Added MatrixBase::Unit*() static function to easily create unit/basis vectors.

Removed EulerAngles, addes typdefs for Quaternion and AngleAxis,
and added automatic conversions from Quaternion/AngleAxis to Matrix3 such that:
 Matrix3f m = AngleAxisf(0.2,Vector3f::UnitX) * AngleAxisf(0.2,Vector3f::UnitY);
just works.

disabled/EulerAngles.h

@@ -0,0 +1,164 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_EULERANGLES_H
+#define EIGEN_EULERANGLES_H
+
+template<typename Other,
+         int OtherRows=Other::RowsAtCompileTime,
+         int OtherCols=Other::ColsAtCompileTime>
+struct ei_eulerangles_assign_impl;
+
+// enum {
+//   XYZ,
+//   XYX,
+//
+//
+// };
+
+/** \class EulerAngles
+  *
+  * \brief Represents a rotation in a 3 dimensional space as three Euler angles
+  *
+  * \param _Scalar the scalar type, i.e., the type of the angles.
+  *
+  * \sa class Quaternion, class AngleAxis, class Transform
+  */
+template<typename _Scalar>
+class EulerAngles
+{
+public:
+  enum { Dim = 3 };
+  /** the scalar type of the coefficients */
+  typedef _Scalar Scalar;
+  typedef Matrix<Scalar,3,3> Matrix3;
+  typedef Matrix<Scalar,3,1> Vector3;
+  typedef Quaternion<Scalar> QuaternionType;
+  typedef AngleAxis<Scalar> AngleAxisType;
+
+protected:
+
+  Vector3 m_angles;
+
+public:
+
+  EulerAngles() {}
+  inline EulerAngles(Scalar a0, Scalar a1, Scalar a2) : m_angles(a0, a1, a2) {}
+  inline EulerAngles(const QuaternionType& q) { *this = q; }
+  inline EulerAngles(const AngleAxisType& aa) { *this = aa; }
+  template<typename Derived>
+  inline EulerAngles(const MatrixBase<Derived>& m) { *this = m; }
+
+  Scalar angle(int i) const { return m_angles.coeff(i); }
+  Scalar& angle(int i) { return m_angles.coeffRef(i); }
+
+  const Vector3& coeffs() const { return m_angles; }
+  Vector3& coeffs() { return m_angles; }
+
+  EulerAngles& operator=(const QuaternionType& q);
+  EulerAngles& operator=(const AngleAxisType& ea);
+  template<typename Derived>
+  EulerAngles& operator=(const MatrixBase<Derived>& m);
+
+  template<typename Derived>
+  EulerAngles& fromRotationMatrix(const MatrixBase<Derived>& m);
+  Matrix3 toRotationMatrix(void) const;
+};
+
+/** Set \c *this from a quaternion.
+  * The axis is normalized.
+  */
+template<typename Scalar>
+EulerAngles<Scalar>& EulerAngles<Scalar>::operator=(const QuaternionType& q)
+{
+  Scalar y2 = q.y() * q.y();
+  m_angles.coeffRef(0) = std::atan2(2*(q.w()*q.x() + q.y()*q.z()), (1 - 2*(q.x()*q.x() + y2)));
+  m_angles.coeffRef(1) = std::asin( 2*(q.w()*q.y() - q.z()*q.x()));
+  m_angles.coeffRef(2) = std::atan2(2*(q.w()*q.z() + q.x()*q.y()), (1 - 2*(y2 + q.z()*q.z())));
+  return *this;
+}
+
+/** Set \c *this from Euler angles \a ea.
+  */
+template<typename Scalar>
+EulerAngles<Scalar>& EulerAngles<Scalar>::operator=(const AngleAxisType& aa)
+{
+  return *this = QuaternionType(aa);
+}
+
+/** Set \c *this from the expression \a xpr:
+  *   - if \a xpr is a 3x1 vector, then \a xpr is assumed to be a vector of angles
+  *   - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix
+  *     and \a xpr is converted to Euler angles
+  */
+template<typename Scalar>
+template<typename Derived>
+EulerAngles<Scalar>& EulerAngles<Scalar>::operator=(const MatrixBase<Derived>& other)
+{
+  ei_eulerangles_assign_impl<Derived>::run(*this,other.derived());
+  return *this;
+}
+
+/** Constructs and \returns an equivalent 3x3 rotation matrix.
+  */
+template<typename Scalar>
+typename EulerAngles<Scalar>::Matrix3
+EulerAngles<Scalar>::toRotationMatrix(void) const
+{
+  Vector3 c = m_angles.cwise().cos();
+  Vector3 s = m_angles.cwise().sin();
+  return Matrix3() <<
+    c.y()*c.z(),                    -c.y()*s.z(),                   s.y(),
+    c.z()*s.x()*s.y()+c.x()*s.z(),  c.x()*c.z()-s.x()*s.y()*s.z(),  -c.y()*s.x(),
+    -c.x()*c.z()*s.y()+s.x()*s.z(), c.z()*s.x()+c.x()*s.y()*s.z(),  c.x()*c.y();
+}
+
+// set from a rotation matrix
+template<typename Other>
+struct ei_eulerangles_assign_impl<Other,3,3>
+{
+  typedef typename Other::Scalar Scalar;
+  inline static void run(EulerAngles<Scalar>& ea, const Other& mat)
+  {
+    // mat =  cy*cz          -cy*sz           sy
+    //        cz*sx*sy+cx*sz  cx*cz-sx*sy*sz -cy*sx
+    //       -cx*cz*sy+sx*sz  cz*sx+cx*sy*sz  cx*cy
+    ea.angle(1) = std::asin(mat.coeff(0,2));
+    ea.angle(0) = std::atan2(-mat.coeff(1,2),mat.coeff(2,2));
+    ea.angle(2) = std::atan2(-mat.coeff(0,1),mat.coeff(0,0));
+  }
+};
+
+// set from a vector of angles
+template<typename Other>
+struct ei_eulerangles_assign_impl<Other,3,1>
+{
+  typedef typename Other::Scalar Scalar;
+  inline static void run(EulerAngles<Scalar>& ea, const Other& vec)
+  {
+    ea.coeffs() = vec;
+  }
+};
+
+#endif // EIGEN_EULERANGLES_H