docs/glyphs/glyphs-6.html - third_party/freetype2 - Git at Google

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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 The FreeType Development Team (<a
   href="mailto:devel@freetype.org">devel@freetype.org</a>)
 </h3>

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   <table width="100%">
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       valign=center><td>
     <h2>
       VI. FreeType outlines
     </h2>
   </td></tr>
   </table>

     <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>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>

       <center>
       <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>
       </center>


       <h4>
         b. Outline descriptor
       </h4>

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

       <center>
       <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>

     <center>
     <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>
     </center>

     <p>Control and bounding boxes can be computed automatically through the
     functions <tt>FT_Get_Outline_CBox()</tt> and
     <tt>FT_Get_Outline_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 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>


   <p><hr></p>

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 </html>
	<!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="David Turner">
	<title>FreeType Glyph Conventions</title>
	</head>

	<body text="#000000"
	bgcolor="#FFFFFF"
	link="#0000EF"
	vlink="#51188E"
	alink="#FF0000">

	<h1 align=center>
	FreeType Glyph Conventions
	</h1>

	<h2 align=center>
	Version 2.1
	</h2>

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

	<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-5.html">Previous</a>
	</td>
	<td align=center
	width="30%">
	<a href="index.html">Contents</a>
	</td>
	<td align=center
	width="30%">
	<a href="glyphs-7.html">Next</a>
	</td>
	</tr>
	</table>
	</center>

	<p><hr></p>

	<table width="100%">
	<tr bgcolor="#CCCCFF"
	valign=center><td>
	<h2>
	VI. FreeType outlines
	</h2>
	</td></tr>
	</table>

	<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
	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
	Type 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
	Bézier 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 Bézier
	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 Bézier
	arc.</p>
	</td>
	</tr>
	</table>
	</center>

	<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
	Bézier 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 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).
	</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
	Bézier 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>

	<center>
	<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>
	</center>


	<h4>
	b. Outline descriptor
	</h4>

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

	<center>
	<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 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 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, Bézier control points are not necessarily
	contained within an outline's (smallest) bounding box.</p>

	<p>This situation happens when 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 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>

	<center>
	<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>
	</center>

	<p>Control and bounding boxes can be computed automatically through the
	functions <tt>FT_Get_Outline_CBox()</tt> and
	<tt>FT_Get_Outline_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 format, i.e. in 1/64th of a pixel, hence 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 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. 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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