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| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="boost_quaternions.quaternions.value_op"></a><a class="link" href="value_op.html" title="Quaternion Value Operations"> Quaternion Value |
| Operations</a> |
| </h3></div></div></div> |
| <a name="boost_quaternions.quaternions.value_op.real_and_unreal"></a><h5> |
| <a name="id784593"></a> |
| <a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.real_and_unreal">real |
| and unreal</a> |
| </h5> |
| <pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">real</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">unreal</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span> |
| </pre> |
| <p> |
| These return <code class="computeroutput"><span class="identifier">q</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span></code> |
| and <code class="computeroutput"><span class="identifier">q</span><span class="special">.</span><span class="identifier">unreal</span><span class="special">()</span></code> |
| respectively. |
| </p> |
| <a name="boost_quaternions.quaternions.value_op.conj"></a><h5> |
| <a name="id784840"></a> |
| <a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.conj">conj</a> |
| </h5> |
| <pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">conj</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span> |
| </pre> |
| <p> |
| This returns the conjugate of the quaternion. |
| </p> |
| <a name="boost_quaternions.quaternions.value_op.sup"></a><h5> |
| <a name="id784961"></a> |
| <a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.sup">sup</a> |
| </h5> |
| <p> |
| template<typename T> T sup(quaternion<T> const & q); |
| </p> |
| <p> |
| This return the sup norm (the greatest among <code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())...</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()))</span></code> of the quaternion. |
| </p> |
| <a name="boost_quaternions.quaternions.value_op.l1"></a><h5> |
| <a name="id785048"></a> |
| <a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.l1">l1</a> |
| </h5> |
| <pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">l1</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span> |
| </pre> |
| <p> |
| This return the l1 norm <code class="computeroutput"><span class="special">(</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())+...+</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()))</span></code> of the quaternion. |
| </p> |
| <a name="boost_quaternions.quaternions.value_op.abs"></a><h5> |
| <a name="id785217"></a> |
| <a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.abs">abs</a> |
| </h5> |
| <pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span> |
| </pre> |
| <p> |
| This return the magnitude (Euclidian norm) of the quaternion. |
| </p> |
| <a name="boost_quaternions.quaternions.value_op.norm"></a><h5> |
| <a name="id785324"></a> |
| <a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.norm">norm</a> |
| </h5> |
| <pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">norm</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span><span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span> |
| </pre> |
| <p> |
| This return the (Cayley) norm of the quaternion. The term "norm" |
| might be confusing, as most people associate it with the Euclidian norm (and |
| quadratic functionals). For this version of (the mathematical objects known |
| as) quaternions, the Euclidian norm (also known as magnitude) is the square |
| root of the Cayley norm. |
| </p> |
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| <td align="right"><div class="copyright-footer">Copyright © 2001 -2003 Hubert Holin<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
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