diff -rc v6/Makefile v6.1/Makefile
*** v6/Makefile	Sun Nov 16 19:27:53 2008
--- v6.1/Makefile	Wed Nov 19 02:59:21 2008
***************
*** 1,19 ****
  all:	Pub/.copied
  
! VER=v6
  
  SOURCES=makeindex.php.txt hilbert.py hilbert_test.py hilbert_pic.py \
  	Makefile
  
! DIFFS=v4_${VER}_diff.txt v5_${VER}_diff.txt 
  
  PUBFILES=${SOURCES} ${DIFFS} index.html hilbert_thumb.gif hilbert_pic.pdf
  
  v4_${VER}_diff.txt:	old/${VER}/.copied
  	(cd old; diff -rc v4 ${VER} >../v4_${VER}_diff.txt; true)
  
! v5_${VER}_diff.txt:	old/${VER}/.copied
! 	(cd old; diff -rc v5 ${VER} >../v5_${VER}_diff.txt; true)
  
  old/${VER}/.copied:	${SOURCES}
  	cp ${SOURCES} old/${VER}
--- 1,22 ----
  all:	Pub/.copied
  
! VERNUM=6.1
! PREVNUM=6
! VER=v${VERNUM}
! PREV=v${PREVNUM}
  
  SOURCES=makeindex.php.txt hilbert.py hilbert_test.py hilbert_pic.py \
  	Makefile
  
! DIFFS=v4_${VER}_diff.txt ${PREV}_${VER}_diff.txt 
  
  PUBFILES=${SOURCES} ${DIFFS} index.html hilbert_thumb.gif hilbert_pic.pdf
  
  v4_${VER}_diff.txt:	old/${VER}/.copied
  	(cd old; diff -rc v4 ${VER} >../v4_${VER}_diff.txt; true)
  
! ${PREV}_${VER}_diff.txt:	old/${VER}/.copied
! 	(cd old; diff -rc ${PREV} ${VER} >../${PREV}_${VER}_diff.txt; true)
  
  old/${VER}/.copied:	${SOURCES}
  	cp ${SOURCES} old/${VER}
***************
*** 26,32 ****
  index.html:	${SOURCES} ${DIFFS}
  	rm -f index.html
  	touch datefile
! 	php makeindex.php.txt >index.html
  	chmod a-w index.html
  
  hilbert_pic.pdf:	hilbert.py hilbert_pic.py
--- 29,35 ----
  index.html:	${SOURCES} ${DIFFS}
  	rm -f index.html
  	touch datefile
! 	php makeindex.php.txt ${VERNUM} >index.html
  	chmod a-w index.html
  
  hilbert_pic.pdf:	hilbert.py hilbert_pic.py
diff -rc v6/hilbert_pic.py v6.1/hilbert_pic.py
*** v6/hilbert_pic.py	Sun Nov 16 19:27:53 2008
--- v6.1/hilbert_pic.py	Wed Nov 19 02:59:21 2008
***************
*** 15,20 ****
--- 15,27 ----
  from hilbert import int_to_Hilbert, Hilbert_to_int
  
  
+ # unit_vector -- Unit vector in the same direction as ( dx, dy ),
+ #                or (0,0) if given (0,0).
+ def unit_vector( dx, dy ):
+     d = sqrt( dx*dx + dy*dy )
+     if d == 0:  return 0, 0
+     else:       return dx / d, dy / d
+ 
  
  def draw_hilbert_pic( c, size ):
      nD = 3
***************
*** 49,72 ****
          pt = 0+0j
          for d in range( 3 ):
              pt += stretch( xyz[d] ) * projection[d]
!         return pt
  
      # Scale it...
!     # NOTE: THIS MEANS LINE WIDTHS AND FONTS AREN'T IN POINTS ANY MORE.
!     farcorner = project( ( size-1, size-1, size-1 ) )
!     stepsize = 6 * inch / farcorner.real
      c.scale( stepsize, stepsize )
      point /= ( stepsize )
  
-     prevpt = 0.+0.j
      # Collect 3D lines in a list:
      lines = []
!     prev_xyz = tuple( [0] * nD )
!     for i in range( 1, size*size*size ):
          pt_xyz = int_to_Hilbert( i, 3 )
          lines.append( ( prev_xyz, pt_xyz ) )
          prev_xyz = pt_xyz
  
      def avg_z( line ):
          start, end = line
          return( ( start[2] + end[2] ) * .5 )
--- 56,81 ----
          pt = 0+0j
          for d in range( 3 ):
              pt += stretch( xyz[d] ) * projection[d]
!         return ( pt.real, pt.imag )
  
      # Scale it...
!     # NOTE: THIS MEANS POINT != 1 FOR LINE WIDTHS AND FONTS.
!     farcorner_x, farcorner_y = project( ( size-1, size-1, size-1 ) )
!     stepsize = 6. * inch / farcorner_x
      c.scale( stepsize, stepsize )
      point /= ( stepsize )
  
      # Collect 3D lines in a list:
      lines = []
!     prev_xyz = int_to_Hilbert( 0, 3 )
!     for i in range( 1, size ** 3 ):
          pt_xyz = int_to_Hilbert( i, 3 )
          lines.append( ( prev_xyz, pt_xyz ) )
          prev_xyz = pt_xyz
  
+     width = 48 * point / farcorner_x
+     shadow_width = width * 3
+ 
      def avg_z( line ):
          start, end = line
          return( ( start[2] + end[2] ) * .5 )
***************
*** 74,100 ****
      def highest_avg_z_first( line1, line2 ):
          return -cmp( avg_z( line1 ), avg_z( line2 ) )
  
-     width = 48 * point / farcorner.real
- 
      # Display furthest-back-first, with white "shadows":
      lines.sort( highest_avg_z_first )
      for line in lines:
!         pt0 = project( line[0] )
!         pt1 = project( line[1] )
!         x0, y0 = pt0.real, pt0.imag
!         x1, y1 = pt1.real, pt1.imag
!         dx, dy  =  x1-x0, y1-y0
!         d = sqrt( dx*dx + dy*dy )
!         shadow_width = width * 3
!         if d < shadow_width * 2:
!             continue
  
!         dx, dy = dx / d, dy / d
          c.setLineWidth( shadow_width )
          c.setStrokeColorRGB(255,255,255)
-         # The shadow is a little shorter than the black line:
          c.line( x0 + dx * shadow_width, y0 + dy * shadow_width, 
                  x1 - dx * shadow_width, y1 - dy * shadow_width )
          c.setLineWidth( width )
          c.setStrokeColorRGB(0,0,0)
          c.line( x0, y0, x1, y1 )
--- 83,102 ----
      def highest_avg_z_first( line1, line2 ):
          return -cmp( avg_z( line1 ), avg_z( line2 ) )
  
      # Display furthest-back-first, with white "shadows":
      lines.sort( highest_avg_z_first )
      for line in lines:
!         x0, y0 = project( line[0] )
!         x1, y1 = project( line[1] )
!         dx, dy = unit_vector( x1-x0, y1-y0 )
  
!         # The shadow is a little shorter than the black line:
          c.setLineWidth( shadow_width )
          c.setStrokeColorRGB(255,255,255)
          c.line( x0 + dx * shadow_width, y0 + dy * shadow_width, 
                  x1 - dx * shadow_width, y1 - dy * shadow_width )
+ 
+         # Now the actual line:
          c.setLineWidth( width )
          c.setStrokeColorRGB(0,0,0)
          c.line( x0, y0, x1, y1 )
diff -rc v6/makeindex.php.txt v6.1/makeindex.php.txt
*** v6/makeindex.php.txt	Sun Nov 16 19:27:53 2008
--- v6.1/makeindex.php.txt	Wed Nov 19 02:59:21 2008
***************
*** 1,5 ****
  <?php // I create the actual index.html file like this:
!       //     php makeindex.php.txt >index.html
  ?>
  <HTML>
  <!--
--- 1,5 ----
  <?php // I create the actual index.html file like this:
!       //     php makeindex.php.txt (version-number) >index.html
  ?>
  <HTML>
  <!--
***************
*** 32,38 ****
      <td valign="top"> 
  <p>
  <h3>Hilbert Curves in More (or fewer) than Two Dimensions</h3>
! <font size="-1">version 0.6</font>
      </td>
    </tr>
  </table>
--- 32,38 ----
      <td valign="top"> 
  <p>
  <h3>Hilbert Curves in More (or fewer) than Two Dimensions</h3>
! <font size="-1">version <?php echo "$argv[1]"?></font>
      </td>
    </tr>
  </table>
***************
*** 357,366 ****
      return 0,  2**( ( -nChunks - 1 ) % nD )  # in Python 0 <=  a % b  < b.
  </font></pre>
  
! <h3>The Code and Test Code</h3>
  
  <?php
  $cmt = array(
  "hilbert.py" => "index <==> Hilbert and support functions.",
  "hilbert_test.py" => "Tests hilbert.py functions for 1 to 3 dimensions.",
  "makeindex.php.txt" => "PHP source for this page (inserts this listing).",
--- 357,367 ----
      return 0,  2**( ( -nChunks - 1 ) % nD )  # in Python 0 <=  a % b  < b.
  </font></pre>
  
! <h3>The Code, Tests &amp; Demos</h3>
  
  <?php
  $cmt = array(
+ "Makefile" => "how this directory is prepared for publishing",
  "hilbert.py" => "index <==> Hilbert and support functions.",
  "hilbert_test.py" => "Tests hilbert.py functions for 1 to 3 dimensions.",
  "makeindex.php.txt" => "PHP source for this page (inserts this listing).",
***************
*** 372,378 ****
  );
  
  echo "<table>\n";
! exec( "/bin/ls -ld hilbert.py hilbert_test.py makeindex.php.txt *diff.txt hilbert_pic.py hilbert_pic.pdf", $lines );
  foreach( $lines as $line ) {
     echo "<tr>\n";
     $parts=explode( " ", $line );
--- 373,379 ----
  );
  
  echo "<table>\n";
! exec( "/bin/ls -ld hilbert.py hilbert_test.py makeindex.php.txt *diff.txt hilbert_pic.py hilbert_pic.pdf Makefile", $lines );
  foreach( $lines as $line ) {
     echo "<tr>\n";
     $parts=explode( " ", $line );
***************
*** 382,394 ****
     foreach( $pieces as $file ) {
     } ; // Empty loop leaves file as last part
     $size=ceil( filesize($file) / 1024 );
!    echo '<td width="40%" valign="top">';
     if( isset( $subst_url[$file] ) )  $url = $subst_url[ $file ];
     else                              $url = $file;
     if( $line[0]=="d" ) {
        echo "<code><a href=\"$url/index.html\"\n>$file/</a></code>";
     } else {
!       echo "<code><a href=\"$url\"\n>$file</a> (${size}K)</code>";
     }
     echo "</td>\n";
     if( isset( $cmt[$file] ) ) {
--- 383,397 ----
     foreach( $pieces as $file ) {
     } ; // Empty loop leaves file as last part
     $size=ceil( filesize($file) / 1024 );
!    echo '<td valign="top">';
     if( isset( $subst_url[$file] ) )  $url = $subst_url[ $file ];
     else                              $url = $file;
     if( $line[0]=="d" ) {
        echo "<code><a href=\"$url/index.html\"\n>$file/</a></code>";
+       echo '</td><td valign="top">';
     } else {
!       echo "<code><a href=\"$url\"\n>$file</a></code>";
!       echo "</td><td valign=\"top\"><code>(${size}K)</code>";
     }
     echo "</td>\n";
     if( isset( $cmt[$file] ) ) {
***************
*** 452,458 ****
     ~999999999999      == -1000000000000</pre>
  <p>
  
! Unlike in C and Java, Python's '/' is divide-with-floor, and '%' is
  modulo, so that, e.g.,<pre>
     -5 / 2 == -3
     -5 % 2 == 1</pre>
--- 455,462 ----
     ~999999999999      == -1000000000000</pre>
  <p>
  
! Unlike in C and Java, Python's '/' with integer arguments is 
! divide-with-floor, and '%' is
  modulo, so that, e.g.,<pre>
     -5 / 2 == -3
     -5 % 2 == 1</pre>
***************
*** 472,478 ****
  <p>
  
  <a id="Jaffer">
! [Jaffer] Aubrey Jaffer, <a href="http://people.csail.mit.edu/jaffer/Geometry/HSFC">Hilbert Space-Filling Curves</a>
  <p>
  
  <a id="Lawder">
--- 476,482 ----
  <p>
  
  <a id="Jaffer">
! [Jaffer] Aubrey Jaffer, <a href="http://people.csail.mit.edu/jaffer/Geometry/MDSFC">Multidimensional Space-Filling Curves</a>
  <p>
  
  <a id="Lawder">