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 | // Copyright (C) 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_PARAMETRIZEDLINE_H
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12 | #define EIGEN_PARAMETRIZEDLINE_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 \ingroup Geometry_Module
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17 | *
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18 | * \class ParametrizedLine
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19 | *
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20 | * \brief A parametrized line
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21 | *
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22 | * A parametrized line is defined by an origin point \f$ \mathbf{o} \f$ and a unit
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23 | * direction vector \f$ \mathbf{d} \f$ such that the line corresponds to
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24 | * the set \f$ l(t) = \mathbf{o} + t \mathbf{d} \f$, \f$ t \in \mathbf{R} \f$.
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25 | *
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26 | * \param _Scalar the scalar type, i.e., the type of the coefficients
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27 | * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
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28 | */
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29 | template <typename _Scalar, int _AmbientDim, int _Options>
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30 | class ParametrizedLine
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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 {
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35 | AmbientDimAtCompileTime = _AmbientDim,
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36 | Options = _Options
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37 | };
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38 | typedef _Scalar Scalar;
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39 | typedef typename NumTraits<Scalar>::Real RealScalar;
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40 | typedef DenseIndex Index;
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41 | typedef Matrix<Scalar,AmbientDimAtCompileTime,1,Options> VectorType;
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42 |
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43 | /** Default constructor without initialization */
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44 | inline ParametrizedLine() {}
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45 |
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46 | template<int OtherOptions>
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47 | ParametrizedLine(const ParametrizedLine<Scalar,AmbientDimAtCompileTime,OtherOptions>& other)
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48 | : m_origin(other.origin()), m_direction(other.direction())
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49 | {}
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50 |
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51 | /** Constructs a dynamic-size line with \a _dim the dimension
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52 | * of the ambient space */
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53 | inline explicit ParametrizedLine(Index _dim) : m_origin(_dim), m_direction(_dim) {}
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54 |
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55 | /** Initializes a parametrized line of direction \a direction and origin \a origin.
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56 | * \warning the vector direction is assumed to be normalized.
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57 | */
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58 | ParametrizedLine(const VectorType& origin, const VectorType& direction)
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59 | : m_origin(origin), m_direction(direction) {}
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60 |
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61 | template <int OtherOptions>
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62 | explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane);
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63 |
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64 | /** Constructs a parametrized line going from \a p0 to \a p1. */
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65 | static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1)
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66 | { return ParametrizedLine(p0, (p1-p0).normalized()); }
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67 |
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68 | ~ParametrizedLine() {}
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69 |
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70 | /** \returns the dimension in which the line holds */
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71 | inline Index dim() const { return m_direction.size(); }
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72 |
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73 | const VectorType& origin() const { return m_origin; }
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74 | VectorType& origin() { return m_origin; }
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75 |
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76 | const VectorType& direction() const { return m_direction; }
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77 | VectorType& direction() { return m_direction; }
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78 |
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79 | /** \returns the squared distance of a point \a p to its projection onto the line \c *this.
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80 | * \sa distance()
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81 | */
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82 | RealScalar squaredDistance(const VectorType& p) const
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83 | {
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84 | VectorType diff = p - origin();
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85 | return (diff - direction().dot(diff) * direction()).squaredNorm();
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86 | }
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87 | /** \returns the distance of a point \a p to its projection onto the line \c *this.
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88 | * \sa squaredDistance()
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89 | */
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90 | RealScalar distance(const VectorType& p) const { using std::sqrt; return sqrt(squaredDistance(p)); }
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91 |
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92 | /** \returns the projection of a point \a p onto the line \c *this. */
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93 | VectorType projection(const VectorType& p) const
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94 | { return origin() + direction().dot(p-origin()) * direction(); }
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95 |
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96 | VectorType pointAt(const Scalar& t) const;
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97 |
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98 | template <int OtherOptions>
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99 | Scalar intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
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100 |
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101 | template <int OtherOptions>
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102 | Scalar intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
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103 |
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104 | template <int OtherOptions>
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105 | VectorType intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
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106 |
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107 | /** \returns \c *this with scalar type casted to \a NewScalarType
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108 | *
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109 | * Note that if \a NewScalarType is equal to the current scalar type of \c *this
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110 | * then this function smartly returns a const reference to \c *this.
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111 | */
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112 | template<typename NewScalarType>
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113 | inline typename internal::cast_return_type<ParametrizedLine,
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114 | ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type cast() const
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115 | {
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116 | return typename internal::cast_return_type<ParametrizedLine,
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117 | ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this);
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118 | }
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119 |
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120 | /** Copy constructor with scalar type conversion */
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121 | template<typename OtherScalarType,int OtherOptions>
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122 | inline explicit ParametrizedLine(const ParametrizedLine<OtherScalarType,AmbientDimAtCompileTime,OtherOptions>& other)
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123 | {
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124 | m_origin = other.origin().template cast<Scalar>();
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125 | m_direction = other.direction().template cast<Scalar>();
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126 | }
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127 |
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128 | /** \returns \c true if \c *this is approximately equal to \a other, within the precision
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129 | * determined by \a prec.
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130 | *
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131 | * \sa MatrixBase::isApprox() */
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132 | bool isApprox(const ParametrizedLine& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
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133 | { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); }
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134 |
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135 | protected:
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136 |
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137 | VectorType m_origin, m_direction;
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138 | };
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139 |
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140 | /** Constructs a parametrized line from a 2D hyperplane
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141 | *
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142 | * \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line
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143 | */
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144 | template <typename _Scalar, int _AmbientDim, int _Options>
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145 | template <int OtherOptions>
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146 | inline ParametrizedLine<_Scalar, _AmbientDim,_Options>::ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim,OtherOptions>& hyperplane)
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147 | {
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148 | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
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149 | direction() = hyperplane.normal().unitOrthogonal();
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150 | origin() = -hyperplane.normal()*hyperplane.offset();
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151 | }
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152 |
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153 | /** \returns the point at \a t along this line
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154 | */
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155 | template <typename _Scalar, int _AmbientDim, int _Options>
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156 | inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType
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157 | ParametrizedLine<_Scalar, _AmbientDim,_Options>::pointAt(const _Scalar& t) const
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158 | {
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159 | return origin() + (direction()*t);
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160 | }
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161 |
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162 | /** \returns the parameter value of the intersection between \c *this and the given \a hyperplane
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163 | */
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164 | template <typename _Scalar, int _AmbientDim, int _Options>
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165 | template <int OtherOptions>
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166 | inline _Scalar ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
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167 | {
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168 | return -(hyperplane.offset()+hyperplane.normal().dot(origin()))
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169 | / hyperplane.normal().dot(direction());
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170 | }
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171 |
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172 |
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173 | /** \deprecated use intersectionParameter()
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174 | * \returns the parameter value of the intersection between \c *this and the given \a hyperplane
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175 | */
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176 | template <typename _Scalar, int _AmbientDim, int _Options>
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177 | template <int OtherOptions>
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178 | inline _Scalar ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
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179 | {
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180 | return intersectionParameter(hyperplane);
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181 | }
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182 |
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183 | /** \returns the point of the intersection between \c *this and the given hyperplane
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184 | */
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185 | template <typename _Scalar, int _AmbientDim, int _Options>
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186 | template <int OtherOptions>
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187 | inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType
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188 | ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
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189 | {
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190 | return pointAt(intersectionParameter(hyperplane));
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191 | }
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192 |
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193 | } // end namespace Eigen
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194 |
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195 | #endif // EIGEN_PARAMETRIZEDLINE_H
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