antkeeper
/
superbuild


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                                <li class="md-nav__item">      <a href="ft2-header_inclusion.html" class="md-nav__link">        FreeType's header inclusion scheme      </a>    </li>  
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                                <li class="md-nav__item">      <a href="ft2-basic_types.html" class="md-nav__link">        Basic Data Types      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-base_interface.html" class="md-nav__link">        Base Interface      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-glyph_variants.html" class="md-nav__link">        Unicode Variation Sequences      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-color_management.html" class="md-nav__link">        Glyph Color Management      </a>    </li>  
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                                <li class="md-nav__item">      <a href="ft2-mac_specific.html" class="md-nav__link">        Mac Specific Interface      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-sizes_management.html" class="md-nav__link">        Size Management      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-header_file_macros.html" class="md-nav__link">        Header File Macros      </a>    </li>  
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                                <li class="md-nav__item">      <a href="ft2-truetype_tables.html" class="md-nav__link">        TrueType Tables      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-type1_tables.html" class="md-nav__link">        Type 1 Tables      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-sfnt_names.html" class="md-nav__link">        SFNT Names      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-bdf_fonts.html" class="md-nav__link">        BDF and PCF Files      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-cid_fonts.html" class="md-nav__link">        CID Fonts      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-pfr_fonts.html" class="md-nav__link">        PFR Fonts      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-winfnt_fonts.html" class="md-nav__link">        Window FNT Files      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-font_formats.html" class="md-nav__link">        Font Formats      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-gasp_table.html" class="md-nav__link">        Gasp Table      </a>    </li>  
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              <li class="md-nav__item md-nav__item--nested">                    <input class="md-nav__toggle md-toggle" data-md-toggle="__nav_6" type="checkbox" id="__nav_6" >            <label class="md-nav__link" for="__nav_6">        Controlling FreeType Modules        <span class="md-nav__icon md-icon"></span>      </label>      <nav class="md-nav" aria-label="Controlling FreeType Modules" data-md-level="1">        <label class="md-nav__title" for="__nav_6">          <span class="md-nav__icon md-icon"></span>          Controlling FreeType Modules        </label>        <ul class="md-nav__list" data-md-scrollfix>                                <li class="md-nav__item">      <a href="ft2-auto_hinter.html" class="md-nav__link">        The auto-hinter      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-cff_driver.html" class="md-nav__link">        The CFF driver      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-t1_cid_driver.html" class="md-nav__link">        The Type 1 and CID drivers      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-tt_driver.html" class="md-nav__link">        The TrueType driver      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-pcf_driver.html" class="md-nav__link">        The PCF driver      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-properties.html" class="md-nav__link">        Driver properties      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-parameter_tags.html" class="md-nav__link">        Parameter Tags      </a>    </li>  
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                                <li class="md-nav__item">      <a href="ft2-list_processing.html" class="md-nav__link">        List Processing      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-outline_processing.html" class="md-nav__link">        Outline Processing      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-quick_advance.html" class="md-nav__link">        Quick retrieval of advance values      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-bitmap_handling.html" class="md-nav__link">        Bitmap Handling      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-raster.html" class="md-nav__link">        Scanline Converter      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-glyph_stroker.html" class="md-nav__link">        Glyph Stroker      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-system_interface.html" class="md-nav__link">        System Interface      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-module_management.html" class="md-nav__link">        Module Management      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-gzip.html" class="md-nav__link">        GZIP Streams      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-lzw.html" class="md-nav__link">        LZW Streams      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-bzip2.html" class="md-nav__link">        BZIP2 Streams      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-debugging_apis.html" class="md-nav__link">        External Debugging APIs      </a>    </li>  
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              <li class="md-nav__item md-nav__item--nested">                    <input class="md-nav__toggle md-toggle" data-md-toggle="__nav_9" type="checkbox" id="__nav_9" >            <label class="md-nav__link" for="__nav_9">        Error Codes        <span class="md-nav__icon md-icon"></span>      </label>      <nav class="md-nav" aria-label="Error Codes" data-md-level="1">        <label class="md-nav__title" for="__nav_9">          <span class="md-nav__icon md-icon"></span>          Error Codes        </label>        <ul class="md-nav__list" data-md-scrollfix>                                <li class="md-nav__item">      <a href="ft2-error_enumerations.html" class="md-nav__link">        Error Enumerations      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-error_code_values.html" class="md-nav__link">        Error Code Values      </a>    </li>  
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              <li class="md-nav__item md-nav__item--nested">                    <input class="md-nav__toggle md-toggle" data-md-toggle="__nav_10" type="checkbox" id="__nav_10" >            <label class="md-nav__link" for="__nav_10">        Miscellaneous        <span class="md-nav__icon md-icon"></span>      </label>      <nav class="md-nav" aria-label="Miscellaneous" data-md-level="1">        <label class="md-nav__title" for="__nav_10">          <span class="md-nav__icon md-icon"></span>          Miscellaneous        </label>        <ul class="md-nav__list" data-md-scrollfix>                                <li class="md-nav__item">      <a href="ft2-gx_validation.html" class="md-nav__link">        TrueTypeGX/AAT Validation      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-incremental.html" class="md-nav__link">        Incremental Loading      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-truetype_engine.html" class="md-nav__link">        The TrueType Engine      </a>    </li>  
                                <li class="md-nav__item">      <a href="ft2-ot_validation.html" class="md-nav__link">        OpenType Validation      </a>    </li>  
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      </ul></nav>                  </div>                </div>              </div>                                                    <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >                <div class="md-sidebar__scrollwrap">                  <div class="md-sidebar__inner">                    <nav class="md-nav md-nav--secondary" aria-label="Table of contents">                  <label class="md-nav__title" for="__toc">      <span class="md-nav__icon md-icon"></span>      Table of contents    </label>    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>              <li class="md-nav__item">  <a href="#synopsis" class="md-nav__link">    Synopsis  </a>  </li>              <li class="md-nav__item">  <a href="#ft_muldiv" class="md-nav__link">    FT_MulDiv  </a>  </li>              <li class="md-nav__item">  <a href="#ft_mulfix" class="md-nav__link">    FT_MulFix  </a>  </li>              <li class="md-nav__item">  <a href="#ft_divfix" class="md-nav__link">    FT_DivFix  </a>  </li>              <li class="md-nav__item">  <a href="#ft_roundfix" class="md-nav__link">    FT_RoundFix  </a>  </li>              <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" data-md-component="content">            <article class="md-content__inner md-typeset">                                                              <p><a href="https://www.freetype.org">FreeType</a> &raquo; <a href="../">Docs</a> &raquo; <a href="index.html#support-api">Support API</a> &raquo; Computations</p><hr /><h1 id="computations">Computations<a class="headerlink" href="#computations" title="Permanent link">&para;</a></h1><h2 id="synopsis">Synopsis<a class="headerlink" href="#synopsis" title="Permanent link">&para;</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">&para;</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 &lsquo;MaxInt&rsquo; or &lsquo;MinInt&rsquo; 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">&para;</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">&para;</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">&para;</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">&para;</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">&para;</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">&para;</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">&para;</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">&para;</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&nbsp;means success.</p><hr>
<h2 id="ft_angle">FT_Angle<a class="headerlink" href="#ft_angle" title="Permanent link">&para;</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">&para;</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 &lt;&lt; 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">&para;</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">&para;</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">&para;</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">&para;</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">&para;</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">&para;</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">&para;</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">&para;</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">&para;</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">&para;</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">&para;</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">&para;</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">&para;</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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