projects / ceph.git / blame
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1 | <!DOCTYPE html PUBLIC '-//W3C//DTD XHTML 1.0 Strict//EN' |
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| 6 | <title>quaternions, vectors, matrices</title> | |
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| 9 | <body> | |
| 10 | <div class="body-0"> | |
| 11 | <div class="body-1"> | |
| 12 | <div class="body-2"> | |
| 13 | <div> | |
| 14 | <h1>QVM: Quaternions, Vectors, Matrices</h1> | |
| 15 | </div> | |
| 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 <<span class="RenoLink"><a href="boost_qvm_quat_hpp.html">boost/qvm/quat.hpp</a></span>> | |
| 23 | #include <<span class="RenoLink"><a href="boost_qvm_quat_operations_hpp.html">boost/qvm/quat_operations.hpp</a></span>> | |
| 24 | ||
| 25 | .... | |
| 26 | <span class="RenoLink"><a href="quat.html">quat</a></span><float> 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 <<span class="RenoLink"><a href="boost_qvm_mat_hpp.html">boost/qvm/mat.hpp</a></span>> | |
| 29 | #include <<span class="RenoLink"><a href="boost_qvm_vec_hpp.html">boost/qvm/vec.hpp</a></span>> | |
| 30 | #include <<span class="RenoLink"><a href="boost_qvm_map_vec_mat_hpp.html">boost/qvm/map_vec_mat.hpp</a></span>> | |
| 31 | ||
| 32 | .... | |
| 33 | <span class="RenoLink"><a href="vec.html">vec</a></span><float,3> v={0,0,7}; | |
| 34 | <span class="RenoLink"><a href="mat.html">mat</a></span><float,4,4> 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 <<span class="RenoLink"><a href="boost_qvm_vec_traits_hpp.html">boost/qvm/vec_traits.hpp</a></span>> | |
| 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 <> | |
| 46 | struct <span class="RenoLink"><a href="vec_traits.html">vec_traits</a></span><float3> | |
| 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 <int I> 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_write_element.html">write_element</a></span>( float3 & v ) { return v.a[I]; } | |
| 52 | template <int I> 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 & v ) { return v.a[I]; } | |
| 53 | ||
| 54 | 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_write_element_idx.html">write_element_idx</a></span>( int i, float3 & 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 & 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><3>(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"> </span><br/><span class="RenoBR"> </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> | |
| 79 | </p> | |
| 80 | </div> | |
| 81 | </div> | |
| 82 | </div> | |
| 83 | </div> | |
| 84 | </body> | |
| 85 | </html> |