Quaternion could now map an array of 4 scalars :

new classes :
* QuaternionBase
* Map<Quaternion>

3 files changed, 567 insertions, 0 deletions

diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index 65e5ce687..025904734 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -129,6 +129,7 @@ template<typename Scalar>     class PlanarRotation;
 // Geometry module:
 template<typename Derived, int _Dim> class RotationBase;
 template<typename Lhs, typename Rhs> class Cross;
+template<typename Derived> class QuaternionBase;
 template<typename Scalar> class Quaternion;
 template<typename Scalar> class Rotation2D;
 template<typename Scalar> class AngleAxis;
diff --git a/Eigen/src/Geometry/Quaternion.h b/Eigen/src/Geometry/Quaternion.h
index 2f9f97807..f3f60a08a 100644
--- a/Eigen/src/Geometry/Quaternion.h
+++ b/Eigen/src/Geometry/Quaternion.h
@@ -507,4 +507,549 @@ struct ei_quaternion_assign_impl<Other,4,1>
   }
 };
 
+/*###################################################################
+      QuaternionBase and Map<Quaternion> and Quat
+  ###################################################################*/
+
+template<typename Other,
+         int OtherRows=Other::RowsAtCompileTime,
+         int OtherCols=Other::ColsAtCompileTime>
+struct ei_quaternionbase_assign_impl;
+
+template<typename Scalar> class Quat; // [XXX] => remove when Quat becomes Quaternion
+
+template<typename Derived>
+struct ei_traits<QuaternionBase<Derived> >
+{
+  typedef typename ei_traits<Derived>::Scalar Scalar;
+  enum {
+    PacketAccess = ei_traits<Derived>::PacketAccess
+  };
+};
+
+template<class Derived>
+class QuaternionBase : public RotationBase<Derived, 3> {
+  typedef RotationBase<Derived, 3> Base;
+public:
+  using Base::operator*;
+
+  typedef typename ei_traits<QuaternionBase<Derived> >::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ // typedef typename Matrix<Scalar,4,1> Coefficients;
+  /** the type of a 3D vector */
+  typedef Matrix<Scalar,3,1> Vector3;
+  /** the equivalent rotation matrix type */
+  typedef Matrix<Scalar,3,3> Matrix3;
+  /** the equivalent angle-axis type */
+  typedef AngleAxis<Scalar> AngleAxisType;
+
+  /** \returns the \c x coefficient */
+  inline Scalar x() const { return this->derived().coeffs().coeff(0); }
+  /** \returns the \c y coefficient */
+  inline Scalar y() const { return this->derived().coeffs().coeff(1); }
+  /** \returns the \c z coefficient */
+  inline Scalar z() const { return this->derived().coeffs().coeff(2); }
+  /** \returns the \c w coefficient */
+  inline Scalar w() const { return this->derived().coeffs().coeff(3); }
+
+  /** \returns a reference to the \c x coefficient */
+  inline Scalar& x() { return this->derived().coeffs().coeffRef(0); }
+  /** \returns a reference to the \c y coefficient */
+  inline Scalar& y() { return this->derived().coeffs().coeffRef(1); }
+  /** \returns a reference to the \c z coefficient */
+  inline Scalar& z() { return this->derived().coeffs().coeffRef(2); }
+  /** \returns a reference to the \c w coefficient */
+  inline Scalar& w() { return this->derived().coeffs().coeffRef(3); }
+
+  /** \returns a read-only vector expression of the imaginary part (x,y,z) */
+  inline const VectorBlock<typename ei_traits<Derived>::Coefficients,3,1> vec() const { return this->derived().coeffs().template start<3>(); }
+
+  /** \returns a vector expression of the imaginary part (x,y,z) */
+  inline VectorBlock<typename ei_traits<Derived>::Coefficients,3,1> vec() { return this->derived().coeffs().template start<3>(); }
+
+  /** \returns a read-only vector expression of the coefficients (x,y,z,w) */
+  inline const typename ei_traits<Derived>::Coefficients& coeffs() const { return this->derived().coeffs(); }
+
+  /** \returns a vector expression of the coefficients (x,y,z,w) */
+  inline typename ei_traits<Derived>::Coefficients& coeffs() { return this->derived().coeffs(); }
+
+  template<class OtherDerived> QuaternionBase& operator=(const QuaternionBase<OtherDerived>& other);
+  QuaternionBase& operator=(const AngleAxisType& aa);
+  template<class OtherDerived>
+  QuaternionBase& operator=(const MatrixBase<OtherDerived>& m);
+
+  /** \returns a quaternion representing an identity rotation
+    * \sa MatrixBase::Identity()
+    */
+  inline static Quat<Scalar> Identity() { return Quat<Scalar>(1, 0, 0, 0); }
+
+  /** \sa Quaternion2::Identity(), MatrixBase::setIdentity()
+    */
+  inline QuaternionBase& setIdentity() { coeffs() << 0, 0, 0, 1; return *this; }
+
+  /** \returns the squared norm of the quaternion's coefficients
+    * \sa Quaternion2::norm(), MatrixBase::squaredNorm()
+    */
+  inline Scalar squaredNorm() const { return coeffs().squaredNorm(); }
+
+  /** \returns the norm of the quaternion's coefficients
+    * \sa Quaternion2::squaredNorm(), MatrixBase::norm()
+    */
+  inline Scalar norm() const { return coeffs().norm(); }
+
+  /** Normalizes the quaternion \c *this
+    * \sa normalized(), MatrixBase::normalize() */
+  inline void normalize() { coeffs().normalize(); }
+  /** \returns a normalized version of \c *this
+    * \sa normalize(), MatrixBase::normalized() */
+  inline Quat<Scalar> normalized() const { return Quat<Scalar>(coeffs().normalized()); }
+
+    /** \returns the dot product of \c *this and \a other
+    * Geometrically speaking, the dot product of two unit quaternions
+    * corresponds to the cosine of half the angle between the two rotations.
+    * \sa angularDistance()
+    */
+  template<class OtherDerived> inline Scalar dot(const QuaternionBase<OtherDerived>& other) const { return coeffs().dot(other.coeffs()); }
+
+  template<class OtherDerived> inline Scalar angularDistance(const QuaternionBase<OtherDerived>& other) const;
+
+  Matrix3 toRotationMatrix(void) const;
+
+  template<typename Derived1, typename Derived2>
+  QuaternionBase& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
+
+  template<class OtherDerived> inline Quat<Scalar> operator* (const QuaternionBase<OtherDerived>& q) const;
+  template<class OtherDerived> inline QuaternionBase& operator*= (const QuaternionBase<OtherDerived>& q);
+
+  Quat<Scalar> inverse(void) const;
+  Quat<Scalar> conjugate(void) const;
+
+  template<class OtherDerived> Quat<Scalar> slerp(Scalar t, const QuaternionBase<OtherDerived>& other) const;
+
+  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+    * determined by \a prec.
+    *
+    * \sa MatrixBase::isApprox() */
+  bool isApprox(const QuaternionBase& other, typename RealScalar prec = precision<Scalar>()) const
+  { return coeffs().isApprox(other.coeffs(), prec); }
+
+  Vector3 _transformVector(Vector3 v) const;
+
+};
+
+/* ########### Quat -> Quaternion */
+
+template<typename _Scalar>
+struct ei_traits<Quat<_Scalar> >
+{
+  typedef _Scalar Scalar;
+  typedef Matrix<_Scalar,4,1> Coefficients;
+  enum{
+    PacketAccess = Aligned 
+  };
+};
+
+template<typename _Scalar>
+class Quat : public QuaternionBase<Quat<_Scalar> >{
+  typedef QuaternionBase<Quat<_Scalar> > Base;
+public:
+  using Base::operator=;
+
+  typedef _Scalar Scalar;
+
+  typedef typename ei_traits<Quat<Scalar> >::Coefficients Coefficients;
+  typedef typename Base::AngleAxisType AngleAxisType;
+
+  /** Default constructor leaving the quaternion uninitialized. */
+  inline Quat() {}
+
+  /** Constructs and initializes the quaternion \f$ w+xi+yj+zk \f$ from
+    * its four coefficients \a w, \a x, \a y and \a z.
+    *
+    * \warning Note the order of the arguments: the real \a w coefficient first,
+    * while internally the coefficients are stored in the following order:
+    * [\c x, \c y, \c z, \c w]
+    */
+  inline Quat(Scalar w, Scalar x, Scalar y, Scalar z)
+  { coeffs() << x, y, z, w; }
+
+  /** Constructs and initialize a quaternion from the array data
+    * This constructor is also used to map an array */
+  inline Quat(const Scalar* data) : m_coeffs(data) {}
+
+  /** Copy constructor */
+//  template<class Derived> inline Quat(const QuaternionBase<Derived>& other) { m_coeffs = other.coeffs(); } [XXX] redundant with 703
+
+  /** Constructs and initializes a quaternion from the angle-axis \a aa */
+  explicit inline Quat(const AngleAxisType& aa) { *this = aa; }
+
+  /** Constructs and initializes a quaternion from either:
+    *  - a rotation matrix expression,
+    *  - a 4D vector expression representing quaternion coefficients.
+    */
+  template<typename Derived>
+  explicit inline Quat(const MatrixBase<Derived>& other) { *this = other; } 
+
+  /** \returns \c *this with scalar type casted to \a NewScalarType
+    *
+    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+    * then this function smartly returns a const reference to \c *this.
+    */
+  template<class Derived>
+  inline typename ei_cast_return_type<Quat, QuaternionBase<Derived> >::type cast() const
+  { return typename ei_cast_return_type<Quat, QuaternionBase<Derived> >::type(*this); }
+
+  /** Copy constructor with scalar type conversion */
+  template<class Derived>
+  inline explicit Quat(const QuaternionBase<Derived>& other)
+  { m_coeffs = other.coeffs().template cast<Scalar>(); }
+
+  inline Coefficients& coeffs() { return m_coeffs;}
+  inline const Coefficients& coeffs() const { return m_coeffs;}
+
+protected:
+  Coefficients m_coeffs;
+};
+
+/* ########### Map<Quat> */
+
+/** \class Map<Quat>
+  * \nonstableyet
+  *
+  * \brief Expression of a quaternion
+  *
+  * \param Scalar the type of the vector of diagonal coefficients
+  *
+  * \sa class Quaternion, class QuaternionBase
+  */
+template<typename _Scalar, int _PacketAccess>
+struct ei_traits<Map<Quat<_Scalar>, _PacketAccess> >:
+ei_traits<Quat<_Scalar> >
+{
+  typedef _Scalar Scalar;
+  typedef Map<Matrix<_Scalar,4,1> > Coefficients;
+  enum {
+    PacketAccess = _PacketAccess
+  };
+};
+
+template<typename _Scalar, int PacketAccess>
+class Map<Quat<_Scalar>, PacketAccess > : public QuaternionBase<Map<Quat<_Scalar>, PacketAccess> >, ei_no_assignment_operator {
+  public:
+    
+    typedef _Scalar Scalar;
+
+    typedef typename ei_traits<Map<Quat<Scalar>, PacketAccess> >::Coefficients Coefficients;
+
+    inline Map<Quat<Scalar>, PacketAccess >(const Scalar* coeffs) : m_coeffs(coeffs) {}
+    
+    inline Coefficients& coeffs() { return m_coeffs;}
+    inline const Coefficients& coeffs() const { return m_coeffs;}
+
+  protected:
+    Coefficients m_coeffs;
+};
+
+typedef Map<Quat<double> > QuaternionMapd;
+typedef Map<Quat<float> > QuaternionMapf;
+typedef Map<Quat<double>, Aligned> QuaternionMapAlignedd;
+typedef Map<Quat<float>, Aligned> QuaternionMapAlignedf;
+
+// Generic Quaternion * Quaternion product
+template<int Arch, class Derived, class OtherDerived, typename Scalar, int PacketAccess> struct ei_quat_product
+{
+  inline static Quat<Scalar> run(const QuaternionBase<Derived>& a, const QuaternionBase<OtherDerived>& b){
+    return Quat<Scalar>
+    (
+      a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
+      a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
+      a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
+      a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
+    );
+  }
+};
+
+/** \returns the concatenation of two rotations as a quaternion-quaternion product */
+template <class Derived>
+template <class OtherDerived>
+inline Quat<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::operator* (const QuaternionBase<OtherDerived>& other) const
+{
+  EIGEN_STATIC_ASSERT((ei_is_same_type<typename Derived::Scalar, typename OtherDerived::Scalar>::ret),
+   YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+   return ei_quat_product<EiArch, Derived, OtherDerived, 
+                          ei_traits<Derived>::Scalar, 
+                          ei_traits<Derived>::PacketAccess && ei_traits<OtherDerived>::PacketAccess>::run(*this, other);
+}
+
+/** \sa operator*(Quaternion) */
+template <class Derived>
+template <class OtherDerived>
+inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other)
+{
+  return (*this = *this * other);
+}
+
+/** Rotation of a vector by a quaternion.
+  * \remarks If the quaternion is used to rotate several points (>1)
+  * then it is much more efficient to first convert it to a 3x3 Matrix.
+  * Comparison of the operation cost for n transformations:
+  *   - Quaternion2:    30n
+  *   - Via a Matrix3: 24 + 15n
+  */
+template <class Derived>
+inline typename QuaternionBase<Derived>::Vector3
+QuaternionBase<Derived>::_transformVector(Vector3 v) const
+{
+    // Note that this algorithm comes from the optimization by hand
+    // of the conversion to a Matrix followed by a Matrix/Vector product.
+    // It appears to be much faster than the common algorithm found
+    // in the litterature (30 versus 39 flops). It also requires two
+    // Vector3 as temporaries.
+    Vector3 uv = Scalar(2) * this->vec().cross(v);
+    return v + this->w() * uv + this->vec().cross(uv);
+}
+
+template<class Derived>
+template<class OtherDerived>
+inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other)
+{
+  coeffs() = other.coeffs();
+  return *this;
+}
+
+/** Set \c *this from an angle-axis \a aa and returns a reference to \c *this
+  */
+template<class Derived>
+inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)
+{
+  Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
+  this->w() = ei_cos(ha);
+  this->vec() = ei_sin(ha) * aa.axis();
+  return *this;
+}
+
+/** Set \c *this from the expression \a xpr:
+  *   - if \a xpr is a 4x1 vector, then \a xpr is assumed to be a quaternion
+  *   - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix
+  *     and \a xpr is converted to a quaternion
+  */
+
+template<class Derived>
+template<class MatrixDerived>
+inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerived>& xpr)
+{
+  EIGEN_STATIC_ASSERT((ei_is_same_type<typename Derived::Scalar, typename MatrixDerived::Scalar>::ret),
+   YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+  ei_quaternionbase_assign_impl<MatrixDerived>::run(*this, xpr.derived());
+  return *this;
+}
+
+/** Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to
+  * be normalized, otherwise the result is undefined.
+  */
+template<class Derived>
+inline typename QuaternionBase<Derived>::Matrix3
+QuaternionBase<Derived>::toRotationMatrix(void) const
+{
+  // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)
+  // if not inlined then the cost of the return by value is huge ~ +35%,
+  // however, not inlining this function is an order of magnitude slower, so
+  // it has to be inlined, and so the return by value is not an issue
+  Matrix3 res;
+
+  const Scalar tx  = 2*this->x();
+  const Scalar ty  = 2*this->y();
+  const Scalar tz  = 2*this->z();
+  const Scalar twx = tx*this->w();
+  const Scalar twy = ty*this->w();
+  const Scalar twz = tz*this->w();
+  const Scalar txx = tx*this->x();
+  const Scalar txy = ty*this->x();
+  const Scalar txz = tz*this->x();
+  const Scalar tyy = ty*this->y();
+  const Scalar tyz = tz*this->y();
+  const Scalar tzz = tz*this->z();
+
+  res.coeffRef(0,0) = 1-(tyy+tzz);
+  res.coeffRef(0,1) = txy-twz;
+  res.coeffRef(0,2) = txz+twy;
+  res.coeffRef(1,0) = txy+twz;
+  res.coeffRef(1,1) = 1-(txx+tzz);
+  res.coeffRef(1,2) = tyz-twx;
+  res.coeffRef(2,0) = txz-twy;
+  res.coeffRef(2,1) = tyz+twx;
+  res.coeffRef(2,2) = 1-(txx+tyy);
+
+  return res;
+}
+
+/** Sets \c *this to be a quaternion representing a rotation between
+  * the two arbitrary vectors \a a and \a b. In other words, the built
+  * rotation represent a rotation sending the line of direction \a a
+  * to the line of direction \a b, both lines passing through the origin.
+  *
+  * \returns a reference to \c *this.
+  *
+  * Note that the two input vectors do \b not have to be normalized, and
+  * do not need to have the same norm.
+  */
+template<class Derived>
+template<typename Derived1, typename Derived2>
+inline QuaternionBase<Derived>& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
+{
+  Vector3 v0 = a.normalized();
+  Vector3 v1 = b.normalized();
+  Scalar c = v1.dot(v0);
+
+  // if dot == -1, vectors are nearly opposites
+  // => accuraletly compute the rotation axis by computing the
+  //    intersection of the two planes. This is done by solving:
+  //       x^T v0 = 0
+  //       x^T v1 = 0
+  //    under the constraint:
+  //       ||x|| = 1
+  //    which yields a singular value problem
+  if (c < Scalar(-1)+precision<Scalar>())
+  {
+    c = std::max<Scalar>(c,-1);
+    Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
+    SVD<Matrix<Scalar,2,3> > svd(m);
+    Vector3 axis = svd.matrixV().col(2);
+
+    Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
+    this->w() = ei_sqrt(w2);
+    this->vec() = axis * ei_sqrt(Scalar(1) - w2);
+    return *this;
+  }
+  Vector3 axis = v0.cross(v1);
+  Scalar s = ei_sqrt((Scalar(1)+c)*Scalar(2));
+  Scalar invs = Scalar(1)/s;
+  this->vec() = axis * invs;
+  this->w() = s * Scalar(0.5);
+
+  return *this;
+}
+
+/** \returns the multiplicative inverse of \c *this
+  * Note that in most cases, i.e., if you simply want the opposite rotation,
+  * and/or the quaternion is normalized, then it is enough to use the conjugate.
+  *
+  * \sa Quaternion2::conjugate()
+  */
+template <class Derived>
+inline Quat<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::inverse() const
+{
+  // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite()  ??
+  Scalar n2 = this->squaredNorm();
+  if (n2 > 0)
+    return Quat<Scalar>(conjugate().coeffs() / n2);
+  else
+  {
+    // return an invalid result to flag the error
+    return Quat<Scalar>(ei_traits<Derived>::Coefficients::Zero());
+  }
+}
+
+/** \returns the conjugate of the \c *this which is equal to the multiplicative inverse
+  * if the quaternion is normalized.
+  * The conjugate of a quaternion represents the opposite rotation.
+  *
+  * \sa Quaternion2::inverse()
+  */
+template <class Derived>
+inline Quat<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::conjugate() const
+{
+  return Quat<Scalar>(this->w(),-this->x(),-this->y(),-this->z());
+}
+
+/** \returns the angle (in radian) between two rotations
+  * \sa dot()
+  */
+template <class Derived>
+template <class OtherDerived>
+inline typename ei_traits<QuaternionBase<Derived> >::Scalar QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const
+{
+  double d = ei_abs(this->dot(other));
+  if (d>=1.0)
+    return 0;
+  return Scalar(2) * std::acos(d);
+}
+
+/** \returns the spherical linear interpolation between the two quaternions
+  * \c *this and \a other at the parameter \a t
+  */
+template <class Derived>
+template <class OtherDerived>
+Quat<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::slerp(Scalar t, const QuaternionBase<OtherDerived>& other) const
+{
+  static const Scalar one = Scalar(1) - precision<Scalar>();
+  Scalar d = this->dot(other);
+  Scalar absD = ei_abs(d);
+  if (absD>=one)
+    return Quat<Scalar>(*this);
+
+  // theta is the angle between the 2 quaternions
+  Scalar theta = std::acos(absD);
+  Scalar sinTheta = ei_sin(theta);
+
+  Scalar scale0 = ei_sin( ( Scalar(1) - t ) * theta) / sinTheta;
+  Scalar scale1 = ei_sin( ( t * theta) ) / sinTheta;
+  if (d<0)
+    scale1 = -scale1;
+
+  return Quat<Scalar>(scale0 * coeffs() + scale1 * other.coeffs());
+}
+
+// set from a rotation matrix
+template<typename Other>
+struct ei_quaternionbase_assign_impl<Other,3,3>
+{
+  typedef typename Other::Scalar Scalar;
+  template<class Derived> inline static void run(QuaternionBase<Derived>& q, const Other& mat)
+  {
+    // This algorithm comes from  "Quaternion Calculus and Fast Animation",
+    // Ken Shoemake, 1987 SIGGRAPH course notes
+    Scalar t = mat.trace();
+    if (t > 0)
+    {
+      t = ei_sqrt(t + Scalar(1.0));
+      q.w() = Scalar(0.5)*t;
+      t = Scalar(0.5)/t;
+      q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
+      q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
+      q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
+    }
+    else
+    {
+      int i = 0;
+      if (mat.coeff(1,1) > mat.coeff(0,0))
+        i = 1;
+      if (mat.coeff(2,2) > mat.coeff(i,i))
+        i = 2;
+      int j = (i+1)%3;
+      int k = (j+1)%3;
+
+      t = ei_sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
+      q.coeffs().coeffRef(i) = Scalar(0.5) * t;
+      t = Scalar(0.5)/t;
+      q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
+      q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
+      q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
+    }
+  }
+};
+
+// set from a vector of coefficients assumed to be a quaternion
+template<typename Other>
+struct ei_quaternionbase_assign_impl<Other,4,1>
+{
+  typedef typename Other::Scalar Scalar;
+  template<class Derived> inline static void run(QuaternionBase<Derived>& q, const Other& vec)
+  {
+    q.coeffs() = vec;
+  }
+};
+
+
 #endif // EIGEN_QUATERNION_H
diff --git a/Eigen/src/Geometry/arch/Geometry_SSE.h b/Eigen/src/Geometry/arch/Geometry_SSE.h
index d0342febc..c608e4843 100644
--- a/Eigen/src/Geometry/arch/Geometry_SSE.h
+++ b/Eigen/src/Geometry/arch/Geometry_SSE.h
@@ -45,6 +45,27 @@ ei_quaternion_product<EiArch_SSE,float>(const Quaternion<float>& _a, const Quate
   return res;
 }
 
+template<class Derived, class OtherDerived> struct ei_quat_product<EiArch_SSE, Derived, OtherDerived, float, Aligned>
+{
+  inline static Quat<float> run(const QuaternionBase<Derived>& _a, const QuaternionBase<OtherDerived>& _b)
+  {
+    const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0,0,0,0x80000000));
+    Quat<float> res;
+    __m128 a = _a.coeffs().packet<Aligned>(0);
+    __m128 b = _b.coeffs().packet<Aligned>(0);
+    __m128 flip1 = _mm_xor_ps(_mm_mul_ps(ei_vec4f_swizzle1(a,1,2,0,2),
+                                         ei_vec4f_swizzle1(b,2,0,1,2)),mask);
+    __m128 flip2 = _mm_xor_ps(_mm_mul_ps(ei_vec4f_swizzle1(a,3,3,3,1),
+                                         ei_vec4f_swizzle1(b,0,1,2,1)),mask);
+    ei_pstore(&res.x(),
+              _mm_add_ps(_mm_sub_ps(_mm_mul_ps(a,ei_vec4f_swizzle1(b,3,3,3,3)),
+                                    _mm_mul_ps(ei_vec4f_swizzle1(a,2,0,1,0),
+                                               ei_vec4f_swizzle1(b,1,2,0,0))),
+                         _mm_add_ps(flip1,flip2)));
+    return res;
+  }
+};
+
 template<typename VectorLhs,typename VectorRhs>
 struct ei_cross3_impl<EiArch_SSE,VectorLhs,VectorRhs,float,true> {
   inline static typename ei_plain_matrix_type<VectorLhs>::type