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.

4 files changed, 96 insertions, 11 deletions

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