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<div class="header">
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<a href="classEigen_1_1Rotation2D-members.html">List of all members</a> &#124;
<a href="#pub-types">Public Types</a> &#124;
<a href="#pub-methods">Public Member Functions</a>  </div>
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<div class="title">Rotation2D&lt; Scalar &gt; Class Template Reference<div class="ingroups"><a class="el" href="group__Geometry__Module.html">Geometry module</a></div></div>  </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename Scalar&gt;<br/>
class Eigen::Rotation2D&lt; Scalar &gt;</h3>

<p>Represents a rotation/orientation in a 2 dimensional space. </p>
<p>This is defined in the Geometry module.</p>
<div class="fragment"><div class="line"><span class="preprocessor">#include &lt;Eigen/Geometry&gt;</span> </div>
</div><!-- fragment --><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">_Scalar</td><td>the scalar type, i.e., the type of the coefficients</td></tr>
  </table>
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</dl>
<p>This class is equivalent to a single scalar representing a counter clock wise rotation as a single angle in radian. It provides some additional features such as the automatic conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar interface to <a class="el" href="classEigen_1_1Quaternion.html" title="The quaternion class used to represent 3D orientations and rotations. ">Quaternion</a> in order to facilitate the writing of generic algorithms dealing with rotations.</p>
<dl class="section see"><dt>See Also</dt><dd>class <a class="el" href="classEigen_1_1Quaternion.html" title="The quaternion class used to represent 3D orientations and rotations. ">Quaternion</a>, class <a class="el" href="classEigen_1_1Transform.html" title="Represents an homogeneous transformation in a N dimensional space. ">Transform</a> </dd></dl>
</div><div id="dynsection-0" onclick="return toggleVisibility(this)" class="dynheader closed" style="cursor:pointer;">
  <img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for Rotation2D&lt; Scalar &gt;:</div>
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<map name="Rotation2D_3_01Scalar_01_4_inherit__map" id="Rotation2D_3_01Scalar_01_4_inherit__map">
<area shape="rect" id="node2" href="classEigen_1_1RotationBase.html" title="{RotationBase\&lt; Rotation2D\l\&lt; _Scalar \&gt;, 2 \&gt;\n||+ _transformVector()\l+ derived()\l+ derived()\l+ inverse()\l+ matrix()\l+ operator*()\l+ operator*()\l+ operator*()\l+ operator*()\l+ toRotationMatrix()\l}" alt="" coords="5,5,184,229"/></map>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-types"></a>
Public Types</h2></td></tr>
<tr class="memitem:abb59a4f54aebad6325389d49d48de310"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="classEigen_1_1Matrix.html">Matrix</a>&lt; <a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>, Dim, Dim &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RotationBase.html#abb59a4f54aebad6325389d49d48de310">RotationMatrixType</a></td></tr>
<tr class="separator:abb59a4f54aebad6325389d49d48de310"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aea29b63b6c32046ae9a471d82c5cf869"><td class="memItemLeft" align="right" valign="top">typedef _Scalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a></td></tr>
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</table><table class="memberdecls">
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Public Member Functions</h2></td></tr>
<tr class="memitem:a0779e44b0f389bec959428f203bc766e"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Rotation2D.html#a0779e44b0f389bec959428f203bc766e">angle</a> () const </td></tr>
<tr class="separator:a0779e44b0f389bec959428f203bc766e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a83ab19e0cf6095c27248a0136d521172"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Rotation2D.html#a83ab19e0cf6095c27248a0136d521172">angle</a> ()</td></tr>
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<tr class="memitem:aff949e81cb0f149761413b5c020b4d5c"><td class="memTemplParams" colspan="2">template&lt;typename NewScalarType &gt; </td></tr>
<tr class="memitem:aff949e81cb0f149761413b5c020b4d5c"><td class="memTemplItemLeft" align="right" valign="top">internal::cast_return_type<br class="typebreak"/>
&lt; <a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a>, <a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a><br class="typebreak"/>
&lt; NewScalarType &gt; &gt;::type&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Rotation2D.html#aff949e81cb0f149761413b5c020b4d5c">cast</a> () const </td></tr>
<tr class="separator:aff949e81cb0f149761413b5c020b4d5c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad46a27f9af696b194058db333a95f7d9"><td class="memTemplParams" colspan="2">template&lt;typename Derived &gt; </td></tr>
<tr class="memitem:ad46a27f9af696b194058db333a95f7d9"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a>&lt; <a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> &gt; &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Rotation2D.html#ad46a27f9af696b194058db333a95f7d9">fromRotationMatrix</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Derived &gt; &amp;mat)</td></tr>
<tr class="separator:ad46a27f9af696b194058db333a95f7d9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab8aa19861bb0513691b920826c75aa43"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Rotation2D.html#ab8aa19861bb0513691b920826c75aa43">inverse</a> () const </td></tr>
<tr class="separator:ab8aa19861bb0513691b920826c75aa43"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:acbcfcb4bf11ad867602619fb454d776d"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Rotation2D.html#acbcfcb4bf11ad867602619fb454d776d">isApprox</a> (const <a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a> &amp;other, const typename <a class="el" href="structEigen_1_1NumTraits.html">NumTraits</a>&lt; <a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> &gt;::Real &amp;prec=<a class="el" href="structEigen_1_1NumTraits.html">NumTraits</a>&lt; <a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> &gt;::dummy_precision()) const </td></tr>
<tr class="separator:acbcfcb4bf11ad867602619fb454d776d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a137458fc1a96a26c9fd58d7b2b61336d"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1RotationBase.html#abb59a4f54aebad6325389d49d48de310">RotationMatrixType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RotationBase.html#a137458fc1a96a26c9fd58d7b2b61336d">matrix</a> () const</td></tr>
<tr class="separator:a137458fc1a96a26c9fd58d7b2b61336d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a39e946f5ec63f80d28cf7988e6ba80b9"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; <a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>, Dim, <a class="el" href="group__enums.html#gga302a826315506a7217d4b477ea78425fac6ccc3814bb6d2a8bf7f75d7131c6b17">Isometry</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RotationBase.html#a39e946f5ec63f80d28cf7988e6ba80b9">operator*</a> (const <a class="el" href="classEigen_1_1Translation.html">Translation</a>&lt; <a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>, Dim &gt; &amp;t) const</td></tr>
<tr class="separator:a39e946f5ec63f80d28cf7988e6ba80b9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a84d2f46dbcd54e3a3b8ebcc673ad3920"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1RotationBase.html#abb59a4f54aebad6325389d49d48de310">RotationMatrixType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RotationBase.html#a84d2f46dbcd54e3a3b8ebcc673ad3920">operator*</a> (const UniformScaling&lt; <a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> &gt; &amp;s) const</td></tr>
<tr class="separator:a84d2f46dbcd54e3a3b8ebcc673ad3920"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:acd4f0475d084e54c0dde2ef3f78822c0"><td class="memItemLeft" align="right" valign="top">internal::rotation_base_generic_product_selector<br class="typebreak"/>
&lt; <a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a>&lt; _Scalar &gt;<br class="typebreak"/>
, OtherDerived, <br class="typebreak"/>
OtherDerived::IsVectorAtCompileTime &gt;<br class="typebreak"/>
::ReturnType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RotationBase.html#acd4f0475d084e54c0dde2ef3f78822c0">operator*</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; OtherDerived &gt; &amp;e) const</td></tr>
<tr class="separator:acd4f0475d084e54c0dde2ef3f78822c0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae0c6c089ae4f8aa3069d1de268522ab9"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Rotation2D.html#ae0c6c089ae4f8aa3069d1de268522ab9">operator*</a> (const <a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a> &amp;other) const </td></tr>
<tr class="separator:ae0c6c089ae4f8aa3069d1de268522ab9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad34dc61aab8108f6b660a19d1fdf000a"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Matrix.html">Vector2</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Rotation2D.html#ad34dc61aab8108f6b660a19d1fdf000a">operator*</a> (const <a class="el" href="classEigen_1_1Matrix.html">Vector2</a> &amp;vec) const </td></tr>
<tr class="separator:ad34dc61aab8108f6b660a19d1fdf000a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4905e372221a7ca6eaf7f11056bc1b7a"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; <a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>, Dim, Mode &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RotationBase.html#a4905e372221a7ca6eaf7f11056bc1b7a">operator*</a> (const <a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; <a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>, Dim, Mode, Options &gt; &amp;t) const</td></tr>
<tr class="separator:a4905e372221a7ca6eaf7f11056bc1b7a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a38e158a4156cbc2978e31a6256ae1d4e"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Rotation2D.html#a38e158a4156cbc2978e31a6256ae1d4e">operator*=</a> (const <a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a> &amp;other)</td></tr>
<tr class="separator:a38e158a4156cbc2978e31a6256ae1d4e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4c944f17c4f3d932a892cada1b927625"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Rotation2D.html#a4c944f17c4f3d932a892cada1b927625">Rotation2D</a> (const <a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> &amp;a)</td></tr>
<tr class="separator:a4c944f17c4f3d932a892cada1b927625"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4b8dc04e709066f966d91ce8d14d3036"><td class="memTemplParams" colspan="2">template&lt;typename OtherScalarType &gt; </td></tr>
<tr class="memitem:a4b8dc04e709066f966d91ce8d14d3036"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Rotation2D.html#a4b8dc04e709066f966d91ce8d14d3036">Rotation2D</a> (const <a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a>&lt; OtherScalarType &gt; &amp;other)</td></tr>
<tr class="separator:a4b8dc04e709066f966d91ce8d14d3036"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a56fb619ede8412eec05b51c22b1465c8"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Rotation2D.html#a56fb619ede8412eec05b51c22b1465c8">slerp</a> (const <a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> &amp;t, const <a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a> &amp;other) const </td></tr>
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<tr class="memitem:af10119ceb1241b50e13faef3ecf2ea00"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Matrix.html">Matrix2</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Rotation2D.html#af10119ceb1241b50e13faef3ecf2ea00">toRotationMatrix</a> (void) const </td></tr>
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<h2 class="groupheader">Member Typedef Documentation</h2>
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          <td class="memname">typedef <a class="el" href="classEigen_1_1Matrix.html">Matrix</a>&lt;<a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>,Dim,Dim&gt; <a class="el" href="classEigen_1_1RotationBase.html#abb59a4f54aebad6325389d49d48de310">RotationMatrixType</a></td>
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<p>corresponding linear transformation matrix type </p>

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<p>the scalar type of the coefficients </p>

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<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<p>Construct a 2D counter clock wise rotation from the angle <em>a</em> in radian. </p>

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<p>Copy constructor with scalar type conversion </p>

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<h2 class="groupheader">Member Function Documentation</h2>
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          <td class="memname"><a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a> angle </td>
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<dl class="section return"><dt>Returns</dt><dd>the rotation angle </dd></dl>

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          <td class="memname"><a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>&amp; angle </td>
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<dl class="section return"><dt>Returns</dt><dd>a read-write reference to the rotation angle </dd></dl>

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          <td class="memname">internal::cast_return_type&lt;<a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a>,<a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a>&lt;NewScalarType&gt; &gt;::type cast </td>
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<dl class="section return"><dt>Returns</dt><dd><code>*this</code> with scalar type casted to <em>NewScalarType</em> </dd></dl>
<p>Note that if <em>NewScalarType</em> is equal to the current scalar type of <code>*this</code> then this function smartly returns a const reference to <code>*this</code>. </p>

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<p>Set <code>*this</code> from a 2x2 rotation matrix <em>mat</em>. In other words, this function extract the rotation angle from the rotation matrix. </p>

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<dl class="section return"><dt>Returns</dt><dd>the inverse rotation </dd></dl>

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          <td class="paramname"><em>prec</em> = <code><a class="el" href="structEigen_1_1NumTraits.html">NumTraits</a>&lt;<a class="el" href="classEigen_1_1Rotation2D.html#aea29b63b6c32046ae9a471d82c5cf869">Scalar</a>&gt;::dummy_precision()</code>&#160;</td>
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<dl class="section return"><dt>Returns</dt><dd><code>true</code> if <code>*this</code> is approximately equal to <em>other</em>, within the precision determined by <em>prec</em>.</dd></dl>
<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classEigen_1_1DenseBase.html#a158c2184951e6e415c2e9b98db8e8966">MatrixBase::isApprox()</a> </dd></dl>

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<dl class="section return"><dt>Returns</dt><dd>an equivalent rotation matrix This function is added to be conform with the Transform class' naming scheme. </dd></dl>

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          <td>(</td>
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<dl class="section return"><dt>Returns</dt><dd>the concatenation of the rotation <code>*this</code> with a translation <em>t</em> </dd></dl>

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<dl class="section return"><dt>Returns</dt><dd>the concatenation of the rotation <code>*this</code> with a uniform scaling <em>s</em> </dd></dl>

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          <td class="memname">internal::rotation_base_generic_product_selector&lt;<a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a>&lt; _Scalar &gt; ,OtherDerived,OtherDerived::IsVectorAtCompileTime&gt;::ReturnType operator* </td>
          <td>(</td>
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<dl class="section return"><dt>Returns</dt><dd>the concatenation of the rotation <code>*this</code> with a generic expression <em>e</em> <em>e</em> can be:<ul>
<li>a DimxDim linear transformation matrix</li>
<li>a DimxDim diagonal matrix (axis aligned scaling)</li>
<li>a vector of size Dim </li>
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<p>Concatenates two rotations </p>

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<p>Applies the rotation to a 2D vector </p>

<p>References <a class="el" href="classEigen_1_1Rotation2D.html#af10119ceb1241b50e13faef3ecf2ea00">Rotation2D&lt; Scalar &gt;::toRotationMatrix()</a>.</p>

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          <td>(</td>
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<dl class="section return"><dt>Returns</dt><dd>the concatenation of the rotation <code>*this</code> with a transformation <em>t</em> </dd></dl>

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<p>Concatenates two rotations </p>

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          <td class="memname"><a class="el" href="classEigen_1_1Rotation2D.html">Rotation2D</a> slerp </td>
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<dl class="section return"><dt>Returns</dt><dd>the spherical interpolation between <code>*this</code> and <em>other</em> using parameter <em>t</em>. It is in fact equivalent to a linear interpolation. </dd></dl>

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<p>Constructs and </p>
<dl class="section return"><dt>Returns</dt><dd>an equivalent 2x2 rotation matrix. </dd></dl>

<p>Referenced by <a class="el" href="classEigen_1_1Rotation2D.html#ad34dc61aab8108f6b660a19d1fdf000a">Rotation2D&lt; Scalar &gt;::operator*()</a>.</p>

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<hr/>The documentation for this class was generated from the following files:<ul>
<li><a class="el" href="ForwardDeclarations_8h_source.html">ForwardDeclarations.h</a></li>
<li><a class="el" href="Rotation2D_8h_source.html">Rotation2D.h</a></li>
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