diff options
Diffstat (limited to 'Eigen/src/Eigen2Support/Geometry/Transform.h')
| -rw-r--r-- | Eigen/src/Eigen2Support/Geometry/Transform.h | 786 |
1 files changed, 0 insertions, 786 deletions
diff --git a/Eigen/src/Eigen2Support/Geometry/Transform.h b/Eigen/src/Eigen2Support/Geometry/Transform.h deleted file mode 100644 index fab60b251..000000000 --- a/Eigen/src/Eigen2Support/Geometry/Transform.h +++ /dev/null @@ -1,786 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> -// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway - -namespace Eigen { - -// Note that we have to pass Dim and HDim because it is not allowed to use a template -// parameter to define a template specialization. To be more precise, in the following -// specializations, it is not allowed to use Dim+1 instead of HDim. -template< typename Other, - int Dim, - int HDim, - int OtherRows=Other::RowsAtCompileTime, - int OtherCols=Other::ColsAtCompileTime> -struct ei_transform_product_impl; - -/** \geometry_module \ingroup Geometry_Module - * - * \class Transform - * - * \brief Represents an homogeneous transformation in a N dimensional space - * - * \param _Scalar the scalar type, i.e., the type of the coefficients - * \param _Dim the dimension of the space - * - * The homography is internally represented and stored as a (Dim+1)^2 matrix which - * is available through the matrix() method. - * - * Conversion methods from/to Qt's QMatrix and QTransform are available if the - * preprocessor token EIGEN_QT_SUPPORT is defined. - * - * \sa class Matrix, class Quaternion - */ -template<typename _Scalar, int _Dim> -class Transform -{ -public: - EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim==Dynamic ? Dynamic : (_Dim+1)*(_Dim+1)) - enum { - Dim = _Dim, ///< space dimension in which the transformation holds - HDim = _Dim+1 ///< size of a respective homogeneous vector - }; - /** the scalar type of the coefficients */ - typedef _Scalar Scalar; - /** type of the matrix used to represent the transformation */ - typedef Matrix<Scalar,HDim,HDim> MatrixType; - /** type of the matrix used to represent the linear part of the transformation */ - typedef Matrix<Scalar,Dim,Dim> LinearMatrixType; - /** type of read/write reference to the linear part of the transformation */ - typedef Block<MatrixType,Dim,Dim> LinearPart; - /** type of read/write reference to the linear part of the transformation */ - typedef const Block<const MatrixType,Dim,Dim> ConstLinearPart; - /** type of a vector */ - typedef Matrix<Scalar,Dim,1> VectorType; - /** type of a read/write reference to the translation part of the rotation */ - typedef Block<MatrixType,Dim,1> TranslationPart; - /** type of a read/write reference to the translation part of the rotation */ - typedef const Block<const MatrixType,Dim,1> ConstTranslationPart; - /** corresponding translation type */ - typedef Translation<Scalar,Dim> TranslationType; - /** corresponding scaling transformation type */ - typedef Scaling<Scalar,Dim> ScalingType; - -protected: - - MatrixType m_matrix; - -public: - - /** Default constructor without initialization of the coefficients. */ - inline Transform() { } - - inline Transform(const Transform& other) - { - m_matrix = other.m_matrix; - } - - inline explicit Transform(const TranslationType& t) { *this = t; } - inline explicit Transform(const ScalingType& s) { *this = s; } - template<typename Derived> - inline explicit Transform(const RotationBase<Derived, Dim>& r) { *this = r; } - - inline Transform& operator=(const Transform& other) - { m_matrix = other.m_matrix; return *this; } - - template<typename OtherDerived, bool BigMatrix> // MSVC 2005 will commit suicide if BigMatrix has a default value - struct construct_from_matrix - { - static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other) - { - transform->matrix() = other; - } - }; - - template<typename OtherDerived> struct construct_from_matrix<OtherDerived, true> - { - static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other) - { - transform->linear() = other; - transform->translation().setZero(); - transform->matrix()(Dim,Dim) = Scalar(1); - transform->matrix().template block<1,Dim>(Dim,0).setZero(); - } - }; - - /** Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. */ - template<typename OtherDerived> - inline explicit Transform(const MatrixBase<OtherDerived>& other) - { - construct_from_matrix<OtherDerived, int(OtherDerived::RowsAtCompileTime) == Dim>::run(this, other); - } - - /** Set \c *this from a (Dim+1)^2 matrix. */ - template<typename OtherDerived> - inline Transform& operator=(const MatrixBase<OtherDerived>& other) - { m_matrix = other; return *this; } - - #ifdef EIGEN_QT_SUPPORT - inline Transform(const QMatrix& other); - inline Transform& operator=(const QMatrix& other); - inline QMatrix toQMatrix(void) const; - inline Transform(const QTransform& other); - inline Transform& operator=(const QTransform& other); - inline QTransform toQTransform(void) const; - #endif - - /** shortcut for m_matrix(row,col); - * \sa MatrixBase::operaror(int,int) const */ - inline Scalar operator() (int row, int col) const { return m_matrix(row,col); } - /** shortcut for m_matrix(row,col); - * \sa MatrixBase::operaror(int,int) */ - inline Scalar& operator() (int row, int col) { return m_matrix(row,col); } - - /** \returns a read-only expression of the transformation matrix */ - inline const MatrixType& matrix() const { return m_matrix; } - /** \returns a writable expression of the transformation matrix */ - inline MatrixType& matrix() { return m_matrix; } - - /** \returns a read-only expression of the linear (linear) part of the transformation */ - inline ConstLinearPart linear() const { return m_matrix.template block<Dim,Dim>(0,0); } - /** \returns a writable expression of the linear (linear) part of the transformation */ - inline LinearPart linear() { return m_matrix.template block<Dim,Dim>(0,0); } - - /** \returns a read-only expression of the translation vector of the transformation */ - inline ConstTranslationPart translation() const { return m_matrix.template block<Dim,1>(0,Dim); } - /** \returns a writable expression of the translation vector of the transformation */ - inline TranslationPart translation() { return m_matrix.template block<Dim,1>(0,Dim); } - - /** \returns an expression of the product between the transform \c *this and a matrix expression \a other - * - * The right hand side \a other might be either: - * \li a vector of size Dim, - * \li an homogeneous vector of size Dim+1, - * \li a transformation matrix of size Dim+1 x Dim+1. - */ - // note: this function is defined here because some compilers cannot find the respective declaration - template<typename OtherDerived> - inline const typename ei_transform_product_impl<OtherDerived,_Dim,_Dim+1>::ResultType - operator * (const MatrixBase<OtherDerived> &other) const - { return ei_transform_product_impl<OtherDerived,Dim,HDim>::run(*this,other.derived()); } - - /** \returns the product expression of a transformation matrix \a a times a transform \a b - * The transformation matrix \a a must have a Dim+1 x Dim+1 sizes. */ - template<typename OtherDerived> - friend inline const typename ProductReturnType<OtherDerived,MatrixType>::Type - operator * (const MatrixBase<OtherDerived> &a, const Transform &b) - { return a.derived() * b.matrix(); } - - /** Contatenates two transformations */ - inline const Transform - operator * (const Transform& other) const - { return Transform(m_matrix * other.matrix()); } - - /** \sa MatrixBase::setIdentity() */ - void setIdentity() { m_matrix.setIdentity(); } - static const typename MatrixType::IdentityReturnType Identity() - { - return MatrixType::Identity(); - } - - template<typename OtherDerived> - inline Transform& scale(const MatrixBase<OtherDerived> &other); - - template<typename OtherDerived> - inline Transform& prescale(const MatrixBase<OtherDerived> &other); - - inline Transform& scale(Scalar s); - inline Transform& prescale(Scalar s); - - template<typename OtherDerived> - inline Transform& translate(const MatrixBase<OtherDerived> &other); - - template<typename OtherDerived> - inline Transform& pretranslate(const MatrixBase<OtherDerived> &other); - - template<typename RotationType> - inline Transform& rotate(const RotationType& rotation); - - template<typename RotationType> - inline Transform& prerotate(const RotationType& rotation); - - Transform& shear(Scalar sx, Scalar sy); - Transform& preshear(Scalar sx, Scalar sy); - - inline Transform& operator=(const TranslationType& t); - inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); } - inline Transform operator*(const TranslationType& t) const; - - inline Transform& operator=(const ScalingType& t); - inline Transform& operator*=(const ScalingType& s) { return scale(s.coeffs()); } - inline Transform operator*(const ScalingType& s) const; - friend inline Transform operator*(const LinearMatrixType& mat, const Transform& t) - { - Transform res = t; - res.matrix().row(Dim) = t.matrix().row(Dim); - res.matrix().template block<Dim,HDim>(0,0) = (mat * t.matrix().template block<Dim,HDim>(0,0)).lazy(); - return res; - } - - template<typename Derived> - inline Transform& operator=(const RotationBase<Derived,Dim>& r); - template<typename Derived> - inline Transform& operator*=(const RotationBase<Derived,Dim>& r) { return rotate(r.toRotationMatrix()); } - template<typename Derived> - inline Transform operator*(const RotationBase<Derived,Dim>& r) const; - - LinearMatrixType rotation() const; - template<typename RotationMatrixType, typename ScalingMatrixType> - void computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const; - template<typename ScalingMatrixType, typename RotationMatrixType> - void computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const; - - template<typename PositionDerived, typename OrientationType, typename ScaleDerived> - Transform& fromPositionOrientationScale(const MatrixBase<PositionDerived> &position, - const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale); - - inline const MatrixType inverse(TransformTraits traits = Affine) const; - - /** \returns a const pointer to the column major internal matrix */ - const Scalar* data() const { return m_matrix.data(); } - /** \returns a non-const pointer to the column major internal matrix */ - Scalar* data() { return m_matrix.data(); } - - /** \returns \c *this with scalar type casted to \a NewScalarType - * - * Note that if \a NewScalarType is equal to the current scalar type of \c *this - * then this function smartly returns a const reference to \c *this. - */ - template<typename NewScalarType> - inline typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type cast() const - { return typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type(*this); } - - /** Copy constructor with scalar type conversion */ - template<typename OtherScalarType> - inline explicit Transform(const Transform<OtherScalarType,Dim>& other) - { m_matrix = other.matrix().template cast<Scalar>(); } - - /** \returns \c true if \c *this is approximately equal to \a other, within the precision - * determined by \a prec. - * - * \sa MatrixBase::isApprox() */ - bool isApprox(const Transform& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const - { return m_matrix.isApprox(other.m_matrix, prec); } - - #ifdef EIGEN_TRANSFORM_PLUGIN - #include EIGEN_TRANSFORM_PLUGIN - #endif - -protected: - -}; - -/** \ingroup Geometry_Module */ -typedef Transform<float,2> Transform2f; -/** \ingroup Geometry_Module */ -typedef Transform<float,3> Transform3f; -/** \ingroup Geometry_Module */ -typedef Transform<double,2> Transform2d; -/** \ingroup Geometry_Module */ -typedef Transform<double,3> Transform3d; - -/************************** -*** Optional QT support *** -**************************/ - -#ifdef EIGEN_QT_SUPPORT -/** Initialises \c *this from a QMatrix assuming the dimension is 2. - * - * This function is available only if the token EIGEN_QT_SUPPORT is defined. - */ -template<typename Scalar, int Dim> -Transform<Scalar,Dim>::Transform(const QMatrix& other) -{ - *this = other; -} - -/** Set \c *this from a QMatrix assuming the dimension is 2. - * - * This function is available only if the token EIGEN_QT_SUPPORT is defined. - */ -template<typename Scalar, int Dim> -Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QMatrix& other) -{ - EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE) - m_matrix << other.m11(), other.m21(), other.dx(), - other.m12(), other.m22(), other.dy(), - 0, 0, 1; - return *this; -} - -/** \returns a QMatrix from \c *this assuming the dimension is 2. - * - * \warning this convertion might loss data if \c *this is not affine - * - * This function is available only if the token EIGEN_QT_SUPPORT is defined. - */ -template<typename Scalar, int Dim> -QMatrix Transform<Scalar,Dim>::toQMatrix(void) const -{ - EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE) - return QMatrix(m_matrix.coeff(0,0), m_matrix.coeff(1,0), - m_matrix.coeff(0,1), m_matrix.coeff(1,1), - m_matrix.coeff(0,2), m_matrix.coeff(1,2)); -} - -/** Initialises \c *this from a QTransform assuming the dimension is 2. - * - * This function is available only if the token EIGEN_QT_SUPPORT is defined. - */ -template<typename Scalar, int Dim> -Transform<Scalar,Dim>::Transform(const QTransform& other) -{ - *this = other; -} - -/** Set \c *this from a QTransform assuming the dimension is 2. - * - * This function is available only if the token EIGEN_QT_SUPPORT is defined. - */ -template<typename Scalar, int Dim> -Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QTransform& other) -{ - EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE) - m_matrix << other.m11(), other.m21(), other.dx(), - other.m12(), other.m22(), other.dy(), - other.m13(), other.m23(), other.m33(); - return *this; -} - -/** \returns a QTransform from \c *this assuming the dimension is 2. - * - * This function is available only if the token EIGEN_QT_SUPPORT is defined. - */ -template<typename Scalar, int Dim> -QTransform Transform<Scalar,Dim>::toQTransform(void) const -{ - EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE) - return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0), m_matrix.coeff(2,0), - m_matrix.coeff(0,1), m_matrix.coeff(1,1), m_matrix.coeff(2,1), - m_matrix.coeff(0,2), m_matrix.coeff(1,2), m_matrix.coeff(2,2)); -} -#endif - -/********************* -*** Procedural API *** -*********************/ - -/** Applies on the right the non uniform scale transformation represented - * by the vector \a other to \c *this and returns a reference to \c *this. - * \sa prescale() - */ -template<typename Scalar, int Dim> -template<typename OtherDerived> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::scale(const MatrixBase<OtherDerived> &other) -{ - EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim)) - linear() = (linear() * other.asDiagonal()).lazy(); - return *this; -} - -/** Applies on the right a uniform scale of a factor \a c to \c *this - * and returns a reference to \c *this. - * \sa prescale(Scalar) - */ -template<typename Scalar, int Dim> -inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::scale(Scalar s) -{ - linear() *= s; - return *this; -} - -/** Applies on the left the non uniform scale transformation represented - * by the vector \a other to \c *this and returns a reference to \c *this. - * \sa scale() - */ -template<typename Scalar, int Dim> -template<typename OtherDerived> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::prescale(const MatrixBase<OtherDerived> &other) -{ - EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim)) - m_matrix.template block<Dim,HDim>(0,0) = (other.asDiagonal() * m_matrix.template block<Dim,HDim>(0,0)).lazy(); - return *this; -} - -/** Applies on the left a uniform scale of a factor \a c to \c *this - * and returns a reference to \c *this. - * \sa scale(Scalar) - */ -template<typename Scalar, int Dim> -inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::prescale(Scalar s) -{ - m_matrix.template corner<Dim,HDim>(TopLeft) *= s; - return *this; -} - -/** Applies on the right the translation matrix represented by the vector \a other - * to \c *this and returns a reference to \c *this. - * \sa pretranslate() - */ -template<typename Scalar, int Dim> -template<typename OtherDerived> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::translate(const MatrixBase<OtherDerived> &other) -{ - EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim)) - translation() += linear() * other; - return *this; -} - -/** Applies on the left the translation matrix represented by the vector \a other - * to \c *this and returns a reference to \c *this. - * \sa translate() - */ -template<typename Scalar, int Dim> -template<typename OtherDerived> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::pretranslate(const MatrixBase<OtherDerived> &other) -{ - EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim)) - translation() += other; - return *this; -} - -/** Applies on the right the rotation represented by the rotation \a rotation - * to \c *this and returns a reference to \c *this. - * - * The template parameter \a RotationType is the type of the rotation which - * must be known by ei_toRotationMatrix<>. - * - * Natively supported types includes: - * - any scalar (2D), - * - a Dim x Dim matrix expression, - * - a Quaternion (3D), - * - a AngleAxis (3D) - * - * This mechanism is easily extendable to support user types such as Euler angles, - * or a pair of Quaternion for 4D rotations. - * - * \sa rotate(Scalar), class Quaternion, class AngleAxis, prerotate(RotationType) - */ -template<typename Scalar, int Dim> -template<typename RotationType> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::rotate(const RotationType& rotation) -{ - linear() *= ei_toRotationMatrix<Scalar,Dim>(rotation); - return *this; -} - -/** Applies on the left the rotation represented by the rotation \a rotation - * to \c *this and returns a reference to \c *this. - * - * See rotate() for further details. - * - * \sa rotate() - */ -template<typename Scalar, int Dim> -template<typename RotationType> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::prerotate(const RotationType& rotation) -{ - m_matrix.template block<Dim,HDim>(0,0) = ei_toRotationMatrix<Scalar,Dim>(rotation) - * m_matrix.template block<Dim,HDim>(0,0); - return *this; -} - -/** Applies on the right the shear transformation represented - * by the vector \a other to \c *this and returns a reference to \c *this. - * \warning 2D only. - * \sa preshear() - */ -template<typename Scalar, int Dim> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::shear(Scalar sx, Scalar sy) -{ - EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE) - VectorType tmp = linear().col(0)*sy + linear().col(1); - linear() << linear().col(0) + linear().col(1)*sx, tmp; - return *this; -} - -/** Applies on the left the shear transformation represented - * by the vector \a other to \c *this and returns a reference to \c *this. - * \warning 2D only. - * \sa shear() - */ -template<typename Scalar, int Dim> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::preshear(Scalar sx, Scalar sy) -{ - EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE) - m_matrix.template block<Dim,HDim>(0,0) = LinearMatrixType(1, sx, sy, 1) * m_matrix.template block<Dim,HDim>(0,0); - return *this; -} - -/****************************************************** -*** Scaling, Translation and Rotation compatibility *** -******************************************************/ - -template<typename Scalar, int Dim> -inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const TranslationType& t) -{ - linear().setIdentity(); - translation() = t.vector(); - m_matrix.template block<1,Dim>(Dim,0).setZero(); - m_matrix(Dim,Dim) = Scalar(1); - return *this; -} - -template<typename Scalar, int Dim> -inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const TranslationType& t) const -{ - Transform res = *this; - res.translate(t.vector()); - return res; -} - -template<typename Scalar, int Dim> -inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const ScalingType& s) -{ - m_matrix.setZero(); - linear().diagonal() = s.coeffs(); - m_matrix.coeffRef(Dim,Dim) = Scalar(1); - return *this; -} - -template<typename Scalar, int Dim> -inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const ScalingType& s) const -{ - Transform res = *this; - res.scale(s.coeffs()); - return res; -} - -template<typename Scalar, int Dim> -template<typename Derived> -inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const RotationBase<Derived,Dim>& r) -{ - linear() = ei_toRotationMatrix<Scalar,Dim>(r); - translation().setZero(); - m_matrix.template block<1,Dim>(Dim,0).setZero(); - m_matrix.coeffRef(Dim,Dim) = Scalar(1); - return *this; -} - -template<typename Scalar, int Dim> -template<typename Derived> -inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const RotationBase<Derived,Dim>& r) const -{ - Transform res = *this; - res.rotate(r.derived()); - return res; -} - -/************************ -*** Special functions *** -************************/ - -/** \returns the rotation part of the transformation - * \nonstableyet - * - * \svd_module - * - * \sa computeRotationScaling(), computeScalingRotation(), class SVD - */ -template<typename Scalar, int Dim> -typename Transform<Scalar,Dim>::LinearMatrixType -Transform<Scalar,Dim>::rotation() const -{ - LinearMatrixType result; - computeRotationScaling(&result, (LinearMatrixType*)0); - return result; -} - - -/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being - * not necessarily positive. - * - * If either pointer is zero, the corresponding computation is skipped. - * - * \nonstableyet - * - * \svd_module - * - * \sa computeScalingRotation(), rotation(), class SVD - */ -template<typename Scalar, int Dim> -template<typename RotationMatrixType, typename ScalingMatrixType> -void Transform<Scalar,Dim>::computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const -{ - JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU|ComputeFullV); - Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1 - Matrix<Scalar, Dim, 1> sv(svd.singularValues()); - sv.coeffRef(0) *= x; - if(scaling) - { - scaling->noalias() = svd.matrixV() * sv.asDiagonal() * svd.matrixV().adjoint(); - } - if(rotation) - { - LinearMatrixType m(svd.matrixU()); - m.col(0) /= x; - rotation->noalias() = m * svd.matrixV().adjoint(); - } -} - -/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being - * not necessarily positive. - * - * If either pointer is zero, the corresponding computation is skipped. - * - * \nonstableyet - * - * \svd_module - * - * \sa computeRotationScaling(), rotation(), class SVD - */ -template<typename Scalar, int Dim> -template<typename ScalingMatrixType, typename RotationMatrixType> -void Transform<Scalar,Dim>::computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const -{ - JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU|ComputeFullV); - Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1 - Matrix<Scalar, Dim, 1> sv(svd.singularValues()); - sv.coeffRef(0) *= x; - if(scaling) - { - scaling->noalias() = svd.matrixU() * sv.asDiagonal() * svd.matrixU().adjoint(); - } - if(rotation) - { - LinearMatrixType m(svd.matrixU()); - m.col(0) /= x; - rotation->noalias() = m * svd.matrixV().adjoint(); - } -} - -/** Convenient method to set \c *this from a position, orientation and scale - * of a 3D object. - */ -template<typename Scalar, int Dim> -template<typename PositionDerived, typename OrientationType, typename ScaleDerived> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::fromPositionOrientationScale(const MatrixBase<PositionDerived> &position, - const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale) -{ - linear() = ei_toRotationMatrix<Scalar,Dim>(orientation); - linear() *= scale.asDiagonal(); - translation() = position; - m_matrix.template block<1,Dim>(Dim,0).setZero(); - m_matrix(Dim,Dim) = Scalar(1); - return *this; -} - -/** \nonstableyet - * - * \returns the inverse transformation matrix according to some given knowledge - * on \c *this. - * - * \param traits allows to optimize the inversion process when the transformion - * is known to be not a general transformation. The possible values are: - * - Projective if the transformation is not necessarily affine, i.e., if the - * last row is not guaranteed to be [0 ... 0 1] - * - Affine is the default, the last row is assumed to be [0 ... 0 1] - * - Isometry if the transformation is only a concatenations of translations - * and rotations. - * - * \warning unless \a traits is always set to NoShear or NoScaling, this function - * requires the generic inverse method of MatrixBase defined in the LU module. If - * you forget to include this module, then you will get hard to debug linking errors. - * - * \sa MatrixBase::inverse() - */ -template<typename Scalar, int Dim> -inline const typename Transform<Scalar,Dim>::MatrixType -Transform<Scalar,Dim>::inverse(TransformTraits traits) const -{ - if (traits == Projective) - { - return m_matrix.inverse(); - } - else - { - MatrixType res; - if (traits == Affine) - { - res.template corner<Dim,Dim>(TopLeft) = linear().inverse(); - } - else if (traits == Isometry) - { - res.template corner<Dim,Dim>(TopLeft) = linear().transpose(); - } - else - { - ei_assert("invalid traits value in Transform::inverse()"); - } - // translation and remaining parts - res.template corner<Dim,1>(TopRight) = - res.template corner<Dim,Dim>(TopLeft) * translation(); - res.template corner<1,Dim>(BottomLeft).setZero(); - res.coeffRef(Dim,Dim) = Scalar(1); - return res; - } -} - -/***************************************************** -*** Specializations of operator* with a MatrixBase *** -*****************************************************/ - -template<typename Other, int Dim, int HDim> -struct ei_transform_product_impl<Other,Dim,HDim, HDim,HDim> -{ - typedef Transform<typename Other::Scalar,Dim> TransformType; - typedef typename TransformType::MatrixType MatrixType; - typedef typename ProductReturnType<MatrixType,Other>::Type ResultType; - static ResultType run(const TransformType& tr, const Other& other) - { return tr.matrix() * other; } -}; - -template<typename Other, int Dim, int HDim> -struct ei_transform_product_impl<Other,Dim,HDim, Dim,Dim> -{ - typedef Transform<typename Other::Scalar,Dim> TransformType; - typedef typename TransformType::MatrixType MatrixType; - typedef TransformType ResultType; - static ResultType run(const TransformType& tr, const Other& other) - { - TransformType res; - res.translation() = tr.translation(); - res.matrix().row(Dim) = tr.matrix().row(Dim); - res.linear() = (tr.linear() * other).lazy(); - return res; - } -}; - -template<typename Other, int Dim, int HDim> -struct ei_transform_product_impl<Other,Dim,HDim, HDim,1> -{ - typedef Transform<typename Other::Scalar,Dim> TransformType; - typedef typename TransformType::MatrixType MatrixType; - typedef typename ProductReturnType<MatrixType,Other>::Type ResultType; - static ResultType run(const TransformType& tr, const Other& other) - { return tr.matrix() * other; } -}; - -template<typename Other, int Dim, int HDim> -struct ei_transform_product_impl<Other,Dim,HDim, Dim,1> -{ - typedef typename Other::Scalar Scalar; - typedef Transform<Scalar,Dim> TransformType; - typedef Matrix<Scalar,Dim,1> ResultType; - static ResultType run(const TransformType& tr, const Other& other) - { return ((tr.linear() * other) + tr.translation()) - * (Scalar(1) / ( (tr.matrix().template block<1,Dim>(Dim,0) * other).coeff(0) + tr.matrix().coeff(Dim,Dim))); } -}; - -} // end namespace Eigen |