// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2010 Hauke Heibel <hauke.heibel@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/.
#ifndef EIGEN_TRANSFORM_H
#define EIGEN_TRANSFORM_H
namespace Eigen {
namespace internal {
template<typename Transform>
struct transform_traits
{
enum
{
Dim = Transform::Dim,
HDim = Transform::HDim,
Mode = Transform::Mode,
IsProjective = (int(Mode)==int(Projective))
};
};
template< typename TransformType,
typename MatrixType,
int Case = transform_traits<TransformType>::IsProjective ? 0
: int(MatrixType::RowsAtCompileTime) == int(transform_traits<TransformType>::HDim) ? 1
: 2,
int RhsCols = MatrixType::ColsAtCompileTime>
struct transform_right_product_impl;
template< typename Other,
int Mode,
int Options,
int Dim,
int HDim,
int OtherRows=Other::RowsAtCompileTime,
int OtherCols=Other::ColsAtCompileTime>
struct transform_left_product_impl;
template< typename Lhs,
typename Rhs,
bool AnyProjective =
transform_traits<Lhs>::IsProjective ||
transform_traits<Rhs>::IsProjective>
struct transform_transform_product_impl;
template< typename Other,
int Mode,
int Options,
int Dim,
int HDim,
int OtherRows=Other::RowsAtCompileTime,
int OtherCols=Other::ColsAtCompileTime>
struct transform_construct_from_matrix;
template<typename TransformType> struct transform_take_affine_part;
template<typename _Scalar, int _Dim, int _Mode, int _Options>
struct traits<Transform<_Scalar,_Dim,_Mode,_Options> >
{
typedef _Scalar Scalar;
typedef Eigen::Index StorageIndex;
typedef Dense StorageKind;
enum {
Dim1 = _Dim==Dynamic ? _Dim : _Dim + 1,
RowsAtCompileTime = _Mode==Projective ? Dim1 : _Dim,
ColsAtCompileTime = Dim1,
MaxRowsAtCompileTime = RowsAtCompileTime,
MaxColsAtCompileTime = ColsAtCompileTime,
Flags = 0
};
};
template<int Mode> struct transform_make_affine;
} // end namespace internal
/** \geometry_module \ingroup Geometry_Module
*
* \class Transform
*
* \brief Represents an homogeneous transformation in a N dimensional space
*
* \tparam _Scalar the scalar type, i.e., the type of the coefficients
* \tparam _Dim the dimension of the space
* \tparam _Mode the type of the transformation. Can be:
* - #Affine: the transformation is stored as a (Dim+1)^2 matrix,
* where the last row is assumed to be [0 ... 0 1].
* - #AffineCompact: the transformation is stored as a (Dim)x(Dim+1) matrix.
* - #Projective: the transformation is stored as a (Dim+1)^2 matrix
* without any assumption.
* \tparam _Options has the same meaning as in class Matrix. It allows to specify DontAlign and/or RowMajor.
* These Options are passed directly to the underlying matrix type.
*
* The homography is internally represented and stored by a matrix which
* is available through the matrix() method. To understand the behavior of
* this class you have to think a Transform object as its internal
* matrix representation. The chosen convention is right multiply:
*
* \code v' = T * v \endcode
*
* Therefore, an affine transformation matrix M is shaped like this:
*
* \f$ \left( \begin{array}{cc}
* linear & translation\\
* 0 ... 0 & 1
* \end{array} \right) \f$
*
* Note that for a projective transformation the last row can be anything,
* and then the interpretation of different parts might be sightly different.
*
* However, unlike a plain matrix, the Transform class provides many features
* simplifying both its assembly and usage. In particular, it can be composed
* with any other transformations (Transform,Translation,RotationBase,DiagonalMatrix)
* and can be directly used to transform implicit homogeneous vectors. All these
* operations are handled via the operator*. For the composition of transformations,
* its principle consists to first convert the right/left hand sides of the product
* to a compatible (Dim+1)^2 matrix and then perform a pure matrix product.
* Of course, internally, operator* tries to perform the minimal number of operations
* according to the nature of each terms. Likewise, when applying the transform
* to points, the latters are automatically promoted to homogeneous vectors
* before doing the matrix product. The conventions to homogeneous representations
* are performed as follow:
*
* \b Translation t (Dim)x(1):
* \f$ \left( \begin{array}{cc}
* I & t \\
* 0\,...\,0 & 1
* \end{array} \right) \f$
*
* \b Rotation R (Dim)x(Dim):
* \f$ \left( \begin{array}{cc}
* R & 0\\
* 0\,...\,0 & 1
* \end{array} \right) \f$
*<!--
* \b Linear \b Matrix L (Dim)x(Dim):
* \f$ \left( \begin{array}{cc}
* L & 0\\
* 0\,...\,0 & 1
* \end{array} \right) \f$
*
* \b Affine \b Matrix A (Dim)x(Dim+1):
* \f$ \left( \begin{array}{c}
* A\\
* 0\,...\,0\,1
* \end{array} \right) \f$
*-->
* \b Scaling \b DiagonalMatrix S (Dim)x(Dim):
* \f$ \left( \begin{array}{cc}
* S & 0\\
* 0\,...\,0 & 1
* \end{array} \right) \f$
*
* \b Column \b point v (Dim)x(1):
* \f$ \left( \begin{array}{c}
* v\\
* 1
* \end{array} \right) \f$
*
* \b Set \b of \b column \b points V1...Vn (Dim)x(n):
* \f$ \left( \begin{array}{ccc}
* v_1 & ... & v_n\\
* 1 & ... & 1
* \end{array} \right) \f$
*
* The concatenation of a Transform object with any kind of other transformation
* always returns a Transform object.
*
* A little exception to the "as pure matrix product" rule is the case of the
* transformation of non homogeneous vectors by an affine transformation. In
* that case the last matrix row can be ignored, and the product returns non
* homogeneous vectors.
*
* Since, for instance, a Dim x Dim matrix is interpreted as a linear transformation,
* it is not possible to directly transform Dim vectors stored in a Dim x Dim matrix.
* The solution is either to use a Dim x Dynamic matrix or explicitly request a
* vector transformation by making the vector homogeneous:
* \code
* m' = T * m.colwise().homogeneous();
* \endcode
* Note that there is zero overhead.
*
* Conversion methods from/to Qt's QMatrix and QTransform are available if the
* preprocessor token EIGEN_QT_SUPPORT is defined.
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_TRANSFORM_PLUGIN.
*
* \sa class Matrix, class Quaternion
*/
template<typename _Scalar, int _Dim, int _Mode, int _Options>
class Transform
{
public:
EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim==Dynamic ? Dynamic : (_Dim+1)*(_Dim+1))
enum {
Mode = _Mode,
Options = _Options,
Dim = _Dim, ///< space dimension in which the transformation holds
HDim = _Dim+1, ///< size of a respective homogeneous vector
Rows = int(Mode)==(AffineCompact) ? Dim : HDim
};
/** the scalar type of the coefficients */
typedef _Scalar Scalar;
typedef Eigen::Index StorageIndex;
typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
/** type of the matrix used to represent the transformation */
typedef typename internal::make_proper_matrix_type<Scalar,Rows,HDim,Options>::type MatrixType;
/** constified MatrixType */
typedef const MatrixType ConstMatrixType;
/** type of the matrix used to represent the linear part of the transformation */
typedef Matrix<Scalar,Dim,Dim,Options> LinearMatrixType;
/** type of read/write reference to the linear part of the transformation */
typedef Block<MatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (Options&RowMajor)==0> LinearPart;
/** type of read reference to the linear part of the transformation */
typedef const Block<ConstMatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (Options&RowMajor)==0> ConstLinearPart;
/** type of read/write reference to the affine part of the transformation */
typedef typename internal::conditional<int(Mode)==int(AffineCompact),
MatrixType&,
Block<MatrixType,Dim,HDim> >::type AffinePart;
/** type of read reference to the affine part of the transformation */
typedef typename internal::conditional<int(Mode)==int(AffineCompact),
const MatrixType&,
const Block<const MatrixType,Dim,HDim> >::type ConstAffinePart;
/** 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,!(internal::traits<MatrixType>::Flags & RowMajorBit)> TranslationPart;
/** type of a read reference to the translation part of the rotation */
typedef const Block<ConstMatrixType,Dim,1,!(internal::traits<MatrixType>::Flags & RowMajorBit)> ConstTranslationPart;
/** corresponding translation type */
typedef Translation<Scalar,Dim> TranslationType;
// this intermediate enum is needed to avoid an ICE with gcc 3.4 and 4.0
enum { TransformTimeDiagonalMode = ((Mode==int(Isometry))?Affine:int(Mode)) };
/** The return type of the product between a diagonal matrix and a transform */
typedef Transform<Scalar,Dim,TransformTimeDiagonalMode> TransformTimeDiagonalReturnType;
protected:
MatrixType m_matrix;
public:
/** Default constructor without initialization of the meaningful coefficients.
* If Mode==Affine, then the last row is set to [0 ... 0 1] */
EIGEN_DEVICE_FUNC inline Transform()
{
check_template_params();
internal::transform_make_affine<(int(Mode)==Affine) ? Affine : AffineCompact>::run(m_matrix);
}
EIGEN_DEVICE_FUNC inline Transform(const Transform& other)
{
check_template_params();
m_matrix = other.m_matrix;
}
EIGEN_DEVICE_FUNC inline explicit Transform(const TranslationType& t)
{
check_template_params();
*this = t;
}
EIGEN_DEVICE_FUNC inline explicit Transform(const UniformScaling<Scalar>& s)
{
check_template_params();
*this = s;
}
template<typename Derived>
EIGEN_DEVICE_FUNC inline explicit Transform(const RotationBase<Derived, Dim>& r)
{
check_template_params();
*this = r;
}
EIGEN_DEVICE_FUNC inline Transform& operator=(const Transform& other)
{ m_matrix = other.m_matrix; return *this; }
typedef internal::transform_take_affine_part<Transform> take_affine_part;
/** Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. */
template<typename OtherDerived>
EIGEN_DEVICE_FUNC inline explicit Transform(const EigenBase<OtherDerived>& other)
{
EIGEN_STATIC_ASSERT((internal::is_same<Scalar,typename OtherDerived::Scalar>::value),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY);
check_template_params();
internal::transform_construct_from_matrix<OtherDerived,Mode,Options,Dim,HDim>::run(this, other.derived());
}
/** Set \c *this from a Dim^2 or (Dim+1)^2 matrix. */
template<typename OtherDerived>
EIGEN_DEVICE_FUNC inline Transform& operator=(const EigenBase<OtherDerived>& other)
{
EIGEN_STATIC_ASSERT((internal::is_same<Scalar,typename OtherDerived::Scalar>::value),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY);
internal::transform_construct_from_matrix<OtherDerived,Mode,Options,Dim,HDim>::run(this, other.derived());
return *this;
}
template<int OtherOptions>
EIGEN_DEVICE_FUNC inline Transform(const Transform<Scalar,Dim,Mode,OtherOptions>& other)
{
check_template_params();
// only the options change, we can directly copy the matrices
m_matrix = other.matrix();
}
template<int OtherMode,int OtherOptions>
EIGEN_DEVICE_FUNC inline Transform(const Transform<Scalar,Dim,OtherMode,OtherOptions>& other)
{
check_template_params();
// prevent conversions as:
// Affine | AffineCompact | Isometry = Projective
EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(OtherMode==int(Projective), Mode==int(Projective)),
YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION)
// prevent conversions as:
// Isometry = Affine | AffineCompact
EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(OtherMode==int(Affine)||OtherMode==int(AffineCompact), Mode!=int(Isometry)),
YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION)
enum { ModeIsAffineCompact = Mode == int(AffineCompact),
OtherModeIsAffineCompact = OtherMode == int(AffineCompact)
};
if(ModeIsAffineCompact == OtherModeIsAffineCompact)
{
// We need the block expression because the code is compiled for all
// combinations of transformations and will trigger a compile time error
// if one tries to assign the matrices directly
m_matrix.template block<Dim,Dim+1>(0,0) = other.matrix().template block<Dim,Dim+1>(0,0);
makeAffine();
}
else if(OtherModeIsAffineCompact)
{
typedef typename Transform<Scalar,Dim,OtherMode,OtherOptions>::MatrixType OtherMatrixType;
internal::transform_construct_from_matrix<OtherMatrixType,Mode,Options,Dim,HDim>::run(this, other.matrix());
}
else
{
// here we know that Mode == AffineCompact and OtherMode != AffineCompact.
// if OtherMode were Projective, the static assert above would already have caught it.
// So the only possibility is that OtherMode == Affine
linear() = other.linear();
translation() = other.translation();
}
}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC Transform(const ReturnByValue<OtherDerived>& other)
{
check_template_params();
other.evalTo(*this);
}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC Transform& operator=(const ReturnByValue<OtherDerived>& other)
{
other.evalTo(*this);
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
EIGEN_DEVICE_FUNC Index rows() const { return int(Mode)==int(Projective) ? m_matrix.cols() : (m_matrix.cols()-1); }
EIGEN_DEVICE_FUNC Index cols() const { return m_matrix.cols(); }
/** shortcut for m_matrix(row,col);
* \sa MatrixBase::operator(Index,Index) const */
EIGEN_DEVICE_FUNC inline Scalar operator() (Index row, Index col) const { return m_matrix(row,col); }
/** shortcut for m_matrix(row,col);
* \sa MatrixBase::operator(Index,Index) */
EIGEN_DEVICE_FUNC inline Scalar& operator() (Index row, Index col) { return m_matrix(row,col); }
/** \returns a read-only expression of the transformation matrix */
EIGEN_DEVICE_FUNC inline const MatrixType& matrix() const { return m_matrix; }
/** \returns a writable expression of the transformation matrix */
EIGEN_DEVICE_FUNC inline MatrixType& matrix() { return m_matrix; }
/** \returns a read-only expression of the linear part of the transformation */
EIGEN_DEVICE_FUNC inline ConstLinearPart linear() const { return ConstLinearPart(m_matrix,0,0); }
/** \returns a writable expression of the linear part of the transformation */
EIGEN_DEVICE_FUNC inline LinearPart linear() { return LinearPart(m_matrix,0,0); }
/** \returns a read-only expression of the Dim x HDim affine part of the transformation */
EIGEN_DEVICE_FUNC inline ConstAffinePart affine() const { return take_affine_part::run(m_matrix); }
/** \returns a writable expression of the Dim x HDim affine part of the transformation */
EIGEN_DEVICE_FUNC inline AffinePart affine() { return take_affine_part::run(m_matrix); }
/** \returns a read-only expression of the translation vector of the transformation */
EIGEN_DEVICE_FUNC inline ConstTranslationPart translation() const { return ConstTranslationPart(m_matrix,0,Dim); }
/** \returns a writable expression of the translation vector of the transformation */
EIGEN_DEVICE_FUNC inline TranslationPart translation() { return TranslationPart(m_matrix,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 can be either:
* \li an homogeneous vector of size Dim+1,
* \li a set of homogeneous vectors of size Dim+1 x N,
* \li a transformation matrix of size Dim+1 x Dim+1.
*
* Moreover, if \c *this represents an affine transformation (i.e., Mode!=Projective), then \a other can also be:
* \li a point of size Dim (computes: \code this->linear() * other + this->translation()\endcode),
* \li a set of N points as a Dim x N matrix (computes: \code (this->linear() * other).colwise() + this->translation()\endcode),
*
* In all cases, the return type is a matrix or vector of same sizes as the right-hand-side \a other.
*
* If you want to interpret \a other as a linear or affine transformation, then first convert it to a Transform<> type,
* or do your own cooking.
*
* Finally, if you want to apply Affine transformations to vectors, then explicitly apply the linear part only:
* \code
* Affine3f A;
* Vector3f v1, v2;
* v2 = A.linear() * v1;
* \endcode
*
*/
// note: this function is defined here because some compilers cannot find the respective declaration
template<typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename internal::transform_right_product_impl<Transform, OtherDerived>::ResultType
operator * (const EigenBase<OtherDerived> &other) const
{ return internal::transform_right_product_impl<Transform, OtherDerived>::run(*this,other.derived()); }
/** \returns the product expression of a transformation matrix \a a times a transform \a b
*
* The left hand side \a other can be either:
* \li a linear transformation matrix of size Dim x Dim,
* \li an affine transformation matrix of size Dim x Dim+1,
* \li a general transformation matrix of size Dim+1 x Dim+1.
*/
template<typename OtherDerived> friend
EIGEN_DEVICE_FUNC inline const typename internal::transform_left_product_impl<OtherDerived,Mode,Options,_Dim,_Dim+1>::ResultType
operator * (const EigenBase<OtherDerived> &a, const Transform &b)
{ return internal::transform_left_product_impl<OtherDerived,Mode,Options,Dim,HDim>::run(a.derived(),b); }
/** \returns The product expression of a transform \a a times a diagonal matrix \a b
*
* The rhs diagonal matrix is interpreted as an affine scaling transformation. The
* product results in a Transform of the same type (mode) as the lhs only if the lhs
* mode is no isometry. In that case, the returned transform is an affinity.
*/
template<typename DiagonalDerived>
EIGEN_DEVICE_FUNC inline const TransformTimeDiagonalReturnType
operator * (const DiagonalBase<DiagonalDerived> &b) const
{
TransformTimeDiagonalReturnType res(*this);
res.linearExt() *= b;
return res;
}
/** \returns The product expression of a diagonal matrix \a a times a transform \a b
*
* The lhs diagonal matrix is interpreted as an affine scaling transformation. The
* product results in a Transform of the same type (mode) as the lhs only if the lhs
* mode is no isometry. In that case, the returned transform is an affinity.
*/
template<typename DiagonalDerived>
EIGEN_DEVICE_FUNC friend inline TransformTimeDiagonalReturnType
operator * (const DiagonalBase<DiagonalDerived> &a, const Transform &b)
{
TransformTimeDiagonalReturnType res;
res.linear().noalias() = a*b.linear();
res.translation().noalias() = a*b.translation();
if (Mode!=int(AffineCompact))
res.matrix().row(Dim) = b.matrix().row(Dim);
return res;
}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC inline Transform& operator*=(const EigenBase<OtherDerived>& other) { return *this = *this * other; }
/** Concatenates two transformations */
EIGEN_DEVICE_FUNC inline const Transform operator * (const Transform& other) const
{
return internal::transform_transform_product_impl<Transform,Transform>::run(*this,other);
}
#if EIGEN_COMP_ICC
private:
// this intermediate structure permits to workaround a bug in ICC 11:
// error: template instantiation resulted in unexpected function type of "Eigen::Transform<double, 3, 32, 0>
// (const Eigen::Transform<double, 3, 2, 0> &) const"
// (the meaning of a name may have changed since the template declaration -- the type of the template is:
// "Eigen::internal::transform_transform_product_impl<Eigen::Transform<double, 3, 32, 0>,
// Eigen::Transform<double, 3, Mode, Options>, <expression>>::ResultType (const Eigen::Transform<double, 3, Mode, Options> &) const")
//
template<int OtherMode,int OtherOptions> struct icc_11_workaround
{
typedef internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> > ProductType;
typedef typename ProductType::ResultType ResultType;
};
public:
/** Concatenates two different transformations */
template<int OtherMode,int OtherOptions>
inline typename icc_11_workaround<OtherMode,OtherOptions>::ResultType
operator * (const Transform<Scalar,Dim,OtherMode,OtherOptions>& other) const
{
typedef typename icc_11_workaround<OtherMode,OtherOptions>::ProductType ProductType;
return ProductType::run(*this,other);
}
#else
/** Concatenates two different transformations */
template<int OtherMode,int OtherOptions>
EIGEN_DEVICE_FUNC inline typename internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> >::ResultType
operator * (const Transform<Scalar,Dim,OtherMode,OtherOptions>& other) const
{
return internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> >::run(*this,other);
}
#endif
/** \sa MatrixBase::setIdentity() */
EIGEN_DEVICE_FUNC void setIdentity() { m_matrix.setIdentity(); }
/**
* \brief Returns an identity transformation.
* \todo In the future this function should be returning a Transform expression.
*/
EIGEN_DEVICE_FUNC static const Transform Identity()
{
return Transform(MatrixType::Identity());
}
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
inline Transform& scale(const MatrixBase<OtherDerived> &other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
inline Transform& prescale(const MatrixBase<OtherDerived> &other);
EIGEN_DEVICE_FUNC inline Transform& scale(const Scalar& s);
EIGEN_DEVICE_FUNC inline Transform& prescale(const Scalar& s);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
inline Transform& translate(const MatrixBase<OtherDerived> &other);
template<typename OtherDerived>
EIGEN_DEVICE_FUNC
inline Transform& pretranslate(const MatrixBase<OtherDerived> &other);
template<typename RotationType>
EIGEN_DEVICE_FUNC
inline Transform& rotate(const RotationType& rotation);
template<typename RotationType>
EIGEN_DEVICE_FUNC
inline Transform& prerotate(const RotationType& rotation);
EIGEN_DEVICE_FUNC Transform& shear(const Scalar& sx, const Scalar& sy);
EIGEN_DEVICE_FUNC Transform& preshear(const Scalar& sx, const Scalar& sy);
EIGEN_DEVICE_FUNC inline Transform& operator=(const TranslationType& t);
EIGEN_DEVICE_FUNC
inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); }
EIGEN_DEVICE_FUNC inline Transform operator*(const TranslationType& t) const;
EIGEN_DEVICE_FUNC
inline Transform& operator=(const UniformScaling<Scalar>& t);
EIGEN_DEVICE_FUNC
inline Transform& operator*=(const UniformScaling<Scalar>& s) { return scale(s.factor()); }
EIGEN_DEVICE_FUNC
inline TransformTimeDiagonalReturnType operator*(const UniformScaling<Scalar>& s) const
{
TransformTimeDiagonalReturnType res = *this;
res.scale(s.factor());
return res;
}
EIGEN_DEVICE_FUNC
inline Transform& operator*=(const DiagonalMatrix<Scalar,Dim>& s) { linearExt() *= s; return *this; }
template<typename Derived>
EIGEN_DEVICE_FUNC inline Transform& operator=(const RotationBase<Derived,Dim>& r);
template<typename Derived>
EIGEN_DEVICE_FUNC inline Transform& operator*=(const RotationBase<Derived,Dim>& r) { return rotate(r.toRotationMatrix()); }
template<typename Derived>
EIGEN_DEVICE_FUNC inline Transform operator*(const RotationBase<Derived,Dim>& r) const;
EIGEN_DEVICE_FUNC const LinearMatrixType rotation() const;
template<typename RotationMatrixType, typename ScalingMatrixType>
EIGEN_DEVICE_FUNC
void computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const;
template<typename ScalingMatrixType, typename RotationMatrixType>
EIGEN_DEVICE_FUNC
void computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const;
template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
EIGEN_DEVICE_FUNC
Transform& fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale);
EIGEN_DEVICE_FUNC
inline Transform inverse(TransformTraits traits = (TransformTraits)Mode) const;
/** \returns a const pointer to the column major internal matrix */
EIGEN_DEVICE_FUNC const Scalar* data() const { return m_matrix.data(); }
/** \returns a non-const pointer to the column major internal matrix */
EIGEN_DEVICE_FUNC 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>
EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim,Mode,Options> >::type cast() const
{ return typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim,Mode,Options> >::type(*this); }
/** Copy constructor with scalar type conversion */
template<typename OtherScalarType>
EIGEN_DEVICE_FUNC inline explicit Transform(const Transform<OtherScalarType,Dim,Mode,Options>& other)
{
check_template_params();
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() */
EIGEN_DEVICE_FUNC bool isApprox(const Transform& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
{ return m_matrix.isApprox(other.m_matrix, prec); }
/** Sets the last row to [0 ... 0 1]
*/
EIGEN_DEVICE_FUNC void makeAffine()
{
internal::transform_make_affine<int(Mode)>::run(m_matrix);
}
/** \internal
* \returns the Dim x Dim linear part if the transformation is affine,
* and the HDim x Dim part for projective transformations.
*/
EIGEN_DEVICE_FUNC inline Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,Dim> linearExt()
{ return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,Dim>(0,0); }
/** \internal
* \returns the Dim x Dim linear part if the transformation is affine,
* and the HDim x Dim part for projective transformations.
*/
EIGEN_DEVICE_FUNC inline const Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,Dim> linearExt() const
{ return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,Dim>(0,0); }
/** \internal
* \returns the translation part if the transformation is affine,
* and the last column for projective transformations.
*/
EIGEN_DEVICE_FUNC inline Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,1> translationExt()
{ return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,1>(0,Dim); }
/** \internal
* \returns the translation part if the transformation is affine,
* and the last column for projective transformations.
*/
EIGEN_DEVICE_FUNC inline const Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,1> translationExt() const
{ return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,1>(0,Dim); }
#ifdef EIGEN_TRANSFORM_PLUGIN
#include EIGEN_TRANSFORM_PLUGIN
#endif
protected:
#ifndef EIGEN_PARSED_BY_DOXYGEN
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void check_template_params()
{
EIGEN_STATIC_ASSERT((Options & (DontAlign|RowMajor)) == Options, INVALID_MATRIX_TEMPLATE_PARAMETERS)
}
#endif
};
/** \ingroup Geometry_Module */
typedef Transform<float,2,Isometry> Isometry2f;
/** \ingroup Geometry_Module */
typedef Transform<float,3,Isometry> Isometry3f;
/** \ingroup Geometry_Module */
typedef Transform<double,2,Isometry> Isometry2d;
/** \ingroup Geometry_Module */
typedef Transform<double,3,Isometry> Isometry3d;
/** \ingroup Geometry_Module */
typedef Transform<float,2,Affine> Affine2f;
/** \ingroup Geometry_Module */
typedef Transform<float,3,Affine> Affine3f;
/** \ingroup Geometry_Module */
typedef Transform<double,2,Affine> Affine2d;
/** \ingroup Geometry_Module */
typedef Transform<double,3,Affine> Affine3d;
/** \ingroup Geometry_Module */
typedef Transform<float,2,AffineCompact> AffineCompact2f;
/** \ingroup Geometry_Module */
typedef Transform<float,3,AffineCompact> AffineCompact3f;
/** \ingroup Geometry_Module */
typedef Transform<double,2,AffineCompact> AffineCompact2d;
/** \ingroup Geometry_Module */
typedef Transform<double,3,AffineCompact> AffineCompact3d;
/** \ingroup Geometry_Module */
typedef Transform<float,2,Projective> Projective2f;
/** \ingroup Geometry_Module */
typedef Transform<float,3,Projective> Projective3f;
/** \ingroup Geometry_Module */
typedef Transform<double,2,Projective> Projective2d;
/** \ingroup Geometry_Module */
typedef Transform<double,3,Projective> Projective3d;
/**************************
*** Optional QT support ***
**************************/
#ifdef EIGEN_QT_SUPPORT
/** Initializes \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, int Mode,int Options>
Transform<Scalar,Dim,Mode,Options>::Transform(const QMatrix& other)
{
check_template_params();
*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, int Mode,int Options>
Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const QMatrix& other)
{
EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
if (Mode == int(AffineCompact))
m_matrix << other.m11(), other.m21(), other.dx(),
other.m12(), other.m22(), other.dy();
else
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 conversion 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, int Mode, int Options>
QMatrix Transform<Scalar,Dim,Mode,Options>::toQMatrix(void) const
{
check_template_params();
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));
}
/** Initializes \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, int Mode,int Options>
Transform<Scalar,Dim,Mode,Options>::Transform(const QTransform& other)
{
check_template_params();
*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, int Mode, int Options>
Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const QTransform& other)
{
check_template_params();
EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
if (Mode == int(AffineCompact))
m_matrix << other.m11(), other.m21(), other.dx(),
other.m12(), other.m22(), other.dy();
else
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, int Mode, int Options>
QTransform Transform<Scalar,Dim,Mode,Options>::toQTransform(void) const
{
EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
if (Mode == int(AffineCompact))
return QTransform(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));
else
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, int Mode, int Options>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
Transform<Scalar,Dim,Mode,Options>::scale(const MatrixBase<OtherDerived> &other)
{
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
linearExt().noalias() = (linearExt() * other.asDiagonal());
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, int Mode, int Options>
EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::scale(const Scalar& s)
{
EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
linearExt() *= 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, int Mode, int Options>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
Transform<Scalar,Dim,Mode,Options>::prescale(const MatrixBase<OtherDerived> &other)
{
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
affine().noalias() = (other.asDiagonal() * affine());
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, int Mode, int Options>
EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::prescale(const Scalar& s)
{
EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
m_matrix.template topRows<Dim>() *= 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, int Mode, int Options>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
Transform<Scalar,Dim,Mode,Options>::translate(const MatrixBase<OtherDerived> &other)
{
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
translationExt() += linearExt() * 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, int Mode, int Options>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
Transform<Scalar,Dim,Mode,Options>::pretranslate(const MatrixBase<OtherDerived> &other)
{
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
if(int(Mode)==int(Projective))
affine() += other * m_matrix.row(Dim);
else
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 internal::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, int Mode, int Options>
template<typename RotationType>
EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
Transform<Scalar,Dim,Mode,Options>::rotate(const RotationType& rotation)
{
linearExt() *= internal::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, int Mode, int Options>
template<typename RotationType>
EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
Transform<Scalar,Dim,Mode,Options>::prerotate(const RotationType& rotation)
{
m_matrix.template block<Dim,HDim>(0,0) = internal::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, int Mode, int Options>
EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
Transform<Scalar,Dim,Mode,Options>::shear(const Scalar& sx, const Scalar& sy)
{
EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
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, int Mode, int Options>
EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
Transform<Scalar,Dim,Mode,Options>::preshear(const Scalar& sx, const Scalar& sy)
{
EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
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, int Mode, int Options>
EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const TranslationType& t)
{
linear().setIdentity();
translation() = t.vector();
makeAffine();
return *this;
}
template<typename Scalar, int Dim, int Mode, int Options>
EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options> Transform<Scalar,Dim,Mode,Options>::operator*(const TranslationType& t) const
{
Transform res = *this;
res.translate(t.vector());
return res;
}
template<typename Scalar, int Dim, int Mode, int Options>
EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const UniformScaling<Scalar>& s)
{
m_matrix.setZero();
linear().diagonal().fill(s.factor());
makeAffine();
return *this;
}
template<typename Scalar, int Dim, int Mode, int Options>
template<typename Derived>
EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const RotationBase<Derived,Dim>& r)
{
linear() = internal::toRotationMatrix<Scalar,Dim>(r);
translation().setZero();
makeAffine();
return *this;
}
template<typename Scalar, int Dim, int Mode, int Options>
template<typename Derived>
EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options> Transform<Scalar,Dim,Mode,Options>::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
*
*
* \svd_module
*
* \sa computeRotationScaling(), computeScalingRotation(), class SVD
*/
template<typename Scalar, int Dim, int Mode, int Options>
EIGEN_DEVICE_FUNC const typename Transform<Scalar,Dim,Mode,Options>::LinearMatrixType
Transform<Scalar,Dim,Mode,Options>::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.
*
*
*
* \svd_module
*
* \sa computeScalingRotation(), rotation(), class SVD
*/
template<typename Scalar, int Dim, int Mode, int Options>
template<typename RotationMatrixType, typename ScalingMatrixType>
EIGEN_DEVICE_FUNC void Transform<Scalar,Dim,Mode,Options>::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
VectorType sv(svd.singularValues());
sv.coeffRef(0) *= x;
if(scaling) scaling->lazyAssign(svd.matrixV() * sv.asDiagonal() * svd.matrixV().adjoint());
if(rotation)
{
LinearMatrixType m(svd.matrixU());
m.col(0) /= x;
rotation->lazyAssign(m * svd.matrixV().adjoint());
}
}
/** decomposes the linear part of the transformation as a product scaling x rotation, the scaling being
* not necessarily positive.
*
* If either pointer is zero, the corresponding computation is skipped.
*
*
*
* \svd_module
*
* \sa computeRotationScaling(), rotation(), class SVD
*/
template<typename Scalar, int Dim, int Mode, int Options>
template<typename ScalingMatrixType, typename RotationMatrixType>
EIGEN_DEVICE_FUNC void Transform<Scalar,Dim,Mode,Options>::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
VectorType sv(svd.singularValues());
sv.coeffRef(0) *= x;
if(scaling) scaling->lazyAssign(svd.matrixU() * sv.asDiagonal() * svd.matrixU().adjoint());
if(rotation)
{
LinearMatrixType m(svd.matrixU());
m.col(0) /= x;
rotation->lazyAssign(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, int Mode, int Options>
template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
Transform<Scalar,Dim,Mode,Options>::fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale)
{
linear() = internal::toRotationMatrix<Scalar,Dim>(orientation);
linear() *= scale.asDiagonal();
translation() = position;
makeAffine();
return *this;
}
namespace internal {
template<int Mode>
struct transform_make_affine
{
template<typename MatrixType>
EIGEN_DEVICE_FUNC static void run(MatrixType &mat)
{
static const int Dim = MatrixType::ColsAtCompileTime-1;
mat.template block<1,Dim>(Dim,0).setZero();
mat.coeffRef(Dim,Dim) = typename MatrixType::Scalar(1);
}
};
template<>
struct transform_make_affine<AffineCompact>
{
template<typename MatrixType> EIGEN_DEVICE_FUNC static void run(MatrixType &) { }
};
// selector needed to avoid taking the inverse of a 3x4 matrix
template<typename TransformType, int Mode=TransformType::Mode>
struct projective_transform_inverse
{
EIGEN_DEVICE_FUNC static inline void run(const TransformType&, TransformType&)
{}
};
template<typename TransformType>
struct projective_transform_inverse<TransformType, Projective>
{
EIGEN_DEVICE_FUNC static inline void run(const TransformType& m, TransformType& res)
{
res.matrix() = m.matrix().inverse();
}
};
} // end namespace internal
/**
*
* \returns the inverse transformation according to some given knowledge
* on \c *this.
*
* \param hint allows to optimize the inversion process when the transformation
* is known to be not a general transformation (optional). 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 if the last row can be assumed to be [0 ... 0 1]
* - #Isometry if the transformation is only a concatenations of translations
* and rotations.
* The default is the template class parameter \c Mode.
*
* \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, int Mode, int Options>
EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>
Transform<Scalar,Dim,Mode,Options>::inverse(TransformTraits hint) const
{
Transform res;
if (hint == Projective)
{
internal::projective_transform_inverse<Transform>::run(*this, res);
}
else
{
if (hint == Isometry)
{
res.matrix().template topLeftCorner<Dim,Dim>() = linear().transpose();
}
else if(hint&Affine)
{
res.matrix().template topLeftCorner<Dim,Dim>() = linear().inverse();
}
else
{
eigen_assert(false && "Invalid transform traits in Transform::Inverse");
}
// translation and remaining parts
res.matrix().template topRightCorner<Dim,1>()
= - res.matrix().template topLeftCorner<Dim,Dim>() * translation();
res.makeAffine(); // we do need this, because in the beginning res is uninitialized
}
return res;
}
namespace internal {
/*****************************************************
*** Specializations of take affine part ***
*****************************************************/
template<typename TransformType> struct transform_take_affine_part {
typedef typename TransformType::MatrixType MatrixType;
typedef typename TransformType::AffinePart AffinePart;
typedef typename TransformType::ConstAffinePart ConstAffinePart;
static inline AffinePart run(MatrixType& m)
{ return m.template block<TransformType::Dim,TransformType::HDim>(0,0); }
static inline ConstAffinePart run(const MatrixType& m)
{ return m.template block<TransformType::Dim,TransformType::HDim>(0,0); }
};
template<typename Scalar, int Dim, int Options>
struct transform_take_affine_part<Transform<Scalar,Dim,AffineCompact, Options> > {
typedef typename Transform<Scalar,Dim,AffineCompact,Options>::MatrixType MatrixType;
static inline MatrixType& run(MatrixType& m) { return m; }
static inline const MatrixType& run(const MatrixType& m) { return m; }
};
/*****************************************************
*** Specializations of construct from matrix ***
*****************************************************/
template<typename Other, int Mode, int Options, int Dim, int HDim>
struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, Dim,Dim>
{
static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
{
transform->linear() = other;
transform->translation().setZero();
transform->makeAffine();
}
};
template<typename Other, int Mode, int Options, int Dim, int HDim>
struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, Dim,HDim>
{
static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
{
transform->affine() = other;
transform->makeAffine();
}
};
template<typename Other, int Mode, int Options, int Dim, int HDim>
struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, HDim,HDim>
{
static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
{ transform->matrix() = other; }
};
template<typename Other, int Options, int Dim, int HDim>
struct transform_construct_from_matrix<Other, AffineCompact,Options,Dim,HDim, HDim,HDim>
{
static inline void run(Transform<typename Other::Scalar,Dim,AffineCompact,Options> *transform, const Other& other)
{ transform->matrix() = other.template block<Dim,HDim>(0,0); }
};
/**********************************************************
*** Specializations of operator* with rhs EigenBase ***
**********************************************************/
template<int LhsMode,int RhsMode>
struct transform_product_result
{
enum
{
Mode =
(LhsMode == (int)Projective || RhsMode == (int)Projective ) ? Projective :
(LhsMode == (int)Affine || RhsMode == (int)Affine ) ? Affine :
(LhsMode == (int)AffineCompact || RhsMode == (int)AffineCompact ) ? AffineCompact :
(LhsMode == (int)Isometry || RhsMode == (int)Isometry ) ? Isometry : Projective
};
};
template< typename TransformType, typename MatrixType, int RhsCols>
struct transform_right_product_impl< TransformType, MatrixType, 0, RhsCols>
{
typedef typename MatrixType::PlainObject ResultType;
static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
{
return T.matrix() * other;
}
};
template< typename TransformType, typename MatrixType, int RhsCols>
struct transform_right_product_impl< TransformType, MatrixType, 1, RhsCols>
{
enum {
Dim = TransformType::Dim,
HDim = TransformType::HDim,
OtherRows = MatrixType::RowsAtCompileTime,
OtherCols = MatrixType::ColsAtCompileTime
};
typedef typename MatrixType::PlainObject ResultType;
static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
{
EIGEN_STATIC_ASSERT(OtherRows==HDim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
typedef Block<ResultType, Dim, OtherCols, int(MatrixType::RowsAtCompileTime)==Dim> TopLeftLhs;
ResultType res(other.rows(),other.cols());
TopLeftLhs(res, 0, 0, Dim, other.cols()).noalias() = T.affine() * other;
res.row(OtherRows-1) = other.row(OtherRows-1);
return res;
}
};
template< typename TransformType, typename MatrixType, int RhsCols>
struct transform_right_product_impl< TransformType, MatrixType, 2, RhsCols>
{
enum {
Dim = TransformType::Dim,
HDim = TransformType::HDim,
OtherRows = MatrixType::RowsAtCompileTime,
OtherCols = MatrixType::ColsAtCompileTime
};
typedef typename MatrixType::PlainObject ResultType;
static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
{
EIGEN_STATIC_ASSERT(OtherRows==Dim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
typedef Block<ResultType, Dim, OtherCols, true> TopLeftLhs;
ResultType res(Replicate<typename TransformType::ConstTranslationPart, 1, OtherCols>(T.translation(),1,other.cols()));
TopLeftLhs(res, 0, 0, Dim, other.cols()).noalias() += T.linear() * other;
return res;
}
};
template< typename TransformType, typename MatrixType >
struct transform_right_product_impl< TransformType, MatrixType, 2, 1> // rhs is a vector of size Dim
{
typedef typename TransformType::MatrixType TransformMatrix;
enum {
Dim = TransformType::Dim,
HDim = TransformType::HDim,
OtherRows = MatrixType::RowsAtCompileTime,
WorkingRows = EIGEN_PLAIN_ENUM_MIN(TransformMatrix::RowsAtCompileTime,HDim)
};
typedef typename MatrixType::PlainObject ResultType;
static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
{
EIGEN_STATIC_ASSERT(OtherRows==Dim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
Matrix<typename ResultType::Scalar, Dim+1, 1> rhs;
rhs.template head<Dim>() = other; rhs[Dim] = typename ResultType::Scalar(1);
Matrix<typename ResultType::Scalar, WorkingRows, 1> res(T.matrix() * rhs);
return res.template head<Dim>();
}
};
/**********************************************************
*** Specializations of operator* with lhs EigenBase ***
**********************************************************/
// generic HDim x HDim matrix * T => Projective
template<typename Other,int Mode, int Options, int Dim, int HDim>
struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, HDim,HDim>
{
typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
typedef typename TransformType::MatrixType MatrixType;
typedef Transform<typename Other::Scalar,Dim,Projective,Options> ResultType;
static ResultType run(const Other& other,const TransformType& tr)
{ return ResultType(other * tr.matrix()); }
};
// generic HDim x HDim matrix * AffineCompact => Projective
template<typename Other, int Options, int Dim, int HDim>
struct transform_left_product_impl<Other,AffineCompact,Options,Dim,HDim, HDim,HDim>
{
typedef Transform<typename Other::Scalar,Dim,AffineCompact,Options> TransformType;
typedef typename TransformType::MatrixType MatrixType;
typedef Transform<typename Other::Scalar,Dim,Projective,Options> ResultType;
static ResultType run(const Other& other,const TransformType& tr)
{
ResultType res;
res.matrix().noalias() = other.template block<HDim,Dim>(0,0) * tr.matrix();
res.matrix().col(Dim) += other.col(Dim);
return res;
}
};
// affine matrix * T
template<typename Other,int Mode, int Options, int Dim, int HDim>
struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, Dim,HDim>
{
typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
typedef typename TransformType::MatrixType MatrixType;
typedef TransformType ResultType;
static ResultType run(const Other& other,const TransformType& tr)
{
ResultType res;
res.affine().noalias() = other * tr.matrix();
res.matrix().row(Dim) = tr.matrix().row(Dim);
return res;
}
};
// affine matrix * AffineCompact
template<typename Other, int Options, int Dim, int HDim>
struct transform_left_product_impl<Other,AffineCompact,Options,Dim,HDim, Dim,HDim>
{
typedef Transform<typename Other::Scalar,Dim,AffineCompact,Options> TransformType;
typedef typename TransformType::MatrixType MatrixType;
typedef TransformType ResultType;
static ResultType run(const Other& other,const TransformType& tr)
{
ResultType res;
res.matrix().noalias() = other.template block<Dim,Dim>(0,0) * tr.matrix();
res.translation() += other.col(Dim);
return res;
}
};
// linear matrix * T
template<typename Other,int Mode, int Options, int Dim, int HDim>
struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, Dim,Dim>
{
typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
typedef typename TransformType::MatrixType MatrixType;
typedef TransformType ResultType;
static ResultType run(const Other& other, const TransformType& tr)
{
TransformType res;
if(Mode!=int(AffineCompact))
res.matrix().row(Dim) = tr.matrix().row(Dim);
res.matrix().template topRows<Dim>().noalias()
= other * tr.matrix().template topRows<Dim>();
return res;
}
};
/**********************************************************
*** Specializations of operator* with another Transform ***
**********************************************************/
template<typename Scalar, int Dim, int LhsMode, int LhsOptions, int RhsMode, int RhsOptions>
struct transform_transform_product_impl<Transform<Scalar,Dim,LhsMode,LhsOptions>,Transform<Scalar,Dim,RhsMode,RhsOptions>,false >
{
enum { ResultMode = transform_product_result<LhsMode,RhsMode>::Mode };
typedef Transform<Scalar,Dim,LhsMode,LhsOptions> Lhs;
typedef Transform<Scalar,Dim,RhsMode,RhsOptions> Rhs;
typedef Transform<Scalar,Dim,ResultMode,LhsOptions> ResultType;
static ResultType run(const Lhs& lhs, const Rhs& rhs)
{
ResultType res;
res.linear() = lhs.linear() * rhs.linear();
res.translation() = lhs.linear() * rhs.translation() + lhs.translation();
res.makeAffine();
return res;
}
};
template<typename Scalar, int Dim, int LhsMode, int LhsOptions, int RhsMode, int RhsOptions>
struct transform_transform_product_impl<Transform<Scalar,Dim,LhsMode,LhsOptions>,Transform<Scalar,Dim,RhsMode,RhsOptions>,true >
{
typedef Transform<Scalar,Dim,LhsMode,LhsOptions> Lhs;
typedef Transform<Scalar,Dim,RhsMode,RhsOptions> Rhs;
typedef Transform<Scalar,Dim,Projective> ResultType;
static ResultType run(const Lhs& lhs, const Rhs& rhs)
{
return ResultType( lhs.matrix() * rhs.matrix() );
}
};
template<typename Scalar, int Dim, int LhsOptions, int RhsOptions>
struct transform_transform_product_impl<Transform<Scalar,Dim,AffineCompact,LhsOptions>,Transform<Scalar,Dim,Projective,RhsOptions>,true >
{
typedef Transform<Scalar,Dim,AffineCompact,LhsOptions> Lhs;
typedef Transform<Scalar,Dim,Projective,RhsOptions> Rhs;
typedef Transform<Scalar,Dim,Projective> ResultType;
static ResultType run(const Lhs& lhs, const Rhs& rhs)
{
ResultType res;
res.matrix().template topRows<Dim>() = lhs.matrix() * rhs.matrix();
res.matrix().row(Dim) = rhs.matrix().row(Dim);
return res;
}
};
template<typename Scalar, int Dim, int LhsOptions, int RhsOptions>
struct transform_transform_product_impl<Transform<Scalar,Dim,Projective,LhsOptions>,Transform<Scalar,Dim,AffineCompact,RhsOptions>,true >
{
typedef Transform<Scalar,Dim,Projective,LhsOptions> Lhs;
typedef Transform<Scalar,Dim,AffineCompact,RhsOptions> Rhs;
typedef Transform<Scalar,Dim,Projective> ResultType;
static ResultType run(const Lhs& lhs, const Rhs& rhs)
{
ResultType res(lhs.matrix().template leftCols<Dim>() * rhs.matrix());
res.matrix().col(Dim) += lhs.matrix().col(Dim);
return res;
}
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_TRANSFORM_H