boost-react-native-bundle

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<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Overview</title> <link rel="stylesheet" href="../math.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> <link rel="home" href="../index.html" title="Math Toolkit 2.1.0"> <link rel="up" href="../quaternions.html" title="Chapter 9. Quaternions"> <link rel="prev" href="../quaternions.html" title="Chapter 9. Quaternions"> <link rel="next" href="quat_header.html" title="Header File"> </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="../quaternions.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="quat_header.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.quat_overview"></a><a class="link" href="quat_overview.html" title="Overview">Overview</a> </h2></div></div></div> Quaternions are a relative of complex numbers. Quaternions are in fact part of a small hierarchy of structures built upon the real numbers, which comprise only the set of real numbers (traditionally named R), the set of complex numbers (traditionally named C), the set of quaternions (traditionally named H) and the set of octonions (traditionally named O), which possess interesting mathematical properties (chief among which is the fact that they are division algebras, i.e. where the following property is true: if <code class="literal">y</code> is an element of that algebra and is not equal to zero, then <code class="literal">yx = yx'</code>, where <code class="literal">x</code> and <code class="literal">x'</code> denote elements of that algebra, implies that <code class="literal">x = x'</code>). Each member of the hierarchy is a super-set of the former. One of the most important aspects of quaternions is that they provide an efficient way to parameterize rotations in R3 (the usual three-dimensional space) and R4. In practical terms, a quaternion is simply a quadruple of real numbers (α,β,γ,δ), which we can write in the form <code class="literal">q = α + βi + γj + δk</code>, where <code class="literal">i</code> is the same object as for complex numbers, and <code class="literal">j</code> and <code class="literal">k</code> are distinct objects which play essentially the same kind of role as <code class="literal">i</code>. An addition and a multiplication is defined on the set of quaternions, which generalize their real and complex counterparts. The main novelty here is that the multiplication is not commutative (i.e. there are quaternions <code class="literal">x</code> and <code class="literal">y</code> such that <code class="literal">xy ≠ yx</code>). A good mnemotechnical way of remembering things is by using the formula <code class="literal">i*i = j*j = k*k = -1</code>. Quaternions (and their kin) are described in far more details in this other <a href="../../../quaternion/TQE.pdf" target="_top">document</a> (with <a href="../../../quaternion/TQE_EA.pdf" target="_top">errata and addenda</a>). Some traditional constructs, such as the exponential, carry over without too much change into the realms of quaternions, but other, such as taking a square root, do not. </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 © 2006-2010, 2012-2014 Nikhar Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang 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>) </div></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="../quaternions.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="quat_header.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html>