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- // 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 or Mode==Isometry, 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 || int(Mode)==Isometry) ? 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
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