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 <gael.guennebaud@inria.fr>
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5 | //
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6 | // This Source Code Form is subject to the terms of the Mozilla
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7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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9 |
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10 | #ifndef EIGEN_TRANSLATION_H
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11 | #define EIGEN_TRANSLATION_H
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12 |
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13 | namespace Eigen {
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14 |
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15 | /** \geometry_module \ingroup Geometry_Module
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16 | *
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17 | * \class Translation
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18 | *
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19 | * \brief Represents a translation transformation
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20 | *
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21 | * \param _Scalar the scalar type, i.e., the type of the coefficients.
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22 | * \param _Dim the dimension of the space, can be a compile time value or Dynamic
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23 | *
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24 | * \note This class is not aimed to be used to store a translation transformation,
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25 | * but rather to make easier the constructions and updates of Transform objects.
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26 | *
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27 | * \sa class Scaling, class Transform
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28 | */
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29 | template<typename _Scalar, int _Dim>
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30 | class Translation
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31 | {
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32 | public:
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33 | EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim)
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34 | /** dimension of the space */
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35 | enum { Dim = _Dim };
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36 | /** the scalar type of the coefficients */
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37 | typedef _Scalar Scalar;
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38 | /** corresponding vector type */
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39 | typedef Matrix<Scalar,Dim,1> VectorType;
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40 | /** corresponding linear transformation matrix type */
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41 | typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
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42 | /** corresponding affine transformation type */
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43 | typedef Transform<Scalar,Dim,Affine> AffineTransformType;
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44 | /** corresponding isometric transformation type */
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45 | typedef Transform<Scalar,Dim,Isometry> IsometryTransformType;
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46 |
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47 | protected:
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48 |
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49 | VectorType m_coeffs;
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50 |
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51 | public:
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52 |
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53 | /** Default constructor without initialization. */
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54 | Translation() {}
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55 | /** */
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56 | inline Translation(const Scalar& sx, const Scalar& sy)
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57 | {
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58 | eigen_assert(Dim==2);
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59 | m_coeffs.x() = sx;
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60 | m_coeffs.y() = sy;
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61 | }
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62 | /** */
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63 | inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz)
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64 | {
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65 | eigen_assert(Dim==3);
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66 | m_coeffs.x() = sx;
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67 | m_coeffs.y() = sy;
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68 | m_coeffs.z() = sz;
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69 | }
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70 | /** Constructs and initialize the translation transformation from a vector of translation coefficients */
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71 | explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {}
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72 |
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73 | /** \brief Retruns the x-translation by value. **/
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74 | inline Scalar x() const { return m_coeffs.x(); }
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75 | /** \brief Retruns the y-translation by value. **/
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76 | inline Scalar y() const { return m_coeffs.y(); }
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77 | /** \brief Retruns the z-translation by value. **/
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78 | inline Scalar z() const { return m_coeffs.z(); }
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79 |
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80 | /** \brief Retruns the x-translation as a reference. **/
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81 | inline Scalar& x() { return m_coeffs.x(); }
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82 | /** \brief Retruns the y-translation as a reference. **/
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83 | inline Scalar& y() { return m_coeffs.y(); }
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84 | /** \brief Retruns the z-translation as a reference. **/
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85 | inline Scalar& z() { return m_coeffs.z(); }
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86 |
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87 | const VectorType& vector() const { return m_coeffs; }
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88 | VectorType& vector() { return m_coeffs; }
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89 |
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90 | const VectorType& translation() const { return m_coeffs; }
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91 | VectorType& translation() { return m_coeffs; }
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92 |
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93 | /** Concatenates two translation */
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94 | inline Translation operator* (const Translation& other) const
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95 | { return Translation(m_coeffs + other.m_coeffs); }
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96 |
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97 | /** Concatenates a translation and a uniform scaling */
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98 | inline AffineTransformType operator* (const UniformScaling<Scalar>& other) const;
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99 |
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100 | /** Concatenates a translation and a linear transformation */
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101 | template<typename OtherDerived>
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102 | inline AffineTransformType operator* (const EigenBase<OtherDerived>& linear) const;
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103 |
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104 | /** Concatenates a translation and a rotation */
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105 | template<typename Derived>
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106 | inline IsometryTransformType operator*(const RotationBase<Derived,Dim>& r) const
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107 | { return *this * IsometryTransformType(r); }
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108 |
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109 | /** \returns the concatenation of a linear transformation \a l with the translation \a t */
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110 | // its a nightmare to define a templated friend function outside its declaration
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111 | template<typename OtherDerived> friend
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112 | inline AffineTransformType operator*(const EigenBase<OtherDerived>& linear, const Translation& t)
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113 | {
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114 | AffineTransformType res;
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115 | res.matrix().setZero();
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116 | res.linear() = linear.derived();
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117 | res.translation() = linear.derived() * t.m_coeffs;
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118 | res.matrix().row(Dim).setZero();
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119 | res(Dim,Dim) = Scalar(1);
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120 | return res;
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121 | }
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122 |
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123 | /** Concatenates a translation and a transformation */
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124 | template<int Mode, int Options>
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125 | inline Transform<Scalar,Dim,Mode> operator* (const Transform<Scalar,Dim,Mode,Options>& t) const
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126 | {
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127 | Transform<Scalar,Dim,Mode> res = t;
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128 | res.pretranslate(m_coeffs);
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129 | return res;
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130 | }
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131 |
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132 | /** Applies translation to vector */
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133 | inline VectorType operator* (const VectorType& other) const
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134 | { return m_coeffs + other; }
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135 |
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136 | /** \returns the inverse translation (opposite) */
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137 | Translation inverse() const { return Translation(-m_coeffs); }
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138 |
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139 | Translation& operator=(const Translation& other)
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140 | {
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141 | m_coeffs = other.m_coeffs;
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142 | return *this;
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143 | }
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144 |
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145 | static const Translation Identity() { return Translation(VectorType::Zero()); }
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146 |
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147 | /** \returns \c *this with scalar type casted to \a NewScalarType
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148 | *
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149 | * Note that if \a NewScalarType is equal to the current scalar type of \c *this
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150 | * then this function smartly returns a const reference to \c *this.
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151 | */
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152 | template<typename NewScalarType>
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153 | inline typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type cast() const
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154 | { return typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type(*this); }
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155 |
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156 | /** Copy constructor with scalar type conversion */
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157 | template<typename OtherScalarType>
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158 | inline explicit Translation(const Translation<OtherScalarType,Dim>& other)
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159 | { m_coeffs = other.vector().template cast<Scalar>(); }
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160 |
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161 | /** \returns \c true if \c *this is approximately equal to \a other, within the precision
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162 | * determined by \a prec.
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163 | *
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164 | * \sa MatrixBase::isApprox() */
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165 | bool isApprox(const Translation& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
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166 | { return m_coeffs.isApprox(other.m_coeffs, prec); }
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167 |
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168 | };
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169 |
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170 | /** \addtogroup Geometry_Module */
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171 | //@{
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172 | typedef Translation<float, 2> Translation2f;
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173 | typedef Translation<double,2> Translation2d;
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174 | typedef Translation<float, 3> Translation3f;
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175 | typedef Translation<double,3> Translation3d;
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176 | //@}
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177 |
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178 | template<typename Scalar, int Dim>
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179 | inline typename Translation<Scalar,Dim>::AffineTransformType
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180 | Translation<Scalar,Dim>::operator* (const UniformScaling<Scalar>& other) const
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181 | {
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182 | AffineTransformType res;
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183 | res.matrix().setZero();
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184 | res.linear().diagonal().fill(other.factor());
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185 | res.translation() = m_coeffs;
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186 | res(Dim,Dim) = Scalar(1);
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187 | return res;
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188 | }
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189 |
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190 | template<typename Scalar, int Dim>
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191 | template<typename OtherDerived>
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192 | inline typename Translation<Scalar,Dim>::AffineTransformType
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193 | Translation<Scalar,Dim>::operator* (const EigenBase<OtherDerived>& linear) const
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194 | {
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195 | AffineTransformType res;
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196 | res.matrix().setZero();
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197 | res.linear() = linear.derived();
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198 | res.translation() = m_coeffs;
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199 | res.matrix().row(Dim).setZero();
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200 | res(Dim,Dim) = Scalar(1);
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201 | return res;
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202 | }
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203 |
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204 | } // end namespace Eigen
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205 |
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206 | #endif // EIGEN_TRANSLATION_H
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