1 | // This file is part of Eigen, a lightweight C++ template library |
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2 | // for linear algebra. Eigen itself is part of the KDE project. |
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3 | // |
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4 | // Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> |
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5 | // Copyright (C) 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 | // no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway |
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12 | |
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13 | namespace Eigen { |
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14 | |
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15 | /** \geometry_module \ingroup Geometry_Module |
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16 | * |
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17 | * \class ParametrizedLine |
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18 | * |
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19 | * \brief A parametrized line |
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20 | * |
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21 | * A parametrized line is defined by an origin point \f$ \mathbf{o} \f$ and a unit |
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22 | * direction vector \f$ \mathbf{d} \f$ such that the line corresponds to |
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23 | * the set \f$ l(t) = \mathbf{o} + t \mathbf{d} \f$, \f$ l \in \mathbf{R} \f$. |
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24 | * |
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25 | * \param _Scalar the scalar type, i.e., the type of the coefficients |
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26 | * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic. |
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27 | */ |
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28 | template <typename _Scalar, int _AmbientDim> |
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29 | class ParametrizedLine |
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30 | { |
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31 | public: |
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32 | EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim) |
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33 | enum { AmbientDimAtCompileTime = _AmbientDim }; |
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34 | typedef _Scalar Scalar; |
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35 | typedef typename NumTraits<Scalar>::Real RealScalar; |
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36 | typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType; |
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37 | |
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38 | /** Default constructor without initialization */ |
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39 | inline explicit ParametrizedLine() {} |
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40 | |
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41 | /** Constructs a dynamic-size line with \a _dim the dimension |
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42 | * of the ambient space */ |
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43 | inline explicit ParametrizedLine(int _dim) : m_origin(_dim), m_direction(_dim) {} |
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44 | |
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45 | /** Initializes a parametrized line of direction \a direction and origin \a origin. |
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46 | * \warning the vector direction is assumed to be normalized. |
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47 | */ |
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48 | ParametrizedLine(const VectorType& origin, const VectorType& direction) |
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49 | : m_origin(origin), m_direction(direction) {} |
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50 | |
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51 | explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim>& hyperplane); |
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52 | |
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53 | /** Constructs a parametrized line going from \a p0 to \a p1. */ |
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54 | static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1) |
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55 | { return ParametrizedLine(p0, (p1-p0).normalized()); } |
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56 | |
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57 | ~ParametrizedLine() {} |
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58 | |
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59 | /** \returns the dimension in which the line holds */ |
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60 | inline int dim() const { return m_direction.size(); } |
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61 | |
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62 | const VectorType& origin() const { return m_origin; } |
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63 | VectorType& origin() { return m_origin; } |
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64 | |
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65 | const VectorType& direction() const { return m_direction; } |
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66 | VectorType& direction() { return m_direction; } |
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67 | |
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68 | /** \returns the squared distance of a point \a p to its projection onto the line \c *this. |
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69 | * \sa distance() |
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70 | */ |
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71 | RealScalar squaredDistance(const VectorType& p) const |
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72 | { |
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73 | VectorType diff = p-origin(); |
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74 | return (diff - diff.eigen2_dot(direction())* direction()).squaredNorm(); |
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75 | } |
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76 | /** \returns the distance of a point \a p to its projection onto the line \c *this. |
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77 | * \sa squaredDistance() |
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78 | */ |
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79 | RealScalar distance(const VectorType& p) const { return ei_sqrt(squaredDistance(p)); } |
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80 | |
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81 | /** \returns the projection of a point \a p onto the line \c *this. */ |
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82 | VectorType projection(const VectorType& p) const |
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83 | { return origin() + (p-origin()).eigen2_dot(direction()) * direction(); } |
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84 | |
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85 | Scalar intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane); |
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86 | |
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87 | /** \returns \c *this with scalar type casted to \a NewScalarType |
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88 | * |
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89 | * Note that if \a NewScalarType is equal to the current scalar type of \c *this |
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90 | * then this function smartly returns a const reference to \c *this. |
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91 | */ |
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92 | template<typename NewScalarType> |
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93 | inline typename internal::cast_return_type<ParametrizedLine, |
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94 | ParametrizedLine<NewScalarType,AmbientDimAtCompileTime> >::type cast() const |
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95 | { |
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96 | return typename internal::cast_return_type<ParametrizedLine, |
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97 | ParametrizedLine<NewScalarType,AmbientDimAtCompileTime> >::type(*this); |
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98 | } |
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99 | |
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100 | /** Copy constructor with scalar type conversion */ |
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101 | template<typename OtherScalarType> |
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102 | inline explicit ParametrizedLine(const ParametrizedLine<OtherScalarType,AmbientDimAtCompileTime>& other) |
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103 | { |
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104 | m_origin = other.origin().template cast<Scalar>(); |
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105 | m_direction = other.direction().template cast<Scalar>(); |
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106 | } |
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107 | |
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108 | /** \returns \c true if \c *this is approximately equal to \a other, within the precision |
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109 | * determined by \a prec. |
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110 | * |
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111 | * \sa MatrixBase::isApprox() */ |
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112 | bool isApprox(const ParametrizedLine& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const |
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113 | { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); } |
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114 | |
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115 | protected: |
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116 | |
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117 | VectorType m_origin, m_direction; |
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118 | }; |
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119 | |
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120 | /** Constructs a parametrized line from a 2D hyperplane |
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121 | * |
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122 | * \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line |
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123 | */ |
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124 | template <typename _Scalar, int _AmbientDim> |
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125 | inline ParametrizedLine<_Scalar, _AmbientDim>::ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim>& hyperplane) |
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126 | { |
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127 | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2) |
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128 | direction() = hyperplane.normal().unitOrthogonal(); |
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129 | origin() = -hyperplane.normal()*hyperplane.offset(); |
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130 | } |
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131 | |
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132 | /** \returns the parameter value of the intersection between \c *this and the given hyperplane |
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133 | */ |
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134 | template <typename _Scalar, int _AmbientDim> |
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135 | inline _Scalar ParametrizedLine<_Scalar, _AmbientDim>::intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane) |
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136 | { |
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137 | return -(hyperplane.offset()+origin().eigen2_dot(hyperplane.normal())) |
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138 | /(direction().eigen2_dot(hyperplane.normal())); |
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139 | } |
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140 | |
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141 | } // end namespace Eigen |
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