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// 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/>.
// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
namespace Eigen {
/** \geometry_module \ingroup Geometry_Module
*
* \class Scaling
*
* \brief Represents a possibly non uniform scaling 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
*
* \note This class is not aimed to be used to store a scaling transformation,
* but rather to make easier the constructions and updates of Transform objects.
*
* \sa class Translation, class Transform
*/
template<typename _Scalar, int _Dim>
class Scaling
{
public:
EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim)
/** dimension of the space */
enum { Dim = _Dim };
/** the scalar type of the coefficients */
typedef _Scalar Scalar;
/** corresponding vector type */
typedef Matrix<Scalar,Dim,1> VectorType;
/** corresponding linear transformation matrix type */
typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
/** corresponding translation type */
typedef Translation<Scalar,Dim> TranslationType;
/** corresponding affine transformation type */
typedef Transform<Scalar,Dim> TransformType;
protected:
VectorType m_coeffs;
public:
/** Default constructor without initialization. */
Scaling() {}
/** Constructs and initialize a uniform scaling transformation */
explicit inline Scaling(const Scalar& s) { m_coeffs.setConstant(s); }
/** 2D only */
inline Scaling(const Scalar& sx, const Scalar& sy)
{
ei_assert(Dim==2);
m_coeffs.x() = sx;
m_coeffs.y() = sy;
}
/** 3D only */
inline Scaling(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 Scaling(const VectorType& coeffs) : m_coeffs(coeffs) {}
const VectorType& coeffs() const { return m_coeffs; }
VectorType& coeffs() { return m_coeffs; }
/** Concatenates two scaling */
inline Scaling operator* (const Scaling& other) const
{ return Scaling(coeffs().cwise() * other.coeffs()); }
/** Concatenates a scaling and a translation */
inline TransformType operator* (const TranslationType& t) const;
/** Concatenates a scaling and an affine transformation */
inline TransformType operator* (const TransformType& t) const;
/** Concatenates a scaling and a linear transformation matrix */
// TODO returns an expression
inline LinearMatrixType operator* (const LinearMatrixType& other) const
{ return coeffs().asDiagonal() * other; }
/** Concatenates a linear transformation matrix and a scaling */
// TODO returns an expression
friend inline LinearMatrixType operator* (const LinearMatrixType& other, const Scaling& s)
{ return other * s.coeffs().asDiagonal(); }
template<typename Derived>
inline LinearMatrixType operator*(const RotationBase<Derived,Dim>& r) const
{ return *this * r.toRotationMatrix(); }
/** Applies scaling to vector */
inline VectorType operator* (const VectorType& other) const
{ return coeffs().asDiagonal() * other; }
/** \returns the inverse scaling */
inline Scaling inverse() const
{ return Scaling(coeffs().cwise().inverse()); }
inline Scaling& operator=(const Scaling& other)
{
m_coeffs = other.m_coeffs;
return *this;
}
/** \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<typename NewScalarType>
inline typename internal::cast_return_type<Scaling,Scaling<NewScalarType,Dim> >::type cast() const
{ return typename internal::cast_return_type<Scaling,Scaling<NewScalarType,Dim> >::type(*this); }
/** Copy constructor with scalar type conversion */
template<typename OtherScalarType>
inline explicit Scaling(const Scaling<OtherScalarType,Dim>& other)
{ m_coeffs = other.coeffs().template cast<Scalar>(); }
/** \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 Scaling& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
{ return m_coeffs.isApprox(other.m_coeffs, prec); }
};
/** \addtogroup Geometry_Module */
//@{
typedef Scaling<float, 2> Scaling2f;
typedef Scaling<double,2> Scaling2d;
typedef Scaling<float, 3> Scaling3f;
typedef Scaling<double,3> Scaling3d;
//@}
template<typename Scalar, int Dim>
inline typename Scaling<Scalar,Dim>::TransformType
Scaling<Scalar,Dim>::operator* (const TranslationType& t) const
{
TransformType res;
res.matrix().setZero();
res.linear().diagonal() = coeffs();
res.translation() = m_coeffs.cwise() * t.vector();
res(Dim,Dim) = Scalar(1);
return res;
}
template<typename Scalar, int Dim>
inline typename Scaling<Scalar,Dim>::TransformType
Scaling<Scalar,Dim>::operator* (const TransformType& t) const
{
TransformType res = t;
res.prescale(m_coeffs);
return res;
}
} // end namespace Eigen
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