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_ALIGNEDBOX_H
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11 | #define EIGEN_ALIGNEDBOX_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 | *
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18 | * \class AlignedBox
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19 | *
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20 | * \brief An axis aligned box
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21 | *
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22 | * \tparam _Scalar the type of the scalar coefficients
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23 | * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
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24 | *
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25 | * This class represents an axis aligned box as a pair of the minimal and maximal corners.
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26 | * \warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using isEmpty().
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27 | * \sa alignedboxtypedefs
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28 | */
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29 | template <typename _Scalar, int _AmbientDim>
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30 | class AlignedBox
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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,_AmbientDim)
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34 | enum { AmbientDimAtCompileTime = _AmbientDim };
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35 | typedef _Scalar Scalar;
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36 | typedef NumTraits<Scalar> ScalarTraits;
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37 | typedef DenseIndex Index;
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38 | typedef typename ScalarTraits::Real RealScalar;
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39 | typedef typename ScalarTraits::NonInteger NonInteger;
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40 | typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
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41 |
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42 | /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
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43 | enum CornerType
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44 | {
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45 | /** 1D names @{ */
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46 | Min=0, Max=1,
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47 | /** @} */
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48 |
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49 | /** Identifier for 2D corner @{ */
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50 | BottomLeft=0, BottomRight=1,
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51 | TopLeft=2, TopRight=3,
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52 | /** @} */
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53 |
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54 | /** Identifier for 3D corner @{ */
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55 | BottomLeftFloor=0, BottomRightFloor=1,
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56 | TopLeftFloor=2, TopRightFloor=3,
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57 | BottomLeftCeil=4, BottomRightCeil=5,
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58 | TopLeftCeil=6, TopRightCeil=7
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59 | /** @} */
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60 | };
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61 |
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62 |
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63 | /** Default constructor initializing a null box. */
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64 | inline AlignedBox()
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65 | { if (AmbientDimAtCompileTime!=Dynamic) setEmpty(); }
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66 |
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67 | /** Constructs a null box with \a _dim the dimension of the ambient space. */
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68 | inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim)
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69 | { setEmpty(); }
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70 |
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71 | /** Constructs a box with extremities \a _min and \a _max.
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72 | * \warning If either component of \a _min is larger than the same component of \a _max, the constructed box is empty. */
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73 | template<typename OtherVectorType1, typename OtherVectorType2>
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74 | inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {}
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75 |
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76 | /** Constructs a box containing a single point \a p. */
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77 | template<typename Derived>
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78 | inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min)
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79 | { }
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80 |
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81 | ~AlignedBox() {}
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82 |
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83 | /** \returns the dimension in which the box holds */
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84 | inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); }
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85 |
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86 | /** \deprecated use isEmpty() */
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87 | inline bool isNull() const { return isEmpty(); }
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88 |
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89 | /** \deprecated use setEmpty() */
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90 | inline void setNull() { setEmpty(); }
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91 |
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92 | /** \returns true if the box is empty.
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93 | * \sa setEmpty */
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94 | inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }
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95 |
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96 | /** Makes \c *this an empty box.
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97 | * \sa isEmpty */
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98 | inline void setEmpty()
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99 | {
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100 | m_min.setConstant( ScalarTraits::highest() );
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101 | m_max.setConstant( ScalarTraits::lowest() );
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102 | }
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103 |
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104 | /** \returns the minimal corner */
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105 | inline const VectorType& (min)() const { return m_min; }
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106 | /** \returns a non const reference to the minimal corner */
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107 | inline VectorType& (min)() { return m_min; }
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108 | /** \returns the maximal corner */
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109 | inline const VectorType& (max)() const { return m_max; }
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110 | /** \returns a non const reference to the maximal corner */
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111 | inline VectorType& (max)() { return m_max; }
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112 |
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113 | /** \returns the center of the box */
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114 | inline const CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>,
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115 | const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> >
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116 | center() const
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117 | { return (m_min+m_max)/2; }
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118 |
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119 | /** \returns the lengths of the sides of the bounding box.
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120 | * Note that this function does not get the same
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121 | * result for integral or floating scalar types: see
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122 | */
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123 | inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> sizes() const
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124 | { return m_max - m_min; }
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125 |
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126 | /** \returns the volume of the bounding box */
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127 | inline Scalar volume() const
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128 | { return sizes().prod(); }
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129 |
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130 | /** \returns an expression for the bounding box diagonal vector
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131 | * if the length of the diagonal is needed: diagonal().norm()
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132 | * will provide it.
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133 | */
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134 | inline CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> diagonal() const
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135 | { return sizes(); }
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136 |
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137 | /** \returns the vertex of the bounding box at the corner defined by
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138 | * the corner-id corner. It works only for a 1D, 2D or 3D bounding box.
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139 | * For 1D bounding boxes corners are named by 2 enum constants:
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140 | * BottomLeft and BottomRight.
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141 | * For 2D bounding boxes, corners are named by 4 enum constants:
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142 | * BottomLeft, BottomRight, TopLeft, TopRight.
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143 | * For 3D bounding boxes, the following names are added:
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144 | * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil.
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145 | */
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146 | inline VectorType corner(CornerType corner) const
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147 | {
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148 | EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE);
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149 |
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150 | VectorType res;
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151 |
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152 | Index mult = 1;
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153 | for(Index d=0; d<dim(); ++d)
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154 | {
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155 | if( mult & corner ) res[d] = m_max[d];
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156 | else res[d] = m_min[d];
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157 | mult *= 2;
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158 | }
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159 | return res;
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160 | }
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161 |
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162 | /** \returns a random point inside the bounding box sampled with
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163 | * a uniform distribution */
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164 | inline VectorType sample() const
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165 | {
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166 | VectorType r(dim());
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167 | for(Index d=0; d<dim(); ++d)
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168 | {
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169 | if(!ScalarTraits::IsInteger)
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170 | {
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171 | r[d] = m_min[d] + (m_max[d]-m_min[d])
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172 | * internal::random<Scalar>(Scalar(0), Scalar(1));
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173 | }
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174 | else
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175 | r[d] = internal::random(m_min[d], m_max[d]);
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176 | }
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177 | return r;
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178 | }
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179 |
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180 | /** \returns true if the point \a p is inside the box \c *this. */
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181 | template<typename Derived>
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182 | inline bool contains(const MatrixBase<Derived>& p) const
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183 | {
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184 | typename internal::nested<Derived,2>::type p_n(p.derived());
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185 | return (m_min.array()<=p_n.array()).all() && (p_n.array()<=m_max.array()).all();
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186 | }
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187 |
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188 | /** \returns true if the box \a b is entirely inside the box \c *this. */
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189 | inline bool contains(const AlignedBox& b) const
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190 | { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); }
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191 |
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192 | /** \returns true if the box \a b is intersecting the box \c *this.
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193 | * \sa intersection, clamp */
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194 | inline bool intersects(const AlignedBox& b) const
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195 | { return (m_min.array()<=(b.max)().array()).all() && ((b.min)().array()<=m_max.array()).all(); }
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196 |
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197 | /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this.
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198 | * \sa extend(const AlignedBox&) */
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199 | template<typename Derived>
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200 | inline AlignedBox& extend(const MatrixBase<Derived>& p)
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201 | {
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202 | typename internal::nested<Derived,2>::type p_n(p.derived());
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203 | m_min = m_min.cwiseMin(p_n);
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204 | m_max = m_max.cwiseMax(p_n);
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205 | return *this;
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206 | }
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207 |
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208 | /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this.
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209 | * \sa merged, extend(const MatrixBase&) */
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210 | inline AlignedBox& extend(const AlignedBox& b)
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211 | {
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212 | m_min = m_min.cwiseMin(b.m_min);
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213 | m_max = m_max.cwiseMax(b.m_max);
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214 | return *this;
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215 | }
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216 |
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217 | /** Clamps \c *this by the box \a b and returns a reference to \c *this.
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218 | * \note If the boxes don't intersect, the resulting box is empty.
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219 | * \sa intersection(), intersects() */
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220 | inline AlignedBox& clamp(const AlignedBox& b)
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221 | {
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222 | m_min = m_min.cwiseMax(b.m_min);
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223 | m_max = m_max.cwiseMin(b.m_max);
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224 | return *this;
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225 | }
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226 |
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227 | /** Returns an AlignedBox that is the intersection of \a b and \c *this
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228 | * \note If the boxes don't intersect, the resulting box is empty.
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229 | * \sa intersects(), clamp, contains() */
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230 | inline AlignedBox intersection(const AlignedBox& b) const
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231 | {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); }
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232 |
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233 | /** Returns an AlignedBox that is the union of \a b and \c *this.
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234 | * \note Merging with an empty box may result in a box bigger than \c *this.
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235 | * \sa extend(const AlignedBox&) */
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236 | inline AlignedBox merged(const AlignedBox& b) const
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237 | { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); }
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238 |
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239 | /** Translate \c *this by the vector \a t and returns a reference to \c *this. */
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240 | template<typename Derived>
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241 | inline AlignedBox& translate(const MatrixBase<Derived>& a_t)
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242 | {
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243 | const typename internal::nested<Derived,2>::type t(a_t.derived());
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244 | m_min += t;
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245 | m_max += t;
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246 | return *this;
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247 | }
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248 |
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249 | /** \returns the squared distance between the point \a p and the box \c *this,
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250 | * and zero if \a p is inside the box.
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251 | * \sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&)
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252 | */
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253 | template<typename Derived>
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254 | inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const;
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255 |
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256 | /** \returns the squared distance between the boxes \a b and \c *this,
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257 | * and zero if the boxes intersect.
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258 | * \sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&)
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259 | */
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260 | inline Scalar squaredExteriorDistance(const AlignedBox& b) const;
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261 |
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262 | /** \returns the distance between the point \a p and the box \c *this,
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263 | * and zero if \a p is inside the box.
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264 | * \sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&)
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265 | */
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266 | template<typename Derived>
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267 | inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const
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268 | { using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(p))); }
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269 |
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270 | /** \returns the distance between the boxes \a b and \c *this,
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271 | * and zero if the boxes intersect.
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272 | * \sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&)
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273 | */
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274 | inline NonInteger exteriorDistance(const AlignedBox& b) const
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275 | { using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(b))); }
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276 |
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277 | /** \returns \c *this with scalar type casted to \a NewScalarType
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278 | *
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279 | * Note that if \a NewScalarType is equal to the current scalar type of \c *this
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280 | * then this function smartly returns a const reference to \c *this.
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281 | */
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282 | template<typename NewScalarType>
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283 | inline typename internal::cast_return_type<AlignedBox,
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284 | AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
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285 | {
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286 | return typename internal::cast_return_type<AlignedBox,
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287 | AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
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288 | }
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289 |
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290 | /** Copy constructor with scalar type conversion */
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291 | template<typename OtherScalarType>
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292 | inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other)
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293 | {
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294 | m_min = (other.min)().template cast<Scalar>();
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295 | m_max = (other.max)().template cast<Scalar>();
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296 | }
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297 |
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298 | /** \returns \c true if \c *this is approximately equal to \a other, within the precision
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299 | * determined by \a prec.
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300 | *
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301 | * \sa MatrixBase::isApprox() */
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302 | bool isApprox(const AlignedBox& other, const RealScalar& prec = ScalarTraits::dummy_precision()) const
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303 | { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
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304 |
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305 | protected:
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306 |
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307 | VectorType m_min, m_max;
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308 | };
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309 |
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310 |
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311 |
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312 | template<typename Scalar,int AmbientDim>
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313 | template<typename Derived>
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314 | inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const
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315 | {
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316 | typename internal::nested<Derived,2*AmbientDim>::type p(a_p.derived());
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317 | Scalar dist2(0);
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318 | Scalar aux;
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319 | for (Index k=0; k<dim(); ++k)
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320 | {
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321 | if( m_min[k] > p[k] )
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322 | {
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323 | aux = m_min[k] - p[k];
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324 | dist2 += aux*aux;
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325 | }
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326 | else if( p[k] > m_max[k] )
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327 | {
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328 | aux = p[k] - m_max[k];
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329 | dist2 += aux*aux;
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330 | }
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331 | }
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332 | return dist2;
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333 | }
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334 |
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335 | template<typename Scalar,int AmbientDim>
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336 | inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const
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337 | {
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338 | Scalar dist2(0);
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339 | Scalar aux;
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340 | for (Index k=0; k<dim(); ++k)
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341 | {
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342 | if( m_min[k] > b.m_max[k] )
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343 | {
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344 | aux = m_min[k] - b.m_max[k];
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345 | dist2 += aux*aux;
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346 | }
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347 | else if( b.m_min[k] > m_max[k] )
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348 | {
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349 | aux = b.m_min[k] - m_max[k];
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350 | dist2 += aux*aux;
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351 | }
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352 | }
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353 | return dist2;
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354 | }
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355 |
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356 | /** \defgroup alignedboxtypedefs Global aligned box typedefs
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357 | *
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358 | * \ingroup Geometry_Module
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359 | *
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360 | * Eigen defines several typedef shortcuts for most common aligned box types.
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361 | *
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362 | * The general patterns are the following:
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363 | *
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364 | * \c AlignedBoxSizeType where \c Size can be \c 1, \c 2,\c 3,\c 4 for fixed size boxes or \c X for dynamic size,
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365 | * and where \c Type can be \c i for integer, \c f for float, \c d for double.
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366 | *
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367 | * For example, \c AlignedBox3d is a fixed-size 3x3 aligned box type of doubles, and \c AlignedBoxXf is a dynamic-size aligned box of floats.
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368 | *
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369 | * \sa class AlignedBox
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370 | */
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371 |
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372 | #define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
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373 | /** \ingroup alignedboxtypedefs */ \
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374 | typedef AlignedBox<Type, Size> AlignedBox##SizeSuffix##TypeSuffix;
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375 |
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376 | #define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
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377 | EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \
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378 | EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
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379 | EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
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380 | EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
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381 | EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)
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382 |
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383 | EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i)
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384 | EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f)
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385 | EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d)
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386 |
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387 | #undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
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388 | #undef EIGEN_MAKE_TYPEDEFS
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389 |
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390 | } // end namespace Eigen
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391 |
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392 | #endif // EIGEN_ALIGNEDBOX_H
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