ceph/src/boost/libs/qvm/doc/quaternions_vectors_matrices.html

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  14 <h1>QVM: Quaternions, Vectors, Matrices</h1>
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  16 <!-- Copyright (c) 2008-2016 Emil Dotchevski and Reverge Studios, Inc. -->
  17 <!-- Distributed under the Boost Software License, Version 1.0. (See accompanying -->
  18 <!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
  19 <div class="RenoIncludeDIV"><div class="RenoAutoDIV"><h3>Quaternions, Vectors, Matrices</h3>
  20 </div>
  21 <p>Out of the box Boost QVM defines generic yet simple <i><span class="RenoLink"><a href="quat.html">quat</a></span></i>, <i><span class="RenoLink"><a href="vec.html">vec</a></span></i> and <i><span class="RenoLink"><a href="mat.html">mat</a></span></i> types. For example, the following snippet creates a quaternion object that rotates around the X axis:</p>
  22 <pre>#include &lt;<span class="RenoLink"><a href="boost_qvm_quat_hpp.html">boost/qvm/quat.hpp</a></span>&gt;
  23 #include &lt;<span class="RenoLink"><a href="boost_qvm_quat_operations_hpp.html">boost/qvm/quat_operations.hpp</a></span>&gt;
  24
  25 ....
  26 <span class="RenoLink"><a href="quat.html">quat</a></span>&lt;float&gt; rx=<span class="RenoLink"><a href="rotx_quat_scalar_.html">rotx_quat</a></span>(3.14159f);</pre>
  27 <p>Similarly, a matrix that translates by a given vector can be created as follows:</p>
  28 <pre>#include &lt;<span class="RenoLink"><a href="boost_qvm_mat_hpp.html">boost/qvm/mat.hpp</a></span>&gt;
  29 #include &lt;<span class="RenoLink"><a href="boost_qvm_vec_hpp.html">boost/qvm/vec.hpp</a></span>&gt;
  30 #include &lt;<span class="RenoLink"><a href="boost_qvm_map_vec_mat_hpp.html">boost/qvm/map_vec_mat.hpp</a></span>&gt;
  31
  32 ....
  33 <span class="RenoLink"><a href="vec.html">vec</a></span>&lt;float,3&gt; v={0,0,7};
  34 <span class="RenoLink"><a href="mat.html">mat</a></span>&lt;float,4,4&gt; tr=<span class="RenoLink"><a href="translation_mat.html">translation_mat</a></span>(v);</pre>
  35 <p>The usual quaternion, vector and matrix operations work on these Boost QVM types, however <i>the operations are decoupled from any specific types</i>: they work on any suitable type that has been registered by specializing the <i><span class="RenoLink"><a href="quat_traits.html">quat_traits</a></span></i>, <i><span class="RenoLink"><a href="vec_traits.html">vec_traits</a></span></i> and <i><span class="RenoLink"><a href="mat_traits.html">mat_traits</a></span></i> templates.</p>
  36 <p>For example, a user-defined 3D vector type <i>float3</i> can be introduced to Boost QVM as follows:</p>
  37 <div class="RenoIncludeDIV"><pre>#include &lt;<span class="RenoLink"><a href="boost_qvm_vec_traits_hpp.html">boost/qvm/vec_traits.hpp</a></span>&gt;
  38
  39 struct float3 { float a[3]; };
  40
  41 namespace boost
  42 {
  43     namespace <span class="RenoLink"><a href="qvm.html">qvm</a></span>
  44     {
  45         template &lt;&gt;
  46         struct <span class="RenoLink"><a href="vec_traits.html">vec_traits</a></span>&lt;float3&gt;
  47         {
  48             static int const <span class="RenoLink"><a href="vec_traits_Vector_dim.html">dim</a></span>=3;
  49             typedef float <span class="RenoLink"><a href="vec_traits_V_scalar_type.html">scalar_type</a></span>;
  50
  51             template &lt;int I&gt; static inline <span class="RenoLink"><a href="vec_traits_V_scalar_type.html">scalar_type</a></span> &amp; <span class="RenoLink"><a href="vec_traits_V_write_element.html">write_element</a></span>( float3 &amp; v ) { return v.a[I]; }
  52             template &lt;int I&gt; static inline <span class="RenoLink"><a href="vec_traits_V_scalar_type.html">scalar_type</a></span> <span class="RenoLink"><a href="vec_traits_V_read_element.html">read_element</a></span>( float3 const &amp; v ) { return v.a[I]; }
  53
  54             static inline <span class="RenoLink"><a href="vec_traits_V_scalar_type.html">scalar_type</a></span> &amp; <span class="RenoLink"><a href="vec_traits_V_write_element_idx.html">write_element_idx</a></span>( int i, float3 &amp; v ) { return v.a[i]; } //optional
  55             static inline <span class="RenoLink"><a href="vec_traits_V_scalar_type.html">scalar_type</a></span> <span class="RenoLink"><a href="vec_traits_V_read_element_idx.html">read_element_idx</a></span>( int i, float3 const &amp; v ) { return v.a[i]; } //optional
  56         };
  57     }
  58 }</pre>
  59 </div><p>After a similar specialization of the <i><span class="RenoLink"><a href="mat_traits.html">mat_traits</a></span></i> template for a user-defined 3x3 matrix type <i>float33</i>, the full range of vector and matrix operations defined by Boost QVM headers becomes available automatically:</p>
  60 <pre>float3 v;
  61 <span class="RenoLink"><a href="accessing_vector_elements.html">X</a></span>(v) = 0;
  62 <span class="RenoLink"><a href="accessing_vector_elements.html">Y</a></span>(v) = 0;
  63 <span class="RenoLink"><a href="accessing_vector_elements.html">Z</a></span>(v) = 7;
  64 float vmag = <span class="RenoLink"><a href="mag_vec_.html">mag</a></span>(v);
  65 float33 m = <span class="RenoLink"><a href="rotx_mat_scalar_.html">rotx_mat</a></span>&lt;3&gt;(3.14159f);
  66 float3 vrot = m <span class="RenoLink"><a href="operator_times_mat_vec_.html">*</a></span> v;</pre>
  67 <p>User-defined quaternion types are similarly introduced to Boost QVM by specializing the <i><span class="RenoLink"><a href="quat_traits.html">quat_traits</a></span></i> template.</p>
  68 </div><div class="RenoIncludeDIV"><div class="RenoHR"><hr/></div>
  69 <p><b>Tutorial navigation:</b> <span class="RenoLink">Quaternions, Vectors, Matrices</span> | <span class="RenoLink"><a href="c_arrays.html">C Arrays</a></span> | <span class="RenoLink"><a href="Views.html">Views</a></span> | <span class="RenoLink"><a href="Swizzling.html">Swizzling</a></span> | <span class="RenoLink"><a href="Interoperability.html">Interoperability</a></span><span class="RenoBR">&nbsp;</span><br/><span class="RenoBR">&nbsp;</span><br/>See also: <span class="RenoLink"><a href="index.html">Boost QVM</a></span></p>
  70 </div><!-- Copyright (c) 2008-2016 Emil Dotchevski and Reverge Studios, Inc. -->
  71 <!-- Distributed under the Boost Software License, Version 1.0. (See accompanying -->
  72 <!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
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  77 <small>Copyright (c) 2008-2016 by Emil Dotchevski and Reverge Studios, Inc.<br/>
  78 Distributed under the <a href="http://www.boost.org/LICENSE_1_0.txt">Boost Software License, Version 1.0</a>.</small>
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