right of array index
       if ($i>=200) { return (200,200,0); }
@@ -553,9 +556,37 @@ sub func_val {
    unless (defined($fl) || defined($fh)) { return undef; }
    unless (defined($fl)) { return $fh; }
    unless (defined($fh)) { return $fl; }
-   my $func=$fl+$factor*($fh-$fl);
-   &Apache::lonnet::logthis("x:$x func:$func factor:$factor il:$il ih:$ih fil:$fl fih:$fh");
-   return $func;
+   return $fl+$factor*($fh-$fl);
+}
+
+#
+# First derivative
+#
+
+sub dfuncdx_val {
+   my ($xmin,$xmax,$x)=@_;
+   my ($il,$ih,$factor)=&indices_scale($xmin,$xmax,$x);
+   my $fl=$Apache::functionplotresponse::dfuncdx[$il];
+   my $fh=$Apache::functionplotresponse::dfuncdx[$ih];
+   unless (defined($fl) || defined($fh)) { return undef; }
+   unless (defined($fl)) { return $fh; }
+   unless (defined($fh)) { return $fl; }
+   return $fl+$factor*($fh-$fl);
+}
+
+#
+# Second derivative
+#
+
+sub d2funcdx2_val {
+   my ($xmin,$xmax,$x)=@_;
+   my ($il,$ih,$factor)=&indices_scale($xmin,$xmax,$x);
+   my $fl=$Apache::functionplotresponse::d2funcdx2[$il];
+   my $fh=$Apache::functionplotresponse::d2funcdx2[$ih];
+   unless (defined($fl) || defined($fh)) { return undef; }
+   unless (defined($fl)) { return $fh; }
+   unless (defined($fh)) { return $fl; }
+   return $fl+$factor*($fh-$fl);
 }
 
 #
@@ -566,7 +597,7 @@ sub populate_arrays {
     my ($id,$xmin,$xmax)=@_;
     for (my $i=0; $i<=200; $i++) {
        $Apache::functionplotresponse::func[$i]=undef;
-       $Apache::functionplotresponse::dfunddx[$i]=undef;
+       $Apache::functionplotresponse::dfuncdx[$i]=undef;
        $Apache::functionplotresponse::d2funcd2x[$i]=undef;
     }
     unless ($xmax>$xmin) { return 'no_func'; }
@@ -591,7 +622,18 @@ sub populate_arrays {
                 if (($xi>$xiold) && ($xi>=0) && ($xi<=200)) {
                    if (defined($Apache::functionplotresponse::func[$xi])) { return 'no_func'; }
                    $xiold=$xi;
+# Function value
                    $Apache::functionplotresponse::func[$xi]=&cubic_hermite($t,@yparms);
+# dy/dx=dy/dt/(dx/dt)
+                   my $dxdt=&ddt_cubic_hermite($t,@xparms);
+                   if ($dxdt) {
+                      $Apache::functionplotresponse::dfuncdx[$xi]=&ddt_cubic_hermite($t,@yparms)/$dxdt;
+                   }
+# d^2y/dx^2
+                   my $d2xdt2=&d2dt2_cubic_hermite($t,@xparms);
+                   if ($d2xdt2) {
+                      $Apache::functionplotresponse::d2funcd2x[$xi]=&d2dt2_cubic_hermite($t,@yparms)/$d2xdt2;
+                   }
                 }
             }
         }
@@ -722,25 +764,6 @@ sub end_functionplotresponse {
         } else {
            $ad='INCORRECT';
         }
-        &func_val($xmin,$xmax,3.96);
-
-        &func_val($xmin,$xmax,3.965);
-
-        &func_val($xmin,$xmax,3.97);
-        &func_val($xmin,$xmax,3.975);
-        &func_val($xmin,$xmax,3.98);
-
-        &func_val($xmin,$xmax,3.985);
-        &func_val($xmin,$xmax,3.99);
-        &func_val($xmin,$xmax,3.995);
-
-        &func_val($xmin,$xmax,4);
-        &func_val($xmin,$xmax,4.05);
-        &func_val($xmin,$xmax,4.1);
-
-        &func_val($xmin,$xmax,4.15);
-        &func_val($xmin,$xmax,4.2);
-        &func_val($xmin,$xmax,4.25);
 
 #
 # Store grading info