Commit 0901f653dbc5d121501168a9248dc95660b96a16

Werner Lemberg 2000-11-09T08:01:18

Revised.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
diff --git a/docs/glyphs/glyphs-1.html b/docs/glyphs/glyphs-1.html
index df4bee7..4b409af 100644
--- a/docs/glyphs/glyphs-1.html
+++ b/docs/glyphs/glyphs-1.html
@@ -56,6 +56,8 @@
   </table>
   </center>
 
+  <p><hr></p>
+
   <table width="100%">
   <tr bgcolor="#CCCCFF"
       valign=center><td>
@@ -166,6 +168,8 @@
     they are usually expressed in pixels then.</p>
 
 
+  <p><hr></p>
+
   <center>
   <table width="100%"
          border=0
diff --git a/docs/glyphs/glyphs-2.html b/docs/glyphs/glyphs-2.html
index ba84e9d..70ece64 100644
--- a/docs/glyphs/glyphs-2.html
+++ b/docs/glyphs/glyphs-2.html
@@ -1,12 +1,13 @@
-<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
+<!doctype html public "-//w3c//dtd html 4.0 transitional//en"
+          "http://www.w3.org/TR/REC-html40/loose.dtd">
 <html>
 <head>
-   <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
-   <meta name="Author" content="blob">
-   <meta name="GENERATOR" content="Mozilla/4.5 [fr] (Win98; I) [Netscape]">
-   <title>FreeType Glyph Conventions</title>
+  <meta http-equiv="Content-Type"
+        content="text/html; charset=iso-8859-1">
+  <meta name="Author"
+        content="David Turner">
+  <title>FreeType Glyph Conventions</title>
 </head>
-<body>
 
 <body text="#000000"
       bgcolor="#FFFFFF"
@@ -14,354 +15,381 @@
       vlink="#51188E"
       alink="#FF0000">
 
-<center><h1>
-FreeType Glyph Conventions
-</h1></center>
-
-<center><h2>
-version 2.1
-</h2></center>
-
-<center><h3>
-Copyright 1998-2000 David Turner (<a href="mailto:david@freetype.org">david@freetype.org</a>)<br>
-Copyright 2000 The FreeType Development Team (<a href="devel@freetype.org">devel@freetype.org</a>)
-</h3></center>
-
-<center><table width=650><tr><td>
-
-<center><table width="100%" border=0 cellpadding=5><tr bgcolor="#CCFFCC" valign=center>
-<td align=center width="30%">
-<a href="glyphs-1.html">Previous</a>
-</td>
-<td align=center width="30%">
-<a href="index.html">Contents</a>
-</td>
-<td align=center width="30%">
-<a href="glyphs-3.html">Next</a>
-</td>
-</tr></table></center>
-
-<table width="100%" cellpadding=4><tr bgcolor="#CCCCFF" valign=center><td><h2>
-II. Glyph Outlines
-</h2></td></tr></table>
-
-<p>This section describes the way scalable representation of glyph images,
-   called outlines, are used by FreeType as well as client applications.</p>
-
-<h3><a name="section-1">
-1. Pixels, Points and Device Resolutions :
-</h3><blockquote>
-
-<p>Though it is a very common assumption when dealing with computer
-graphics programs, the physical dimensions of a given pixel (be it for
-screens or printers) are not squared. Often, the output device, be it a
-screen or printer exhibits varying resolutions in the horizontal and vertical
-directions, and this must be taken care of when rendering text.
-</p>
-
-<p>It is thus common to define a device's characteristics through two numbers
-expressed in <b>dpi</b> (dots per inch). For example, a printer with a
-resolution of 300x600 dpi has 300 pixels per inch in the horizontal
-direction, and 600 in the vertical one. The resolution of a typical computer
-monitor varies with its size (a 15" and 17" monitors don't have the same
-pixel sizes at 640x480), and of course the graphics mode resolution.
-</p>
-
-<p>As a consequence, the size of text is usually given in <b>points</b>,
-rather than device-specific pixels. Points are a simple <i>physical</i>
-unit, where 1 point = 1/72th of an inch, in digital typography. As an
-example, most roman books are printed with a body text which size is
-chosen between 10 and 14 points.</p>
-
-<p>It is thus possible to compute the size of text in pixels from the size
-in points through the following computation :</p>
+<h1 align=center>
+  FreeType Glyph Conventions
+</h1>
 
-<center>
-<p><tt>pixel_size = point_size * resolution / 72</tt></center>
-
-<p>Where resolution is expressed in <em>dpi</em>. Note that because the
-horizontal and vertical resolutions may differ, a single point size
-usually defines different text width and height in pixels.</p>
-
-<p><b>IMPORTANT NOTE:</b>
-<br><i>Unlike what is often thought, the "size of text in pixels" is not
-directly related to the real dimensions of characters when they're displayed
-or printed. The relationship between these two concepts is a bit more complex
-and relate to some design choice made by the font designer. This is described
-in more details the next sub-section (see the explanations on the EM square).
-</i></p>
-
-
-
-</blockquote><h3><a name="section-2">
-2. Vectorial representation :
-</h3><blockquote>
-
-
-
-<p>The source format of outlines is a collection of closed paths
-called <b>contours</b>. Each contour delimits an outer or inner <i>region</i>
-of the glyph, and can be made of either <b>line segments</b> or <b>bezier
-arcs</b>.</p>
-
-<p>The arcs are defined through <b>control points</b>, and can be either
-second-order (these are "conic" beziers) or third-order ("cubic" beziers) polynomials, depending on
-the font format. Note that conic beziers are usually called "quadratic"
-beziers in the literature. Hence, each point of the outline has an
-associated <b>flag</b> indicating its type (normal or control point).
-And scaling the points will scale the whole outline.
-</p>
-
-<p>Each glyph's original outline points are located on a grid of indivisible
-units. The points are usually stored in a font file as 16-bit integer grid
-coordinates, with the grid origin's being at (0,0); they thus range from
--16384 to 16383. (even though point coordinates can be floats in other
-formats such as Type 1, we'll restrict our analysis to integer ones, driven
-by the need for simplicity..).
-</p>
-
-<p><b>IMPORTANT NOTE:</b>
-<br><i>The grid is always oriented like the traditional mathematical 2D
-plane, i.e. the X axis from the left to the right, and the Y axis from
-bottom to top.</i></p>
-
-<p>In creating the glyph outlines, a type designer uses an imaginary square
-called the "EM square". Typically, the EM square can be thought of as a
-tablet on which the character are drawn. The square's size, i.e., the number
-of grid units on its sides, is very important for two reasons:</p>
-
-<ul>
-<li><p>
-it is the reference used to scale the outlines to a given text dimension.
-For example, a size of 12pt at 300x300 dpi corresponds to 12*300/72 = 50
-pixels. This is the size the EM square would appear on the output device
-if it was rendered directly. In other words, scaling from grid units to
-pixels uses the formula:</p>
-
-<p><center><tt>pixel_size = point_size * resolution / 72</tt>
-<br><tt>pixel_coordinate = grid_coordinate * pixel_size / EM_size</tt>
-</center></p>
-
-
-<li><p>
-the greater the EM size is, the larger resolution the designer can use
-when digitizing outlines. For example, in the extreme example of an EM
-size of 4 units, there are only 25 point positions available within the
-EM square which is clearly not enough. Typical TrueType fonts use an EM
-size of 2048 units (note: with Type 1 PostScript fonts, the EM size is
-fixed to 1000 grid units. However, point coordinates can be expressed in
-floating values).
-</p></li>
-</ul>
-
-<p>Note that glyphs can freely extend beyond the EM square if the font
-designer wants so. The EM is used as a convenience, and is a valuable
-convenience from traditional typography.</p>
+<h2 align=center>
+  Version&nbsp;2.1
+</h2>
 
-<center>
-<p><b>Note : Grid units are very often called "font units" or "EM units".</b></center>
-
-<p><b>NOTE:</b>
-<br><i>As said before, the pixel_size computed in&nbsp; the above formula
-does not relate directly to the size of characters on the screen. It simply
-is the size of the EM square if it was to be displayed directly. Each font
-designer is free to place its glyphs as it pleases him within the square.
-This explains why the letters of the following text have not the same height,
-even though they're displayed at the same point size with distinct fonts
-:</i>
-<center>
-<p><img SRC="body_comparison.png" height=40 width=580></center>
-
-<p>As one can see, the glyphs of the Courier family are smaller than those
-of Times New Roman, which themselves are slightly smaller than those of
-Arial, even though everything is displayed or printed&nbsp; at a size of
-16 points. This only reflect design choices.
-</p>
-
-
-
-</blockquote><h3><a name="section-3">
-3. Hinting and Bitmap rendering
-</h3><blockquote>
-
-<p>The outline as stored in a font file is called the "master"
-outline, as its points coordinates are expressed in font units. Before
-it can be converted into a bitmap, it must be scaled to a given
-size/resolution. This is done through a very simple transform, but always
-creates undesirable artifacts, e.g. stems of different widths or heights
-in letters like "E" or "H".
-</p>
-
-<p>As a consequence, proper glyph rendering needs the scaled points to
-be aligned along the target device pixel grid, through an operation called
-"grid-fitting", and often "hinting". One of its main purpose is to ensure
-that important widths and heights are respected throughout the whole font
-(for example, it is very often desirable that the "I" and the "T" have
-their central vertical line of the same pixel width), as well as manage
-features like stems and overshoots, which can cause problems at small pixel
-sizes.
-</p>
-
-<p>There are several ways to perform grid-fitting properly, for example
-most scalable formats associate some control data or programs with each
-glyph outline. Here is an overview :</p>
-
-<blockquote>
-<blockquote><b>explicit grid-fitting :</b>
-<blockquote>The TrueType format defines a stack-based virtual machine,
-for which programs can be written with the help of more than 200 opcodes
-(most of these relating to geometrical operations). Each glyph is thus
-made of both an outline and a control program, its purpose being to perform
-the actual grid-fitting in the way defined by the font designer.</blockquote>
-
-<p><br><b>implicit grid-fitting (also called hinting) :</b>
-<blockquote>The Type 1 format takes a much simpler approach : each glyph
-is made of an outline as well as several pieces called "hints" which are
-used to describe some important features of the glyph, like the presence
-of stems, some width regularities, and the like. There aren't a lot of
-hint types, and it's up to the final renderer to interpret the hints in
-order to produce a fitted outline.</blockquote>
-
-<p><br><b>automatic grid-fitting :</b>
-<blockquote>Some formats simply include no control information with each
-glyph outline, apart metrics like the advance width and height. It's then
-up to the renderer to "guess" the more interesting features of the outline
-in order to perform some decent grid-fitting.</blockquote>
-</blockquote>
-</blockquote>
+<h3 align=center>
+  Copyright&nbsp;1998-2000 David Turner (<a
+  href="mailto:david@freetype.org">david@freetype.org</a>)<br>
+  Copyright&nbsp;2000 The FreeType Development Team (<a
+  href="mailto:devel@freetype.org">devel@freetype.org</a>)
+</h3>
 
 <center>
-<p><br>The following table summarises the pros and cons of each scheme
-:</center>
-</blockquote>
-
-<center><table BORDER=0 WIDTH="80%" BGCOLOR="#CCCCCC" >
-<tr BGCOLOR="#999999">
-<td>
-<blockquote>
-<center><b><font color="#000000">Grid-fitting scheme</font></b></center>
-</blockquote>
-</td>
-
-<td>
-<blockquote>
-<center><b><font color="#000000">Pros</font></b></center>
-</blockquote>
-</td>
-
-<td>
-<blockquote>
-<center><b><font color="#000000">Cons</font></b></center>
-</blockquote>
-</td>
-</tr>
-
-<tr>
-<td>
-<blockquote>
-<center><b><font color="#000000">Explicit</font></b></center>
-</blockquote>
-</td>
-
-<td>
-<blockquote>
-<center><b><font color="#000000">Quality</font></b>
-<br><font color="#000000">excellence at small sizes is possible. This is
-very important for screen display.</font>
-<p><b><font color="#000000">Consistency</font></b>
-<br><font color="#000000">all renderers produce the same glyph bitmaps.</font></center>
-</blockquote>
-</td>
-
-<td>
-<blockquote>
-<center><b><font color="#000000">Speed</font></b>
-<br><font color="#000000">intepreting bytecode can be slow if the glyph
-programs are complex.</font>
-<p><b><font color="#000000">Size</font></b>
-<br><font color="#000000">glyph programs can be long</font>
-<p><b><font color="#000000">Technicity</font></b>
-<br><font color="#000000">it is extremely difficult to write good hinting
-programs. Very few tools available.</font></center>
-</blockquote>
-</td>
-</tr>
-
-<tr>
-<td>
-<blockquote>
-<center><b><font color="#000000">Implicit</font></b></center>
-</blockquote>
-</td>
-
-<td>
-<blockquote>
-<center><b><font color="#000000">Size</font></b>
-<br><font color="#000000">hints are usually much smaller than explicit
-glyph programs.</font>
-<p><b><font color="#000000">Speed</font></b>
-<br><font color="#000000">grid-fitting is usually a fast process</font></center>
-</blockquote>
-</td>
-
-<td>
-<blockquote>
-<center><b><font color="#000000">Quality</font></b>
-<br><font color="#000000">often questionable at small sizes. Better with
-anti-aliasing though.</font>
-<p><b><font color="#000000">Inconsistency</font></b>
-<br><font color="#000000">results can vary between different renderers,
-or even distinct versions of the same engine.</font></center>
-</blockquote>
-</td>
-</tr>
-
-<tr>
-<td>
-<blockquote>
-<center><b><font color="#000000">Automatic</font></b></center>
-</blockquote>
-</td>
-
-<td>
-<blockquote>
-<center><b><font color="#000000">Size</font></b>
-<br><font color="#000000">no need for control information, resulting in
-smaller font files.</font>
-<p><b><font color="#000000">Speed</font></b>
-<br><font color="#000000">depends on the grid-fitting algo.Usually faster
-than explicit grid-fitting.</font></center>
-</blockquote>
-</td>
-
-<td>
-<blockquote>
-<center><b><font color="#000000">Quality</font></b>
-<br><font color="#000000">often questionable at small sizes. Better with
-anti-aliasing though</font>
-<p><b><font color="#000000">Speed</font></b>
-<br><font color="#000000">depends on the grid-fitting algo.</font>
-<p><b><font color="#000000">Inconsistency</font></b>
-<br><font color="#000000">results can vary between different renderers,
-or even distinct versions of the same engine.</font></center>
-</blockquote>
-</td>
-</tr>
-</table></center>
-</blockquote>
-
-<center><table width="100%" border=0 cellpadding=5><tr bgcolor="#CCFFCC" valign=center>
-<td align=center width="30%">
-<a href="glyphs-1.html">Previous</a>
-</td>
-<td align=center width="30%">
-<a href="index.html">Contents</a>
-</td>
-<td align=center width="30%">
-<a href="glyphs-3.html">Next</a>
-</td>
-</tr></table></center>
-
-</td></tr></table></center>
+<table width="65%">
+<tr><td>
+
+  <center>
+  <table width="100%"
+         border=0
+         cellpadding=5>
+  <tr bgcolor="#CCFFCC"
+      valign=center>
+    <td align=center
+        width="30%">
+      <a href="glyphs-1.html">Previous</a>
+    </td>
+    <td align=center
+        width="30%">
+      <a href="index.html">Contents</a>
+    </td>
+    <td align=center
+        width="30%">
+      <a href="glyphs-3.html">Next</a>
+    </td>
+  </tr>
+  </table>
+  </center>
+
+  <p><hr></p>
+
+  <table width="100%">
+  <tr bgcolor="#CCCCFF"
+      valign=center><td>
+    <h2>
+      II. Glyph Outlines
+    </h2>
+  </td></tr>
+  </table>
+
+  <p>This section describes the way scalable representation of glyph images,
+  called outlines, are used by FreeType as well as client applications.</p>
+
+    <a name="section-1">
+    <h3>
+      1. Pixels, points and device resolutions
+    </h3>
+
+    <p>Though it is a very common assumption when dealing with computer
+    graphics programs, the physical dimensions of a given pixel (be it for
+    screens or printers) are not squared.  Often, the output device, be it a
+    screen or printer, exhibits varying resolutions in both horizontal and
+    vertical direction, and this must be taken care of when rendering
+    text.</p>
+
+    <p>It is thus common to define a device's characteristics through two
+    numbers expressed in <em>dpi</em> (dots per inch).  For example, a
+    printer with a resolution of 300x600&nbsp;dpi has 300&nbsp;pixels per
+    inch in the horizontal direction, and 600 in the vertical one.  The
+    resolution of a typical computer monitor varies with its size
+    (15"&nbsp;and 17"&nbsp;monitors don't have the same pixel sizes at
+    640x480), and of course the graphics mode resolution.</p>
+
+    <p>As a consequence, the size of text is usually given in
+    <em>points</em>, rather than device-specific pixels.  Points are a
+    simple <em>physical</em> unit, where 1&nbsp;point&nbsp;=&nbsp;1/72th of
+    an inch, in digital typography.  As an example, most Roman books are
+    printed with a body text which size is chosen between 10 and
+    14&nbsp;points.</p>
+
+    <p>It is thus possible to compute the size of text in pixels from the
+    size in points with the following formula:</p>
+
+    <center>
+      <tt>pixel_size = point_size * resolution / 72</tt>
+    </center>
+
+    <p>The resolution is expressed in <em>dpi</em>.  Since horizontal and
+    vertical resolutions may differ, a single point size usually defines a
+    different text width and height in pixels.</p>
+
+    <p><em>Unlike what is often thought, the "size of text in pixels" is not
+    directly related to the real dimensions of characters when they are
+    displayed or printed.  The relationship between these two concepts is a
+    bit more complex and relate to some design choices made by the font
+    designer.  This is described in more detail in the next sub-section (see
+    the explanations on the EM square).</em></p>
+
+
+    <a name="section-2">
+    <h3>
+      2. Vectorial representation
+    </h3>
+
+    <p>The source format of outlines is a collection of closed paths called
+    <em>contours</em>.  Each contour delimits an outer or inner
+    <em>region</em> of the glyph, and can be made of either <em>line
+    segments</em> or <em>B&eacute;zier arcs</em>.</p>
+
+    <p>The arcs are defined through <em>control points</em>, and can be
+    either second-order (these are <em>conic</em> B&eacute;ziers) or
+    third-order (<em>cubic</em> B&eacute;ziers) polynomials, depending on
+    the font format.  Note that conic B&eacute;ziers are usually called
+    <em>quadratic</em> B&eacute;ziers in the literature.  Hence, each point
+    of the outline has an associated flag indicating its type (normal or
+    control point).  And scaling the points will scale the whole
+    outline.</p>
+
+    <p>Each glyph's original outline points are located on a grid of
+    indivisible units.  The points are usually stored in a font file as
+    16-bit integer grid coordinates, with the grid origin's being at (0,0);
+    they thus range from -16384 to&nbsp;16383.  (Even though point
+    coordinates can be floats in other formats such as Type&nbsp;1, we will
+    restrict our analysis to integer values for simplicity).</p>
+
+    <p><em>The grid is always oriented like the traditional mathematical
+    two-dimensional plane, i.e., the <i>X</i>&nbsp;axis from the left to the
+    right, and the <i>Y</i>&nbsp;axis from bottom to top.</em></p>
+
+    <p>In creating the glyph outlines, a type designer uses an imaginary
+    square called the <em>EM square</em>.  Typically, the EM square can be
+    thought of as a tablet on which the character are drawn.  The square's
+    size, i.e., the number of grid units on its sides, is very important for
+    two reasons:</p>
+
+    <ul>
+      <li>
+        <p>It is the reference used to scale the outlines to a given text
+        dimension.  For example, a size of 12pt at 300x300&nbsp;dpi
+        corresponds to 12*300/72&nbsp;=&nbsp;50&nbsp;pixels.  This is the
+        size the EM square would appear on the output device if it was
+        rendered directly.  In other words, scaling from grid units to
+        pixels uses the formula:</p>
+
+        <p><center>
+          <tt>pixel_size = point_size * resolution / 72</tt><br>
+          <tt>pixel_coord = grid_coord * pixel_size / EM_size</tt>
+        </center></p>
+      </li>
+      <li>
+        <p>The greater the EM size is, the larger resolution the designer
+        can use when digitizing outlines.  For example, in the extreme
+        example of an EM size of 4&nbsp;units, there are only 25&nbsp;point
+        positions available within the EM square which is clearly not
+        enough.  Typical TrueType fonts use an EM size of 2048&nbsp;units;
+        Type&nbsp;1 PostScript fonts have a fixed EM size of 1000&nbsp;grid
+        units but point coordinates can be expressed as floating values.</p>
+      </li>
+    </ul>
+
+    <p>Note that glyphs can freely extend beyond the EM square if the font
+    designer wants so.  The EM is used as a convenience, and is a valuable
+    convenience from traditional typography.</p>
+
+    <p>Grid units are very often called <em>font units</em> or <em>EM
+    units</em>.</p>
+
+    <p><em>As said before, <tt>pixel_size</tt> computed in the above formula
+    does not relate directly to the size of characters on the screen.  It
+    simply is the size of the EM square if it was to be displayed.  Each
+    font designer is free to place its glyphs as it pleases him within the
+    square.  This explains why the letters of the following text have not
+    the same height, even though they are displayed at the same point size
+    with distinct fonts:</em>
+
+    <p><center>
+      <img src="body_comparison.png"
+           height=40 width=580
+           alt="Comparison of font heights">
+    </center></p>
+
+    <p>As one can see, the glyphs of the Courier family are smaller than
+    those of Times New Roman, which themselves are slightly smaller than
+    those of Arial, even though everything is displayed or printed at a size
+    of 16&nbsp;points.  This only reflects design choices.</p>
+
+
+    <a name="section-3">
+    <h3>
+      3. Hinting and Bitmap rendering
+    </h3>
+
+    <p>The outline as stored in a font file is called the "master" outline,
+    as its points coordinates are expressed in font units.  Before it can be
+    converted into a bitmap, it must be scaled to a given size/resolution. 
+    This is done through a very simple transformation, but always creates
+    undesirable artifacts, e.g. stems of different widths or heights in
+    letters like "E" or "H".</p>
+
+    <p>As a consequence, proper glyph rendering needs the scaled points to
+    be aligned along the target device pixel grid, through an operation
+    called <em>grid-fitting</em>, and often <em>hinting</em>.  One of its
+    main purposes is to ensure that important widths and heights are
+    respected throughout the whole font (for example, it is very often
+    desirable that the "I" and the "T" have their central vertical line of
+    the same pixel width), as well as to manage features like stems and
+    overshoots, which can cause problems at small pixel sizes.</p>
+
+    <p>There are several ways to perform grid-fitting properly; most
+    scalable formats associate some control data or programs with each glyph
+    outline.  Here is an overview:</p>
+
+    <ul>
+      <li>
+        <p><em>explicit grid-fitting</em></p>
+
+        <p>The TrueType format defines a stack-based virtual machine, for
+        which programs can be written with the help of more than
+        200&nbsp;opcodes (most of these relating to geometrical operations). 
+        Each glyph is thus made of both an outline and a control program to
+        perform the actual grid-fitting in the way defined by the font
+        designer.</p>
+      </li>
+      <li>
+        <p><em>implicit grid-fitting (also called hinting)</em></p>
+
+        <p>The Type&nbsp;1 format takes a much simpler approach: Each glyph
+        is made of an outline as well as several pieces called
+        <em>hints</em> which are used to describe some important features of
+        the glyph, like the presence of stems, some width regularities, and
+        the like.  There aren't a lot of hint types, and it is up to the
+        final renderer to interpret the hints in order to produce a fitted
+        outline.</p>
+      </li>
+      <li>
+        <p><em>automatic grid-fitting</em></p>
+
+        <p>Some formats simply include no control information with each
+        glyph outline, apart metrics like the advance width and height.  It
+        is then up to the renderer to "guess" the more interesting features
+        of the outline in order to perform some decent grid-fitting.</p>
+      </li>
+    </ul>
+
+    <p>The following table summarises the pros and cons of each scheme.</p>
+
+    <center>
+      <table width="90%"
+             bgcolor="#CCCCCC"
+             cellpadding=5>
+      <tr bgcolor="#999999">
+        <td>
+          <center>
+            <b>grid-fitting scheme</b>
+          </center>
+        </td>
+        <td>
+          <center>
+            <b>advantages</b>
+          </center>
+        </td>
+        <td>
+          <center>
+            <b>disadvantages</b>
+          </center>
+        </td>
+      </tr>
+
+      <tr>
+        <td valign=top>
+          <center>
+            <b>explicit</b>
+          </center>
+        </td>
+
+        <td valign=top>
+          <p><b>Quality.</b> Excellent results at small sizes are possible. 
+          This is very important for screen display.</p>
+
+          <p><b>Consistency.</b> All renderers produce the same glyph
+          bitmaps.</p>
+        </td>
+
+        <td valign=top>
+          <p><b>Speed.</b> Intepreting bytecode can be slow if the glyph
+          programs are complex.</p>
+
+          <p><b>Size.</b> Glyph programs can be long.</p>
+
+          <p><b>Technicity.</b>
+          It is extremely difficult to write good hinting
+          programs.  Very few tools available.</p>
+        </td>
+      </tr>
+      <tr>
+        <td valign=top>
+          <center>
+            <b>implicit</b>
+          </center>
+        </td>
+
+        <td valign=top>
+          <p><b>Size.</b> Hints are usually much smaller than explicit glyph
+          programs.</p>
+
+          <p><b>Speed.</b>
+          Grid-fitting is usually a fast process.</p>
+        </td>
+
+        <td valign=top>
+          <p><b>Quality.</b> Often questionable at small sizes.  Better with
+          anti-aliasing though.</p>
+
+          <p><b>Inconsistency.</b> Results can vary between different
+          renderers, or even distinct versions of the same engine.</p>
+        </td>
+      </tr>
+
+      <tr>
+        <td valign=top>
+          <center>
+            <b>automatic</b>
+          </center>
+        </td>
+
+        <td valign=top>
+          <p><b>Size.</b> No need for control information, resulting in
+          smaller font files.</p>
+
+          <p><b>Speed.</b> Depends on the grid-fitting algorithm.  Usually
+          faster than explicit grid-fitting.</p>
+        </td>
+
+        <td valign=top>
+          <p><b>Quality.</b> Often questionable at small sizes.  Better with
+          anti-aliasing though.</p>
+
+          <p><b>Speed.</b> Depends on the grid-fitting algorithm.</p>
+
+          <p><b>Inconsistency.</b> Results can vary between different
+          renderers, or even distinct versions of the same engine.</p>
+        </td>
+      </tr>
+      </table>
+    </center>
+
+    <p><hr></p>
+
+  <center>
+  <table width="100%"
+         border=0
+         cellpadding=5>
+  <tr bgcolor="#CCFFCC"
+      valign=center>
+    <td align=center
+        width="30%">
+      <a href="glyphs-1.html">Previous</a>
+    </td>
+    <td align=center
+        width="30%">
+      <a href="index.html">Contents</a>
+    </td>
+    <td align=center
+        width="30%">
+      <a href="glyphs-3.html">Next</a>
+    </td>
+  </tr>
+  </table>
+  </center>
+
+</td></tr>
+</table>
+</center>
+
 </body>
 </html>