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<a href="slerp_8h.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/* +---------------------------------------------------------------------------+</span>
<a name="l00002"></a>00002 <span class="comment"> | The Mobile Robot Programming Toolkit (MRPT) C++ library |</span>
<a name="l00003"></a>00003 <span class="comment"> | |</span>
<a name="l00004"></a>00004 <span class="comment"> | http://www.mrpt.org/ |</span>
<a name="l00005"></a>00005 <span class="comment"> | |</span>
<a name="l00006"></a>00006 <span class="comment"> | Copyright (C) 2005-2011 University of Malaga |</span>
<a name="l00007"></a>00007 <span class="comment"> | |</span>
<a name="l00008"></a>00008 <span class="comment"> | This software was written by the Machine Perception and Intelligent |</span>
<a name="l00009"></a>00009 <span class="comment"> | Robotics Lab, University of Malaga (Spain). |</span>
<a name="l00010"></a>00010 <span class="comment"> | Contact: Jose-Luis Blanco <jlblanco@ctima.uma.es> |</span>
<a name="l00011"></a>00011 <span class="comment"> | |</span>
<a name="l00012"></a>00012 <span class="comment"> | This file is part of the MRPT project. |</span>
<a name="l00013"></a>00013 <span class="comment"> | |</span>
<a name="l00014"></a>00014 <span class="comment"> | MRPT is free software: you can redistribute it and/or modify |</span>
<a name="l00015"></a>00015 <span class="comment"> | it under the terms of the GNU General Public License as published by |</span>
<a name="l00016"></a>00016 <span class="comment"> | the Free Software Foundation, either version 3 of the License, or |</span>
<a name="l00017"></a>00017 <span class="comment"> | (at your option) any later version. |</span>
<a name="l00018"></a>00018 <span class="comment"> | |</span>
<a name="l00019"></a>00019 <span class="comment"> | MRPT is distributed in the hope that it will be useful, |</span>
<a name="l00020"></a>00020 <span class="comment"> | but WITHOUT ANY WARRANTY; without even the implied warranty of |</span>
<a name="l00021"></a>00021 <span class="comment"> | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |</span>
<a name="l00022"></a>00022 <span class="comment"> | GNU General Public License for more details. |</span>
<a name="l00023"></a>00023 <span class="comment"> | |</span>
<a name="l00024"></a>00024 <span class="comment"> | You should have received a copy of the GNU General Public License |</span>
<a name="l00025"></a>00025 <span class="comment"> | along with MRPT. If not, see <http://www.gnu.org/licenses/>. |</span>
<a name="l00026"></a>00026 <span class="comment"> | |</span>
<a name="l00027"></a>00027 <span class="comment"> +---------------------------------------------------------------------------+ */</span>
<a name="l00028"></a>00028 <span class="preprocessor">#ifndef mrpt_math_slerp_H</span>
<a name="l00029"></a>00029 <span class="preprocessor"></span><span class="preprocessor">#define mrpt_math_slerp_H</span>
<a name="l00030"></a>00030 <span class="preprocessor"></span>
<a name="l00031"></a>00031 <span class="preprocessor">#include <<a class="code" href="_c_quaternion_8h.html">mrpt/math/CQuaternion.h</a>></span>
<a name="l00032"></a>00032
<a name="l00033"></a>00033 <span class="keyword">namespace </span>mrpt
<a name="l00034"></a>00034 {
<a name="l00035"></a>00035 <span class="keyword">namespace </span>poses { <span class="keyword">class </span>CPose3D; <span class="keyword">class </span><a class="code" href="namespacemrpt_1_1poses.html#a1d4ae634d5f0417a36ca15a4d928300d">CPose3DQuat</a>; }
<a name="l00036"></a>00036
<a name="l00037"></a>00037 <span class="keyword">namespace </span>math
<a name="l00038"></a>00038 {
<a name="l00039"></a>00039 <span class="keyword">using namespace </span>mrpt::poses;
<a name="l00040"></a>00040 <span class="comment"></span>
<a name="l00041"></a>00041 <span class="comment"> /** \addtogroup geometry_grp</span>
<a name="l00042"></a>00042 <span class="comment"> * @{ */</span>
<a name="l00043"></a>00043 <span class="comment"></span>
<a name="l00044"></a>00044 <span class="comment"> /** @name SLERP (Spherical Linear Interpolation) functions</span>
<a name="l00045"></a>00045 <span class="comment"> @{ */</span>
<a name="l00046"></a>00046 <span class="comment"></span>
<a name="l00047"></a>00047 <span class="comment"> /** SLERP interpolation between two quaternions</span>
<a name="l00048"></a>00048 <span class="comment"> * \param[in] q0 The quaternion for t=0</span>
<a name="l00049"></a>00049 <span class="comment"> * \param[in] q1 The quaternion for t=1</span>
<a name="l00050"></a>00050 <span class="comment"> * \param[in] t A "time" parameter, in the range [0,1].</span>
<a name="l00051"></a>00051 <span class="comment"> * \param[out] q The output, interpolated quaternion.</span>
<a name="l00052"></a>00052 <span class="comment"> * \tparam T The type of the quaternion (e.g. float, double).</span>
<a name="l00053"></a>00053 <span class="comment"> * \exception std::exception Only in Debug, if t is not in the valid range.</span>
<a name="l00054"></a>00054 <span class="comment"> * \sa http://en.wikipedia.org/wiki/Slerp</span>
<a name="l00055"></a>00055 <span class="comment"> */</span>
<a name="l00056"></a>00056 <span class="keyword">template</span> <<span class="keyword">typename</span> T>
<a name="l00057"></a><a class="code" href="group__geometry__grp.html#ga3e9a5920971ffc3caa6649159bc5a156">00057</a> <span class="keywordtype">void</span> <a class="code" href="group__geometry__grp.html#ga3e9a5920971ffc3caa6649159bc5a156" title="SLERP interpolation between two quaternions.">slerp</a>(
<a name="l00058"></a>00058 <span class="keyword">const</span> <a class="code" href="classmrpt_1_1math_1_1_c_quaternion.html" title="A quaternion, which can represent a 3D rotation as pair , with a real part "r" and a 3D vector ...">CQuaternion<T></a> & q0,
<a name="l00059"></a>00059 <span class="keyword">const</span> <a class="code" href="classmrpt_1_1math_1_1_c_quaternion.html" title="A quaternion, which can represent a 3D rotation as pair , with a real part "r" and a 3D vector ...">CQuaternion<T></a> & q1,
<a name="l00060"></a>00060 <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code" href="eigen__plugins_8h.html#a7b88b312dc3827120dbfc60da344625d" title="Transpose.">t</a>,
<a name="l00061"></a>00061 <a class="code" href="classmrpt_1_1math_1_1_c_quaternion.html" title="A quaternion, which can represent a 3D rotation as pair , with a real part "r" and a 3D vector ...">CQuaternion<T></a> & q)
<a name="l00062"></a>00062 {
<a name="l00063"></a>00063 <a class="code" href="mrpt__macros_8h.html#a5ad4d8d68e2f6664f247407bf89aac55" title="Defines an assertion mechanism - only when compiled in debug.">ASSERTDEB_</a>(t>=0 && t<=1)
<a name="l00064"></a>00064 <span class="comment">// See: http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/index.htm</span>
<a name="l00065"></a>00065 <span class="comment">// Angle between q0-q1:</span>
<a name="l00066"></a>00066 <span class="keywordtype">double</span> cosHalfTheta = q0[0]*q1[0]+q0[1]*q1[1]+q0[2]*q1[2]+q0[3]*q1[3];
<a name="l00067"></a>00067 <span class="comment">// if qa=qb or qa=-qb then theta = 0 and we can return qa</span>
<a name="l00068"></a>00068 <span class="keywordflow">if</span> (<a class="code" href="group__metric__grp.html#gaf15608f8914516f8d949a8c053d55021">std::abs</a>(cosHalfTheta) >= 1.0)
<a name="l00069"></a>00069 {
<a name="l00070"></a>00070 q = q0;
<a name="l00071"></a>00071 <span class="keywordflow">return</span>;
<a name="l00072"></a>00072 }
<a name="l00073"></a>00073 <span class="keywordtype">bool</span> reverse_q1 = <span class="keyword">false</span>;
<a name="l00074"></a>00074 <span class="keywordflow">if</span> (cosHalfTheta < 0) <span class="comment">// Always follow the shortest path</span>
<a name="l00075"></a>00075 {
<a name="l00076"></a>00076 reverse_q1 = <span class="keyword">true</span>;
<a name="l00077"></a>00077 cosHalfTheta = -cosHalfTheta;
<a name="l00078"></a>00078 }
<a name="l00079"></a>00079 <span class="comment">// Calculate temporary values.</span>
<a name="l00080"></a>00080 <span class="keyword">const</span> <span class="keywordtype">double</span> halfTheta = acos(cosHalfTheta);
<a name="l00081"></a>00081 <span class="keyword">const</span> <span class="keywordtype">double</span> sinHalfTheta = std::sqrt(1.0 - <a class="code" href="namespacemrpt_1_1utils.html#a67cb05bb8ad4e725875a7ee54b7042ae" title="Inline function for the square of a number.">square</a>(cosHalfTheta));
<a name="l00082"></a>00082 <span class="comment">// if theta = 180 degrees then result is not fully defined</span>
<a name="l00083"></a>00083 <span class="comment">// we could rotate around any axis normal to qa or qb</span>
<a name="l00084"></a>00084 <span class="keywordflow">if</span> (<a class="code" href="group__metric__grp.html#gaf15608f8914516f8d949a8c053d55021">std::abs</a>(sinHalfTheta) < 0.001)
<a name="l00085"></a>00085 {
<a name="l00086"></a>00086 <span class="keywordflow">if</span> (!reverse_q1)
<a name="l00087"></a>00087 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0;i<4;i++) q[i] = (1-t)*q0[i] + t*q1[i];
<a name="l00088"></a>00088 <span class="keywordflow">else</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0;i<4;i++) q[i] = (1-t)*q0[i] - t*q1[i];
<a name="l00089"></a>00089 <span class="keywordflow">return</span>;
<a name="l00090"></a>00090 }
<a name="l00091"></a>00091 <span class="keyword">const</span> <span class="keywordtype">double</span> A = sin((1-t) * halfTheta)/sinHalfTheta;
<a name="l00092"></a>00092 <span class="keyword">const</span> <span class="keywordtype">double</span> B = sin(t*halfTheta)/sinHalfTheta;
<a name="l00093"></a>00093 <span class="keywordflow">if</span> (!reverse_q1)
<a name="l00094"></a>00094 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0;i<4;i++) q[i] = A*q0[i] + B*q1[i];
<a name="l00095"></a>00095 <span class="keywordflow">else</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0;i<4;i++) q[i] = A*q0[i] - B*q1[i];
<a name="l00096"></a>00096 }
<a name="l00097"></a>00097 <span class="comment"></span>
<a name="l00098"></a>00098 <span class="comment"> /** SLERP interpolation between two 6D poses - like mrpt::math::slerp for quaternions, but interpolates the [X,Y,Z] coordinates as well.</span>
<a name="l00099"></a>00099 <span class="comment"> * \param[in] p0 The pose for t=0</span>
<a name="l00100"></a>00100 <span class="comment"> * \param[in] p1 The pose for t=1</span>
<a name="l00101"></a>00101 <span class="comment"> * \param[in] t A "time" parameter, in the range [0,1].</span>
<a name="l00102"></a>00102 <span class="comment"> * \param[out] p The output, interpolated pose.</span>
<a name="l00103"></a>00103 <span class="comment"> * \exception std::exception Only in Debug, if t is not in the valid range.</span>
<a name="l00104"></a>00104 <span class="comment"> */</span>
<a name="l00105"></a>00105 <span class="keywordtype">void</span> <a class="code" href="base_2include_2mrpt_2base_2link__pragmas_8h.html#a6045fa0129b1a3d6c8bf895470e66574">BASE_IMPEXP</a> <a class="code" href="group__geometry__grp.html#ga3e9a5920971ffc3caa6649159bc5a156" title="SLERP interpolation between two quaternions.">slerp</a>(
<a name="l00106"></a>00106 <span class="keyword">const</span> <a class="code" href="classmrpt_1_1poses_1_1_c_pose3_d.html" title="A class used to store a 3D pose (a 3D translation + a rotation in 3D).">CPose3D</a> & q0,
<a name="l00107"></a>00107 <span class="keyword">const</span> <a class="code" href="classmrpt_1_1poses_1_1_c_pose3_d.html" title="A class used to store a 3D pose (a 3D translation + a rotation in 3D).">CPose3D</a> & q1,
<a name="l00108"></a>00108 <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code" href="eigen__plugins_8h.html#a7b88b312dc3827120dbfc60da344625d" title="Transpose.">t</a>,
<a name="l00109"></a>00109 <a class="code" href="classmrpt_1_1poses_1_1_c_pose3_d.html" title="A class used to store a 3D pose (a 3D translation + a rotation in 3D).">CPose3D</a> & p);
<a name="l00110"></a>00110 <span class="comment"></span>
<a name="l00111"></a>00111 <span class="comment"> //! \overload</span>
<a name="l00112"></a>00112 <span class="comment"></span> <span class="keywordtype">void</span> <a class="code" href="base_2include_2mrpt_2base_2link__pragmas_8h.html#a6045fa0129b1a3d6c8bf895470e66574">BASE_IMPEXP</a> <a class="code" href="group__geometry__grp.html#ga3e9a5920971ffc3caa6649159bc5a156" title="SLERP interpolation between two quaternions.">slerp</a>(
<a name="l00113"></a>00113 <span class="keyword">const</span> <a class="code" href="classmrpt_1_1poses_1_1_c_pose3_d_quat.html" title="A class used to store a 3D pose as a translation (x,y,z) and a quaternion (qr,qx,qy,qz).">CPose3DQuat</a> & q0,
<a name="l00114"></a>00114 <span class="keyword">const</span> <a class="code" href="classmrpt_1_1poses_1_1_c_pose3_d_quat.html" title="A class used to store a 3D pose as a translation (x,y,z) and a quaternion (qr,qx,qy,qz).">CPose3DQuat</a> & q1,
<a name="l00115"></a>00115 <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code" href="eigen__plugins_8h.html#a7b88b312dc3827120dbfc60da344625d" title="Transpose.">t</a>,
<a name="l00116"></a>00116 <a class="code" href="classmrpt_1_1poses_1_1_c_pose3_d_quat.html" title="A class used to store a 3D pose as a translation (x,y,z) and a quaternion (qr,qx,qy,qz).">CPose3DQuat</a> & p);
<a name="l00117"></a>00117 <span class="comment"></span>
<a name="l00118"></a>00118 <span class="comment"> /** @} */</span>
<a name="l00119"></a>00119 <span class="comment"></span>
<a name="l00120"></a>00120 <span class="comment"> /** @} */</span> <span class="comment">// grouping</span>
<a name="l00121"></a>00121 }
<a name="l00122"></a>00122 }
<a name="l00123"></a>00123 <span class="preprocessor">#endif</span>
</pre></div></div>
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