EulerAngles.h

00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
00005 //
00006 // This Source Code Form is subject to the terms of the Mozilla
00007 // Public License v. 2.0. If a copy of the MPL was not distributed
00008 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00009 
00010 #ifndef EIGEN_EULERANGLES_H
00011 #define EIGEN_EULERANGLES_H
00012 
00013 namespace Eigen { 
00014 
00015 /** \geometry_module \ingroup Geometry_Module
00016   *
00017   *
00018   * \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
00019   *
00020   * Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
00021   * For instance, in:
00022   * \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode
00023   * "2" represents the z axis and "0" the x axis, etc. The returned angles are such that
00024   * we have the following equality:
00025   * \code
00026   * mat == AngleAxisf(ea[0], Vector3f::UnitZ())
00027   *      * AngleAxisf(ea[1], Vector3f::UnitX())
00028   *      * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
00029   * This corresponds to the right-multiply conventions (with right hand side frames).
00030   * 
00031   * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
00032   * 
00033   * \sa class AngleAxis
00034   */
00035 template<typename Derived>
00036 inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
00037 MatrixBase<Derived>::eulerAngles (Index a0, Index a1, Index a2) const
00038 {
00039   using std::atan2;
00040   using std::sin;
00041   using std::cos;
00042   /* Implemented from Graphics Gems IV */
00043   EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
00044 
00045   Matrix<Scalar,3,1>  res;
00046   typedef Matrix<typename Derived::Scalar,2,1> Vector2;
00047 
00048   const Index odd = ((a0+1)%3 == a1) ? 0 : 1;
00049   const Index i = a0;
00050   const Index j = (a0 + 1 + odd)%3;
00051   const Index k = (a0 + 2 - odd)%3;
00052   
00053   if (a0==a2)
00054   {
00055     res[0] = atan2(coeff(j,i), coeff(k,i));
00056     if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0)))
00057     {
00058       res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI);
00059       Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
00060       res[1] = -atan2(s2, coeff(i,i));
00061     }
00062     else
00063     {
00064       Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
00065       res[1] = atan2(s2, coeff(i,i));
00066     }
00067     
00068     // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
00069     // we can compute their respective rotation, and apply its inverse to M. Since the result must
00070     // be a rotation around x, we have:
00071     //
00072     //  c2  s1.s2 c1.s2                   1  0   0 
00073     //  0   c1    -s1       *    M    =   0  c3  s3
00074     //  -s2 s1.c2 c1.c2                   0 -s3  c3
00075     //
00076     //  Thus:  m11.c1 - m21.s1 = c3  &   m12.c1 - m22.s1 = s3
00077     
00078     Scalar s1 = sin(res[0]);
00079     Scalar c1 = cos(res[0]);
00080     res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
00081   } 
00082   else
00083   {
00084     res[0] = atan2(coeff(j,k), coeff(k,k));
00085     Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
00086     if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) {
00087       res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI);
00088       res[1] = atan2(-coeff(i,k), -c2);
00089     }
00090     else
00091       res[1] = atan2(-coeff(i,k), c2);
00092     Scalar s1 = sin(res[0]);
00093     Scalar c1 = cos(res[0]);
00094     res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
00095   }
00096   if (!odd)
00097     res = -res;
00098   
00099   return res;
00100 }
00101 
00102 } // end namespace Eigen
00103 
00104 #endif // EIGEN_EULERANGLES_H