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 | // |
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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 | // no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway |
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11 | |
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12 | namespace Eigen { |
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13 | |
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14 | /** \geometry_module \ingroup Geometry_Module |
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15 | * |
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16 | * \class Rotation2D |
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17 | * |
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18 | * \brief Represents a rotation/orientation in a 2 dimensional space. |
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19 | * |
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20 | * \param _Scalar the scalar type, i.e., the type of the coefficients |
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21 | * |
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22 | * This class is equivalent to a single scalar representing a counter clock wise rotation |
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23 | * as a single angle in radian. It provides some additional features such as the automatic |
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24 | * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar |
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25 | * interface to Quaternion in order to facilitate the writing of generic algorithms |
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26 | * dealing with rotations. |
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27 | * |
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28 | * \sa class Quaternion, class Transform |
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29 | */ |
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30 | template<typename _Scalar> struct ei_traits<Rotation2D<_Scalar> > |
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31 | { |
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32 | typedef _Scalar Scalar; |
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33 | }; |
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34 | |
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35 | template<typename _Scalar> |
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36 | class Rotation2D : public RotationBase<Rotation2D<_Scalar>,2> |
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37 | { |
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38 | typedef RotationBase<Rotation2D<_Scalar>,2> Base; |
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39 | |
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40 | public: |
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41 | |
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42 | using Base::operator*; |
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43 | |
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44 | enum { Dim = 2 }; |
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45 | /** the scalar type of the coefficients */ |
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46 | typedef _Scalar Scalar; |
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47 | typedef Matrix<Scalar,2,1> Vector2; |
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48 | typedef Matrix<Scalar,2,2> Matrix2; |
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49 | |
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50 | protected: |
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51 | |
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52 | Scalar m_angle; |
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53 | |
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54 | public: |
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55 | |
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56 | /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */ |
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57 | inline Rotation2D(Scalar a) : m_angle(a) {} |
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58 | |
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59 | /** \returns the rotation angle */ |
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60 | inline Scalar angle() const { return m_angle; } |
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61 | |
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62 | /** \returns a read-write reference to the rotation angle */ |
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63 | inline Scalar& angle() { return m_angle; } |
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64 | |
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65 | /** \returns the inverse rotation */ |
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66 | inline Rotation2D inverse() const { return -m_angle; } |
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67 | |
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68 | /** Concatenates two rotations */ |
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69 | inline Rotation2D operator*(const Rotation2D& other) const |
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70 | { return m_angle + other.m_angle; } |
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71 | |
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72 | /** Concatenates two rotations */ |
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73 | inline Rotation2D& operator*=(const Rotation2D& other) |
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74 | { return m_angle += other.m_angle; return *this; } |
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75 | |
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76 | /** Applies the rotation to a 2D vector */ |
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77 | Vector2 operator* (const Vector2& vec) const |
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78 | { return toRotationMatrix() * vec; } |
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79 | |
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80 | template<typename Derived> |
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81 | Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m); |
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82 | Matrix2 toRotationMatrix(void) const; |
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83 | |
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84 | /** \returns the spherical interpolation between \c *this and \a other using |
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85 | * parameter \a t. It is in fact equivalent to a linear interpolation. |
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86 | */ |
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87 | inline Rotation2D slerp(Scalar t, const Rotation2D& other) const |
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88 | { return m_angle * (1-t) + other.angle() * t; } |
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89 | |
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90 | /** \returns \c *this with scalar type casted to \a NewScalarType |
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91 | * |
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92 | * Note that if \a NewScalarType is equal to the current scalar type of \c *this |
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93 | * then this function smartly returns a const reference to \c *this. |
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94 | */ |
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95 | template<typename NewScalarType> |
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96 | inline typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type cast() const |
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97 | { return typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type(*this); } |
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98 | |
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99 | /** Copy constructor with scalar type conversion */ |
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100 | template<typename OtherScalarType> |
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101 | inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other) |
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102 | { |
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103 | m_angle = Scalar(other.angle()); |
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104 | } |
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105 | |
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106 | /** \returns \c true if \c *this is approximately equal to \a other, within the precision |
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107 | * determined by \a prec. |
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108 | * |
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109 | * \sa MatrixBase::isApprox() */ |
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110 | bool isApprox(const Rotation2D& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const |
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111 | { return ei_isApprox(m_angle,other.m_angle, prec); } |
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112 | }; |
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113 | |
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114 | /** \ingroup Geometry_Module |
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115 | * single precision 2D rotation type */ |
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116 | typedef Rotation2D<float> Rotation2Df; |
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117 | /** \ingroup Geometry_Module |
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118 | * double precision 2D rotation type */ |
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119 | typedef Rotation2D<double> Rotation2Dd; |
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120 | |
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121 | /** Set \c *this from a 2x2 rotation matrix \a mat. |
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122 | * In other words, this function extract the rotation angle |
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123 | * from the rotation matrix. |
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124 | */ |
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125 | template<typename Scalar> |
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126 | template<typename Derived> |
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127 | Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat) |
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128 | { |
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129 | EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE) |
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130 | m_angle = ei_atan2(mat.coeff(1,0), mat.coeff(0,0)); |
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131 | return *this; |
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132 | } |
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133 | |
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134 | /** Constructs and \returns an equivalent 2x2 rotation matrix. |
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135 | */ |
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136 | template<typename Scalar> |
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137 | typename Rotation2D<Scalar>::Matrix2 |
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138 | Rotation2D<Scalar>::toRotationMatrix(void) const |
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139 | { |
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140 | Scalar sinA = ei_sin(m_angle); |
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141 | Scalar cosA = ei_cos(m_angle); |
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142 | return (Matrix2() << cosA, -sinA, sinA, cosA).finished(); |
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143 | } |
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144 | |
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145 | } // end namespace Eigen |
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