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| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="boost_octonions.octonions.oct_create"></a><a class="link" href="oct_create.html" title="Octonion Creation Functions"> Octonion Creation |
| Functions</a> |
| </h3></div></div></div> |
| <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">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">spherical</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi6</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">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">multipolar</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta4</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">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">cylindrical</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">angle</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h6</span><span class="special">);</span> |
| </pre> |
| <p> |
| These build octonions in a way similar to the way polar builds complex numbers, |
| as there is no strict equivalent to polar coordinates for octonions. |
| </p> |
| <p> |
| <code class="computeroutput"><span class="identifier">spherical</span></code> is a simple transposition |
| of <code class="computeroutput"><span class="identifier">polar</span></code>, it takes as inputs |
| a (positive) magnitude and a point on the hypersphere, given by three angles. |
| The first of these, <span class="emphasis"><em>theta</em></span> has a natural range of -pi |
| to +pi, and the other two have natural ranges of -pi/2 to +pi/2 (as is the |
| case with the usual spherical coordinates in <span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span>). |
| Due to the many symmetries and periodicities, nothing untoward happens if |
| the magnitude is negative or the angles are outside their natural ranges. |
| The expected degeneracies (a magnitude of zero ignores the angles settings...) |
| do happen however. |
| </p> |
| <p> |
| <code class="computeroutput"><span class="identifier">cylindrical</span></code> is likewise a |
| simple transposition of the usual cylindrical coordinates in <span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span>, which in turn is another derivative of |
| planar polar coordinates. The first two inputs are the polar coordinates |
| of the first <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span> component |
| of the octonion. The third and fourth inputs are placed into the third and |
| fourth <span class="emphasis"><em><span class="bold"><strong>R</strong></span></em></span> components |
| of the octonion, respectively. |
| </p> |
| <p> |
| <code class="computeroutput"><span class="identifier">multipolar</span></code> is yet another |
| simple generalization of polar coordinates. This time, both <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span> components of the octonion are given |
| in polar coordinates. |
| </p> |
| <p> |
| In this version of our implementation of octonions, there is no analogue |
| of the complex value operation arg as the situation is somewhat more complicated. |
| </p> |
| </div> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
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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>) |
| </p> |
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