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<h1><a href="http://freetype.org/index.html">FreeType</a> Glyph
Conventions / II</h1>
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<h2>II. Glyph Outlines</h2>
<p>This section describes the way scalable representations
of glyph images, called outlines, are used by FreeType as
well as client applications.</p>
<h3 id="section-1">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 exhibits varying
resolutions in both 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 <em>dpi</em> (dots per
inch). For example, a printer with a resolution of
300×600 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 (10″ and 25″ monitors don't
have the same pixel sizes at 1024×768), 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 <em>physical</em> unit, where 1 point
equals 1/72 of an inch in digital typography. As an
example, most books using the Latin script are printed
with a body text size somewhere between 10 and
14 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>
<code>pixel_size = point_size * resolution / 72</code>
</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 depends on 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>
<h3 id="section-2">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>Bézier
arcs</em>.</p>
<p>The arcs are defined through <em>control points</em>, and
can be either second-order (these are <em>conic</em>
Béziers) or third-order (<em>cubic</em>
Béziers) polynomials, depending on the font format.
Note that conic Béziers are usually called
<em>quadratic</em> Béziers in the literature.
Hence, FreeType associates each point of the outline with
flags to indicate its type (normal or control point). As
a consequence, 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's origin being at (0,0); they thus range from
-32768 to 32767. (Even though point coordinates can
be floats in other formats such as Type 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> axis goes from the left to the right,
and the <i>Y</i> 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 characters 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 size used to scale the outlines
to a given text dimension. For example, a size of
12pt at 300×300 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 align="center">
<code>pixel_size = point_size * resolution / 72</code><br>
<code>pixel_coord = grid_coord * pixel_size / EM_size</code>
</p>
<p>Another acronym used for the pixel size
is <em>ppem</em> (pixel per EM); this value can be
fractional also. Note that fractional ppem values are
not supported everywhere.</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 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; Type 1 or CFF PostScript fonts
traditionally use an EM size of 1000 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 square is thus just
a convention in 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, <code>pixel_size</code> computed in
the above formula does not directly relate 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>
<p align="center">
<img src="font-comparison.svg"
height="80%"
width="80%"
alt="Comparison of font heights">
</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.</p>
<h3 id="section-3">3. Hinting and Bitmap rendering</h3>
<p>The outline as stored in a font file is called the
‘master’ outline, as its point coordinates are
expressed in font units. Before it can be converted into
a bitmap, it must be scaled to a given size and
resolution. This is done with a very simple
transformation, but especially at small sizes undesirable
artifacts can appear, in particular stems of different
width or height in letters like ‘E’ or
‘H’ can occur.</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> (often
called <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’
glyphs 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 class="emph">
<p>explicit grid-fitting</p>
<p>The TrueType format defines a stack-based virtual
machine, for which programs (also
called <em>bytecode</em>) can be written with the help
of more than 200 operators, most of them related
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 class="emph">
<p>implicit grid-fitting (also called hinting)</p>
<p>The Type 1, CFF, and CFF2 formats take 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 class="emph">
<p>automatic grid-fitting</p>
<p>Some formats include no control information with each
glyph outline, apart from font 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 summarizes the pros and cons of each
scheme.</p>
<table class="vertical-space">
<thead>
<tr>
<th align="center">
<b>grid-fitting scheme</b>
</th>
<th align="center">
<b>advantages</b>
</th>
<th align="center">
<b>disadvantages</b>
</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="center">
<p><b>explicit</b></p>
</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 (at least in theory).</p>
</td>
<td valign="top">
<p><b>Speed.</b> Interpreting bytecode can be slow
if the glyph programs are complex.</p>
<p><b>Size.</b> Glyph programs can be long.</p>
<p><b>Technical difficulty.</b> It is extremely
difficult to write good hinting programs. Very
few tools available.</p>
</td>
</tr>
<tr>
<td valign="top" align="center">
<p><b>implicit</b></p>
</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" align="center">
<p><b>automatic</b></p>
</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>
</tbody>
</table>
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<div class="updated">
<p>Last update: 23-Oct-2022</p>
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