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<h1><a href="../../../index.html">FreeType</a> Glyph
Conventions / VI</h1>
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<div id="freetype-outlines">
<h2>VI. FreeType outlines</h2>
<p>The purpose of this section is to present the way
FreeType manages vectorial outlines, as well as the most
common operations that can be applied on them.</p>
<h3 id="section-1">1. FreeType outline description and
structure</h3>
<h4>a. Outline curve decomposition</h4>
<p>An outline is described as a series of closed contours in
the 2D plane. Each contour is made of a series of line
segments and Bézier arcs. Depending on the file
format, these can be second-order or third-order
polynomials. The former are also called quadratic or
conic arcs, and they are used in the TrueType format. The
latter are called cubic arcs and are mostly used in the
PostScript Type 1 and Type formats.</p>
<p>Each arc is described through a series of start, end, and
control points. Each point of the outline has a specific
tag which indicates whether it is describes a line segment
or an arc. The tags can take the following values:</p>
<table>
<tr>
<td valign="top">
<p><tt>FT_CURVE_TAG_ON</tt></p>
</td>
<td valign="top">
<p>Used when the point is ‘on’ the curve.
This corresponds to start and end points of segments
and arcs. The other tags specify what is called an
‘off’ point, i.e., a point which isn't
located on the contour itself, but serves as a
control point for a Bézier arc.</p>
</td>
</tr>
<tr>
<td valign="top">
<p><tt>FT_CURVE_TAG_CONIC</tt></p>
</td>
<td valign="top">
<p>Used for an ‘off’ point used to control
a conic Bézier arc.</p>
</td>
</tr>
<tr>
<td valign="top">
<p><tt>FT_CURVE_TAG_CUBIC</tt></p>
</td>
<td valign="top">
<p>Used for an ‘off’ point used to control
a cubic Bézier arc.</p>
</td>
</tr>
</table>
<p>Use the <tt>FT_CURVE_TAG(tag)</tt> macro to filter out
other, internally used flags.
<p>The following rules are applied to decompose the
contour's points into segments and arcs:</p>
<ul>
<li>
<p>Two successive ‘on’ points indicate a
line segment joining them.</p>
</li>
<li>
<p>One conic ‘off’ point between two
‘on’ points indicates a conic
Bézier arc, the ‘off’ point being
the control point, and the ‘on’ ones the
start and end points.</p>
</li>
<li>
<p>Two successive cubic ‘off’ points between
two ‘on’ points indicate a cubic
Bézier arc. There must be exactly two cubic
control points and two ‘on’ points for
each cubic arc (using a single cubic ‘off’
point between two ‘on’ points is
forbidden, for example).</p>
</li>
<li>
<p>Two successive conic ‘off’ points force
the rasterizer to create (during the scan-line
conversion process exclusively) a virtual
‘on’ point inbetween, at their exact
middle. This greatly facilitates the definition of
successive conic Bézier arcs. Moreover, it is
the way outlines are described in the TrueType
specification.</p>
</li>
<li>
<p>The last point in a contour uses the first as an end
point to create a closed contour. For example, if the
last two points of a contour were an ‘on’
point followed by a conic ‘off’ point, the
first point in the contour would be used as final
point to create an ‘on’ –
‘off’ – ‘on’ sequence as
described above.
</li>
<li>
<p>The first point in a contour can be a conic
‘off’ point itself; in that case, use the
last point of the contour as the contour's starting
point. If the last point is a conic ‘off’
point itself, start the contour with the virtual
‘on’ point between the last and first
point of the contour.
</li>
</ul>
<p>Note that it is possible to mix conic and cubic arcs in a
single contour, however, no font driver of FreeType
produces such outlines currently.</p>
<table>
<tr>
<td>
<img src="points_segment.png"
height="166"
width="221"
alt="segment example">
</td>
<td>
<img src="points_conic.png"
height="183"
width="236"
alt="conic arc example">
</td>
</tr>
<tr>
<td>
<img src="points_cubic.png"
height="162"
width="214"
alt="cubic arc example">
</td>
<td>
<img src="points_conic2.png"
height="204"
width="225"
alt="cubic arc with virtual 'on' point">
</td>
</tr>
</table>
<h4>b. The <tt>FT_Outline</tt> descriptor</h4>
<p>A FreeType outline is described through a simple
structure
called <a href="../reference/ft2-outline_processing.html#FT_Outline"><tt>FT_Outline</tt></a>.
Right now, the following fields are of interest:</p>
<table>
<caption>
<b><tt>FT_Outline</tt></b>
</caption>
<tbody>
<tr>
<td>
<tt>n_points</tt>
</td>
<td>
the number of points in the outline
</td>
</tr>
<tr>
<td>
<tt>n_contours</tt>
</td>
<td>
the number of contours in the outline
</td>
</tr>
<tr>
<td>
<tt>points</tt>
</td>
<td>
array of point coordinates
</td>
</tr>
<tr>
<td>
<tt>contours</tt>
</td>
<td>
array of contour end indices
</td>
</tr>
<tr>
<td>
<tt>tags</tt>
</td>
<td>
array of point flags
</td>
</tr>
</tbody>
</table>
<p>Here, <tt>points</tt> is a pointer to an array of
<a href="../reference/ft2-basic_types.html#FT_Vector"><tt>FT_Vector</tt></a>
records, used to store the vectorial coordinates of each
outline point. These are expressed in 1/64th of a pixel,
which is also known as the <em>26.6 fixed-point
format</em>.</p>
<p><tt>contours</tt> is an array of point indices to delimit
contours in the outline. For example, the first contour
always starts at point 0, and ends at
point <tt>contours[0]</tt>. The second contour starts at
point <tt>contours[0]+1</tt> and ends at
<tt>contours[1]</tt>, etc. To traverse these points in a
callback based manner,
use <a href="../reference/ft2-outline_processing.html#FT_Outline_Decompose"><tt>FT_Outline_Decompose</tt></a>.</p>
<p>Note that each contour is closed, and that value
of <tt>n_points</tt> should be equal
to <tt>contours[n_contours-1]+1</tt> for a valid
outline.</p>
<p>Finally, <tt>tags</tt> is an array of bytes, used to
store each outline point's tag.</p>
<h3 id="section-2">2. Bounding and control box
computations</h3>
<p>As described earlier, a <em>bounding box</em> (also
called <em>bbox</em>) is simply a rectangle that
completely encloses the shape of a given outline. The
interesting case is the smallest bounding box possible,
and in the following we subsume this under the term
‘bounding box’. Because of the way arcs are
defined, Bézier control points are not necessarily
contained within an outline's (smallest) bounding box.</p>
<p>Such a situation happens if one Bézier arc is, for
example, the upper edge of an outline and an
‘off’ point happens to be above the bbox.
However, it is very rare in the case of character outlines
because most font designers and creation tools always
place ‘on’ points at the extrema of each
curved edges (as both the TrueType and PostScript
specifications recommend), as it makes hinting much
easier.</p>
<p>We thus define the <em>control box</em> (also
called <em>cbox</em>) as the smallest possible rectangle
that encloses all points of a given outline (including its
‘off’ points). Clearly, it always includes
the bbox, and the two boxes are identical in most
cases.</p>
<p>Unlike the bbox, the cbox is much faster to compute.</p>
<table>
<tr>
<td>
<img src="bbox1.png"
height="264"
width="228"
alt="a glyph with different bbox and cbox">
</td>
<td>
<img src="bbox2.png"
height="229"
width="217"
alt="a glyph with identical bbox and cbox">
</td>
</tr>
</table>
<p>Control and bounding boxes can be computed automatically
using the
functions <a href="../reference/ft2-outline_processing.html#FT_Outline_Get_CBox"><tt>FT_Outline_Get_CBox</tt></a>
and
<a href="../reference/ft2-outline_processing.html#FT_Outline_Get_BBox"><tt>FT_Outline_Get_BBox</tt></a>.
The former function is always very fast, while the
latter <em>may</em> be slow in the case of
‘outside’ control points (as it needs to find
the extreme of conic and cubic arcs for
‘perfect’ computations). If this isn't the
case, it is as fast as computing the control box.
<p>Note also that even though most glyph outlines have equal
cbox and bbox values to ease hinting, this is not
necessarily the case if a transformation like rotation is
applied to them.</p>
<h3 id="section-3">3. Coordinates, scaling and
grid-fitting</h3>
<p>An outline point's vectorial coordinates are expressed in
the 26.6 format, i.e. in 1/64th of a pixel, hence the
coordinates ‘(1.0,-2.5)’ is stored as the
integer pair ‘(64,-192)’, to name an
example.</p>
<p>After a glyph outline is scaled from the EM grid (in font
units) to the current character dimensions, the hinter or
grid-fitter is in charge of aligning important outline
points (mainly edge delimiters) to the pixel grid. Even
though this process is much too complex to be described in
a few lines, its purpose is mainly to round point
positions, while trying to preserve important properties
like widths, stems, etc.</p>
<p>The following operations can be used to round vectorial
distances in the 26.6 format to the grid:</p>
<pre>
round( x ) == ( x + 32 ) & -64
floor( x ) == x & -64
ceiling( x ) == ( x + 63 ) & -64</pre>
<p>Once a glyph outline is grid-fitted or transformed, it
often is interesting to compute the glyph image's pixel
dimensions before rendering it. To do so, one has to
consider the following:</p>
<p>The scan-line converter draws all the pixels
whose <em>centers</em> fall inside the glyph shape. In
B/W rendering mode, it can also detect <em>drop-outs</em>,
i.e., discontinuities coming from extremely thin shape
fragments, in order to draw the ‘missing’
pixels. These new pixels are always located at a distance
less than half of a pixel but it is not easy to predict
where they will appear before rendering.</p>
<p>This leads to the following computations:</p>
<ul>
<li>
<p>compute the bbox</p>
</li>
<li>
<p>grid-fit the bounding box with the following:</p>
<pre>
xmin = floor( bbox.xMin )
xmax = ceiling( bbox.xMax )
ymin = floor( bbox.yMin )
ymax = ceiling( bbox.yMax )</pre>
</li>
<li>
<p>return pixel dimensions, i.e.</p>
<pre>
width = (xmax - xmin)/64</pre>
<p>and</p>
<pre>
height = (ymax - ymin)/64</pre>
</li>
</ul>
<p>By grid-fitting the bounding box, it is guaranteed that
all the pixel centers that are to be drawn, <em>including
those coming from drop-out control</em>, will
be <em>within</em> the adjusted box. Then the box's
dimensions in pixels can be computed.</p>
<p>Note also that, when translating a grid-fitted outline, one should
<em>always use integer distances</em> to move an outline
in the 2D plane. Otherwise, glyph edges won't be aligned
on the pixel grid anymore, and the hinter's work will be
lost, producing <em>very low quality</em> bitmaps and
pixmaps.</p>
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<p>Last update: 1-Jul-2013</p>
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