1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. Eigen itself is part of the KDE project. 3 // 4 // Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> 5 // 6 // This Source Code Form is subject to the terms of the Mozilla 7 // Public License v. 2.0. If a copy of the MPL was not distributed 8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9 10 // no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway 11 12 namespace Eigen { 13 14 /** \geometry_module \ingroup Geometry_Module 15 * 16 * \class Rotation2D 17 * 18 * \brief Represents a rotation/orientation in a 2 dimensional space. 19 * 20 * \param _Scalar the scalar type, i.e., the type of the coefficients 21 * 22 * This class is equivalent to a single scalar representing a counter clock wise rotation 23 * as a single angle in radian. It provides some additional features such as the automatic 24 * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar 25 * interface to Quaternion in order to facilitate the writing of generic algorithms 26 * dealing with rotations. 27 * 28 * \sa class Quaternion, class Transform 29 */ 30 template<typename _Scalar> struct ei_traits<Rotation2D<_Scalar> > 31 { 32 typedef _Scalar Scalar; 33 }; 34 35 template<typename _Scalar> 36 class Rotation2D : public RotationBase<Rotation2D<_Scalar>,2> 37 { 38 typedef RotationBase<Rotation2D<_Scalar>,2> Base; 39 40 public: 41 42 using Base::operator*; 43 44 enum { Dim = 2 }; 45 /** the scalar type of the coefficients */ 46 typedef _Scalar Scalar; 47 typedef Matrix<Scalar,2,1> Vector2; 48 typedef Matrix<Scalar,2,2> Matrix2; 49 50 protected: 51 52 Scalar m_angle; 53 54 public: 55 56 /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */ 57 inline Rotation2D(Scalar a) : m_angle(a) {} 58 59 /** \returns the rotation angle */ 60 inline Scalar angle() const { return m_angle; } 61 62 /** \returns a read-write reference to the rotation angle */ 63 inline Scalar& angle() { return m_angle; } 64 65 /** \returns the inverse rotation */ 66 inline Rotation2D inverse() const { return -m_angle; } 67 68 /** Concatenates two rotations */ 69 inline Rotation2D operator*(const Rotation2D& other) const 70 { return m_angle + other.m_angle; } 71 72 /** Concatenates two rotations */ 73 inline Rotation2D& operator*=(const Rotation2D& other) 74 { return m_angle += other.m_angle; return *this; } 75 76 /** Applies the rotation to a 2D vector */ 77 Vector2 operator* (const Vector2& vec) const 78 { return toRotationMatrix() * vec; } 79 80 template<typename Derived> 81 Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m); 82 Matrix2 toRotationMatrix(void) const; 83 84 /** \returns the spherical interpolation between \c *this and \a other using 85 * parameter \a t. It is in fact equivalent to a linear interpolation. 86 */ 87 inline Rotation2D slerp(Scalar t, const Rotation2D& other) const 88 { return m_angle * (1-t) + other.angle() * t; } 89 90 /** \returns \c *this with scalar type casted to \a NewScalarType 91 * 92 * Note that if \a NewScalarType is equal to the current scalar type of \c *this 93 * then this function smartly returns a const reference to \c *this. 94 */ 95 template<typename NewScalarType> 96 inline typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type cast() const 97 { return typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type(*this); } 98 99 /** Copy constructor with scalar type conversion */ 100 template<typename OtherScalarType> 101 inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other) 102 { 103 m_angle = Scalar(other.angle()); 104 } 105 106 /** \returns \c true if \c *this is approximately equal to \a other, within the precision 107 * determined by \a prec. 108 * 109 * \sa MatrixBase::isApprox() */ 110 bool isApprox(const Rotation2D& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const 111 { return ei_isApprox(m_angle,other.m_angle, prec); } 112 }; 113 114 /** \ingroup Geometry_Module 115 * single precision 2D rotation type */ 116 typedef Rotation2D<float> Rotation2Df; 117 /** \ingroup Geometry_Module 118 * double precision 2D rotation type */ 119 typedef Rotation2D<double> Rotation2Dd; 120 121 /** Set \c *this from a 2x2 rotation matrix \a mat. 122 * In other words, this function extract the rotation angle 123 * from the rotation matrix. 124 */ 125 template<typename Scalar> 126 template<typename Derived> 127 Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat) 128 { 129 EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE) 130 m_angle = ei_atan2(mat.coeff(1,0), mat.coeff(0,0)); 131 return *this; 132 } 133 134 /** Constructs and \returns an equivalent 2x2 rotation matrix. 135 */ 136 template<typename Scalar> 137 typename Rotation2D<Scalar>::Matrix2 138 Rotation2D<Scalar>::toRotationMatrix(void) const 139 { 140 Scalar sinA = ei_sin(m_angle); 141 Scalar cosA = ei_cos(m_angle); 142 return (Matrix2() << cosA, -sinA, sinA, cosA).finished(); 143 } 144 145 } // end namespace Eigen 146