[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
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| 5 | // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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| 6 | //
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| 7 | // This Source Code Form is subject to the terms of the Mozilla
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| 8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 10 |
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| 11 | // no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
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| 12 |
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| 13 | namespace Eigen {
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| 14 |
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| 15 | // Note that we have to pass Dim and HDim because it is not allowed to use a template
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| 16 | // parameter to define a template specialization. To be more precise, in the following
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| 17 | // specializations, it is not allowed to use Dim+1 instead of HDim.
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| 18 | template< typename Other,
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| 19 | int Dim,
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| 20 | int HDim,
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| 21 | int OtherRows=Other::RowsAtCompileTime,
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| 22 | int OtherCols=Other::ColsAtCompileTime>
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| 23 | struct ei_transform_product_impl;
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| 24 |
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| 25 | /** \geometry_module \ingroup Geometry_Module
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| 26 | *
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| 27 | * \class Transform
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| 28 | *
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| 29 | * \brief Represents an homogeneous transformation in a N dimensional space
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| 30 | *
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| 31 | * \param _Scalar the scalar type, i.e., the type of the coefficients
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| 32 | * \param _Dim the dimension of the space
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| 33 | *
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| 34 | * The homography is internally represented and stored as a (Dim+1)^2 matrix which
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| 35 | * is available through the matrix() method.
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| 36 | *
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| 37 | * Conversion methods from/to Qt's QMatrix and QTransform are available if the
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| 38 | * preprocessor token EIGEN_QT_SUPPORT is defined.
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| 39 | *
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| 40 | * \sa class Matrix, class Quaternion
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| 41 | */
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| 42 | template<typename _Scalar, int _Dim>
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| 43 | class Transform
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| 44 | {
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| 45 | public:
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| 46 | EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim==Dynamic ? Dynamic : (_Dim+1)*(_Dim+1))
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| 47 | enum {
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| 48 | Dim = _Dim, ///< space dimension in which the transformation holds
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| 49 | HDim = _Dim+1 ///< size of a respective homogeneous vector
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| 50 | };
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| 51 | /** the scalar type of the coefficients */
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| 52 | typedef _Scalar Scalar;
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| 53 | /** type of the matrix used to represent the transformation */
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| 54 | typedef Matrix<Scalar,HDim,HDim> MatrixType;
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| 55 | /** type of the matrix used to represent the linear part of the transformation */
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| 56 | typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
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| 57 | /** type of read/write reference to the linear part of the transformation */
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| 58 | typedef Block<MatrixType,Dim,Dim> LinearPart;
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| 59 | /** type of read/write reference to the linear part of the transformation */
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| 60 | typedef const Block<const MatrixType,Dim,Dim> ConstLinearPart;
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| 61 | /** type of a vector */
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| 62 | typedef Matrix<Scalar,Dim,1> VectorType;
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| 63 | /** type of a read/write reference to the translation part of the rotation */
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| 64 | typedef Block<MatrixType,Dim,1> TranslationPart;
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| 65 | /** type of a read/write reference to the translation part of the rotation */
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| 66 | typedef const Block<const MatrixType,Dim,1> ConstTranslationPart;
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| 67 | /** corresponding translation type */
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| 68 | typedef Translation<Scalar,Dim> TranslationType;
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| 69 | /** corresponding scaling transformation type */
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| 70 | typedef Scaling<Scalar,Dim> ScalingType;
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| 71 |
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| 72 | protected:
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| 73 |
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| 74 | MatrixType m_matrix;
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| 75 |
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| 76 | public:
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| 77 |
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| 78 | /** Default constructor without initialization of the coefficients. */
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| 79 | inline Transform() { }
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| 80 |
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| 81 | inline Transform(const Transform& other)
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| 82 | {
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| 83 | m_matrix = other.m_matrix;
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| 84 | }
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| 85 |
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| 86 | inline explicit Transform(const TranslationType& t) { *this = t; }
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| 87 | inline explicit Transform(const ScalingType& s) { *this = s; }
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| 88 | template<typename Derived>
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| 89 | inline explicit Transform(const RotationBase<Derived, Dim>& r) { *this = r; }
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| 90 |
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| 91 | inline Transform& operator=(const Transform& other)
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| 92 | { m_matrix = other.m_matrix; return *this; }
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| 93 |
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| 94 | template<typename OtherDerived, bool BigMatrix> // MSVC 2005 will commit suicide if BigMatrix has a default value
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| 95 | struct construct_from_matrix
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| 96 | {
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| 97 | static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other)
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| 98 | {
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| 99 | transform->matrix() = other;
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| 100 | }
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| 101 | };
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| 102 |
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| 103 | template<typename OtherDerived> struct construct_from_matrix<OtherDerived, true>
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| 104 | {
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| 105 | static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other)
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| 106 | {
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| 107 | transform->linear() = other;
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| 108 | transform->translation().setZero();
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| 109 | transform->matrix()(Dim,Dim) = Scalar(1);
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| 110 | transform->matrix().template block<1,Dim>(Dim,0).setZero();
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| 111 | }
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| 112 | };
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| 113 |
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| 114 | /** Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. */
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| 115 | template<typename OtherDerived>
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| 116 | inline explicit Transform(const MatrixBase<OtherDerived>& other)
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| 117 | {
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| 118 | construct_from_matrix<OtherDerived, int(OtherDerived::RowsAtCompileTime) == Dim>::run(this, other);
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| 119 | }
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| 120 |
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| 121 | /** Set \c *this from a (Dim+1)^2 matrix. */
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| 122 | template<typename OtherDerived>
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| 123 | inline Transform& operator=(const MatrixBase<OtherDerived>& other)
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| 124 | { m_matrix = other; return *this; }
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| 125 |
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| 126 | #ifdef EIGEN_QT_SUPPORT
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| 127 | inline Transform(const QMatrix& other);
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| 128 | inline Transform& operator=(const QMatrix& other);
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| 129 | inline QMatrix toQMatrix(void) const;
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| 130 | inline Transform(const QTransform& other);
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| 131 | inline Transform& operator=(const QTransform& other);
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| 132 | inline QTransform toQTransform(void) const;
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| 133 | #endif
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| 134 |
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| 135 | /** shortcut for m_matrix(row,col);
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| 136 | * \sa MatrixBase::operaror(int,int) const */
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| 137 | inline Scalar operator() (int row, int col) const { return m_matrix(row,col); }
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| 138 | /** shortcut for m_matrix(row,col);
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| 139 | * \sa MatrixBase::operaror(int,int) */
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| 140 | inline Scalar& operator() (int row, int col) { return m_matrix(row,col); }
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| 141 |
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| 142 | /** \returns a read-only expression of the transformation matrix */
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| 143 | inline const MatrixType& matrix() const { return m_matrix; }
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| 144 | /** \returns a writable expression of the transformation matrix */
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| 145 | inline MatrixType& matrix() { return m_matrix; }
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| 146 |
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| 147 | /** \returns a read-only expression of the linear (linear) part of the transformation */
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| 148 | inline ConstLinearPart linear() const { return m_matrix.template block<Dim,Dim>(0,0); }
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| 149 | /** \returns a writable expression of the linear (linear) part of the transformation */
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| 150 | inline LinearPart linear() { return m_matrix.template block<Dim,Dim>(0,0); }
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| 151 |
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| 152 | /** \returns a read-only expression of the translation vector of the transformation */
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| 153 | inline ConstTranslationPart translation() const { return m_matrix.template block<Dim,1>(0,Dim); }
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| 154 | /** \returns a writable expression of the translation vector of the transformation */
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| 155 | inline TranslationPart translation() { return m_matrix.template block<Dim,1>(0,Dim); }
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| 156 |
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| 157 | /** \returns an expression of the product between the transform \c *this and a matrix expression \a other
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| 158 | *
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| 159 | * The right hand side \a other might be either:
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| 160 | * \li a vector of size Dim,
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| 161 | * \li an homogeneous vector of size Dim+1,
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| 162 | * \li a transformation matrix of size Dim+1 x Dim+1.
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| 163 | */
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| 164 | // note: this function is defined here because some compilers cannot find the respective declaration
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| 165 | template<typename OtherDerived>
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| 166 | inline const typename ei_transform_product_impl<OtherDerived,_Dim,_Dim+1>::ResultType
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| 167 | operator * (const MatrixBase<OtherDerived> &other) const
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| 168 | { return ei_transform_product_impl<OtherDerived,Dim,HDim>::run(*this,other.derived()); }
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| 169 |
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| 170 | /** \returns the product expression of a transformation matrix \a a times a transform \a b
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| 171 | * The transformation matrix \a a must have a Dim+1 x Dim+1 sizes. */
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| 172 | template<typename OtherDerived>
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| 173 | friend inline const typename ProductReturnType<OtherDerived,MatrixType>::Type
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| 174 | operator * (const MatrixBase<OtherDerived> &a, const Transform &b)
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| 175 | { return a.derived() * b.matrix(); }
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| 176 |
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| 177 | /** Contatenates two transformations */
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| 178 | inline const Transform
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| 179 | operator * (const Transform& other) const
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| 180 | { return Transform(m_matrix * other.matrix()); }
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| 181 |
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| 182 | /** \sa MatrixBase::setIdentity() */
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| 183 | void setIdentity() { m_matrix.setIdentity(); }
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| 184 | static const typename MatrixType::IdentityReturnType Identity()
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| 185 | {
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| 186 | return MatrixType::Identity();
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| 187 | }
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| 188 |
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| 189 | template<typename OtherDerived>
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| 190 | inline Transform& scale(const MatrixBase<OtherDerived> &other);
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| 191 |
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| 192 | template<typename OtherDerived>
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| 193 | inline Transform& prescale(const MatrixBase<OtherDerived> &other);
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| 194 |
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| 195 | inline Transform& scale(Scalar s);
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| 196 | inline Transform& prescale(Scalar s);
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| 197 |
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| 198 | template<typename OtherDerived>
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| 199 | inline Transform& translate(const MatrixBase<OtherDerived> &other);
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| 200 |
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| 201 | template<typename OtherDerived>
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| 202 | inline Transform& pretranslate(const MatrixBase<OtherDerived> &other);
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| 203 |
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| 204 | template<typename RotationType>
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| 205 | inline Transform& rotate(const RotationType& rotation);
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| 206 |
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| 207 | template<typename RotationType>
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| 208 | inline Transform& prerotate(const RotationType& rotation);
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| 209 |
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| 210 | Transform& shear(Scalar sx, Scalar sy);
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| 211 | Transform& preshear(Scalar sx, Scalar sy);
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| 212 |
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| 213 | inline Transform& operator=(const TranslationType& t);
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| 214 | inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); }
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| 215 | inline Transform operator*(const TranslationType& t) const;
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| 216 |
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| 217 | inline Transform& operator=(const ScalingType& t);
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| 218 | inline Transform& operator*=(const ScalingType& s) { return scale(s.coeffs()); }
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| 219 | inline Transform operator*(const ScalingType& s) const;
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| 220 | friend inline Transform operator*(const LinearMatrixType& mat, const Transform& t)
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| 221 | {
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| 222 | Transform res = t;
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| 223 | res.matrix().row(Dim) = t.matrix().row(Dim);
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| 224 | res.matrix().template block<Dim,HDim>(0,0) = (mat * t.matrix().template block<Dim,HDim>(0,0)).lazy();
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| 225 | return res;
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| 226 | }
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| 227 |
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| 228 | template<typename Derived>
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| 229 | inline Transform& operator=(const RotationBase<Derived,Dim>& r);
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| 230 | template<typename Derived>
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| 231 | inline Transform& operator*=(const RotationBase<Derived,Dim>& r) { return rotate(r.toRotationMatrix()); }
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| 232 | template<typename Derived>
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| 233 | inline Transform operator*(const RotationBase<Derived,Dim>& r) const;
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| 234 |
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| 235 | LinearMatrixType rotation() const;
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| 236 | template<typename RotationMatrixType, typename ScalingMatrixType>
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| 237 | void computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const;
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| 238 | template<typename ScalingMatrixType, typename RotationMatrixType>
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| 239 | void computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const;
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| 240 |
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| 241 | template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
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| 242 | Transform& fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
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| 243 | const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale);
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| 244 |
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| 245 | inline const MatrixType inverse(TransformTraits traits = Affine) const;
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| 246 |
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| 247 | /** \returns a const pointer to the column major internal matrix */
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| 248 | const Scalar* data() const { return m_matrix.data(); }
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| 249 | /** \returns a non-const pointer to the column major internal matrix */
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| 250 | Scalar* data() { return m_matrix.data(); }
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| 251 |
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| 252 | /** \returns \c *this with scalar type casted to \a NewScalarType
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| 253 | *
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| 254 | * Note that if \a NewScalarType is equal to the current scalar type of \c *this
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| 255 | * then this function smartly returns a const reference to \c *this.
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| 256 | */
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| 257 | template<typename NewScalarType>
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| 258 | inline typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type cast() const
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| 259 | { return typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type(*this); }
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| 260 |
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| 261 | /** Copy constructor with scalar type conversion */
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| 262 | template<typename OtherScalarType>
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| 263 | inline explicit Transform(const Transform<OtherScalarType,Dim>& other)
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| 264 | { m_matrix = other.matrix().template cast<Scalar>(); }
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| 265 |
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| 266 | /** \returns \c true if \c *this is approximately equal to \a other, within the precision
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| 267 | * determined by \a prec.
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| 268 | *
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| 269 | * \sa MatrixBase::isApprox() */
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| 270 | bool isApprox(const Transform& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
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| 271 | { return m_matrix.isApprox(other.m_matrix, prec); }
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| 272 |
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| 273 | #ifdef EIGEN_TRANSFORM_PLUGIN
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| 274 | #include EIGEN_TRANSFORM_PLUGIN
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| 275 | #endif
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| 276 |
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| 277 | protected:
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| 278 |
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| 279 | };
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| 280 |
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| 281 | /** \ingroup Geometry_Module */
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| 282 | typedef Transform<float,2> Transform2f;
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| 283 | /** \ingroup Geometry_Module */
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| 284 | typedef Transform<float,3> Transform3f;
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| 285 | /** \ingroup Geometry_Module */
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| 286 | typedef Transform<double,2> Transform2d;
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| 287 | /** \ingroup Geometry_Module */
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| 288 | typedef Transform<double,3> Transform3d;
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| 289 |
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| 290 | /**************************
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| 291 | *** Optional QT support ***
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| 292 | **************************/
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| 293 |
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| 294 | #ifdef EIGEN_QT_SUPPORT
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| 295 | /** Initialises \c *this from a QMatrix assuming the dimension is 2.
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| 296 | *
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| 297 | * This function is available only if the token EIGEN_QT_SUPPORT is defined.
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| 298 | */
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| 299 | template<typename Scalar, int Dim>
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| 300 | Transform<Scalar,Dim>::Transform(const QMatrix& other)
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| 301 | {
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| 302 | *this = other;
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| 303 | }
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| 304 |
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| 305 | /** Set \c *this from a QMatrix assuming the dimension is 2.
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| 306 | *
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| 307 | * This function is available only if the token EIGEN_QT_SUPPORT is defined.
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| 308 | */
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| 309 | template<typename Scalar, int Dim>
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| 310 | Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QMatrix& other)
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| 311 | {
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| 312 | EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
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| 313 | m_matrix << other.m11(), other.m21(), other.dx(),
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| 314 | other.m12(), other.m22(), other.dy(),
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| 315 | 0, 0, 1;
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| 316 | return *this;
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| 317 | }
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| 318 |
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| 319 | /** \returns a QMatrix from \c *this assuming the dimension is 2.
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| 320 | *
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| 321 | * \warning this convertion might loss data if \c *this is not affine
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| 322 | *
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| 323 | * This function is available only if the token EIGEN_QT_SUPPORT is defined.
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| 324 | */
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| 325 | template<typename Scalar, int Dim>
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| 326 | QMatrix Transform<Scalar,Dim>::toQMatrix(void) const
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| 327 | {
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| 328 | EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
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| 329 | return QMatrix(m_matrix.coeff(0,0), m_matrix.coeff(1,0),
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| 330 | m_matrix.coeff(0,1), m_matrix.coeff(1,1),
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| 331 | m_matrix.coeff(0,2), m_matrix.coeff(1,2));
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| 332 | }
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| 333 |
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| 334 | /** Initialises \c *this from a QTransform assuming the dimension is 2.
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| 335 | *
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| 336 | * This function is available only if the token EIGEN_QT_SUPPORT is defined.
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| 337 | */
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| 338 | template<typename Scalar, int Dim>
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| 339 | Transform<Scalar,Dim>::Transform(const QTransform& other)
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| 340 | {
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| 341 | *this = other;
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| 342 | }
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| 343 |
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| 344 | /** Set \c *this from a QTransform assuming the dimension is 2.
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| 345 | *
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| 346 | * This function is available only if the token EIGEN_QT_SUPPORT is defined.
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| 347 | */
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| 348 | template<typename Scalar, int Dim>
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| 349 | Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QTransform& other)
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| 350 | {
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| 351 | EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
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| 352 | m_matrix << other.m11(), other.m21(), other.dx(),
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| 353 | other.m12(), other.m22(), other.dy(),
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| 354 | other.m13(), other.m23(), other.m33();
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| 355 | return *this;
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| 356 | }
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| 357 |
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| 358 | /** \returns a QTransform from \c *this assuming the dimension is 2.
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| 359 | *
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| 360 | * This function is available only if the token EIGEN_QT_SUPPORT is defined.
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| 361 | */
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| 362 | template<typename Scalar, int Dim>
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| 363 | QTransform Transform<Scalar,Dim>::toQTransform(void) const
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| 364 | {
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| 365 | EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
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| 366 | return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0), m_matrix.coeff(2,0),
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| 367 | m_matrix.coeff(0,1), m_matrix.coeff(1,1), m_matrix.coeff(2,1),
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| 368 | m_matrix.coeff(0,2), m_matrix.coeff(1,2), m_matrix.coeff(2,2));
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| 369 | }
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| 370 | #endif
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| 371 |
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| 372 | /*********************
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| 373 | *** Procedural API ***
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| 374 | *********************/
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| 375 |
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| 376 | /** Applies on the right the non uniform scale transformation represented
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| 377 | * by the vector \a other to \c *this and returns a reference to \c *this.
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| 378 | * \sa prescale()
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| 379 | */
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| 380 | template<typename Scalar, int Dim>
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| 381 | template<typename OtherDerived>
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| 382 | Transform<Scalar,Dim>&
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| 383 | Transform<Scalar,Dim>::scale(const MatrixBase<OtherDerived> &other)
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| 384 | {
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| 385 | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
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| 386 | linear() = (linear() * other.asDiagonal()).lazy();
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| 387 | return *this;
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| 388 | }
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| 389 |
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| 390 | /** Applies on the right a uniform scale of a factor \a c to \c *this
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| 391 | * and returns a reference to \c *this.
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| 392 | * \sa prescale(Scalar)
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| 393 | */
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| 394 | template<typename Scalar, int Dim>
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| 395 | inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::scale(Scalar s)
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| 396 | {
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| 397 | linear() *= s;
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| 398 | return *this;
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| 399 | }
|
---|
| 400 |
|
---|
| 401 | /** Applies on the left the non uniform scale transformation represented
|
---|
| 402 | * by the vector \a other to \c *this and returns a reference to \c *this.
|
---|
| 403 | * \sa scale()
|
---|
| 404 | */
|
---|
| 405 | template<typename Scalar, int Dim>
|
---|
| 406 | template<typename OtherDerived>
|
---|
| 407 | Transform<Scalar,Dim>&
|
---|
| 408 | Transform<Scalar,Dim>::prescale(const MatrixBase<OtherDerived> &other)
|
---|
| 409 | {
|
---|
| 410 | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
|
---|
| 411 | m_matrix.template block<Dim,HDim>(0,0) = (other.asDiagonal() * m_matrix.template block<Dim,HDim>(0,0)).lazy();
|
---|
| 412 | return *this;
|
---|
| 413 | }
|
---|
| 414 |
|
---|
| 415 | /** Applies on the left a uniform scale of a factor \a c to \c *this
|
---|
| 416 | * and returns a reference to \c *this.
|
---|
| 417 | * \sa scale(Scalar)
|
---|
| 418 | */
|
---|
| 419 | template<typename Scalar, int Dim>
|
---|
| 420 | inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::prescale(Scalar s)
|
---|
| 421 | {
|
---|
| 422 | m_matrix.template corner<Dim,HDim>(TopLeft) *= s;
|
---|
| 423 | return *this;
|
---|
| 424 | }
|
---|
| 425 |
|
---|
| 426 | /** Applies on the right the translation matrix represented by the vector \a other
|
---|
| 427 | * to \c *this and returns a reference to \c *this.
|
---|
| 428 | * \sa pretranslate()
|
---|
| 429 | */
|
---|
| 430 | template<typename Scalar, int Dim>
|
---|
| 431 | template<typename OtherDerived>
|
---|
| 432 | Transform<Scalar,Dim>&
|
---|
| 433 | Transform<Scalar,Dim>::translate(const MatrixBase<OtherDerived> &other)
|
---|
| 434 | {
|
---|
| 435 | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
|
---|
| 436 | translation() += linear() * other;
|
---|
| 437 | return *this;
|
---|
| 438 | }
|
---|
| 439 |
|
---|
| 440 | /** Applies on the left the translation matrix represented by the vector \a other
|
---|
| 441 | * to \c *this and returns a reference to \c *this.
|
---|
| 442 | * \sa translate()
|
---|
| 443 | */
|
---|
| 444 | template<typename Scalar, int Dim>
|
---|
| 445 | template<typename OtherDerived>
|
---|
| 446 | Transform<Scalar,Dim>&
|
---|
| 447 | Transform<Scalar,Dim>::pretranslate(const MatrixBase<OtherDerived> &other)
|
---|
| 448 | {
|
---|
| 449 | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
|
---|
| 450 | translation() += other;
|
---|
| 451 | return *this;
|
---|
| 452 | }
|
---|
| 453 |
|
---|
| 454 | /** Applies on the right the rotation represented by the rotation \a rotation
|
---|
| 455 | * to \c *this and returns a reference to \c *this.
|
---|
| 456 | *
|
---|
| 457 | * The template parameter \a RotationType is the type of the rotation which
|
---|
| 458 | * must be known by ei_toRotationMatrix<>.
|
---|
| 459 | *
|
---|
| 460 | * Natively supported types includes:
|
---|
| 461 | * - any scalar (2D),
|
---|
| 462 | * - a Dim x Dim matrix expression,
|
---|
| 463 | * - a Quaternion (3D),
|
---|
| 464 | * - a AngleAxis (3D)
|
---|
| 465 | *
|
---|
| 466 | * This mechanism is easily extendable to support user types such as Euler angles,
|
---|
| 467 | * or a pair of Quaternion for 4D rotations.
|
---|
| 468 | *
|
---|
| 469 | * \sa rotate(Scalar), class Quaternion, class AngleAxis, prerotate(RotationType)
|
---|
| 470 | */
|
---|
| 471 | template<typename Scalar, int Dim>
|
---|
| 472 | template<typename RotationType>
|
---|
| 473 | Transform<Scalar,Dim>&
|
---|
| 474 | Transform<Scalar,Dim>::rotate(const RotationType& rotation)
|
---|
| 475 | {
|
---|
| 476 | linear() *= ei_toRotationMatrix<Scalar,Dim>(rotation);
|
---|
| 477 | return *this;
|
---|
| 478 | }
|
---|
| 479 |
|
---|
| 480 | /** Applies on the left the rotation represented by the rotation \a rotation
|
---|
| 481 | * to \c *this and returns a reference to \c *this.
|
---|
| 482 | *
|
---|
| 483 | * See rotate() for further details.
|
---|
| 484 | *
|
---|
| 485 | * \sa rotate()
|
---|
| 486 | */
|
---|
| 487 | template<typename Scalar, int Dim>
|
---|
| 488 | template<typename RotationType>
|
---|
| 489 | Transform<Scalar,Dim>&
|
---|
| 490 | Transform<Scalar,Dim>::prerotate(const RotationType& rotation)
|
---|
| 491 | {
|
---|
| 492 | m_matrix.template block<Dim,HDim>(0,0) = ei_toRotationMatrix<Scalar,Dim>(rotation)
|
---|
| 493 | * m_matrix.template block<Dim,HDim>(0,0);
|
---|
| 494 | return *this;
|
---|
| 495 | }
|
---|
| 496 |
|
---|
| 497 | /** Applies on the right the shear transformation represented
|
---|
| 498 | * by the vector \a other to \c *this and returns a reference to \c *this.
|
---|
| 499 | * \warning 2D only.
|
---|
| 500 | * \sa preshear()
|
---|
| 501 | */
|
---|
| 502 | template<typename Scalar, int Dim>
|
---|
| 503 | Transform<Scalar,Dim>&
|
---|
| 504 | Transform<Scalar,Dim>::shear(Scalar sx, Scalar sy)
|
---|
| 505 | {
|
---|
| 506 | EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
|
---|
| 507 | VectorType tmp = linear().col(0)*sy + linear().col(1);
|
---|
| 508 | linear() << linear().col(0) + linear().col(1)*sx, tmp;
|
---|
| 509 | return *this;
|
---|
| 510 | }
|
---|
| 511 |
|
---|
| 512 | /** Applies on the left the shear transformation represented
|
---|
| 513 | * by the vector \a other to \c *this and returns a reference to \c *this.
|
---|
| 514 | * \warning 2D only.
|
---|
| 515 | * \sa shear()
|
---|
| 516 | */
|
---|
| 517 | template<typename Scalar, int Dim>
|
---|
| 518 | Transform<Scalar,Dim>&
|
---|
| 519 | Transform<Scalar,Dim>::preshear(Scalar sx, Scalar sy)
|
---|
| 520 | {
|
---|
| 521 | EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
|
---|
| 522 | m_matrix.template block<Dim,HDim>(0,0) = LinearMatrixType(1, sx, sy, 1) * m_matrix.template block<Dim,HDim>(0,0);
|
---|
| 523 | return *this;
|
---|
| 524 | }
|
---|
| 525 |
|
---|
| 526 | /******************************************************
|
---|
| 527 | *** Scaling, Translation and Rotation compatibility ***
|
---|
| 528 | ******************************************************/
|
---|
| 529 |
|
---|
| 530 | template<typename Scalar, int Dim>
|
---|
| 531 | inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const TranslationType& t)
|
---|
| 532 | {
|
---|
| 533 | linear().setIdentity();
|
---|
| 534 | translation() = t.vector();
|
---|
| 535 | m_matrix.template block<1,Dim>(Dim,0).setZero();
|
---|
| 536 | m_matrix(Dim,Dim) = Scalar(1);
|
---|
| 537 | return *this;
|
---|
| 538 | }
|
---|
| 539 |
|
---|
| 540 | template<typename Scalar, int Dim>
|
---|
| 541 | inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const TranslationType& t) const
|
---|
| 542 | {
|
---|
| 543 | Transform res = *this;
|
---|
| 544 | res.translate(t.vector());
|
---|
| 545 | return res;
|
---|
| 546 | }
|
---|
| 547 |
|
---|
| 548 | template<typename Scalar, int Dim>
|
---|
| 549 | inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const ScalingType& s)
|
---|
| 550 | {
|
---|
| 551 | m_matrix.setZero();
|
---|
| 552 | linear().diagonal() = s.coeffs();
|
---|
| 553 | m_matrix.coeffRef(Dim,Dim) = Scalar(1);
|
---|
| 554 | return *this;
|
---|
| 555 | }
|
---|
| 556 |
|
---|
| 557 | template<typename Scalar, int Dim>
|
---|
| 558 | inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const ScalingType& s) const
|
---|
| 559 | {
|
---|
| 560 | Transform res = *this;
|
---|
| 561 | res.scale(s.coeffs());
|
---|
| 562 | return res;
|
---|
| 563 | }
|
---|
| 564 |
|
---|
| 565 | template<typename Scalar, int Dim>
|
---|
| 566 | template<typename Derived>
|
---|
| 567 | inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const RotationBase<Derived,Dim>& r)
|
---|
| 568 | {
|
---|
| 569 | linear() = ei_toRotationMatrix<Scalar,Dim>(r);
|
---|
| 570 | translation().setZero();
|
---|
| 571 | m_matrix.template block<1,Dim>(Dim,0).setZero();
|
---|
| 572 | m_matrix.coeffRef(Dim,Dim) = Scalar(1);
|
---|
| 573 | return *this;
|
---|
| 574 | }
|
---|
| 575 |
|
---|
| 576 | template<typename Scalar, int Dim>
|
---|
| 577 | template<typename Derived>
|
---|
| 578 | inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const RotationBase<Derived,Dim>& r) const
|
---|
| 579 | {
|
---|
| 580 | Transform res = *this;
|
---|
| 581 | res.rotate(r.derived());
|
---|
| 582 | return res;
|
---|
| 583 | }
|
---|
| 584 |
|
---|
| 585 | /************************
|
---|
| 586 | *** Special functions ***
|
---|
| 587 | ************************/
|
---|
| 588 |
|
---|
| 589 | /** \returns the rotation part of the transformation
|
---|
| 590 | * \nonstableyet
|
---|
| 591 | *
|
---|
| 592 | * \svd_module
|
---|
| 593 | *
|
---|
| 594 | * \sa computeRotationScaling(), computeScalingRotation(), class SVD
|
---|
| 595 | */
|
---|
| 596 | template<typename Scalar, int Dim>
|
---|
| 597 | typename Transform<Scalar,Dim>::LinearMatrixType
|
---|
| 598 | Transform<Scalar,Dim>::rotation() const
|
---|
| 599 | {
|
---|
| 600 | LinearMatrixType result;
|
---|
| 601 | computeRotationScaling(&result, (LinearMatrixType*)0);
|
---|
| 602 | return result;
|
---|
| 603 | }
|
---|
| 604 |
|
---|
| 605 |
|
---|
| 606 | /** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being
|
---|
| 607 | * not necessarily positive.
|
---|
| 608 | *
|
---|
| 609 | * If either pointer is zero, the corresponding computation is skipped.
|
---|
| 610 | *
|
---|
| 611 | * \nonstableyet
|
---|
| 612 | *
|
---|
| 613 | * \svd_module
|
---|
| 614 | *
|
---|
| 615 | * \sa computeScalingRotation(), rotation(), class SVD
|
---|
| 616 | */
|
---|
| 617 | template<typename Scalar, int Dim>
|
---|
| 618 | template<typename RotationMatrixType, typename ScalingMatrixType>
|
---|
| 619 | void Transform<Scalar,Dim>::computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const
|
---|
| 620 | {
|
---|
| 621 | JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU|ComputeFullV);
|
---|
| 622 | Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1
|
---|
| 623 | Matrix<Scalar, Dim, 1> sv(svd.singularValues());
|
---|
| 624 | sv.coeffRef(0) *= x;
|
---|
| 625 | if(scaling)
|
---|
| 626 | {
|
---|
| 627 | scaling->noalias() = svd.matrixV() * sv.asDiagonal() * svd.matrixV().adjoint();
|
---|
| 628 | }
|
---|
| 629 | if(rotation)
|
---|
| 630 | {
|
---|
| 631 | LinearMatrixType m(svd.matrixU());
|
---|
| 632 | m.col(0) /= x;
|
---|
| 633 | rotation->noalias() = m * svd.matrixV().adjoint();
|
---|
| 634 | }
|
---|
| 635 | }
|
---|
| 636 |
|
---|
| 637 | /** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being
|
---|
| 638 | * not necessarily positive.
|
---|
| 639 | *
|
---|
| 640 | * If either pointer is zero, the corresponding computation is skipped.
|
---|
| 641 | *
|
---|
| 642 | * \nonstableyet
|
---|
| 643 | *
|
---|
| 644 | * \svd_module
|
---|
| 645 | *
|
---|
| 646 | * \sa computeRotationScaling(), rotation(), class SVD
|
---|
| 647 | */
|
---|
| 648 | template<typename Scalar, int Dim>
|
---|
| 649 | template<typename ScalingMatrixType, typename RotationMatrixType>
|
---|
| 650 | void Transform<Scalar,Dim>::computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const
|
---|
| 651 | {
|
---|
| 652 | JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU|ComputeFullV);
|
---|
| 653 | Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1
|
---|
| 654 | Matrix<Scalar, Dim, 1> sv(svd.singularValues());
|
---|
| 655 | sv.coeffRef(0) *= x;
|
---|
| 656 | if(scaling)
|
---|
| 657 | {
|
---|
| 658 | scaling->noalias() = svd.matrixU() * sv.asDiagonal() * svd.matrixU().adjoint();
|
---|
| 659 | }
|
---|
| 660 | if(rotation)
|
---|
| 661 | {
|
---|
| 662 | LinearMatrixType m(svd.matrixU());
|
---|
| 663 | m.col(0) /= x;
|
---|
| 664 | rotation->noalias() = m * svd.matrixV().adjoint();
|
---|
| 665 | }
|
---|
| 666 | }
|
---|
| 667 |
|
---|
| 668 | /** Convenient method to set \c *this from a position, orientation and scale
|
---|
| 669 | * of a 3D object.
|
---|
| 670 | */
|
---|
| 671 | template<typename Scalar, int Dim>
|
---|
| 672 | template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
|
---|
| 673 | Transform<Scalar,Dim>&
|
---|
| 674 | Transform<Scalar,Dim>::fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
|
---|
| 675 | const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale)
|
---|
| 676 | {
|
---|
| 677 | linear() = ei_toRotationMatrix<Scalar,Dim>(orientation);
|
---|
| 678 | linear() *= scale.asDiagonal();
|
---|
| 679 | translation() = position;
|
---|
| 680 | m_matrix.template block<1,Dim>(Dim,0).setZero();
|
---|
| 681 | m_matrix(Dim,Dim) = Scalar(1);
|
---|
| 682 | return *this;
|
---|
| 683 | }
|
---|
| 684 |
|
---|
| 685 | /** \nonstableyet
|
---|
| 686 | *
|
---|
| 687 | * \returns the inverse transformation matrix according to some given knowledge
|
---|
| 688 | * on \c *this.
|
---|
| 689 | *
|
---|
| 690 | * \param traits allows to optimize the inversion process when the transformion
|
---|
| 691 | * is known to be not a general transformation. The possible values are:
|
---|
| 692 | * - Projective if the transformation is not necessarily affine, i.e., if the
|
---|
| 693 | * last row is not guaranteed to be [0 ... 0 1]
|
---|
| 694 | * - Affine is the default, the last row is assumed to be [0 ... 0 1]
|
---|
| 695 | * - Isometry if the transformation is only a concatenations of translations
|
---|
| 696 | * and rotations.
|
---|
| 697 | *
|
---|
| 698 | * \warning unless \a traits is always set to NoShear or NoScaling, this function
|
---|
| 699 | * requires the generic inverse method of MatrixBase defined in the LU module. If
|
---|
| 700 | * you forget to include this module, then you will get hard to debug linking errors.
|
---|
| 701 | *
|
---|
| 702 | * \sa MatrixBase::inverse()
|
---|
| 703 | */
|
---|
| 704 | template<typename Scalar, int Dim>
|
---|
| 705 | inline const typename Transform<Scalar,Dim>::MatrixType
|
---|
| 706 | Transform<Scalar,Dim>::inverse(TransformTraits traits) const
|
---|
| 707 | {
|
---|
| 708 | if (traits == Projective)
|
---|
| 709 | {
|
---|
| 710 | return m_matrix.inverse();
|
---|
| 711 | }
|
---|
| 712 | else
|
---|
| 713 | {
|
---|
| 714 | MatrixType res;
|
---|
| 715 | if (traits == Affine)
|
---|
| 716 | {
|
---|
| 717 | res.template corner<Dim,Dim>(TopLeft) = linear().inverse();
|
---|
| 718 | }
|
---|
| 719 | else if (traits == Isometry)
|
---|
| 720 | {
|
---|
| 721 | res.template corner<Dim,Dim>(TopLeft) = linear().transpose();
|
---|
| 722 | }
|
---|
| 723 | else
|
---|
| 724 | {
|
---|
| 725 | ei_assert("invalid traits value in Transform::inverse()");
|
---|
| 726 | }
|
---|
| 727 | // translation and remaining parts
|
---|
| 728 | res.template corner<Dim,1>(TopRight) = - res.template corner<Dim,Dim>(TopLeft) * translation();
|
---|
| 729 | res.template corner<1,Dim>(BottomLeft).setZero();
|
---|
| 730 | res.coeffRef(Dim,Dim) = Scalar(1);
|
---|
| 731 | return res;
|
---|
| 732 | }
|
---|
| 733 | }
|
---|
| 734 |
|
---|
| 735 | /*****************************************************
|
---|
| 736 | *** Specializations of operator* with a MatrixBase ***
|
---|
| 737 | *****************************************************/
|
---|
| 738 |
|
---|
| 739 | template<typename Other, int Dim, int HDim>
|
---|
| 740 | struct ei_transform_product_impl<Other,Dim,HDim, HDim,HDim>
|
---|
| 741 | {
|
---|
| 742 | typedef Transform<typename Other::Scalar,Dim> TransformType;
|
---|
| 743 | typedef typename TransformType::MatrixType MatrixType;
|
---|
| 744 | typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
|
---|
| 745 | static ResultType run(const TransformType& tr, const Other& other)
|
---|
| 746 | { return tr.matrix() * other; }
|
---|
| 747 | };
|
---|
| 748 |
|
---|
| 749 | template<typename Other, int Dim, int HDim>
|
---|
| 750 | struct ei_transform_product_impl<Other,Dim,HDim, Dim,Dim>
|
---|
| 751 | {
|
---|
| 752 | typedef Transform<typename Other::Scalar,Dim> TransformType;
|
---|
| 753 | typedef typename TransformType::MatrixType MatrixType;
|
---|
| 754 | typedef TransformType ResultType;
|
---|
| 755 | static ResultType run(const TransformType& tr, const Other& other)
|
---|
| 756 | {
|
---|
| 757 | TransformType res;
|
---|
| 758 | res.translation() = tr.translation();
|
---|
| 759 | res.matrix().row(Dim) = tr.matrix().row(Dim);
|
---|
| 760 | res.linear() = (tr.linear() * other).lazy();
|
---|
| 761 | return res;
|
---|
| 762 | }
|
---|
| 763 | };
|
---|
| 764 |
|
---|
| 765 | template<typename Other, int Dim, int HDim>
|
---|
| 766 | struct ei_transform_product_impl<Other,Dim,HDim, HDim,1>
|
---|
| 767 | {
|
---|
| 768 | typedef Transform<typename Other::Scalar,Dim> TransformType;
|
---|
| 769 | typedef typename TransformType::MatrixType MatrixType;
|
---|
| 770 | typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
|
---|
| 771 | static ResultType run(const TransformType& tr, const Other& other)
|
---|
| 772 | { return tr.matrix() * other; }
|
---|
| 773 | };
|
---|
| 774 |
|
---|
| 775 | template<typename Other, int Dim, int HDim>
|
---|
| 776 | struct ei_transform_product_impl<Other,Dim,HDim, Dim,1>
|
---|
| 777 | {
|
---|
| 778 | typedef typename Other::Scalar Scalar;
|
---|
| 779 | typedef Transform<Scalar,Dim> TransformType;
|
---|
| 780 | typedef Matrix<Scalar,Dim,1> ResultType;
|
---|
| 781 | static ResultType run(const TransformType& tr, const Other& other)
|
---|
| 782 | { return ((tr.linear() * other) + tr.translation())
|
---|
| 783 | * (Scalar(1) / ( (tr.matrix().template block<1,Dim>(Dim,0) * other).coeff(0) + tr.matrix().coeff(Dim,Dim))); }
|
---|
| 784 | };
|
---|
| 785 |
|
---|
| 786 | } // end namespace Eigen
|
---|