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) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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5 | // Copyright (C) 2006-2008 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 | #ifndef EIGEN_ORTHOMETHODS_H
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12 | #define EIGEN_ORTHOMETHODS_H
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13 |
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14 | namespace Eigen {
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15 |
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16 | /** \geometry_module
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17 | *
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18 | * \returns the cross product of \c *this and \a other
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19 | *
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20 | * Here is a very good explanation of cross-product: http://xkcd.com/199/
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21 | * \sa MatrixBase::cross3()
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22 | */
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23 | template<typename Derived>
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24 | template<typename OtherDerived>
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25 | inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
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26 | MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
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27 | {
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28 | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
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29 | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
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30 |
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31 | // Note that there is no need for an expression here since the compiler
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32 | // optimize such a small temporary very well (even within a complex expression)
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33 | typename internal::nested<Derived,2>::type lhs(derived());
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34 | typename internal::nested<OtherDerived,2>::type rhs(other.derived());
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35 | return typename cross_product_return_type<OtherDerived>::type(
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36 | numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
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37 | numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
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38 | numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
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39 | );
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40 | }
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41 |
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42 | namespace internal {
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43 |
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44 | template< int Arch,typename VectorLhs,typename VectorRhs,
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45 | typename Scalar = typename VectorLhs::Scalar,
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46 | bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>
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47 | struct cross3_impl {
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48 | static inline typename internal::plain_matrix_type<VectorLhs>::type
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49 | run(const VectorLhs& lhs, const VectorRhs& rhs)
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50 | {
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51 | return typename internal::plain_matrix_type<VectorLhs>::type(
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52 | numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
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53 | numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
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54 | numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
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55 | 0
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56 | );
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57 | }
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58 | };
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59 |
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60 | }
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61 |
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62 | /** \geometry_module
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63 | *
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64 | * \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
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65 | *
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66 | * The size of \c *this and \a other must be four. This function is especially useful
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67 | * when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
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68 | *
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69 | * \sa MatrixBase::cross()
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70 | */
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71 | template<typename Derived>
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72 | template<typename OtherDerived>
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73 | inline typename MatrixBase<Derived>::PlainObject
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74 | MatrixBase<Derived>::cross3(const MatrixBase<OtherDerived>& other) const
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75 | {
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76 | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)
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77 | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)
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78 |
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79 | typedef typename internal::nested<Derived,2>::type DerivedNested;
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80 | typedef typename internal::nested<OtherDerived,2>::type OtherDerivedNested;
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81 | DerivedNested lhs(derived());
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82 | OtherDerivedNested rhs(other.derived());
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83 |
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84 | return internal::cross3_impl<Architecture::Target,
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85 | typename internal::remove_all<DerivedNested>::type,
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86 | typename internal::remove_all<OtherDerivedNested>::type>::run(lhs,rhs);
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87 | }
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88 |
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89 | /** \returns a matrix expression of the cross product of each column or row
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90 | * of the referenced expression with the \a other vector.
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91 | *
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92 | * The referenced matrix must have one dimension equal to 3.
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93 | * The result matrix has the same dimensions than the referenced one.
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94 | *
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95 | * \geometry_module
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96 | *
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97 | * \sa MatrixBase::cross() */
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98 | template<typename ExpressionType, int Direction>
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99 | template<typename OtherDerived>
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100 | const typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType
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101 | VectorwiseOp<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& other) const
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102 | {
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103 | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
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104 | EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
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105 | YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
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106 |
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107 | CrossReturnType res(_expression().rows(),_expression().cols());
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108 | if(Direction==Vertical)
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109 | {
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110 | eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
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111 | res.row(0) = (_expression().row(1) * other.coeff(2) - _expression().row(2) * other.coeff(1)).conjugate();
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112 | res.row(1) = (_expression().row(2) * other.coeff(0) - _expression().row(0) * other.coeff(2)).conjugate();
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113 | res.row(2) = (_expression().row(0) * other.coeff(1) - _expression().row(1) * other.coeff(0)).conjugate();
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114 | }
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115 | else
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116 | {
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117 | eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
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118 | res.col(0) = (_expression().col(1) * other.coeff(2) - _expression().col(2) * other.coeff(1)).conjugate();
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119 | res.col(1) = (_expression().col(2) * other.coeff(0) - _expression().col(0) * other.coeff(2)).conjugate();
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120 | res.col(2) = (_expression().col(0) * other.coeff(1) - _expression().col(1) * other.coeff(0)).conjugate();
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121 | }
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122 | return res;
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123 | }
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124 |
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125 | namespace internal {
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126 |
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127 | template<typename Derived, int Size = Derived::SizeAtCompileTime>
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128 | struct unitOrthogonal_selector
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129 | {
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130 | typedef typename plain_matrix_type<Derived>::type VectorType;
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131 | typedef typename traits<Derived>::Scalar Scalar;
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132 | typedef typename NumTraits<Scalar>::Real RealScalar;
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133 | typedef typename Derived::Index Index;
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134 | typedef Matrix<Scalar,2,1> Vector2;
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135 | static inline VectorType run(const Derived& src)
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136 | {
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137 | VectorType perp = VectorType::Zero(src.size());
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138 | Index maxi = 0;
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139 | Index sndi = 0;
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140 | src.cwiseAbs().maxCoeff(&maxi);
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141 | if (maxi==0)
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142 | sndi = 1;
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143 | RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
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144 | perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
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145 | perp.coeffRef(sndi) = numext::conj(src.coeff(maxi)) * invnm;
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146 |
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147 | return perp;
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148 | }
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149 | };
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150 |
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151 | template<typename Derived>
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152 | struct unitOrthogonal_selector<Derived,3>
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153 | {
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154 | typedef typename plain_matrix_type<Derived>::type VectorType;
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155 | typedef typename traits<Derived>::Scalar Scalar;
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156 | typedef typename NumTraits<Scalar>::Real RealScalar;
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157 | static inline VectorType run(const Derived& src)
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158 | {
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159 | VectorType perp;
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160 | /* Let us compute the crossed product of *this with a vector
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161 | * that is not too close to being colinear to *this.
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162 | */
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163 |
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164 | /* unless the x and y coords are both close to zero, we can
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165 | * simply take ( -y, x, 0 ) and normalize it.
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166 | */
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167 | if((!isMuchSmallerThan(src.x(), src.z()))
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168 | || (!isMuchSmallerThan(src.y(), src.z())))
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169 | {
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170 | RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
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171 | perp.coeffRef(0) = -numext::conj(src.y())*invnm;
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172 | perp.coeffRef(1) = numext::conj(src.x())*invnm;
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173 | perp.coeffRef(2) = 0;
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174 | }
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175 | /* if both x and y are close to zero, then the vector is close
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176 | * to the z-axis, so it's far from colinear to the x-axis for instance.
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177 | * So we take the crossed product with (1,0,0) and normalize it.
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178 | */
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179 | else
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180 | {
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181 | RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
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182 | perp.coeffRef(0) = 0;
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183 | perp.coeffRef(1) = -numext::conj(src.z())*invnm;
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184 | perp.coeffRef(2) = numext::conj(src.y())*invnm;
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185 | }
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186 |
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187 | return perp;
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188 | }
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189 | };
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190 |
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191 | template<typename Derived>
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192 | struct unitOrthogonal_selector<Derived,2>
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193 | {
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194 | typedef typename plain_matrix_type<Derived>::type VectorType;
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195 | static inline VectorType run(const Derived& src)
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196 | { return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
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197 | };
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198 |
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199 | } // end namespace internal
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200 |
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201 | /** \returns a unit vector which is orthogonal to \c *this
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202 | *
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203 | * The size of \c *this must be at least 2. If the size is exactly 2,
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204 | * then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
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205 | *
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206 | * \sa cross()
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207 | */
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208 | template<typename Derived>
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209 | typename MatrixBase<Derived>::PlainObject
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210 | MatrixBase<Derived>::unitOrthogonal() const
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211 | {
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212 | EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
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213 | return internal::unitOrthogonal_selector<Derived>::run(derived());
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214 | }
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215 |
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216 | } // end namespace Eigen
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217 |
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218 | #endif // EIGEN_ORTHOMETHODS_H
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