Add Scaling and Translation class as discussed on ML, still missing:

* handling Quaternion, AngleAxis and Rotation2D, 2 options here:
 1- make all of them inheriting a common base class Rotation such that we can
    have a single version of operator* for all the rotation type (they all get converted to a matrix)
 2- write a version for all type (so 3 rotations types * 3 for Transform,Translation and Scaling)
* real documentation

Eigen/src/Geometry/Translation.h

@@ -0,0 +1,165 @@
+// 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_TRANSLATION_H
+#define EIGEN_TRANSLATION_H
+
+/** \geometry_module \ingroup GeometryModule
+  *
+  * \class Translation
+  *
+  * \brief Represents a translation transformation
+  *
+  * \param _Scalar the scalar type, i.e., the type of the coefficients.
+  * \param _Dim the  dimension of the space, can be a compile time value or Dynamic
+  *
+  *
+  * \sa class Scaling, class Transform
+  */
+template<typename _Scalar, int _Dim>
+class Translation
+{
+public:
+  enum { Dim = _Dim };
+  /** the scalar type of the coefficients */
+  typedef _Scalar Scalar;
+  typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
+  typedef Matrix<Scalar,Dim,1> VectorType;
+  typedef Scaling<Scalar,Dim> ScalingType;
+  typedef Transform<Scalar,Dim> TransformType;
+
+protected:
+
+  VectorType m_coeffs;
+
+public:
+
+  /** Default constructor without initialization. */
+  Translation() {}
+  /**  */
+  inline Translation(const Scalar& sx, const Scalar& sy)
+  {
+    ei_assert(Dim==2);
+    m_coeffs.x() = sx;
+    m_coeffs.y() = sy;
+  }
+  /**  */
+  inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz)
+  {
+    ei_assert(Dim==3);
+    m_coeffs.x() = sx;
+    m_coeffs.y() = sy;
+    m_coeffs.z() = sz;
+  }
+  /** Constructs and initialize the scaling transformation from a vector of scaling coefficients */
+  explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {}
+
+  const VectorType& vector() const { return m_coeffs; }
+  VectorType& vector() { return m_coeffs; }
+
+  /** Concatenates two translation */
+  inline Translation operator* (const Translation& other) const
+  { return Translation(m_coeffs + other.m_coeffs); }
+  
+  /** Concatenates a translation and a scaling */
+  inline TransformType operator* (const ScalingType& other) const;
+
+  /** Concatenates a translation and a linear transformation */
+  inline TransformType operator* (const LinearMatrixType& linear) const;
+
+  /** Concatenates a linear transformation and a translation */
+  // its a nightmare to define a templated friend function outside its declaration
+  friend inline TransformType operator* (const LinearMatrixType& linear, const Translation& t)
+  {
+    TransformType res;
+    res.matrix().setZero();
+    res.linear() = linear;
+    res.translation() = linear * t.m_coeffs;
+    res.matrix().row(Dim).setZero();
+    res(Dim,Dim) = Scalar(1);
+    return res;
+  }
+
+  /** Concatenates a translation and an affine transformation */
+  inline TransformType operator* (const TransformType& t) const;
+
+  /** Applies translation to vector */
+  inline VectorType operator* (const VectorType& other) const
+  { return m_coeffs + other; }
+
+  /** \returns the inverse translation (opposite) */
+  Translation inverse() const { return Translation(-m_coeffs); }
+
+  Translation& operator=(const Translation& other)
+  {
+    m_coeffs = other.m_coeffs;
+    return *this;
+  }
+
+};
+
+/** \addtogroup GeometryModule */
+//@{
+typedef Translation<float, 2> Translation2f;
+typedef Translation<double,2> Translation2d;
+typedef Translation<float, 3> Translation3f;
+typedef Translation<double,3> Translation3d;
+//@}
+
+
+template<typename Scalar, int Dim>
+inline typename Translation<Scalar,Dim>::TransformType
+Translation<Scalar,Dim>::operator* (const ScalingType& other) const
+{
+  TransformType res;
+  res.matrix().setZero();
+  res.linear().diagonal() = other.coeffs();
+  res.translation() = m_coeffs;
+  res(Dim,Dim) = Scalar(1);
+  return res;
+}
+
+template<typename Scalar, int Dim>
+inline typename Translation<Scalar,Dim>::TransformType
+Translation<Scalar,Dim>::operator* (const LinearMatrixType& linear) const
+{
+  TransformType res;
+  res.matrix().setZero();
+  res.linear() = linear;
+  res.translation() = m_coeffs;
+  res.matrix().row(Dim).setZero();
+  res(Dim,Dim) = Scalar(1);
+  return res;
+}
+
+template<typename Scalar, int Dim>
+inline typename Translation<Scalar,Dim>::TransformType
+Translation<Scalar,Dim>::operator* (const TransformType& t) const
+{
+  TransformType res = t;
+  res.pretranslate(m_coeffs);
+  return res;
+}
+
+#endif // EIGEN_TRANSLATION_H