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FreeType's header inclusion scheme
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Basic Data Types
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Base Interface
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Unicode Variation Sequences
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Glyph Color Management
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Glyph Layer Management
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Glyph Management
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Mac Specific Interface
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Size Management
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Header File Macros
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Format-Specific API
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Format-Specific API
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Multiple Masters
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TrueType Tables
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Type 1 Tables
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SFNT Names
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BDF and PCF Files
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Window FNT Files
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Font Formats
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Controlling FreeType Modules
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Controlling FreeType Modules
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The CFF driver
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The Type 1 and CID drivers
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The TrueType driver
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The PCF driver
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Driver properties
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Parameter Tags
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Computations
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Computations
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Synopsis
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<a href="#ft_muldiv" class="md-nav__link">
FT_MulDiv
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FT_MulFix
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FT_DivFix
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FT_RoundFix
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FT_CeilFix
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FT_FloorFix
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FT_Vector_Transform
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FT_Matrix_Multiply
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FT_Matrix_Invert
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FT_Angle
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FT_ANGLE_PI
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FT_ANGLE_2PI
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FT_ANGLE_PI2
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FT_ANGLE_PI4
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FT_Sin
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FT_Cos
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FT_Tan
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FT_Atan2
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FT_Angle_Diff
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FT_Vector_Unit
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<li class="md-nav__item">
<a href="#ft_vector_rotate" class="md-nav__link">
FT_Vector_Rotate
</a>
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<a href="#ft_vector_length" class="md-nav__link">
FT_Vector_Length
</a>
</li>
<li class="md-nav__item">
<a href="#ft_vector_polarize" class="md-nav__link">
FT_Vector_Polarize
</a>
</li>
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FT_Vector_From_Polar
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List Processing
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Outline Processing
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Quick retrieval of advance values
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Bitmap Handling
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Scanline Converter
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Glyph Stroker
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System Interface
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Module Management
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GZIP Streams
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LZW Streams
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BZIP2 Streams
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Error Codes
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Error Codes
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Error Enumerations
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Error Code Values
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Miscellaneous
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TrueTypeGX/AAT Validation
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Incremental Loading
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The TrueType Engine
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OpenType Validation
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<li class="md-nav__item">
<a href="#synopsis" class="md-nav__link">
Synopsis
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<li class="md-nav__item">
<a href="#ft_muldiv" class="md-nav__link">
FT_MulDiv
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<li class="md-nav__item">
<a href="#ft_mulfix" class="md-nav__link">
FT_MulFix
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<li class="md-nav__item">
<a href="#ft_divfix" class="md-nav__link">
FT_DivFix
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<a href="#ft_roundfix" class="md-nav__link">
FT_RoundFix
</a>
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<li class="md-nav__item">
<a href="#ft_ceilfix" class="md-nav__link">
FT_CeilFix
</a>
</li>
<li class="md-nav__item">
<a href="#ft_floorfix" class="md-nav__link">
FT_FloorFix
</a>
</li>
<li class="md-nav__item">
<a href="#ft_vector_transform" class="md-nav__link">
FT_Vector_Transform
</a>
</li>
<li class="md-nav__item">
<a href="#ft_matrix_multiply" class="md-nav__link">
FT_Matrix_Multiply
</a>
</li>
<li class="md-nav__item">
<a href="#ft_matrix_invert" class="md-nav__link">
FT_Matrix_Invert
</a>
</li>
<li class="md-nav__item">
<a href="#ft_angle" class="md-nav__link">
FT_Angle
</a>
</li>
<li class="md-nav__item">
<a href="#ft_angle_pi" class="md-nav__link">
FT_ANGLE_PI
</a>
</li>
<li class="md-nav__item">
<a href="#ft_angle_2pi" class="md-nav__link">
FT_ANGLE_2PI
</a>
</li>
<li class="md-nav__item">
<a href="#ft_angle_pi2" class="md-nav__link">
FT_ANGLE_PI2
</a>
</li>
<li class="md-nav__item">
<a href="#ft_angle_pi4" class="md-nav__link">
FT_ANGLE_PI4
</a>
</li>
<li class="md-nav__item">
<a href="#ft_sin" class="md-nav__link">
FT_Sin
</a>
</li>
<li class="md-nav__item">
<a href="#ft_cos" class="md-nav__link">
FT_Cos
</a>
</li>
<li class="md-nav__item">
<a href="#ft_tan" class="md-nav__link">
FT_Tan
</a>
</li>
<li class="md-nav__item">
<a href="#ft_atan2" class="md-nav__link">
FT_Atan2
</a>
</li>
<li class="md-nav__item">
<a href="#ft_angle_diff" class="md-nav__link">
FT_Angle_Diff
</a>
</li>
<li class="md-nav__item">
<a href="#ft_vector_unit" class="md-nav__link">
FT_Vector_Unit
</a>
</li>
<li class="md-nav__item">
<a href="#ft_vector_rotate" class="md-nav__link">
FT_Vector_Rotate
</a>
</li>
<li class="md-nav__item">
<a href="#ft_vector_length" class="md-nav__link">
FT_Vector_Length
</a>
</li>
<li class="md-nav__item">
<a href="#ft_vector_polarize" class="md-nav__link">
FT_Vector_Polarize
</a>
</li>
<li class="md-nav__item">
<a href="#ft_vector_from_polar" class="md-nav__link">
FT_Vector_From_Polar
</a>
</li>
</ul>
</nav>
</div>
</div>
</div>
<div class="md-content">
<article class="md-content__inner md-typeset">
<p><a href="https://www.freetype.org">FreeType</a> » <a href="../">Docs</a> » <a href="index.html#support-api">Support API</a> » Computations</p>
<hr />
<h1 id="computations">Computations<a class="headerlink" href="#computations" title="Permanent link">¶</a></h1>
<h2 id="synopsis">Synopsis<a class="headerlink" href="#synopsis" title="Permanent link">¶</a></h2>
<p>This section contains various functions used to perform computations on 16.16 fixed-float numbers or 2d vectors.</p>
<p><strong>Attention</strong>: Most arithmetic functions take <code>FT_Long</code> as arguments. For historical reasons, FreeType was designed under the assumption that <code>FT_Long</code> is a 32-bit integer; results can thus be undefined if the arguments don't fit into 32 bits.</p>
<h2 id="ft_muldiv">FT_MulDiv<a class="headerlink" href="#ft_muldiv" title="Permanent link">¶</a></h2>
<p>Defined in FT_FREETYPE_H (freetype/freetype.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_long">FT_Long</a> )
<b>FT_MulDiv</b>( <a href="ft2-basic_types.html#ft_long">FT_Long</a> a,
<a href="ft2-basic_types.html#ft_long">FT_Long</a> b,
<a href="ft2-basic_types.html#ft_long">FT_Long</a> c );
</code></pre></div>
<p>Compute <code>(a*b)/c</code> with maximum accuracy, using a 64-bit intermediate integer whenever necessary.</p>
<p>This function isn't necessarily as fast as some processor-specific operations, but is at least completely portable.</p>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="a">a</td><td class="desc">
<p>The first multiplier.</p>
</td></tr>
<tr><td class="val" id="b">b</td><td class="desc">
<p>The second multiplier.</p>
</td></tr>
<tr><td class="val" id="c">c</td><td class="desc">
<p>The divisor.</p>
</td></tr>
</table>
<h4>return</h4>
<p>The result of <code>(a*b)/c</code>. This function never traps when trying to divide by zero; it simply returns ‘MaxInt’ or ‘MinInt’ depending on the signs of <code>a</code> and <code>b</code>.</p>
<hr>
<h2 id="ft_mulfix">FT_MulFix<a class="headerlink" href="#ft_mulfix" title="Permanent link">¶</a></h2>
<p>Defined in FT_FREETYPE_H (freetype/freetype.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_long">FT_Long</a> )
<b>FT_MulFix</b>( <a href="ft2-basic_types.html#ft_long">FT_Long</a> a,
<a href="ft2-basic_types.html#ft_long">FT_Long</a> b );
</code></pre></div>
<p>Compute <code>(a*b)/0x10000</code> with maximum accuracy. Its main use is to multiply a given value by a 16.16 fixed-point factor.</p>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="a">a</td><td class="desc">
<p>The first multiplier.</p>
</td></tr>
<tr><td class="val" id="b">b</td><td class="desc">
<p>The second multiplier. Use a 16.16 factor here whenever possible (see note below).</p>
</td></tr>
</table>
<h4>return</h4>
<p>The result of <code>(a*b)/0x10000</code>.</p>
<h4>note</h4>
<p>This function has been optimized for the case where the absolute value of <code>a</code> is less than 2048, and <code>b</code> is a 16.16 scaling factor. As this happens mainly when scaling from notional units to fractional pixels in FreeType, it resulted in noticeable speed improvements between versions 2.x and 1.x.</p>
<p>As a conclusion, always try to place a 16.16 factor as the <em>second</em> argument of this function; this can make a great difference.</p>
<hr>
<h2 id="ft_divfix">FT_DivFix<a class="headerlink" href="#ft_divfix" title="Permanent link">¶</a></h2>
<p>Defined in FT_FREETYPE_H (freetype/freetype.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_long">FT_Long</a> )
<b>FT_DivFix</b>( <a href="ft2-basic_types.html#ft_long">FT_Long</a> a,
<a href="ft2-basic_types.html#ft_long">FT_Long</a> b );
</code></pre></div>
<p>Compute <code>(a*0x10000)/b</code> with maximum accuracy. Its main use is to divide a given value by a 16.16 fixed-point factor.</p>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="a">a</td><td class="desc">
<p>The numerator.</p>
</td></tr>
<tr><td class="val" id="b">b</td><td class="desc">
<p>The denominator. Use a 16.16 factor here.</p>
</td></tr>
</table>
<h4>return</h4>
<p>The result of <code>(a*0x10000)/b</code>.</p>
<hr>
<h2 id="ft_roundfix">FT_RoundFix<a class="headerlink" href="#ft_roundfix" title="Permanent link">¶</a></h2>
<p>Defined in FT_FREETYPE_H (freetype/freetype.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> )
<b>FT_RoundFix</b>( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> a );
</code></pre></div>
<p>Round a 16.16 fixed number.</p>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="a">a</td><td class="desc">
<p>The number to be rounded.</p>
</td></tr>
</table>
<h4>return</h4>
<p><code>a</code> rounded to the nearest 16.16 fixed integer, halfway cases away from zero.</p>
<h4>note</h4>
<p>The function uses wrap-around arithmetic.</p>
<hr>
<h2 id="ft_ceilfix">FT_CeilFix<a class="headerlink" href="#ft_ceilfix" title="Permanent link">¶</a></h2>
<p>Defined in FT_FREETYPE_H (freetype/freetype.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> )
<b>FT_CeilFix</b>( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> a );
</code></pre></div>
<p>Compute the smallest following integer of a 16.16 fixed number.</p>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="a">a</td><td class="desc">
<p>The number for which the ceiling function is to be computed.</p>
</td></tr>
</table>
<h4>return</h4>
<p><code>a</code> rounded towards plus infinity.</p>
<h4>note</h4>
<p>The function uses wrap-around arithmetic.</p>
<hr>
<h2 id="ft_floorfix">FT_FloorFix<a class="headerlink" href="#ft_floorfix" title="Permanent link">¶</a></h2>
<p>Defined in FT_FREETYPE_H (freetype/freetype.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> )
<b>FT_FloorFix</b>( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> a );
</code></pre></div>
<p>Compute the largest previous integer of a 16.16 fixed number.</p>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="a">a</td><td class="desc">
<p>The number for which the floor function is to be computed.</p>
</td></tr>
</table>
<h4>return</h4>
<p><code>a</code> rounded towards minus infinity.</p>
<hr>
<h2 id="ft_vector_transform">FT_Vector_Transform<a class="headerlink" href="#ft_vector_transform" title="Permanent link">¶</a></h2>
<p>Defined in FT_FREETYPE_H (freetype/freetype.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <span class="keyword">void</span> )
<b>FT_Vector_Transform</b>( <a href="ft2-basic_types.html#ft_vector">FT_Vector</a>* vector,
<span class="keyword">const</span> <a href="ft2-basic_types.html#ft_matrix">FT_Matrix</a>* matrix );
</code></pre></div>
<p>Transform a single vector through a 2x2 matrix.</p>
<h4>inout</h4>
<table class="fields">
<tr><td class="val" id="vector">vector</td><td class="desc">
<p>The target vector to transform.</p>
</td></tr>
</table>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="matrix">matrix</td><td class="desc">
<p>A pointer to the source 2x2 matrix.</p>
</td></tr>
</table>
<h4>note</h4>
<p>The result is undefined if either <code>vector</code> or <code>matrix</code> is invalid.</p>
<hr>
<h2 id="ft_matrix_multiply">FT_Matrix_Multiply<a class="headerlink" href="#ft_matrix_multiply" title="Permanent link">¶</a></h2>
<p>Defined in FT_GLYPH_H (freetype/ftglyph.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <span class="keyword">void</span> )
<b>FT_Matrix_Multiply</b>( <span class="keyword">const</span> <a href="ft2-basic_types.html#ft_matrix">FT_Matrix</a>* a,
<a href="ft2-basic_types.html#ft_matrix">FT_Matrix</a>* b );
</code></pre></div>
<p>Perform the matrix operation <code>b = a*b</code>.</p>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="a">a</td><td class="desc">
<p>A pointer to matrix <code>a</code>.</p>
</td></tr>
</table>
<h4>inout</h4>
<table class="fields">
<tr><td class="val" id="b">b</td><td class="desc">
<p>A pointer to matrix <code>b</code>.</p>
</td></tr>
</table>
<h4>note</h4>
<p>The result is undefined if either <code>a</code> or <code>b</code> is zero.</p>
<p>Since the function uses wrap-around arithmetic, results become meaningless if the arguments are very large.</p>
<hr>
<h2 id="ft_matrix_invert">FT_Matrix_Invert<a class="headerlink" href="#ft_matrix_invert" title="Permanent link">¶</a></h2>
<p>Defined in FT_GLYPH_H (freetype/ftglyph.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_error">FT_Error</a> )
<b>FT_Matrix_Invert</b>( <a href="ft2-basic_types.html#ft_matrix">FT_Matrix</a>* matrix );
</code></pre></div>
<p>Invert a 2x2 matrix. Return an error if it can't be inverted.</p>
<h4>inout</h4>
<table class="fields">
<tr><td class="val" id="matrix">matrix</td><td class="desc">
<p>A pointer to the target matrix. Remains untouched in case of error.</p>
</td></tr>
</table>
<h4>return</h4>
<p>FreeType error code. 0 means success.</p>
<hr>
<h2 id="ft_angle">FT_Angle<a class="headerlink" href="#ft_angle" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code> <span class="keyword">typedef</span> <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> <b>FT_Angle</b>;
</code></pre></div>
<p>This type is used to model angle values in FreeType. Note that the angle is a 16.16 fixed-point value expressed in degrees.</p>
<hr>
<h2 id="ft_angle_pi">FT_ANGLE_PI<a class="headerlink" href="#ft_angle_pi" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code>#<span class="keyword">define</span> <b>FT_ANGLE_PI</b> ( 180L << 16 )
</code></pre></div>
<p>The angle pi expressed in <code><a href="ft2-computations.html#ft_angle">FT_Angle</a></code> units.</p>
<hr>
<h2 id="ft_angle_2pi">FT_ANGLE_2PI<a class="headerlink" href="#ft_angle_2pi" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code>#<span class="keyword">define</span> <b>FT_ANGLE_2PI</b> ( <a href="ft2-computations.html#ft_angle_pi">FT_ANGLE_PI</a> * 2 )
</code></pre></div>
<p>The angle 2*pi expressed in <code><a href="ft2-computations.html#ft_angle">FT_Angle</a></code> units.</p>
<hr>
<h2 id="ft_angle_pi2">FT_ANGLE_PI2<a class="headerlink" href="#ft_angle_pi2" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code>#<span class="keyword">define</span> <b>FT_ANGLE_PI2</b> ( <a href="ft2-computations.html#ft_angle_pi">FT_ANGLE_PI</a> / 2 )
</code></pre></div>
<p>The angle pi/2 expressed in <code><a href="ft2-computations.html#ft_angle">FT_Angle</a></code> units.</p>
<hr>
<h2 id="ft_angle_pi4">FT_ANGLE_PI4<a class="headerlink" href="#ft_angle_pi4" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code>#<span class="keyword">define</span> <b>FT_ANGLE_PI4</b> ( <a href="ft2-computations.html#ft_angle_pi">FT_ANGLE_PI</a> / 4 )
</code></pre></div>
<p>The angle pi/4 expressed in <code><a href="ft2-computations.html#ft_angle">FT_Angle</a></code> units.</p>
<hr>
<h2 id="ft_sin">FT_Sin<a class="headerlink" href="#ft_sin" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> )
<b>FT_Sin</b>( <a href="ft2-computations.html#ft_angle">FT_Angle</a> angle );
</code></pre></div>
<p>Return the sinus of a given angle in fixed-point format.</p>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="angle">angle</td><td class="desc">
<p>The input angle.</p>
</td></tr>
</table>
<h4>return</h4>
<p>The sinus value.</p>
<h4>note</h4>
<p>If you need both the sinus and cosinus for a given angle, use the function <code><a href="ft2-computations.html#ft_vector_unit">FT_Vector_Unit</a></code>.</p>
<hr>
<h2 id="ft_cos">FT_Cos<a class="headerlink" href="#ft_cos" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> )
<b>FT_Cos</b>( <a href="ft2-computations.html#ft_angle">FT_Angle</a> angle );
</code></pre></div>
<p>Return the cosinus of a given angle in fixed-point format.</p>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="angle">angle</td><td class="desc">
<p>The input angle.</p>
</td></tr>
</table>
<h4>return</h4>
<p>The cosinus value.</p>
<h4>note</h4>
<p>If you need both the sinus and cosinus for a given angle, use the function <code><a href="ft2-computations.html#ft_vector_unit">FT_Vector_Unit</a></code>.</p>
<hr>
<h2 id="ft_tan">FT_Tan<a class="headerlink" href="#ft_tan" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> )
<b>FT_Tan</b>( <a href="ft2-computations.html#ft_angle">FT_Angle</a> angle );
</code></pre></div>
<p>Return the tangent of a given angle in fixed-point format.</p>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="angle">angle</td><td class="desc">
<p>The input angle.</p>
</td></tr>
</table>
<h4>return</h4>
<p>The tangent value.</p>
<hr>
<h2 id="ft_atan2">FT_Atan2<a class="headerlink" href="#ft_atan2" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-computations.html#ft_angle">FT_Angle</a> )
<b>FT_Atan2</b>( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> x,
<a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> y );
</code></pre></div>
<p>Return the arc-tangent corresponding to a given vector (x,y) in the 2d plane.</p>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="x">x</td><td class="desc">
<p>The horizontal vector coordinate.</p>
</td></tr>
<tr><td class="val" id="y">y</td><td class="desc">
<p>The vertical vector coordinate.</p>
</td></tr>
</table>
<h4>return</h4>
<p>The arc-tangent value (i.e. angle).</p>
<hr>
<h2 id="ft_angle_diff">FT_Angle_Diff<a class="headerlink" href="#ft_angle_diff" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-computations.html#ft_angle">FT_Angle</a> )
<b>FT_Angle_Diff</b>( <a href="ft2-computations.html#ft_angle">FT_Angle</a> angle1,
<a href="ft2-computations.html#ft_angle">FT_Angle</a> angle2 );
</code></pre></div>
<p>Return the difference between two angles. The result is always constrained to the ]-PI..PI] interval.</p>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="angle1">angle1</td><td class="desc">
<p>First angle.</p>
</td></tr>
<tr><td class="val" id="angle2">angle2</td><td class="desc">
<p>Second angle.</p>
</td></tr>
</table>
<h4>return</h4>
<p>Constrained value of <code>angle2-angle1</code>.</p>
<hr>
<h2 id="ft_vector_unit">FT_Vector_Unit<a class="headerlink" href="#ft_vector_unit" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <span class="keyword">void</span> )
<b>FT_Vector_Unit</b>( <a href="ft2-basic_types.html#ft_vector">FT_Vector</a>* vec,
<a href="ft2-computations.html#ft_angle">FT_Angle</a> angle );
</code></pre></div>
<p>Return the unit vector corresponding to a given angle. After the call, the value of <code>vec.x</code> will be <code>cos(angle)</code>, and the value of <code>vec.y</code> will be <code>sin(angle)</code>.</p>
<p>This function is useful to retrieve both the sinus and cosinus of a given angle quickly.</p>
<h4>output</h4>
<table class="fields">
<tr><td class="val" id="vec">vec</td><td class="desc">
<p>The address of target vector.</p>
</td></tr>
</table>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="angle">angle</td><td class="desc">
<p>The input angle.</p>
</td></tr>
</table>
<hr>
<h2 id="ft_vector_rotate">FT_Vector_Rotate<a class="headerlink" href="#ft_vector_rotate" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <span class="keyword">void</span> )
<b>FT_Vector_Rotate</b>( <a href="ft2-basic_types.html#ft_vector">FT_Vector</a>* vec,
<a href="ft2-computations.html#ft_angle">FT_Angle</a> angle );
</code></pre></div>
<p>Rotate a vector by a given angle.</p>
<h4>inout</h4>
<table class="fields">
<tr><td class="val" id="vec">vec</td><td class="desc">
<p>The address of target vector.</p>
</td></tr>
</table>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="angle">angle</td><td class="desc">
<p>The input angle.</p>
</td></tr>
</table>
<hr>
<h2 id="ft_vector_length">FT_Vector_Length<a class="headerlink" href="#ft_vector_length" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> )
<b>FT_Vector_Length</b>( <a href="ft2-basic_types.html#ft_vector">FT_Vector</a>* vec );
</code></pre></div>
<p>Return the length of a given vector.</p>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="vec">vec</td><td class="desc">
<p>The address of target vector.</p>
</td></tr>
</table>
<h4>return</h4>
<p>The vector length, expressed in the same units that the original vector coordinates.</p>
<hr>
<h2 id="ft_vector_polarize">FT_Vector_Polarize<a class="headerlink" href="#ft_vector_polarize" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <span class="keyword">void</span> )
<b>FT_Vector_Polarize</b>( <a href="ft2-basic_types.html#ft_vector">FT_Vector</a>* vec,
<a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> *length,
<a href="ft2-computations.html#ft_angle">FT_Angle</a> *angle );
</code></pre></div>
<p>Compute both the length and angle of a given vector.</p>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="vec">vec</td><td class="desc">
<p>The address of source vector.</p>
</td></tr>
</table>
<h4>output</h4>
<table class="fields">
<tr><td class="val" id="length">length</td><td class="desc">
<p>The vector length.</p>
</td></tr>
<tr><td class="val" id="angle">angle</td><td class="desc">
<p>The vector angle.</p>
</td></tr>
</table>
<hr>
<h2 id="ft_vector_from_polar">FT_Vector_From_Polar<a class="headerlink" href="#ft_vector_from_polar" title="Permanent link">¶</a></h2>
<p>Defined in FT_TRIGONOMETRY_H (freetype/fttrigon.h).</p>
<div class = "codehilite"><pre><code> FT_EXPORT( <span class="keyword">void</span> )
<b>FT_Vector_From_Polar</b>( <a href="ft2-basic_types.html#ft_vector">FT_Vector</a>* vec,
<a href="ft2-basic_types.html#ft_fixed">FT_Fixed</a> length,
<a href="ft2-computations.html#ft_angle">FT_Angle</a> angle );
</code></pre></div>
<p>Compute vector coordinates from a length and angle.</p>
<h4>output</h4>
<table class="fields">
<tr><td class="val" id="vec">vec</td><td class="desc">
<p>The address of source vector.</p>
</td></tr>
</table>
<h4>input</h4>
<table class="fields">
<tr><td class="val" id="length">length</td><td class="desc">
<p>The vector length.</p>
</td></tr>
<tr><td class="val" id="angle">angle</td><td class="desc">
<p>The vector angle.</p>
</td></tr>
</table>
<hr>
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