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 <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>

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


 <table width="100%"><tr valign=center bgcolor="#CCCCFF"><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>

 <h3><a name="section-1">
 1. FreeType outline description and structure :
 </h3><blockquote>

 <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 bezier
 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
 come from the TrueType format. The latter are called cubic arcs and mostly
 come from the Type1 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 wether 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>
 <p><b>FT_Curve_Tag_On&nbsp;</b></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. one which isn't located on the contour itself,
 but serves as a control point for a bezier arc.</p>
 </td>
 </tr>

 <tr>
 <td>
 <p><b>FT_Curve_Tag_Conic</b></p>
 </td>

 <td>
 <p>Used for an "off" point used to control a conic bezier arc.</p>
 </td>
 </tr>

 <tr>
 <td>
 <p><b>FT_Curve_Tag_Cubic</b></p>
 </td>

 <td>
 <p>Used for an "off" point used to control a cubic bezier 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 bezier
 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
 bezier 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 bezier arcs. Moreover, it's the way outlines are
 described in the TrueType specification.
 </li>
 </ul>

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

 <center><table>
 <tr>
 <td>
 <blockquote><img SRC="points_segment.png" height=166 width=221></blockquote>
 </td>

 <td>
 <blockquote><img SRC="points_conic.png" height=183 width=236></blockquote>
 </td>
 </tr>

 <tr>
 <td>
 <blockquote><img SRC="points_cubic.png" height=162 width=214></blockquote>
 </td>

 <td>
 <blockquote><img SRC="points_conic2.png" height=204 width=225></blockquote>
 </td>
 </tr>
 </table></center>

 <h4>
 b. Outline descriptor :</h4>

 <p>A FreeType outline is described through a simple structure,
 called <tt>FT_Outline</tt>, which fields are :</p>

 <center><table CELLSPACING=3 CELLPADDING=3 BGCOLOR="#CCCCCC">
 <tr>
 <td>
 <p><b><tt>n_points</tt></b></p>
 </td>

 <td>
 <p>the number of points in the outline</p>
 </td>
 </tr>

 <tr>
 <td>
 <p><b><tt>n_contours</tt></b></p>
 </td>

 <td>
 <p>the number of contours in the outline</p>
 </td>
 </tr>

 <tr>
 <td>
 <p><b><tt>points</tt></b></p>
 </td>

 <td>
 <p>array of point coordinates</p>
 </td>
 </tr>

 <tr>
 <td>
 <p><b><tt>contours</tt></b></p>
 </td>

 <td>
 <p>array of contour end indices</p>
 </td>
 </tr>

 <tr>
 <td>
 <p><b><tt>tags</tt></b></p>
 </td>

 <td>
 <p>array of point flags</p>
 </td>
 </tr>
 </table></center>

 <p>Here, <b><tt>points</tt></b> 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 <i>26.6 fixed float format</i>.
 </p>

 <p><b><tt>contours</tt></b> 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 a point <b><tt>contours[0]</tt></b>. The second contour
 starts at point "<b><tt>contours[0]+1</tt></b>" and ends at
 <b><tt>contours[1]</tt></b>, etc..
 </p>

 <p>Note that each contour is closed, and that <b><tt>n_points</tt></b>
 should be equal to "<b><tt>contours[n_contours-1]+1</tt></b>" for a valid
 outline.
 </p>

 <p>Finally, <b><tt>tags</tt></b> is an array of bytes, used to store each
 outline point's tag.
 </p>


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

 <p>A <b>bounding box</b> (also called "<b>bbox</b>") is simply
 the smallest possible rectangle that encloses the shape of a given outline.
 Because of the way arcs are defined, bezier control points are not
 necessarily contained within an outline's bounding box.
 </p>

 <p>This situation happens when one bezier 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 <b>control box</b> (a.k.a. the "<b>cbox</b>") 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 also much faster to compute.</p>

 <center><table>
 <tr>
 <td><img SRC="bbox1.png" height=264 width=228></td>

 <td><img SRC="bbox2.png" height=229 width=217></td>
 </tr>
 </table></center>

 <p>Control and bounding boxes can be computed automatically through the
 functions <b><tt>FT_Get_Outline_CBox</tt></b> and <b><tt>FT_Get_Outline_BBox</tt></b>.
 The former function is always very fast, while the latter <i>may</i> 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's 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
 transform like rotation is applied to them.
 </p>

 </blockquote><h3><a name="section-3">
 &nbsp;3. Coordinates, scaling and grid-fitting :
 </h3><blockquote>

 <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>

 <center>
 <p><tt>round(x)&nbsp;&nbsp; ==&nbsp; (x+32) &amp; -64</tt>
 <br><tt>floor(x)&nbsp;&nbsp; ==&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; x &amp;
 -64</tt>
 <br><tt>ceiling(x) ==&nbsp; (x+63) &amp; -64</tt></center>

 <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>The scan-line converter draws all the pixels whose <i>centers</i> fall
 inside the glyph shape. It can also detect "<b><i>drop-outs</i></b>", 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 one cannot predict easily where they'll appear
 before rendering.
 <p>This leads to the following computations :
 <br>&nbsp;
 <ul>
 <li>
 compute the bbox</li>
 </ul>

 <ul>
 <li>
 grid-fit the bounding box with the following :</li>
 </ul>

 <ul><p>
 <ul><tt>xmin = floor( bbox.xMin )</tt>
 <br><tt>xmax = ceiling( bbox.xMax )</tt>
 <br><tt>ymin = floor( bbox.yMin )</tt>
 <br><tt>ymax = ceiling( bbox.yMax )</tt>
 </p></ul>

 <li>
 return pixel dimensions, i.e.
 <tt>width = (xmax - xmin)/64</tt> and <tt>height = (ymax - ymin)/64</tt>
 </li>
 </ul>

 <p><br>By grid-fitting the bounding box, one guarantees that all the pixel
 centers that are to be drawn, <b><i>including those coming from drop-out
 control</i></b>, will be <b><i>within</i></b> the adjusted box. Then the
 box's dimensions in pixels can be computed.
 <p>Note also that, when <i>translating</i> a <i>grid-fitted outline</i>,
 one should <b><i>always</i></b> use <b><i>integer distances</i></b> 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
 <b><i>very
 low quality </i></b>bitmaps and pixmaps..</blockquote>
 </blockquote>

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 <td align=center width="30%">
 <a href="glyphs-5.html">Previous</a>
 </td>
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 <a href="index.html">Contents</a>
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	<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
	<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>
	</head>
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	<body text="#000000"
	bgcolor="#FFFFFF"
	link="#0000EF"
	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-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>


	<table width="100%"><tr valign=center bgcolor="#CCCCFF"><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>

	<h3><a name="section-1">
	1. FreeType outline description and structure :
	</h3><blockquote>

	<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 bezier
	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
	come from the TrueType format. The latter are called cubic arcs and mostly
	come from the Type1 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 wether 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>
	<p><b>FT_Curve_Tag_On </b></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. one which isn't located on the contour itself,
	but serves as a control point for a bezier arc.</p>
	</td>
	</tr>

	<tr>
	<td>
	<p><b>FT_Curve_Tag_Conic</b></p>
	</td>

	<td>
	<p>Used for an "off" point used to control a conic bezier arc.</p>
	</td>
	</tr>

	<tr>
	<td>
	<p><b>FT_Curve_Tag_Cubic</b></p>
	</td>

	<td>
	<p>Used for an "off" point used to control a cubic bezier 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 bezier
	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
	bezier 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 bezier arcs. Moreover, it's the way outlines are
	described in the TrueType specification.
	</li>
	</ul>

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

	<center><table>
	<tr>
	<td>
	<blockquote><img SRC="points_segment.png" height=166 width=221></blockquote>
	</td>

	<td>
	<blockquote><img SRC="points_conic.png" height=183 width=236></blockquote>
	</td>
	</tr>

	<tr>
	<td>
	<blockquote><img SRC="points_cubic.png" height=162 width=214></blockquote>
	</td>

	<td>
	<blockquote><img SRC="points_conic2.png" height=204 width=225></blockquote>
	</td>
	</tr>
	</table></center>

	<h4>
	b. Outline descriptor :</h4>

	<p>A FreeType outline is described through a simple structure,
	called <tt>FT_Outline</tt>, which fields are :</p>

	<center><table CELLSPACING=3 CELLPADDING=3 BGCOLOR="#CCCCCC">
	<tr>
	<td>
	<p><b><tt>n_points</tt></b></p>
	</td>

	<td>
	<p>the number of points in the outline</p>
	</td>
	</tr>

	<tr>
	<td>
	<p><b><tt>n_contours</tt></b></p>
	</td>

	<td>
	<p>the number of contours in the outline</p>
	</td>
	</tr>

	<tr>
	<td>
	<p><b><tt>points</tt></b></p>
	</td>

	<td>
	<p>array of point coordinates</p>
	</td>
	</tr>

	<tr>
	<td>
	<p><b><tt>contours</tt></b></p>
	</td>

	<td>
	<p>array of contour end indices</p>
	</td>
	</tr>

	<tr>
	<td>
	<p><b><tt>tags</tt></b></p>
	</td>

	<td>
	<p>array of point flags</p>
	</td>
	</tr>
	</table></center>

	<p>Here, <b><tt>points</tt></b> 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 <i>26.6 fixed float format</i>.
	</p>

	<p><b><tt>contours</tt></b> 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 a point <b><tt>contours[0]</tt></b>. The second contour
	starts at point "<b><tt>contours[0]+1</tt></b>" and ends at
	<b><tt>contours[1]</tt></b>, etc..
	</p>

	<p>Note that each contour is closed, and that <b><tt>n_points</tt></b>
	should be equal to "<b><tt>contours[n_contours-1]+1</tt></b>" for a valid
	outline.
	</p>

	<p>Finally, <b><tt>tags</tt></b> is an array of bytes, used to store each
	outline point's tag.
	</p>


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

	<p>A <b>bounding box</b> (also called "<b>bbox</b>") is simply
	the smallest possible rectangle that encloses the shape of a given outline.
	Because of the way arcs are defined, bezier control points are not
	necessarily contained within an outline's bounding box.
	</p>

	<p>This situation happens when one bezier 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 <b>control box</b> (a.k.a. the "<b>cbox</b>") 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 also much faster to compute.</p>

	<center><table>
	<tr>
	<td><img SRC="bbox1.png" height=264 width=228></td>

	<td><img SRC="bbox2.png" height=229 width=217></td>
	</tr>
	</table></center>

	<p>Control and bounding boxes can be computed automatically through the
	functions <b><tt>FT_Get_Outline_CBox</tt></b> and <b><tt>FT_Get_Outline_BBox</tt></b>.
	The former function is always very fast, while the latter <i>may</i> 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's 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
	transform like rotation is applied to them.
	</p>

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

	<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>

	<center>
	<p><tt>round(x)   ==  (x+32) & -64</tt>
	<br><tt>floor(x)   ==       x &
	-64</tt>
	<br><tt>ceiling(x) ==  (x+63) & -64</tt></center>

	<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>The scan-line converter draws all the pixels whose <i>centers</i> fall
	inside the glyph shape. It can also detect "<b><i>drop-outs</i></b>", 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 one cannot predict easily where they'll appear
	before rendering.
	<p>This leads to the following computations :
	<br>
	<ul>
	<li>
	compute the bbox</li>
	</ul>

	<ul>
	<li>
	grid-fit the bounding box with the following :</li>
	</ul>

	<ul><p>
	<ul><tt>xmin = floor( bbox.xMin )</tt>
	<br><tt>xmax = ceiling( bbox.xMax )</tt>
	<br><tt>ymin = floor( bbox.yMin )</tt>
	<br><tt>ymax = ceiling( bbox.yMax )</tt>
	</p></ul>

	<li>
	return pixel dimensions, i.e.
	<tt>width = (xmax - xmin)/64</tt> and <tt>height = (ymax - ymin)/64</tt>
	</li>
	</ul>

	<p><br>By grid-fitting the bounding box, one guarantees that all the pixel
	centers that are to be drawn, <b><i>including those coming from drop-out
	control</i></b>, will be <b><i>within</i></b> the adjusted box. Then the
	box's dimensions in pixels can be computed.
	<p>Note also that, when <i>translating</i> a <i>grid-fitted outline</i>,
	one should <b><i>always</i></b> use <b><i>integer distances</i></b> 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
	<b><i>very
	low quality </i></b>bitmaps and pixmaps..</blockquote>
	</blockquote>

	<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>
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