111 lines
10 KiB
HTML
111 lines
10 KiB
HTML
<html>
|
||
<head>
|
||
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
|
||
<title>Quaternion Value Operations</title>
|
||
<link rel="stylesheet" href="../math.css" type="text/css">
|
||
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
|
||
<link rel="home" href="../index.html" title="Math Toolkit 3.0.0">
|
||
<link rel="up" href="../quaternions.html" title="Chapter 16. Quaternions">
|
||
<link rel="prev" href="quat_non_mem.html" title="Quaternion Non-Member Operators">
|
||
<link rel="next" href="create.html" title="Quaternion Creation Functions">
|
||
</head>
|
||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||
<table cellpadding="2" width="100%"><tr>
|
||
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
|
||
<td align="center"><a href="../../../../../index.html">Home</a></td>
|
||
<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td>
|
||
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
|
||
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
|
||
<td align="center"><a href="../../../../../more/index.htm">More</a></td>
|
||
</tr></table>
|
||
<hr>
|
||
<div class="spirit-nav">
|
||
<a accesskey="p" href="quat_non_mem.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="create.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="math_toolkit.value_op"></a><a class="link" href="value_op.html" title="Quaternion Value Operations">Quaternion Value Operations</a>
|
||
</h2></div></div></div>
|
||
<h5>
|
||
<a name="math_toolkit.value_op.h0"></a>
|
||
<span class="phrase"><a name="math_toolkit.value_op.real_and_unreal"></a></span><a class="link" href="value_op.html#math_toolkit.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>
|
||
<h5>
|
||
<a name="math_toolkit.value_op.h1"></a>
|
||
<span class="phrase"><a name="math_toolkit.value_op.conj"></a></span><a class="link" href="value_op.html#math_toolkit.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>
|
||
<h5>
|
||
<a name="math_toolkit.value_op.h2"></a>
|
||
<span class="phrase"><a name="math_toolkit.value_op.sup"></a></span><a class="link" href="value_op.html#math_toolkit.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>
|
||
<h5>
|
||
<a name="math_toolkit.value_op.h3"></a>
|
||
<span class="phrase"><a name="math_toolkit.value_op.l1"></a></span><a class="link" href="value_op.html#math_toolkit.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>
|
||
<h5>
|
||
<a name="math_toolkit.value_op.h4"></a>
|
||
<span class="phrase"><a name="math_toolkit.value_op.abs"></a></span><a class="link" href="value_op.html#math_toolkit.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 (Euclidean norm) of the quaternion.
|
||
</p>
|
||
<h5>
|
||
<a name="math_toolkit.value_op.h5"></a>
|
||
<span class="phrase"><a name="math_toolkit.value_op.norm"></a></span><a class="link" href="value_op.html#math_toolkit.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 Euclidean norm (also known as magnitude) is the square
|
||
root of the Cayley norm.
|
||
</p>
|
||
</div>
|
||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||
<td align="left"></td>
|
||
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
||
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||
Walker and Xiaogang Zhang<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>)
|
||
</p>
|
||
</div></td>
|
||
</tr></table>
|
||
<hr>
|
||
<div class="spirit-nav">
|
||
<a accesskey="p" href="quat_non_mem.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="create.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
|
||
</div>
|
||
</body>
|
||
</html>
|