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 | }
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400 |
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401 | /** Applies on the left the non uniform scale transformation represented
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402 | * by the vector \a other to \c *this and returns a reference to \c *this.
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403 | * \sa scale()
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404 | */
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405 | template<typename Scalar, int Dim>
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406 | template<typename OtherDerived>
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407 | Transform<Scalar,Dim>&
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408 | Transform<Scalar,Dim>::prescale(const MatrixBase<OtherDerived> &other)
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409 | {
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410 | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
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411 | m_matrix.template block<Dim,HDim>(0,0) = (other.asDiagonal() * m_matrix.template block<Dim,HDim>(0,0)).lazy();
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412 | return *this;
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413 | }
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414 |
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415 | /** Applies on the left a uniform scale of a factor \a c to \c *this
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416 | * and returns a reference to \c *this.
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417 | * \sa scale(Scalar)
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418 | */
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419 | template<typename Scalar, int Dim>
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---|
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
|
---|