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.

11 files changed, 154 insertions, 67 deletions

diff --git a/Eigen/Geometry b/Eigen/Geometry
index 2dd44fb0b..ae3012bfa 100644
--- a/Eigen/Geometry
+++ b/Eigen/Geometry
@@ -8,7 +8,6 @@ namespace Eigen {
 #include "src/Geometry/Cross.h"
 #include "src/Geometry/Quaternion.h"
 #include "src/Geometry/AngleAxis.h"
-#include "src/Geometry/EulerAngles.h"
 #include "src/Geometry/Rotation.h"
 #include "src/Geometry/Transform.h"
 
diff --git a/Eigen/src/Core/CwiseNullaryOp.h b/Eigen/src/Core/CwiseNullaryOp.h
index 167993e02..3cf9070e2 100644
--- a/Eigen/src/Core/CwiseNullaryOp.h
+++ b/Eigen/src/Core/CwiseNullaryOp.h
@@ -43,13 +43,13 @@
 template<typename NullaryOp, typename MatrixType>
 struct ei_traits<CwiseNullaryOp<NullaryOp, MatrixType> >
 {
-  typedef typename MatrixType::Scalar Scalar;
+  typedef typename ei_traits<MatrixType>::Scalar Scalar;
   enum {
-    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
-    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
-    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
-    Flags = (MatrixType::Flags
+    RowsAtCompileTime = ei_traits<MatrixType>::RowsAtCompileTime,
+    ColsAtCompileTime = ei_traits<MatrixType>::ColsAtCompileTime,
+    MaxRowsAtCompileTime = ei_traits<MatrixType>::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = ei_traits<MatrixType>::MaxColsAtCompileTime,
+    Flags = (ei_traits<MatrixType>::Flags
       & (  HereditaryBits
          | (ei_functor_has_linear_access<NullaryOp>::ret ? LinearAccessBit : 0)
          | (ei_functor_traits<NullaryOp>::PacketAccess ? PacketAccessBit : 0)))
@@ -453,7 +453,7 @@ Derived& MatrixBase<Derived>::setOnes()
   * \sa identity(), setIdentity(), isIdentity()
   */
 template<typename Derived>
-inline const CwiseNullaryOp<ei_scalar_identity_op<typename ei_traits<Derived>::Scalar>, Derived>
+inline const typename MatrixBase<Derived>::IdentityReturnType
 MatrixBase<Derived>::identity(int rows, int cols)
 {
   return NullaryExpr(rows, cols, ei_scalar_identity_op<Scalar>());
@@ -470,7 +470,7 @@ MatrixBase<Derived>::identity(int rows, int cols)
   * \sa identity(int,int), setIdentity(), isIdentity()
   */
 template<typename Derived>
-inline const CwiseNullaryOp<ei_scalar_identity_op<typename ei_traits<Derived>::Scalar>, Derived>
+inline const typename MatrixBase<Derived>::IdentityReturnType
 MatrixBase<Derived>::identity()
 {
   EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
@@ -522,4 +522,72 @@ inline Derived& MatrixBase<Derived>::setIdentity()
   return *this = identity(rows(), cols());
 }
 
+/** \returns an expression of the i-th unit (basis) vector.
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(int), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(int size, int i)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+  return BasisReturnType(SquareMatrixType::identity(size,size), i);
+}
+
+/** \returns an expression of the i-th unit (basis) vector.
+  *
+  * \only_for_vectors
+  *
+  * This variant is for fixed-size vector only.
+  *
+  * \sa MatrixBase::Unit(int,int), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(int i)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+  return BasisReturnType(SquareMatrixType::identity(),i);
+}
+
+/** \returns an expression of the X axis unit vector (1{,0}^*)
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(int,int), MatrixBase::Unit(int), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitX()
+{ return Derived::Unit(0); }
+
+/** \returns an expression of the Y axis unit vector (0,1{,0}^*)
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(int,int), MatrixBase::Unit(int), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitY()
+{ return Derived::Unit(1); }
+
+/** \returns an expression of the Z axis unit vector (0,0,1{,0}^*)
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(int,int), MatrixBase::Unit(int), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitZ()
+{ return Derived::Unit(2); }
+
+/** \returns an expression of the W axis unit vector (0,0,0,1)
+  *
+  * \only_for_vectors
+  *
+  * \sa MatrixBase::Unit(int,int), MatrixBase::Unit(int), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+  */
+template<typename Derived>
+const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitW()
+{ return Derived::Unit(3); }
+
 #endif // EIGEN_CWISE_NULLARY_OP_H
diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
index cf6a937d1..c6ea5f14f 100644
--- a/Eigen/src/Core/MatrixBase.h
+++ b/Eigen/src/Core/MatrixBase.h
@@ -148,6 +148,10 @@ template<typename Derived> class MatrixBase
       */
     typedef typename NumTraits<Scalar>::Real RealScalar;
 
+    /** type of the equivalent square matrix */
+    typedef Matrix<Scalar,EIGEN_ENUM_MAX(RowsAtCompileTime,ColsAtCompileTime),
+                          EIGEN_ENUM_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;
+
     /** \returns the number of rows. \sa cols(), RowsAtCompileTime */
     inline int rows() const { return derived().rows(); }
     /** \returns the number of columns. \sa row(), ColsAtCompileTime*/
@@ -193,7 +197,14 @@ template<typename Derived> class MatrixBase
     /** the return type of MatrixBase::adjoint() */
     typedef Transpose<NestByValue<typename ei_unref<ConjugateReturnType>::type> >
             AdjointReturnType;
+    /** the return type of MatrixBase::eigenvalues() */
     typedef Matrix<typename NumTraits<typename ei_traits<Derived>::Scalar>::Real, ei_traits<Derived>::ColsAtCompileTime, 1> EigenvaluesReturnType;
+    /** the return type of identity */
+    typedef CwiseNullaryOp<ei_scalar_identity_op<Scalar>,Derived> IdentityReturnType;
+    /** the return type of unit vectors */
+    typedef Block<CwiseNullaryOp<ei_scalar_identity_op<Scalar>, SquareMatrixType>,
+                  ei_traits<Derived>::RowsAtCompileTime,
+                  ei_traits<Derived>::ColsAtCompileTime> BasisReturnType;
 
 
     /** Copies \a other into *this. \returns a reference to *this. */
@@ -391,8 +402,14 @@ template<typename Derived> class MatrixBase
     static const ConstantReturnType ones(int rows, int cols);
     static const ConstantReturnType ones(int size);
     static const ConstantReturnType ones();
-    static const CwiseNullaryOp<ei_scalar_identity_op<Scalar>,Derived> identity();
-    static const CwiseNullaryOp<ei_scalar_identity_op<Scalar>,Derived> identity(int rows, int cols);
+    static const IdentityReturnType identity();
+    static const IdentityReturnType identity(int rows, int cols);
+    static const BasisReturnType Unit(int size, int i);
+    static const BasisReturnType Unit(int i);
+    static const BasisReturnType UnitX();
+    static const BasisReturnType UnitY();
+    static const BasisReturnType UnitZ();
+    static const BasisReturnType UnitW();
 
     const DiagonalMatrix<Derived> asDiagonal() const;
 
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index beda186f6..0246b43cc 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -102,7 +102,6 @@ template<typename Lhs, typename Rhs> class Cross;
 template<typename Scalar> class Quaternion;
 template<typename Scalar> class Rotation2D;
 template<typename Scalar> class AngleAxis;
-template<typename Scalar> class EulerAngles;
 template<typename Scalar,int Dim> class Transform;
 
 #endif // EIGEN_FORWARDDECLARATIONS_H
diff --git a/Eigen/src/Core/util/Macros.h b/Eigen/src/Core/util/Macros.h
index 9c013f6d1..eaa5df27f 100644
--- a/Eigen/src/Core/util/Macros.h
+++ b/Eigen/src/Core/util/Macros.h
@@ -151,5 +151,6 @@ _EIGEN_GENERIC_PUBLIC_INTERFACE(Derived, Eigen::MatrixBase<Derived>) \
 friend class Eigen::MatrixBase<Derived>;
 
 #define EIGEN_ENUM_MIN(a,b) (((int)a <= (int)b) ? (int)a : (int)b)
+#define EIGEN_ENUM_MAX(a,b) (((int)a >= (int)b) ? (int)a : (int)b)
 
 #endif // EIGEN_MACROS_H
diff --git a/Eigen/src/Geometry/AngleAxis.h b/Eigen/src/Geometry/AngleAxis.h
index c77264e1c..639e75a87 100644
--- a/Eigen/src/Geometry/AngleAxis.h
+++ b/Eigen/src/Geometry/AngleAxis.h
@@ -31,6 +31,10 @@
   *
   * \param _Scalar the scalar type, i.e., the type of the coefficients.
   *
+  * The following two typedefs are provided for convenience:
+  * \li \c AngleAxisf for \c float
+  * \li \c AngleAxisd for \c double
+  *
   * \sa class Quaternion, class EulerAngles, class Transform
   */
 template<typename _Scalar>
@@ -43,7 +47,6 @@ public:
   typedef Matrix<Scalar,3,3> Matrix3;
   typedef Matrix<Scalar,3,1> Vector3;
   typedef Quaternion<Scalar> QuaternionType;
-  typedef EulerAngles<Scalar> EulerAnglesType;
 
 protected:
 
@@ -56,7 +59,6 @@ public:
   template<typename Derived>
   inline AngleAxis(Scalar angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
   inline AngleAxis(const QuaternionType& q) { *this = q; }
-  inline AngleAxis(const EulerAnglesType& ea) { *this = ea; }
   template<typename Derived>
   inline AngleAxis(const MatrixBase<Derived>& m) { *this = m; }
 
@@ -66,8 +68,26 @@ public:
   const Vector3& axis() const { return m_axis; }
   Vector3& axis() { return m_axis; }
 
+  operator Matrix3 () const { return toRotationMatrix(); }
+
+  inline QuaternionType operator* (const AngleAxis& other) const
+  { return QuaternionType(*this) * QuaternionType(other); }
+  
+  inline QuaternionType operator* (const QuaternionType& other) const
+  { return QuaternionType(*this) * other; }
+
+  friend inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b)
+  { return a * QuaternionType(b); }
+
+  inline typename ProductReturnType<Matrix3,Matrix3>::Type
+  operator* (const Matrix3& other) const
+  { return toRotationMatrix() * other; }
+
+  inline friend typename ProductReturnType<Matrix3,Matrix3>::Type
+  operator* (const Matrix3& a, const AngleAxis& b)
+  { return a * b.toRotationMatrix(); }
+
   AngleAxis& operator=(const QuaternionType& q);
-  AngleAxis& operator=(const EulerAnglesType& ea);
   template<typename Derived>
   AngleAxis& operator=(const MatrixBase<Derived>& m);
 
@@ -76,6 +96,9 @@ public:
   Matrix3 toRotationMatrix(void) const;
 };
 
+typedef AngleAxis<float> AngleAxisf;
+typedef AngleAxis<double> AngleAxisd;
+
 /** Set \c *this from a quaternion.
   * The axis is normalized.
   */
@@ -96,14 +119,6 @@ AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionType& q)
   return *this;
 }
 
-/** Set \c *this from Euler angles \a ea.
-  */
-template<typename Scalar>
-AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const EulerAnglesType& ea)
-{
-  return *this = QuaternionType(ea);
-}
-
 /** Set \c *this from a 3x3 rotation matrix \a mat.
   */
 template<typename Scalar>
diff --git a/Eigen/src/Geometry/Quaternion.h b/Eigen/src/Geometry/Quaternion.h
index d8ccf4917..fcc7e21ca 100644
--- a/Eigen/src/Geometry/Quaternion.h
+++ b/Eigen/src/Geometry/Quaternion.h
@@ -40,9 +40,13 @@ struct ei_quaternion_assign_impl;
   * orientations and rotations of objects in three dimensions. Compared to other
   * representations like Euler angles or 3x3 matrices, quatertions offer the
   * following advantages:
-  *   - compact storage (4 scalars)
-  *   - efficient to compose (28 flops),
-  *   - stable spherical interpolation
+  * \li \c compact storage (4 scalars)
+  * \li \c efficient to compose (28 flops),
+  * \li \c stable spherical interpolation
+  *
+  * The following two typedefs are provided for convenience:
+  * \li \c Quaternionf for \c float
+  * \li \c Quaterniond for \c double
   *
   * \sa  class AngleAxis, class EulerAngles, class Transform
   */
@@ -60,7 +64,6 @@ public:
   typedef Matrix<Scalar,3,1> Vector3;
   typedef Matrix<Scalar,3,3> Matrix3;
   typedef AngleAxis<Scalar> AngleAxisType;
-  typedef EulerAngles<Scalar> EulerAnglesType;
 
   inline Scalar x() const { return m_coeffs.coeff(0); }
   inline Scalar y() const { return m_coeffs.coeff(1); }
@@ -97,16 +100,16 @@ public:
   inline Quaternion(const Quaternion& other) { m_coeffs = other.m_coeffs; }
 
   explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }
-  explicit inline Quaternion(const EulerAnglesType& ea) { *this = ea; }
   template<typename Derived>
   explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
 
   Quaternion& operator=(const Quaternion& other);
   Quaternion& operator=(const AngleAxisType& aa);
-  Quaternion& operator=(EulerAnglesType ea);
   template<typename Derived>
   Quaternion& operator=(const MatrixBase<Derived>& m);
 
+  operator Matrix3 () const { return toRotationMatrix(); }
+
   /** \returns a quaternion representing an identity rotation
     * \sa MatrixBase::identity()
     */
@@ -144,6 +147,9 @@ public:
 
 };
 
+typedef Quaternion<float> Quaternionf;
+typedef Quaternion<double> Quaterniond;
+
 /** \returns the concatenation of two rotations as a quaternion-quaternion product */
 template <typename Scalar>
 inline Quaternion<Scalar> Quaternion<Scalar>::operator* (const Quaternion& other) const
@@ -204,30 +210,6 @@ inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const AngleAxisType& aa
   return *this;
 }
 
-/** Set \c *this from the rotation defined by the Euler angles \a ea,
-  * and returns a reference to \c *this
-  */
-template<typename Scalar>
-inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(EulerAnglesType ea)
-{
-  ea.coeffs() *= 0.5;
-
-  Vector3 cosines = ea.coeffs().cwise().cos();
-  Vector3 sines   = ea.coeffs().cwise().sin();
-
-  Scalar cYcZ = cosines.y() * cosines.z();
-  Scalar sYsZ = sines.y() * sines.z();
-  Scalar sYcZ = sines.y() * cosines.z();
-  Scalar cYsZ = cosines.y() * sines.z();
-
-  this->w() = cosines.x() * cYcZ + sines.x()   * sYsZ;
-  this->x() = sines.x()   * cYcZ - cosines.x() * sYsZ;
-  this->y() = cosines.x() * sYcZ + sines.x()   * cYsZ;
-  this->z() = cosines.x() * cYsZ - sines.x()   * sYcZ;
-
-  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
diff --git a/Eigen/src/Geometry/Rotation.h b/Eigen/src/Geometry/Rotation.h
index ba533b9fc..fb4179786 100644
--- a/Eigen/src/Geometry/Rotation.h
+++ b/Eigen/src/Geometry/Rotation.h
@@ -89,14 +89,6 @@ struct ToRotationMatrix<Scalar, 3, AngleAxis<OtherScalarType> >
   { return aa.toRotationMatrix(); }
 };
 
-// euler angles to rotation matrix
-template<typename Scalar, typename OtherScalarType>
-struct ToRotationMatrix<Scalar, 3, EulerAngles<OtherScalarType> >
-{
-  inline static Matrix<Scalar,3,3> convert(const EulerAngles<OtherScalarType>& ea)
-  { return ea.toRotationMatrix(); }
-};
-
 // matrix xpr to matrix xpr
 template<typename Scalar, int Dim, typename OtherDerived>
 struct ToRotationMatrix<Scalar, Dim, MatrixBase<OtherDerived> >
diff --git a/Eigen/src/Geometry/EulerAngles.h b/disabled/EulerAngles.h
index 637744715..65489f225 100644
--- a/Eigen/src/Geometry/EulerAngles.h
+++ b/disabled/EulerAngles.h
@@ -30,6 +30,13 @@ template<typename Other,
          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
diff --git a/test/array.cpp b/test/array.cpp
index 6233aaec8..3acb4ab55 100644
--- a/test/array.cpp
+++ b/test/array.cpp
@@ -53,6 +53,11 @@ template<typename MatrixType> void scalarAdd(const MatrixType& m)
   m3 = m1;
   m3.cwise() -= s1;
   VERIFY_IS_APPROX(m3, m1.cwise() - s1);
+
+  VERIFY_IS_APPROX(m1.colwise().sum().sum(), m1.sum());
+  VERIFY_IS_APPROX(m1.rowwise().sum().sum(), m1.sum());
+  VERIFY_IS_NOT_APPROX((m1.rowwise().sum()*2).sum(), m1.sum());
+  VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(ei_scalar_sum_op<Scalar>()));
 }
 
 template<typename MatrixType> void comparisons(const MatrixType& m)
diff --git a/test/geometry.cpp b/test/geometry.cpp
index 64b096aa8..395d1c2c8 100644
--- a/test/geometry.cpp
+++ b/test/geometry.cpp
@@ -40,12 +40,12 @@ template<typename Scalar> void geometry(void)
   typedef Matrix<Scalar,4,1> Vector4;
   typedef Quaternion<Scalar> Quaternion;
   typedef AngleAxis<Scalar> AngleAxis;
-  typedef EulerAngles<Scalar> EulerAngles;
 
   Quaternion q1, q2;
   Vector3 v0 = Vector3::random(),
     v1 = Vector3::random(),
     v2 = Vector3::random();
+  Matrix3 matrot1;
 
   Scalar a = ei_random<Scalar>(-M_PI, M_PI);
 
@@ -61,11 +61,13 @@ template<typename Scalar> void geometry(void)
   q2 = q1.toRotationMatrix();
   VERIFY_IS_APPROX(q1*v1,q2*v1);
 
-  // Euler angle conversion
-  VERIFY_IS_APPROX(Quaternion(EulerAngles(q1)) * v1, q1 * v1);
-  EulerAngles ea = q2;
-  VERIFY_IS_APPROX(EulerAngles(Quaternion(ea)).coeffs(), ea.coeffs());
-  VERIFY_IS_NOT_APPROX(EulerAngles(Quaternion(EulerAngles(v2.cwise() * Vector3(0.2,-0.2,1)))).coeffs(), v2);
+  matrot1 = AngleAxis(0.1, Vector3::UnitX())
+          * AngleAxis(0.2, Vector3::UnitY())
+          * AngleAxis(0.3, Vector3::UnitZ());
+  VERIFY_IS_APPROX(matrot1 * v1,
+       AngleAxis(0.1, Vector3(1,0,0)).toRotationMatrix()
+    * (AngleAxis(0.2, Vector3(0,1,0)).toRotationMatrix()
+    * (AngleAxis(0.3, Vector3(0,0,1)).toRotationMatrix() * v1)));
 
   // angle-axis conversion
   AngleAxis aa = q1;