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 | //
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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 | #ifndef EIGEN_ROTATION2D_H
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11 | #define EIGEN_ROTATION2D_H
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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 Rotation2D
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18 | *
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19 | * \brief Represents a rotation/orientation in a 2 dimensional space.
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20 | *
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21 | * \param _Scalar the scalar type, i.e., the type of the coefficients
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22 | *
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23 | * This class is equivalent to a single scalar representing a counter clock wise rotation
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24 | * as a single angle in radian. It provides some additional features such as the automatic
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25 | * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar
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26 | * interface to Quaternion in order to facilitate the writing of generic algorithms
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27 | * dealing with rotations.
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28 | *
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29 | * \sa class Quaternion, class Transform
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30 | */
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31 |
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32 | namespace internal {
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33 |
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34 | template<typename _Scalar> struct traits<Rotation2D<_Scalar> >
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35 | {
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36 | typedef _Scalar Scalar;
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37 | };
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38 | } // end namespace internal
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39 |
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40 | template<typename _Scalar>
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41 | class Rotation2D : public RotationBase<Rotation2D<_Scalar>,2>
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42 | {
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43 | typedef RotationBase<Rotation2D<_Scalar>,2> Base;
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44 |
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45 | public:
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46 |
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47 | using Base::operator*;
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48 |
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49 | enum { Dim = 2 };
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50 | /** the scalar type of the coefficients */
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51 | typedef _Scalar Scalar;
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52 | typedef Matrix<Scalar,2,1> Vector2;
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53 | typedef Matrix<Scalar,2,2> Matrix2;
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54 |
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55 | protected:
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56 |
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57 | Scalar m_angle;
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58 |
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59 | public:
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60 |
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61 | /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
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62 | inline Rotation2D(const Scalar& a) : m_angle(a) {}
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63 |
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64 | /** Default constructor wihtout initialization. The represented rotation is undefined. */
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65 | Rotation2D() {}
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66 |
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67 | /** \returns the rotation angle */
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68 | inline Scalar angle() const { return m_angle; }
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69 |
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70 | /** \returns a read-write reference to the rotation angle */
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71 | inline Scalar& angle() { return m_angle; }
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72 |
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73 | /** \returns the inverse rotation */
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74 | inline Rotation2D inverse() const { return -m_angle; }
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75 |
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76 | /** Concatenates two rotations */
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77 | inline Rotation2D operator*(const Rotation2D& other) const
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78 | { return m_angle + other.m_angle; }
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79 |
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80 | /** Concatenates two rotations */
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81 | inline Rotation2D& operator*=(const Rotation2D& other)
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82 | { m_angle += other.m_angle; return *this; }
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83 |
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84 | /** Applies the rotation to a 2D vector */
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85 | Vector2 operator* (const Vector2& vec) const
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86 | { return toRotationMatrix() * vec; }
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87 |
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88 | template<typename Derived>
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89 | Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m);
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90 | Matrix2 toRotationMatrix() const;
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91 |
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92 | /** \returns the spherical interpolation between \c *this and \a other using
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93 | * parameter \a t. It is in fact equivalent to a linear interpolation.
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94 | */
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95 | inline Rotation2D slerp(const Scalar& t, const Rotation2D& other) const
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96 | { return m_angle * (1-t) + other.angle() * t; }
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97 |
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98 | /** \returns \c *this with scalar type casted to \a NewScalarType
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99 | *
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100 | * Note that if \a NewScalarType is equal to the current scalar type of \c *this
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101 | * then this function smartly returns a const reference to \c *this.
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102 | */
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103 | template<typename NewScalarType>
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104 | inline typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type cast() const
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105 | { return typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type(*this); }
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106 |
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107 | /** Copy constructor with scalar type conversion */
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108 | template<typename OtherScalarType>
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109 | inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other)
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110 | {
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111 | m_angle = Scalar(other.angle());
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112 | }
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113 |
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114 | static inline Rotation2D Identity() { return Rotation2D(0); }
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115 |
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116 | /** \returns \c true if \c *this is approximately equal to \a other, within the precision
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117 | * determined by \a prec.
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118 | *
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119 | * \sa MatrixBase::isApprox() */
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120 | bool isApprox(const Rotation2D& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
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121 | { return internal::isApprox(m_angle,other.m_angle, prec); }
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122 | };
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123 |
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124 | /** \ingroup Geometry_Module
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125 | * single precision 2D rotation type */
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126 | typedef Rotation2D<float> Rotation2Df;
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127 | /** \ingroup Geometry_Module
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128 | * double precision 2D rotation type */
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129 | typedef Rotation2D<double> Rotation2Dd;
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130 |
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131 | /** Set \c *this from a 2x2 rotation matrix \a mat.
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132 | * In other words, this function extract the rotation angle
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133 | * from the rotation matrix.
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134 | */
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135 | template<typename Scalar>
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136 | template<typename Derived>
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137 | Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
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138 | {
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139 | using std::atan2;
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140 | EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
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141 | m_angle = atan2(mat.coeff(1,0), mat.coeff(0,0));
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142 | return *this;
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143 | }
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144 |
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145 | /** Constructs and \returns an equivalent 2x2 rotation matrix.
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146 | */
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147 | template<typename Scalar>
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148 | typename Rotation2D<Scalar>::Matrix2
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149 | Rotation2D<Scalar>::toRotationMatrix(void) const
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150 | {
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151 | using std::sin;
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152 | using std::cos;
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153 | Scalar sinA = sin(m_angle);
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154 | Scalar cosA = cos(m_angle);
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155 | return (Matrix2() << cosA, -sinA, sinA, cosA).finished();
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156 | }
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157 |
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158 | } // end namespace Eigen
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159 |
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160 | #endif // EIGEN_ROTATION2D_H
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