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    1 <?xml version='1.0' encoding='UTF-8' standalone='no'?>
    2 <doxygen xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="compound.xsd" version="1.8.13">
    3   <compounddef id="group__rational__rotation__approximation__grp" kind="group">
    4     <compoundname>rational_rotation_approximation_grp</compoundname>
    5     <title>CGAL::rational_rotation_approximation()</title>
    6       <sectiondef kind="func">
    7       <memberdef kind="function" id="group__rational__rotation__approximation__grp_1gac7990dcba1e282368c6140c0afae456b" prot="public" static="no" const="no" explicit="no" inline="no" virt="non-virtual">
    8         <templateparamlist>
    9           <param>
   10             <type><ref refid="classRingNumberType" kindref="compound" external="/home/cgal-testsuite/cgal_doc_build/CGAL-5.0-I-190/doc/scripts/build_doc/doc_tags/Algebraic_foundations.tag">RingNumberType</ref></type>
   11           </param>
   12         </templateparamlist>
   13         <type>void</type>
   14         <definition>void CGAL::rational_rotation_approximation</definition>
   15         <argsstring>(const RingNumberType &amp;dirx, const RingNumberType &amp;diry, RingNumberType &amp;sin_num, RingNumberType &amp;cos_num, RingNumberType &amp;denom, const RingNumberType &amp;eps_num, const RingNumberType &amp;eps_den)</argsstring>
   16         <name>rational_rotation_approximation</name>
   17         <param>
   18           <type>const <ref refid="classRingNumberType" kindref="compound" external="/home/cgal-testsuite/cgal_doc_build/CGAL-5.0-I-190/doc/scripts/build_doc/doc_tags/Algebraic_foundations.tag">RingNumberType</ref> &amp;</type>
   19           <declname>dirx</declname>
   20         </param>
   21         <param>
   22           <type>const <ref refid="classRingNumberType" kindref="compound" external="/home/cgal-testsuite/cgal_doc_build/CGAL-5.0-I-190/doc/scripts/build_doc/doc_tags/Algebraic_foundations.tag">RingNumberType</ref> &amp;</type>
   23           <declname>diry</declname>
   24         </param>
   25         <param>
   26           <type><ref refid="classRingNumberType" kindref="compound" external="/home/cgal-testsuite/cgal_doc_build/CGAL-5.0-I-190/doc/scripts/build_doc/doc_tags/Algebraic_foundations.tag">RingNumberType</ref> &amp;</type>
   27           <declname>sin_num</declname>
   28         </param>
   29         <param>
   30           <type><ref refid="classRingNumberType" kindref="compound" external="/home/cgal-testsuite/cgal_doc_build/CGAL-5.0-I-190/doc/scripts/build_doc/doc_tags/Algebraic_foundations.tag">RingNumberType</ref> &amp;</type>
   31           <declname>cos_num</declname>
   32         </param>
   33         <param>
   34           <type><ref refid="classRingNumberType" kindref="compound" external="/home/cgal-testsuite/cgal_doc_build/CGAL-5.0-I-190/doc/scripts/build_doc/doc_tags/Algebraic_foundations.tag">RingNumberType</ref> &amp;</type>
   35           <declname>denom</declname>
   36         </param>
   37         <param>
   38           <type>const <ref refid="classRingNumberType" kindref="compound" external="/home/cgal-testsuite/cgal_doc_build/CGAL-5.0-I-190/doc/scripts/build_doc/doc_tags/Algebraic_foundations.tag">RingNumberType</ref> &amp;</type>
   39           <declname>eps_num</declname>
   40         </param>
   41         <param>
   42           <type>const <ref refid="classRingNumberType" kindref="compound" external="/home/cgal-testsuite/cgal_doc_build/CGAL-5.0-I-190/doc/scripts/build_doc/doc_tags/Algebraic_foundations.tag">RingNumberType</ref> &amp;</type>
   43           <declname>eps_den</declname>
   44         </param>
   45         <briefdescription>
   46 <para>computes integers <computeroutput>sin_num</computeroutput>, <computeroutput>cos_num</computeroutput> and <computeroutput>denom</computeroutput>, such that <computeroutput>sin_num</computeroutput>/<computeroutput>denom</computeroutput> approximates the sine of direction <formula id="87">$ ($</formula><computeroutput>dirx</computeroutput>,<computeroutput>diry</computeroutput> <formula id="88">$ )$</formula>. </para>        </briefdescription>
   47         <detaileddescription>
   48 <para>The difference between the sine and the approximating rational is bounded by <computeroutput>eps_num</computeroutput>/<computeroutput>eps_den</computeroutput>. <simplesect kind="pre"><para><computeroutput>eps_num</computeroutput> <formula id="89">$ \neq0$</formula>.</para></simplesect>
   49 <bold>Implementation</bold><linebreak/>
   50 </para><para>The approximation is based on Farey sequences as described in the rational rotation method presented by Canny and Ressler at the 8th SoCG 1992. We use a slower version which needs no division operation in the approximation.</para><para><simplesect kind="see"><para><computeroutput><ref refid="classCGAL_1_1Aff__transformation__2" kindref="compound">CGAL::Aff_transformation_2</ref>&lt;<ref refid="classKernel" kindref="compound">Kernel</ref>&gt;</computeroutput> </para></simplesect>
   51 </para>        </detaileddescription>
   52         <inbodydescription>
   53         </inbodydescription>
   54         <location file="CGAL/rational_rotation.h" line="23" column="1"/>
   55       </memberdef>
   56       </sectiondef>
   57     <briefdescription>
   58     </briefdescription>
   59     <detaileddescription>
   60     </detaileddescription>
   61   </compounddef>
   62 </doxygen>