1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Quaternion Value Operations</title> 5<link rel="stylesheet" href="../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../quaternions.html" title="Chapter 16. Quaternions"> 9<link rel="prev" href="quat_non_mem.html" title="Quaternion Non-Member Operators"> 10<link rel="next" href="create.html" title="Quaternion Creation Functions"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<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> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 27<a name="math_toolkit.value_op"></a><a class="link" href="value_op.html" title="Quaternion Value Operations">Quaternion Value Operations</a> 28</h2></div></div></div> 29<h5> 30<a name="math_toolkit.value_op.h0"></a> 31 <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 32 and unreal</a> 33 </h5> 34<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> 35<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> 36</pre> 37<p> 38 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 39 <code class="computeroutput"><span class="identifier">q</span><span class="special">.</span><span class="identifier">unreal</span><span class="special">()</span></code> 40 respectively. 41 </p> 42<h5> 43<a name="math_toolkit.value_op.h1"></a> 44 <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> 45 </h5> 46<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> 47</pre> 48<p> 49 This returns the conjugate of the quaternion. 50 </p> 51<h5> 52<a name="math_toolkit.value_op.h2"></a> 53 <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> 54 </h5> 55<p> 56 template<typename T> T sup(quaternion<T> const & q); 57 </p> 58<p> 59 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. 60 </p> 61<h5> 62<a name="math_toolkit.value_op.h3"></a> 63 <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> 64 </h5> 65<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> 66</pre> 67<p> 68 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. 69 </p> 70<h5> 71<a name="math_toolkit.value_op.h4"></a> 72 <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> 73 </h5> 74<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> 75</pre> 76<p> 77 This return the magnitude (Euclidean norm) of the quaternion. 78 </p> 79<h5> 80<a name="math_toolkit.value_op.h5"></a> 81 <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> 82 </h5> 83<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> 84</pre> 85<p> 86 This return the (Cayley) norm of the quaternion. The term "norm" 87 might be confusing, as most people associate it with the Euclidian norm (and 88 quadratic functionals). For this version of (the mathematical objects known 89 as) quaternions, the Euclidean norm (also known as magnitude) is the square 90 root of the Cayley norm. 91 </p> 92</div> 93<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 94<td align="left"></td> 95<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 96 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 97 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 98 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 99 Daryle Walker and Xiaogang Zhang<p> 100 Distributed under the Boost Software License, Version 1.0. (See accompanying 101 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>) 102 </p> 103</div></td> 104</tr></table> 105<hr> 106<div class="spirit-nav"> 107<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> 108</div> 109</body> 110</html> 111
