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  <div class="navpath"><a class="el" href="namespaceitk.html">itk</a>::<a class="el" href="classitk_1_1Versor.html">Versor</a>
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<h1>itk::Versor&lt; T &gt; Class Template Reference<br>
<small>
[<a class="el" href="group__Geometry.html">Geometry Representation Objects</a>,&nbsp;<a class="el" href="group__DataRepresentation.html">Data Representation Objects</a>]</small>
</h1><!-- doxytag: class="itk::Versor" --><a class="el" href="classA.html">A</a> templated class holding a unit quaternion.  
<a href="#_details">More...</a>
<p>
<code>#include &lt;<a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>&gt;</code>
<p>
<div class="dynheader">
Inheritance diagram for itk::Versor&lt; T &gt;:</div>
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<p><center><img src="classitk_1_1Versor__inherit__graph.png" border="0" usemap="#itk_1_1Versor_3_01T_01_4__inherit__map" alt="Inheritance graph"></center>
<map name="itk_1_1Versor_3_01T_01_4__inherit__map">
<area shape="rect" id="node3" href="classitk_1_1Versor.html" title="itk::Versor\&lt; TScalarType \&gt;" alt="" coords="5,101,205,131"></map>
<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
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Collaboration diagram for itk::Versor&lt; T &gt;:</div>
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<p><center><img src="classitk_1_1Versor__coll__graph.png" border="0" usemap="#itk_1_1Versor_3_01T_01_4__coll__map" alt="Collaboration graph"></center>
<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>

<p>
<a href="classitk_1_1Versor-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Public Types</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">typedef <a class="el" href="classitk_1_1CovariantVector.html">CovariantVector</a>&lt; T, 3 &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#cc335f5a15ed33693fb93f24c8d08e9d">CovariantVectorType</a></td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">typedef <a class="el" href="classitk_1_1Matrix.html">Matrix</a>&lt; T, 3, 3 &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#0a8a1bfdeb3dd64eb7245cdc4dbe0c11">MatrixType</a></td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">typedef <a class="el" href="classitk_1_1Point.html">Point</a>&lt; T, 3 &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#39114efc8e606651f7b6dc5e17525808">PointType</a></td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">typedef NumericTraits<br class="typebreak">
&lt; <a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a> &gt;::<a class="el" href="classitk_1_1Versor.html#ffbdfef95833b33015541c29a27126ed">RealType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#ffbdfef95833b33015541c29a27126ed">RealType</a></td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">typedef <a class="el" href="classitk_1_1Versor.html">Versor</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#5168833b384aa41aa5db77e850e1af21">Self</a></td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">typedef T&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a></td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">typedef <a class="el" href="classitk_1_1Vector.html">Vector</a>&lt; T, 3 &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#747ef420c3854a48e416f50d21496db4">VectorType</a></td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">typedef vnl_quaternion&lt; T &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#52ec040aa0278c862ab37fa167b4b2fb">VnlQuaternionType</a></td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">typedef vnl_vector_fixed&lt; T, 3 &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#855ceff5742080cc4a1c31089564f861">VnlVectorType</a></td></tr>

<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Versor.html">Self</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#4271004f22244e8fee9ec78cbae0fbc9">Exponential</a> (<a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a> exponent) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#44eb824ede24c516dbf7600199a5dbbd">GetAngle</a> (void) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Vector.html">VectorType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#98dbb150e21c9c6cd02f8432d2484c85">GetAxis</a> (void) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Versor.html">Self</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#b17c97cf8c95d49354089d06223a1c4a">GetConjugate</a> (void) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Matrix.html">MatrixType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#4f0f947910bdb1a80ab0553a72cc34e5">GetMatrix</a> (void) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Versor.html">Self</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#7a4e827179aa5bb5c08d733b08e3f144">GetReciprocal</a> (void) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Vector.html">VectorType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#f1a9cb958d24cd34c2bd60024e24b841">GetRight</a> (void) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#184b40d091f937447bfcda86af49d818">GetScalar</a> (void) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#bf44ded0b41b1b6aff8bf9719e561d48">GetTensor</a> (void) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">vnl_quaternion&lt; T &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#5dc32e252b30fcaee4f0c48330f3d2ff">GetVnlQuaternion</a> (void) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#c5497c3ee33a1542c2faee088803e1fe">GetW</a> (void) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#0d83976fe33626aace4e684f39ae3da2">GetX</a> (void) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#40421e9662c4f3e9a968654d02b76ad1">GetY</a> (void) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#afbb686acd55527e05c43cf2e8e42153">GetZ</a> (void) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#e910c46eaaa309f8afae8671a0363ff6">Normalize</a> (void)</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#8a58bd499236bd10d5c4cb3cf4e8dfb7">operator!=</a> (const <a class="el" href="classitk_1_1Versor.html">Self</a> &amp;vec) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Versor.html">Self</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#8b4a1917598e4474f5d49bdb96abaee2">operator*</a> (const <a class="el" href="classitk_1_1Versor.html">Self</a> &amp;vec) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">const <a class="el" href="classitk_1_1Versor.html">Self</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#e8431eb4817b6d46170501bad0b6e5c3">operator*=</a> (const <a class="el" href="classitk_1_1Versor.html">Self</a> &amp;v)</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Versor.html">Self</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#8997dba400b5514ef42eb218205be062">operator/</a> (const <a class="el" href="classitk_1_1Versor.html">Self</a> &amp;vec) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">const <a class="el" href="classitk_1_1Versor.html">Self</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#c82e7509e446e1b04eaf4f3f27184cdd">operator/=</a> (const <a class="el" href="classitk_1_1Versor.html">Self</a> &amp;v)</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">const <a class="el" href="classitk_1_1Versor.html">Self</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#9921cca6464a64d81d5f1d3777b8893a">operator=</a> (const <a class="el" href="classitk_1_1Versor.html">Self</a> &amp;v)</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#9399ffb749237306ca30d586466cc187">operator==</a> (const <a class="el" href="classitk_1_1Versor.html">Self</a> &amp;vec) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#72a0cf968370f95dac5bac84a01f93a0">Set</a> (const <a class="el" href="classitk_1_1Vector.html">VectorType</a> &amp;axis)</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#d22261bee493be34f2fc3941d24604dc">Set</a> (const <a class="el" href="classitk_1_1Matrix.html">MatrixType</a> &amp;m)</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#352e896152c940d754f8f0c83ce3a83e">Set</a> (const <a class="el" href="classitk_1_1Vector.html">VectorType</a> &amp;axis, <a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a> angle)</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#9da1e5c6d1c9a51daae55684021048a1">Set</a> (const <a class="el" href="classitk_1_1Versor.html#52ec040aa0278c862ab37fa167b4b2fb">VnlQuaternionType</a> &amp;)</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#23ca7d20f1af882701447ec571ab0437">SetIdentity</a> ()</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#df882c1fa42c755cfb42c77bea7fdfdf">SetRotationAroundX</a> (<a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a> angle)</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#c11199be1609dcad266f1bdea9d04d84">SetRotationAroundY</a> (<a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a> angle)</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#817c1cab4a5566d40f46035345754539">SetRotationAroundZ</a> (<a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a> angle)</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Versor.html">Self</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#52d7add53c9b883fd1076ff8565b6718">SquareRoot</a> (void) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Versor.html#855ceff5742080cc4a1c31089564f861">VnlVectorType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#89e10b3809ffe03014a34f3a31f18a5f">Transform</a> (const <a class="el" href="classitk_1_1Versor.html#855ceff5742080cc4a1c31089564f861">VnlVectorType</a> &amp;v) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Point.html">PointType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#3f59f624db69b8c1569ffd9093a33718">Transform</a> (const <a class="el" href="classitk_1_1Point.html">PointType</a> &amp;v) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1CovariantVector.html">CovariantVectorType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#f1b1537a964ada2b5004ae0e4a8565d9">Transform</a> (const <a class="el" href="classitk_1_1CovariantVector.html">CovariantVectorType</a> &amp;v) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitk_1_1Vector.html">VectorType</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#084a6f3bfbb0765a3077ffb9d4842d77">Transform</a> (const <a class="el" href="classitk_1_1Vector.html">VectorType</a> &amp;v) const </td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#ede0307b8611788ad7d48659406b976f">Versor</a> (const <a class="el" href="classitk_1_1Versor.html">Self</a> &amp;v)</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#f9a3d71d51822d2f76ae31fa2c53e424">Versor</a> ()</td></tr>

<tr><td colspan="2"><div class="groupHeader"></div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitk_1_1Versor.html#610d6f1705d2a0de95ce92811a4e6bc7">Set</a> (T x, T y, T z, T w)</td></tr>

</table>
<hr><a name="_details"></a><h2>Detailed Description</h2>
<h3>template&lt;class T&gt;<br>
 class itk::Versor&lt; T &gt;</h3>

<a class="el" href="classA.html">A</a> templated class holding a unit quaternion. 
<p>
<a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a> is a templated class that holds a unit quaternion. The difference between versors and quaternions is that quaternions can represent rotations and scale changes while versors are limited to rotations.<p>
This class only implements the operations that maintain versors as a group, that is, any operations between versors result in another versor. For this reason, addition is not defined in this class, even though it is a valid operation between quaternions.<p>
<dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="classitk_1_1Vector.html" title="A templated class holding a n-Dimensional vector.">Vector</a> <p>
<a class="el" href="classitk_1_1Point.html" title="A templated class holding a geometric point in n-Dimensional space.">Point</a> <p>
<a class="el" href="classitk_1_1CovariantVector.html" title="A templated class holding a n-Dimensional covariant vector.">CovariantVector</a> <p>
<a class="el" href="classitk_1_1Matrix.html" title="A templated class holding a M x N size Matrix This class contains a vnl_matrix_fixed...">Matrix</a> </dd></dl>

<p>Definition at line <a class="el" href="itkVersor_8h_source.html#l00052">52</a> of file <a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>.</p>
<hr><h2>Member Typedef Documentation</h2>
<a class="anchor" name="cc335f5a15ed33693fb93f24c8d08e9d"></a><!-- doxytag: member="itk::Versor::CovariantVectorType" ref="cc335f5a15ed33693fb93f24c8d08e9d" args="" -->
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template&lt;class T&gt; </div>
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          <td class="memname">typedef <a class="el" href="classitk_1_1CovariantVector.html">CovariantVector</a>&lt;T,3&gt; <a class="el" href="classitk_1_1Versor.html">itk::Versor</a>&lt; T &gt;::<a class="el" href="classitk_1_1CovariantVector.html">CovariantVectorType</a>          </td>
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<p>
<a class="el" href="classitk_1_1CovariantVector.html" title="A templated class holding a n-Dimensional covariant vector.">CovariantVector</a> type. 
<p>Definition at line <a class="el" href="itkVersor_8h_source.html#l00072">72</a> of file <a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>.</p>

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<a class="anchor" name="0a8a1bfdeb3dd64eb7245cdc4dbe0c11"></a><!-- doxytag: member="itk::Versor::MatrixType" ref="0a8a1bfdeb3dd64eb7245cdc4dbe0c11" args="" -->
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Type of the rotation matrix equivalent to the <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a> 
<p>Definition at line <a class="el" href="itkVersor_8h_source.html#l00081">81</a> of file <a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>.</p>

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<a class="anchor" name="39114efc8e606651f7b6dc5e17525808"></a><!-- doxytag: member="itk::Versor::PointType" ref="39114efc8e606651f7b6dc5e17525808" args="" -->
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<a class="el" href="classitk_1_1Point.html" title="A templated class holding a geometric point in n-Dimensional space.">Point</a> type. 
<p>Definition at line <a class="el" href="itkVersor_8h_source.html#l00069">69</a> of file <a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>.</p>

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<a class="anchor" name="ffbdfef95833b33015541c29a27126ed"></a><!-- doxytag: member="itk::Versor::RealType" ref="ffbdfef95833b33015541c29a27126ed" args="" -->
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          <td class="memname">typedef NumericTraits&lt;<a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a>&gt;::<a class="el" href="classitk_1_1Versor.html#ffbdfef95833b33015541c29a27126ed">RealType</a> <a class="el" href="classitk_1_1Versor.html">itk::Versor</a>&lt; T &gt;::<a class="el" href="classitk_1_1Versor.html#ffbdfef95833b33015541c29a27126ed">RealType</a>          </td>
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Type used for computations on the versor components 
<p>Definition at line <a class="el" href="itkVersor_8h_source.html#l00063">63</a> of file <a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>.</p>

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<a class="anchor" name="5168833b384aa41aa5db77e850e1af21"></a><!-- doxytag: member="itk::Versor::Self" ref="5168833b384aa41aa5db77e850e1af21" args="" -->
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Standard class typedefs. 
<p>Definition at line <a class="el" href="itkVersor_8h_source.html#l00056">56</a> of file <a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>.</p>

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<a class="anchor" name="9dfee332294098f7bda65163c2615588"></a><!-- doxytag: member="itk::Versor::ValueType" ref="9dfee332294098f7bda65163c2615588" args="" -->
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ValueType can be used to declare a variable that is the same type as a data element held in a <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a>. 
<p>Definition at line <a class="el" href="itkVersor_8h_source.html#l00060">60</a> of file <a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>.</p>

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<a class="anchor" name="747ef420c3854a48e416f50d21496db4"></a><!-- doxytag: member="itk::Versor::VectorType" ref="747ef420c3854a48e416f50d21496db4" args="" -->
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<a class="el" href="classitk_1_1Vector.html" title="A templated class holding a n-Dimensional vector.">Vector</a> type used to represent the axis. 
<p>Definition at line <a class="el" href="itkVersor_8h_source.html#l00066">66</a> of file <a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>.</p>

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<a class="anchor" name="52ec040aa0278c862ab37fa167b4b2fb"></a><!-- doxytag: member="itk::Versor::VnlQuaternionType" ref="52ec040aa0278c862ab37fa167b4b2fb" args="" -->
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Vnl Quaternion type. 
<p>Definition at line <a class="el" href="itkVersor_8h_source.html#l00078">78</a> of file <a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>.</p>

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Vnl <a class="el" href="classitk_1_1Vector.html" title="A templated class holding a n-Dimensional vector.">Vector</a> type. 
<p>Definition at line <a class="el" href="itkVersor_8h_source.html#l00075">75</a> of file <a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>.</p>

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<hr><h2>Constructor &amp; Destructor Documentation</h2>
<a class="anchor" name="f9a3d71d51822d2f76ae31fa2c53e424"></a><!-- doxytag: member="itk::Versor::Versor" ref="f9a3d71d51822d2f76ae31fa2c53e424" args="()" -->
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Default constructor creates a null versor (representing 0 degrees rotation). 
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Copy constructor. 
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<hr><h2>Member Function Documentation</h2>
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Compute the Exponential of the unit quaternion Exponentiation by a factor is equivalent to multiplication of the rotaion angle of the quaternion. 
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Returns the rotation angle in radians. 
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<a class="anchor" name="98dbb150e21c9c6cd02f8432d2484c85"></a><!-- doxytag: member="itk::Versor::GetAxis" ref="98dbb150e21c9c6cd02f8432d2484c85" args="(void) const " -->
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Returns the axis of the rotation. It is a unit vector parallel to the axis. 
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Get Conjugate versor. Returns the versor that produce a rotation by the same angle but in opposite direction. 
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Get the matrix representation. 
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Get Reciprocal versor. Returns the versor that composed with this one will result in a scalar operator equals to 1. It is also equivalent to 1/this. 
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Returns the Right part It is a vector part of the <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a>. It is called Right because it is equivalent to a right angle rotation. 
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Returns the Scalar part. 
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Get Tensor part of the <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a>. Given that Versors are normalized quaternions this value is expected to be 1.0 always 
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Get a vnl_quaternion with a copy of the internal memory block. 
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Returns the W component. 
<p>Definition at line <a class="el" href="itkVersor_8h_source.html#l00185">185</a> of file <a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>.</p>

<p>Referenced by <a class="el" href="itkVersor_8h_source.html#l00286">itk::operator&lt;&lt;()</a>.</p>

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Returns the X component. 
<p>Definition at line <a class="el" href="itkVersor_8h_source.html#l00173">173</a> of file <a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>.</p>

<p>Referenced by <a class="el" href="itkVersor_8h_source.html#l00286">itk::operator&lt;&lt;()</a>.</p>

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<a class="anchor" name="40421e9662c4f3e9a968654d02b76ad1"></a><!-- doxytag: member="itk::Versor::GetY" ref="40421e9662c4f3e9a968654d02b76ad1" args="(void) const " -->
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Returns the Y component. 
<p>Definition at line <a class="el" href="itkVersor_8h_source.html#l00177">177</a> of file <a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>.</p>

<p>Referenced by <a class="el" href="itkVersor_8h_source.html#l00286">itk::operator&lt;&lt;()</a>.</p>

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<a class="anchor" name="afbb686acd55527e05c43cf2e8e42153"></a><!-- doxytag: member="itk::Versor::GetZ" ref="afbb686acd55527e05c43cf2e8e42153" args="(void) const " -->
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Returns the Z component. 
<p>Definition at line <a class="el" href="itkVersor_8h_source.html#l00181">181</a> of file <a class="el" href="itkVersor_8h_source.html">itkVersor.h</a>.</p>

<p>Referenced by <a class="el" href="itkVersor_8h_source.html#l00286">itk::operator&lt;&lt;()</a>.</p>

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<a class="anchor" name="e910c46eaaa309f8afae8671a0363ff6"></a><!-- doxytag: member="itk::Versor::Normalize" ref="e910c46eaaa309f8afae8671a0363ff6" args="(void)" -->
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Normalize the <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a>. Given that Versors are normalized quaternions this method is provided only for convinience when it is suspected that a versor could be out of the unit sphere. 
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<a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a> operator!= Performs the comparison between two versors. this operation uses an arbitrary threshold for the comparison. 
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<a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a> operator*. Performs the composition of two versors. this operation is NOT commutative. 
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Composition operator *=. Compose the current versor with the operand and store the result in the current versor. 
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<a class="anchor" name="8997dba400b5514ef42eb218205be062"></a><!-- doxytag: member="itk::Versor::operator/" ref="8997dba400b5514ef42eb218205be062" args="(const Self &amp;vec) const " -->
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<a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a> operator/. Performs the division of two versors. 
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Division operator /=. Divide the current versor with the operand and store the result in the current versor. This is equivalent to compose the <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a> with the reciprocal of the operand <dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="classitk_1_1Versor.html#7a4e827179aa5bb5c08d733b08e3f144">GetReciprocal</a> </dd></dl>

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<a class="anchor" name="9921cca6464a64d81d5f1d3777b8893a"></a><!-- doxytag: member="itk::Versor::operator=" ref="9921cca6464a64d81d5f1d3777b8893a" args="(const Self &amp;v)" -->
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Assignment operator =. Copy the versor argument. 
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<a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a> operator== Performs the comparison between two versors. this operation uses an arbitrary threshold for the comparison. 
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<a class="anchor" name="72a0cf968370f95dac5bac84a01f93a0"></a><!-- doxytag: member="itk::Versor::Set" ref="72a0cf968370f95dac5bac84a01f93a0" args="(const VectorType &amp;axis)" -->
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Set the versor using the right part. the magnitude of the vector given is assumed to be equal to vcl_sin(angle/2). This method will compute internally the scalar part that preserve the <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a> as a unit quaternion. 
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Set the versor using an orthogonal matrix. Based on code from: <a href="http://www.euclideanspace.com/maths/geometry/rotations/">http://www.euclideanspace.com/maths/geometry/rotations/</a> conversions/matrixToQuaternion/index.htm 
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Set the versor using a vector and angle the unit vector parallel to the given vector will be used. The angle is expected in radians. 
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Set the <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a> from Quaternion components. <dl class="warning" compact><dt><b>Warning:</b></dt><dd>After assignment, the corresponding quaternion will be normalized in order to get a consistent <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a>. Also, if the "w" component is negative, the four components will be negated in order to produce a quaternion where "w" is positive, since this is implicitly assumed in other sections of the code, in particular when "w" is computed from (x,y,z) via normalization. The reason why it is valid to negate all the components is that the rotation by angle , is represented by ({}{2}) in the (x,y,z) components and by ({}{2}) in the "w" component. The rotation by any  should be equivalent to a rotation by  + n  , therefore we should be able to replace ({}{2}) with ({}{2} + n   ) and ({}{2}) with ({}{2} + n   ). Considering that ( n   ) = (-1)^{n} we can conclude that if we simultaneously change the signs of all the <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a> components, the rotation that it represents remains unchanged. </dd></dl>

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<a class="anchor" name="9da1e5c6d1c9a51daae55684021048a1"></a><!-- doxytag: member="itk::Versor::Set" ref="9da1e5c6d1c9a51daae55684021048a1" args="(const VnlQuaternionType &amp;)" -->
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Set the <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a> from a Quaternion <dl class="warning" compact><dt><b>Warning:</b></dt><dd>After assignment, the corresponding quaternion will be normalized in order to get a consistent <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a>. </dd></dl>

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Reset the values so the versor is equivalent to an identity transformation. This is equivalent to set a zero angle 
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Sets a rotation around the X axis using the parameter as angle in radians. This is a method provided for convinience to initialize a rotation. The effect of this methods is not cumulative with any value previously stored in the <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a>. <dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="classitk_1_1Versor.html#9da1e5c6d1c9a51daae55684021048a1">Set</a> <p>
<a class="el" href="classitk_1_1Versor.html#c11199be1609dcad266f1bdea9d04d84">SetRotationAroundY</a> <p>
<a class="el" href="classitk_1_1Versor.html#817c1cab4a5566d40f46035345754539">SetRotationAroundZ</a> </dd></dl>

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Sets a rotation around the Y axis using the parameter as angle in radians. This is a method provided for convinience to initialize a rotation. The effect of this methods is not cumulative with any value previously stored in the <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a>. <dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="classitk_1_1Versor.html#9da1e5c6d1c9a51daae55684021048a1">Set</a> <p>
<a class="el" href="classitk_1_1Versor.html#df882c1fa42c755cfb42c77bea7fdfdf">SetRotationAroundX</a> <p>
<a class="el" href="classitk_1_1Versor.html#817c1cab4a5566d40f46035345754539">SetRotationAroundZ</a> </dd></dl>

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<a class="anchor" name="817c1cab4a5566d40f46035345754539"></a><!-- doxytag: member="itk::Versor::SetRotationAroundZ" ref="817c1cab4a5566d40f46035345754539" args="(ValueType angle)" -->
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          <td class="paramtype"><a class="el" href="classitk_1_1Versor.html#9dfee332294098f7bda65163c2615588">ValueType</a>&nbsp;</td>
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Sets a rotation around the Y axis using the parameter as angle in radians. This is a method provided for convinience to initialize a rotation. The effect of this methods is not cumulative with any value previously stored in the <a class="el" href="classitk_1_1Versor.html" title="A templated class holding a unit quaternion.">Versor</a>. <dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="classitk_1_1Versor.html#9da1e5c6d1c9a51daae55684021048a1">Set</a> <p>
<a class="el" href="classitk_1_1Versor.html#df882c1fa42c755cfb42c77bea7fdfdf">SetRotationAroundX</a> <p>
<a class="el" href="classitk_1_1Versor.html#c11199be1609dcad266f1bdea9d04d84">SetRotationAroundY</a> </dd></dl>

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<a class="anchor" name="52d7add53c9b883fd1076ff8565b6718"></a><!-- doxytag: member="itk::Versor::SquareRoot" ref="52d7add53c9b883fd1076ff8565b6718" args="(void) const " -->
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Get the Square root of the unit quaternion. 
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<a class="anchor" name="89e10b3809ffe03014a34f3a31f18a5f"></a><!-- doxytag: member="itk::Versor::Transform" ref="89e10b3809ffe03014a34f3a31f18a5f" args="(const VnlVectorType &amp;v) const " -->
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          <td>(</td>
          <td class="paramtype">const <a class="el" href="classitk_1_1Versor.html#855ceff5742080cc4a1c31089564f861">VnlVectorType</a> &amp;&nbsp;</td>
          <td class="paramname"> <em>v</em>          </td>
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<a class="el" href="classitk_1_1Transform.html" title="Transform points and vector from an input space to an output space.">Transform</a> a <a class="el" href="classvnl__vector.html">vnl_vector</a>. 
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<a class="anchor" name="3f59f624db69b8c1569ffd9093a33718"></a><!-- doxytag: member="itk::Versor::Transform" ref="3f59f624db69b8c1569ffd9093a33718" args="(const PointType &amp;v) const " -->
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          <td>(</td>
          <td class="paramtype">const <a class="el" href="classitk_1_1Point.html">PointType</a> &amp;&nbsp;</td>
          <td class="paramname"> <em>v</em>          </td>
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<a class="el" href="classitk_1_1Transform.html" title="Transform points and vector from an input space to an output space.">Transform</a> a point. 
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<a class="anchor" name="f1b1537a964ada2b5004ae0e4a8565d9"></a><!-- doxytag: member="itk::Versor::Transform" ref="f1b1537a964ada2b5004ae0e4a8565d9" args="(const CovariantVectorType &amp;v) const " -->
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          <td class="paramtype">const <a class="el" href="classitk_1_1CovariantVector.html">CovariantVectorType</a> &amp;&nbsp;</td>
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<a class="el" href="classitk_1_1Transform.html" title="Transform points and vector from an input space to an output space.">Transform</a> a covariant vector. 
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<a class="anchor" name="084a6f3bfbb0765a3077ffb9d4842d77"></a><!-- doxytag: member="itk::Versor::Transform" ref="084a6f3bfbb0765a3077ffb9d4842d77" args="(const VectorType &amp;v) const " -->
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          <td class="memname"><a class="el" href="classitk_1_1Vector.html">VectorType</a> <a class="el" href="classitk_1_1Versor.html">itk::Versor</a>&lt; T &gt;::<a class="el" href="classitk_1_1Transform.html">Transform</a>           </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classitk_1_1Vector.html">VectorType</a> &amp;&nbsp;</td>
          <td class="paramname"> <em>v</em>          </td>
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<a class="el" href="classitk_1_1Transform.html" title="Transform points and vector from an input space to an output space.">Transform</a> a vector. 
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<hr>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="itkVersor_8h_source.html">itkVersor.h</a></ul>
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