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  <title>FreeType Glyph Conventions</title>
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  FreeType Glyph Conventions
</h1>

<h2 align=center>
  Version&nbsp;2.1
</h2>

<h3 align=center>
  Copyright&nbsp;1998-2000 David Turner (<a
  href="mailto:david@freetype.org">david@freetype.org</a>)<br>
  Copyright&nbsp;2000, 2006 The FreeType Development Team (<a
  href="mailto:devel@freetype.org">devel@freetype.org</a>)
</h3>

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    <h2>
      VI. FreeType outlines
    </h2>
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<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>

<a name="section-1">
    <h3>
      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
      B&eacute;zier 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
      Type&nbsp;1 format.</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 used to describe a line segment or an arc.  The tags can
      take the following values:</p>

<center>
      <table cellspacing=5
             cellpadding=5
             width="80%">
      <tr VALIGN=TOP>
        <td valign=top>
          <tt>FT_CURVE_TAG_ON</tt>
        </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
          B&eacute;zier arc.</p>
        </td>
      </tr>

<tr>
        <td valign=top>
          <tt>FT_CURVE_TAG_CONIC</tt>
        </td>
        <td valign=top>
          <p>Used for an "off" point used to control a conic B&eacute;zier
          arc.</p>
        </td>
      </tr>

<tr>
        <td valign=top>
          <tt>FT_CURVE_TAG_CUBIC</tt>
        </td>
        <td valign=top>
          <p>Used for an "off" point used to control a cubic B&eacute;zier
          arc.</p>
        </td>
      </tr>
      </table>
      </center>

<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>
          Two successive "on" points indicate a line segment joining them.
        </li>
        <li>
          One conic "off" point amidst two "on" points indicates a conic
          B&eacute;zier arc, the "off" point being the control point, and
          the "on" ones the start and end points.
        </li>
        <li>
          Two successive cubic "off" points amidst two "on" points indicate
          a cubic B&eacute;zier 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).
        </li>
        <li>
          Finally, two successive conic "off" points forces the rasterizer
          to create (during the scan-line conversion process exclusively) a
          virtual "on" point amidst them, at their exact middle.  This
          greatly facilitates the definition of successive conic
          B&eacute;zier arcs.  Moreover, it is the way outlines are
          described in the TrueType specification.
        </li>
      </ul>

<p>Note that it is possible to mix conic and cubic arcs in a single
      contour, even though no current font driver produces such
      outlines.</p>

<h4>
        b. Outline descriptor
      </h4>

<p>A FreeType outline is described through a simple structure:</p>

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      <table cellspacing=3
             cellpadding=3>
      <caption>
        <b><tt>FT_Outline</tt></b>
      </caption>

<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>
      </table>
      </center>

<p>Here, <tt>points</tt> is a pointer to an array of
      <tt>FT_Vector</tt> 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&nbsp;fixed float format</em>.</p>

<p><tt>contours</tt> is an array of point indices used to delimit
      contours in the outline.  For example, the first contour always starts
      at point&nbsp;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.</p>

<p>Note that each contour is closed, and that <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>

<a name="section-2">
    <h3>
      2. Bounding and control box computations
    </h3>

<p>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, B&eacute;zier control points are not necessarily
    contained within an outline's (smallest) bounding box.</p>

<p>This situation happens when one B&eacute;zier 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 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 equates it in most cases.</p>

<p>Unlike the bbox, the cbox is much faster to compute.</p>

<p>Control and bounding boxes can be computed automatically through the
    functions <tt>FT_Outline_Get_CBox()</tt> and
    <tt>FT_Outline_Get_BBox()</tt>.  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 to ease hinting, this is not necessary the case anymore when a
    transformation like rotation is applied to them.</p>

<a name="section-3">
    <h3>
      3. Coordinates, scaling and grid-fitting
    </h3>

<p>An outline point's vectorial coordinates are expressed in the
    26.6&nbsp;format, i.e. in 1/64th of a pixel, hence the coordinates
    (1.0,-2.5) is stored as the integer pair (x:64,y:-192).</p>

<p>After a master glyph outline is scaled from the EM grid 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&nbsp;format to the grid:</p>

<pre>
    round( x )   == ( x + 32 ) &amp; -64
    floor( x )   ==          x &amp; -64
    ceiling( x ) == ( x + 63 ) &amp; -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.  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>
        return pixel dimensions, i.e.

<pre>
    width = (xmax - xmin)/64</pre>

and

<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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<font size=-1>Last update: 31-Aug-2006</font>

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