// 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>
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
namespace Eigen {
// Note that we have to pass Dim and HDim because it is not allowed to use a template
// parameter to define a template specialization. To be more precise, in the following
// specializations, it is not allowed to use Dim+1 instead of HDim.
template< typename Other,
int Dim,
int HDim,
int OtherRows=Other::RowsAtCompileTime,
int OtherCols=Other::ColsAtCompileTime>
struct ei_transform_product_impl;
/** \geometry_module \ingroup Geometry_Module
*
* \class Transform
*
* \brief Represents an homogeneous transformation in a N dimensional space
*
* \param _Scalar the scalar type, i.e., the type of the coefficients
* \param _Dim the dimension of the space
*
* The homography is internally represented and stored as a (Dim+1)^2 matrix which
* is available through the matrix() method.
*
* Conversion methods from/to Qt's QMatrix and QTransform are available if the
* preprocessor token EIGEN_QT_SUPPORT is defined.
*
* \sa class Matrix, class Quaternion
*/
template<typename _Scalar, int _Dim>
class Transform
{
public:
EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim==Dynamic ? Dynamic : (_Dim+1)*(_Dim+1))
enum {
Dim = _Dim, ///< space dimension in which the transformation holds
HDim = _Dim+1 ///< size of a respective homogeneous vector
};
/** the scalar type of the coefficients */
typedef _Scalar Scalar;
/** type of the matrix used to represent the transformation */
typedef Matrix<Scalar,HDim,HDim> MatrixType;
/** type of the matrix used to represent the linear part of the transformation */
typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
/** type of read/write reference to the linear part of the transformation */
typedef Block<MatrixType,Dim,Dim> LinearPart;
/** type of read/write reference to the linear part of the transformation */
typedef const Block<const MatrixType,Dim,Dim> ConstLinearPart;
/** type of a vector */
typedef Matrix<Scalar,Dim,1> VectorType;
/** type of a read/write reference to the translation part of the rotation */
typedef Block<MatrixType,Dim,1> TranslationPart;
/** type of a read/write reference to the translation part of the rotation */
typedef const Block<const MatrixType,Dim,1> ConstTranslationPart;
/** corresponding translation type */
typedef Translation<Scalar,Dim> TranslationType;
/** corresponding scaling transformation type */
typedef Scaling<Scalar,Dim> ScalingType;
protected:
MatrixType m_matrix;
public:
/** Default constructor without initialization of the coefficients. */
inline Transform() { }
inline Transform(const Transform& other)
{
m_matrix = other.m_matrix;
}
inline explicit Transform(const TranslationType& t) { *this = t; }
inline explicit Transform(const ScalingType& s) { *this = s; }
template<typename Derived>
inline explicit Transform(const RotationBase<Derived, Dim>& r) { *this = r; }
inline Transform& operator=(const Transform& other)
{ m_matrix = other.m_matrix; return *this; }
template<typename OtherDerived, bool BigMatrix> // MSVC 2005 will commit suicide if BigMatrix has a default value
struct construct_from_matrix
{
static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other)
{
transform->matrix() = other;
}
};
template<typename OtherDerived> struct construct_from_matrix<OtherDerived, true>
{
static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other)
{
transform->linear() = other;
transform->translation().setZero();
transform->matrix()(Dim,Dim) = Scalar(1);
transform->matrix().template block<1,Dim>(Dim,0).setZero();
}
};
/** Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. */
template<typename OtherDerived>
inline explicit Transform(const MatrixBase<OtherDerived>& other)
{
construct_from_matrix<OtherDerived, int(OtherDerived::RowsAtCompileTime) == Dim>::run(this, other);
}
/** Set \c *this from a (Dim+1)^2 matrix. */
template<typename OtherDerived>
inline Transform& operator=(const MatrixBase<OtherDerived>& other)
{ m_matrix = other; return *this; }
#ifdef EIGEN_QT_SUPPORT
inline Transform(const QMatrix& other);
inline Transform& operator=(const QMatrix& other);
inline QMatrix toQMatrix(void) const;
inline Transform(const QTransform& other);
inline Transform& operator=(const QTransform& other);
inline QTransform toQTransform(void) const;
#endif
/** shortcut for m_matrix(row,col);
* \sa MatrixBase::operaror(int,int) const */
inline Scalar operator() (int row, int col) const { return m_matrix(row,col); }
/** shortcut for m_matrix(row,col);
* \sa MatrixBase::operaror(int,int) */
inline Scalar& operator() (int row, int col) { return m_matrix(row,col); }
/** \returns a read-only expression of the transformation matrix */
inline const MatrixType& matrix() const { return m_matrix; }
/** \returns a writable expression of the transformation matrix */
inline MatrixType& matrix() { return m_matrix; }
/** \returns a read-only expression of the linear (linear) part of the transformation */
inline ConstLinearPart linear() const { return m_matrix.template block<Dim,Dim>(0,0); }
/** \returns a writable expression of the linear (linear) part of the transformation */
inline LinearPart linear() { return m_matrix.template block<Dim,Dim>(0,0); }
/** \returns a read-only expression of the translation vector of the transformation */
inline ConstTranslationPart translation() const { return m_matrix.template block<Dim,1>(0,Dim); }
/** \returns a writable expression of the translation vector of the transformation */
inline TranslationPart translation() { return m_matrix.template block<Dim,1>(0,Dim); }
/** \returns an expression of the product between the transform \c *this and a matrix expression \a other
*
* The right hand side \a other might be either:
* \li a vector of size Dim,
* \li an homogeneous vector of size Dim+1,
* \li a transformation matrix of size Dim+1 x Dim+1.
*/
// note: this function is defined here because some compilers cannot find the respective declaration
template<typename OtherDerived>
inline const typename ei_transform_product_impl<OtherDerived,_Dim,_Dim+1>::ResultType
operator * (const MatrixBase<OtherDerived> &other) const
{ return ei_transform_product_impl<OtherDerived,Dim,HDim>::run(*this,other.derived()); }
/** \returns the product expression of a transformation matrix \a a times a transform \a b
* The transformation matrix \a a must have a Dim+1 x Dim+1 sizes. */
template<typename OtherDerived>
friend inline const typename ProductReturnType<OtherDerived,MatrixType>::Type
operator * (const MatrixBase<OtherDerived> &a, const Transform &b)
{ return a.derived() * b.matrix(); }
/** Contatenates two transformations */
inline const Transform
operator * (const Transform& other) const
{ return Transform(m_matrix * other.matrix()); }
/** \sa MatrixBase::setIdentity() */
void setIdentity() { m_matrix.setIdentity(); }
static const typename MatrixType::IdentityReturnType Identity()
{
return MatrixType::Identity();
}
template<typename OtherDerived>
inline Transform& scale(const MatrixBase<OtherDerived> &other);
template<typename OtherDerived>
inline Transform& prescale(const MatrixBase<OtherDerived> &other);
inline Transform& scale(Scalar s);
inline Transform& prescale(Scalar s);
template<typename OtherDerived>
inline Transform& translate(const MatrixBase<OtherDerived> &other);
template<typename OtherDerived>
inline Transform& pretranslate(const MatrixBase<OtherDerived> &other);
template<typename RotationType>
inline Transform& rotate(const RotationType& rotation);
template<typename RotationType>
inline Transform& prerotate(const RotationType& rotation);
Transform& shear(Scalar sx, Scalar sy);
Transform& preshear(Scalar sx, Scalar sy);
inline Transform& operator=(const TranslationType& t);
inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); }
inline Transform operator*(const TranslationType& t) const;
inline Transform& operator=(const ScalingType& t);
inline Transform& operator*=(const ScalingType& s) { return scale(s.coeffs()); }
inline Transform operator*(const ScalingType& s) const;
friend inline Transform operator*(const LinearMatrixType& mat, const Transform& t)
{
Transform res = t;
res.matrix().row(Dim) = t.matrix().row(Dim);
res.matrix().template block<Dim,HDim>(0,0) = (mat * t.matrix().template block<Dim,HDim>(0,0)).lazy();
return res;
}
template<typename Derived>
inline Transform& operator=(const RotationBase<Derived,Dim>& r);
template<typename Derived>
inline Transform& operator*=(const RotationBase<Derived,Dim>& r) { return rotate(r.toRotationMatrix()); }
template<typename Derived>
inline Transform operator*(const RotationBase<Derived,Dim>& r) const;
LinearMatrixType rotation() const;
template<typename RotationMatrixType, typename ScalingMatrixType>
void computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const;
template<typename ScalingMatrixType, typename RotationMatrixType>
void computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const;
template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
Transform& fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale);
inline const MatrixType inverse(TransformTraits traits = Affine) const;
/** \returns a const pointer to the column major internal matrix */
const Scalar* data() const { return m_matrix.data(); }
/** \returns a non-const pointer to the column major internal matrix */
Scalar* data() { return m_matrix.data(); }
/** \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<Transform,Transform<NewScalarType,Dim> >::type cast() const
{ return typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type(*this); }
/** Copy constructor with scalar type conversion */
template<typename OtherScalarType>
inline explicit Transform(const Transform<OtherScalarType,Dim>& other)
{ m_matrix = other.matrix().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 Transform& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
{ return m_matrix.isApprox(other.m_matrix, prec); }
#ifdef EIGEN_TRANSFORM_PLUGIN
#include EIGEN_TRANSFORM_PLUGIN
#endif
protected:
};
/** \ingroup Geometry_Module */
typedef Transform<float,2> Transform2f;
/** \ingroup Geometry_Module */
typedef Transform<float,3> Transform3f;
/** \ingroup Geometry_Module */
typedef Transform<double,2> Transform2d;
/** \ingroup Geometry_Module */
typedef Transform<double,3> Transform3d;
/**************************
*** Optional QT support ***
**************************/
#ifdef EIGEN_QT_SUPPORT
/** Initialises \c *this from a QMatrix assuming the dimension is 2.
*
* This function is available only if the token EIGEN_QT_SUPPORT is defined.
*/
template<typename Scalar, int Dim>
Transform<Scalar,Dim>::Transform(const QMatrix& other)
{
*this = other;
}
/** Set \c *this from a QMatrix assuming the dimension is 2.
*
* This function is available only if the token EIGEN_QT_SUPPORT is defined.
*/
template<typename Scalar, int Dim>
Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QMatrix& other)
{
EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
m_matrix << other.m11(), other.m21(), other.dx(),
other.m12(), other.m22(), other.dy(),
0, 0, 1;
return *this;
}
/** \returns a QMatrix from \c *this assuming the dimension is 2.
*
* \warning this convertion might loss data if \c *this is not affine
*
* This function is available only if the token EIGEN_QT_SUPPORT is defined.
*/
template<typename Scalar, int Dim>
QMatrix Transform<Scalar,Dim>::toQMatrix(void) const
{
EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
return QMatrix(m_matrix.coeff(0,0), m_matrix.coeff(1,0),
m_matrix.coeff(0,1), m_matrix.coeff(1,1),
m_matrix.coeff(0,2), m_matrix.coeff(1,2));
}
/** Initialises \c *this from a QTransform assuming the dimension is 2.
*
* This function is available only if the token EIGEN_QT_SUPPORT is defined.
*/
template<typename Scalar, int Dim>
Transform<Scalar,Dim>::Transform(const QTransform& other)
{
*this = other;
}
/** Set \c *this from a QTransform assuming the dimension is 2.
*
* This function is available only if the token EIGEN_QT_SUPPORT is defined.
*/
template<typename Scalar, int Dim>
Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QTransform& other)
{
EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
m_matrix << other.m11(), other.m21(), other.dx(),
other.m12(), other.m22(), other.dy(),
other.m13(), other.m23(), other.m33();
return *this;
}
/** \returns a QTransform from \c *this assuming the dimension is 2.
*
* This function is available only if the token EIGEN_QT_SUPPORT is defined.
*/
template<typename Scalar, int Dim>
QTransform Transform<Scalar,Dim>::toQTransform(void) const
{
EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0), m_matrix.coeff(2,0),
m_matrix.coeff(0,1), m_matrix.coeff(1,1), m_matrix.coeff(2,1),
m_matrix.coeff(0,2), m_matrix.coeff(1,2), m_matrix.coeff(2,2));
}
#endif
/*********************
*** Procedural API ***
*********************/
/** Applies on the right the non uniform scale transformation represented
* by the vector \a other to \c *this and returns a reference to \c *this.
* \sa prescale()
*/
template<typename Scalar, int Dim>
template<typename OtherDerived>
Transform<Scalar,Dim>&
Transform<Scalar,Dim>::scale(const MatrixBase<OtherDerived> &other)
{
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
linear() = (linear() * other.asDiagonal()).lazy();
return *this;
}
/** Applies on the right a uniform scale of a factor \a c to \c *this
* and returns a reference to \c *this.
* \sa prescale(Scalar)
*/
template<typename Scalar, int Dim>
inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::scale(Scalar s)
{
linear() *= s;
return *this;
}
/** Applies on the left the non uniform scale transformation represented
* by the vector \a other to \c *this and returns a reference to \c *this.
* \sa scale()
*/
template<typename Scalar, int Dim>
template<typename OtherDerived>
Transform<Scalar,Dim>&
Transform<Scalar,Dim>::prescale(const MatrixBase<OtherDerived> &other)
{
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
m_matrix.template block<Dim,HDim>(0,0) = (other.asDiagonal() * m_matrix.template block<Dim,HDim>(0,0)).lazy();
return *this;
}
/** Applies on the left a uniform scale of a factor \a c to \c *this
* and returns a reference to \c *this.
* \sa scale(Scalar)
*/
template<typename Scalar, int Dim>
inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::prescale(Scalar s)
{
m_matrix.template corner<Dim,HDim>(TopLeft) *= s;
return *this;
}
/** Applies on the right the translation matrix represented by the vector \a other
* to \c *this and returns a reference to \c *this.
* \sa pretranslate()
*/
template<typename Scalar, int Dim>
template<typename OtherDerived>
Transform<Scalar,Dim>&
Transform<Scalar,Dim>::translate(const MatrixBase<OtherDerived> &other)
{
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
translation() += linear() * other;
return *this;
}
/** Applies on the left the translation matrix represented by the vector \a other
* to \c *this and returns a reference to \c *this.
* \sa translate()
*/
template<typename Scalar, int Dim>
template<typename OtherDerived>
Transform<Scalar,Dim>&
Transform<Scalar,Dim>::pretranslate(const MatrixBase<OtherDerived> &other)
{
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
translation() += other;
return *this;
}
/** Applies on the right the rotation represented by the rotation \a rotation
* to \c *this and returns a reference to \c *this.
*
* The template parameter \a RotationType is the type of the rotation which
* must be known by ei_toRotationMatrix<>.
*
* Natively supported types includes:
* - any scalar (2D),
* - a Dim x Dim matrix expression,
* - a Quaternion (3D),
* - a AngleAxis (3D)
*
* This mechanism is easily extendable to support user types such as Euler angles,
* or a pair of Quaternion for 4D rotations.
*
* \sa rotate(Scalar), class Quaternion, class AngleAxis, prerotate(RotationType)
*/
template<typename Scalar, int Dim>
template<typename RotationType>
Transform<Scalar,Dim>&
Transform<Scalar,Dim>::rotate(const RotationType& rotation)
{
linear() *= ei_toRotationMatrix<Scalar,Dim>(rotation);
return *this;
}
/** Applies on the left the rotation represented by the rotation \a rotation
* to \c *this and returns a reference to \c *this.
*
* See rotate() for further details.
*
* \sa rotate()
*/
template<typename Scalar, int Dim>
template<typename RotationType>
Transform<Scalar,Dim>&
Transform<Scalar,Dim>::prerotate(const RotationType& rotation)
{
m_matrix.template block<Dim,HDim>(0,0) = ei_toRotationMatrix<Scalar,Dim>(rotation)
* m_matrix.template block<Dim,HDim>(0,0);
return *this;
}
/** Applies on the right the shear transformation represented
* by the vector \a other to \c *this and returns a reference to \c *this.
* \warning 2D only.
* \sa preshear()
*/
template<typename Scalar, int Dim>
Transform<Scalar,Dim>&
Transform<Scalar,Dim>::shear(Scalar sx, Scalar sy)
{
EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
VectorType tmp = linear().col(0)*sy + linear().col(1);
linear() << linear().col(0) + linear().col(1)*sx, tmp;
return *this;
}
/** Applies on the left the shear transformation represented
* by the vector \a other to \c *this and returns a reference to \c *this.
* \warning 2D only.
* \sa shear()
*/
template<typename Scalar, int Dim>
Transform<Scalar,Dim>&
Transform<Scalar,Dim>::preshear(Scalar sx, Scalar sy)
{
EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
m_matrix.template block<Dim,HDim>(0,0) = LinearMatrixType(1, sx, sy, 1) * m_matrix.template block<Dim,HDim>(0,0);
return *this;
}
/******************************************************
*** Scaling, Translation and Rotation compatibility ***
******************************************************/
template<typename Scalar, int Dim>
inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const TranslationType& t)
{
linear().setIdentity();
translation() = t.vector();
m_matrix.template block<1,Dim>(Dim,0).setZero();
m_matrix(Dim,Dim) = Scalar(1);
return *this;
}
template<typename Scalar, int Dim>
inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const TranslationType& t) const
{
Transform res = *this;
res.translate(t.vector());
return res;
}
template<typename Scalar, int Dim>
inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const ScalingType& s)
{
m_matrix.setZero();
linear().diagonal() = s.coeffs();
m_matrix.coeffRef(Dim,Dim) = Scalar(1);
return *this;
}
template<typename Scalar, int Dim>
inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const ScalingType& s) const
{
Transform res = *this;
res.scale(s.coeffs());
return res;
}
template<typename Scalar, int Dim>
template<typename Derived>
inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const RotationBase<Derived,Dim>& r)
{
linear() = ei_toRotationMatrix<Scalar,Dim>(r);
translation().setZero();
m_matrix.template block<1,Dim>(Dim,0).setZero();
m_matrix.coeffRef(Dim,Dim) = Scalar(1);
return *this;
}
template<typename Scalar, int Dim>
template<typename Derived>
inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const RotationBase<Derived,Dim>& r) const
{
Transform res = *this;
res.rotate(r.derived());
return res;
}
/************************
*** Special functions ***
************************/
/** \returns the rotation part of the transformation
* \nonstableyet
*
* \svd_module
*
* \sa computeRotationScaling(), computeScalingRotation(), class SVD
*/
template<typename Scalar, int Dim>
typename Transform<Scalar,Dim>::LinearMatrixType
Transform<Scalar,Dim>::rotation() const
{
LinearMatrixType result;
computeRotationScaling(&result, (LinearMatrixType*)0);
return result;
}
/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being
* not necessarily positive.
*
* If either pointer is zero, the corresponding computation is skipped.
*
* \nonstableyet
*
* \svd_module
*
* \sa computeScalingRotation(), rotation(), class SVD
*/
template<typename Scalar, int Dim>
template<typename RotationMatrixType, typename ScalingMatrixType>
void Transform<Scalar,Dim>::computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const
{
JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU|ComputeFullV);
Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1
Matrix<Scalar, Dim, 1> sv(svd.singularValues());
sv.coeffRef(0) *= x;
if(scaling)
{
scaling->noalias() = svd.matrixV() * sv.asDiagonal() * svd.matrixV().adjoint();
}
if(rotation)
{
LinearMatrixType m(svd.matrixU());
m.col(0) /= x;
rotation->noalias() = m * svd.matrixV().adjoint();
}
}
/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being
* not necessarily positive.
*
* If either pointer is zero, the corresponding computation is skipped.
*
* \nonstableyet
*
* \svd_module
*
* \sa computeRotationScaling(), rotation(), class SVD
*/
template<typename Scalar, int Dim>
template<typename ScalingMatrixType, typename RotationMatrixType>
void Transform<Scalar,Dim>::computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const
{
JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU|ComputeFullV);
Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1
Matrix<Scalar, Dim, 1> sv(svd.singularValues());
sv.coeffRef(0) *= x;
if(scaling)
{
scaling->noalias() = svd.matrixU() * sv.asDiagonal() * svd.matrixU().adjoint();
}
if(rotation)
{
LinearMatrixType m(svd.matrixU());
m.col(0) /= x;
rotation->noalias() = m * svd.matrixV().adjoint();
}
}
/** Convenient method to set \c *this from a position, orientation and scale
* of a 3D object.
*/
template<typename Scalar, int Dim>
template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
Transform<Scalar,Dim>&
Transform<Scalar,Dim>::fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale)
{
linear() = ei_toRotationMatrix<Scalar,Dim>(orientation);
linear() *= scale.asDiagonal();
translation() = position;
m_matrix.template block<1,Dim>(Dim,0).setZero();
m_matrix(Dim,Dim) = Scalar(1);
return *this;
}
/** \nonstableyet
*
* \returns the inverse transformation matrix according to some given knowledge
* on \c *this.
*
* \param traits allows to optimize the inversion process when the transformion
* is known to be not a general transformation. The possible values are:
* - Projective if the transformation is not necessarily affine, i.e., if the
* last row is not guaranteed to be [0 ... 0 1]
* - Affine is the default, the last row is assumed to be [0 ... 0 1]
* - Isometry if the transformation is only a concatenations of translations
* and rotations.
*
* \warning unless \a traits is always set to NoShear or NoScaling, this function
* requires the generic inverse method of MatrixBase defined in the LU module. If
* you forget to include this module, then you will get hard to debug linking errors.
*
* \sa MatrixBase::inverse()
*/
template<typename Scalar, int Dim>
inline const typename Transform<Scalar,Dim>::MatrixType
Transform<Scalar,Dim>::inverse(TransformTraits traits) const
{
if (traits == Projective)
{
return m_matrix.inverse();
}
else
{
MatrixType res;
if (traits == Affine)
{
res.template corner<Dim,Dim>(TopLeft) = linear().inverse();
}
else if (traits == Isometry)
{
res.template corner<Dim,Dim>(TopLeft) = linear().transpose();
}
else
{
ei_assert("invalid traits value in Transform::inverse()");
}
// translation and remaining parts
res.template corner<Dim,1>(TopRight) = - res.template corner<Dim,Dim>(TopLeft) * translation();
res.template corner<1,Dim>(BottomLeft).setZero();
res.coeffRef(Dim,Dim) = Scalar(1);
return res;
}
}
/*****************************************************
*** Specializations of operator* with a MatrixBase ***
*****************************************************/
template<typename Other, int Dim, int HDim>
struct ei_transform_product_impl<Other,Dim,HDim, HDim,HDim>
{
typedef Transform<typename Other::Scalar,Dim> TransformType;
typedef typename TransformType::MatrixType MatrixType;
typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
static ResultType run(const TransformType& tr, const Other& other)
{ return tr.matrix() * other; }
};
template<typename Other, int Dim, int HDim>
struct ei_transform_product_impl<Other,Dim,HDim, Dim,Dim>
{
typedef Transform<typename Other::Scalar,Dim> TransformType;
typedef typename TransformType::MatrixType MatrixType;
typedef TransformType ResultType;
static ResultType run(const TransformType& tr, const Other& other)
{
TransformType res;
res.translation() = tr.translation();
res.matrix().row(Dim) = tr.matrix().row(Dim);
res.linear() = (tr.linear() * other).lazy();
return res;
}
};
template<typename Other, int Dim, int HDim>
struct ei_transform_product_impl<Other,Dim,HDim, HDim,1>
{
typedef Transform<typename Other::Scalar,Dim> TransformType;
typedef typename TransformType::MatrixType MatrixType;
typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
static ResultType run(const TransformType& tr, const Other& other)
{ return tr.matrix() * other; }
};
template<typename Other, int Dim, int HDim>
struct ei_transform_product_impl<Other,Dim,HDim, Dim,1>
{
typedef typename Other::Scalar Scalar;
typedef Transform<Scalar,Dim> TransformType;
typedef Matrix<Scalar,Dim,1> ResultType;
static ResultType run(const TransformType& tr, const Other& other)
{ return ((tr.linear() * other) + tr.translation())
* (Scalar(1) / ( (tr.matrix().template block<1,Dim>(Dim,0) * other).coeff(0) + tr.matrix().coeff(Dim,Dim))); }
};
} // end namespace Eigen