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 <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 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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