1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.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 #ifndef EIGEN_ANGLEAXIS_H 11 #define EIGEN_ANGLEAXIS_H 12 13 namespace Eigen { 14 15 /** \geometry_module \ingroup Geometry_Module 16 * 17 * \class AngleAxis 18 * 19 * \brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis 20 * 21 * \param _Scalar the scalar type, i.e., the type of the coefficients. 22 * 23 * \warning When setting up an AngleAxis object, the axis vector \b must \b be \b normalized. 24 * 25 * The following two typedefs are provided for convenience: 26 * \li \c AngleAxisf for \c float 27 * \li \c AngleAxisd for \c double 28 * 29 * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily 30 * mimic Euler-angles. Here is an example: 31 * \include AngleAxis_mimic_euler.cpp 32 * Output: \verbinclude AngleAxis_mimic_euler.out 33 * 34 * \note This class is not aimed to be used to store a rotation transformation, 35 * but rather to make easier the creation of other rotation (Quaternion, rotation Matrix) 36 * and transformation objects. 37 * 38 * \sa class Quaternion, class Transform, MatrixBase::UnitX() 39 */ 40 41 namespace internal { 42 template<typename _Scalar> struct traits<AngleAxis<_Scalar> > 43 { 44 typedef _Scalar Scalar; 45 }; 46 } 47 48 template<typename _Scalar> 49 class AngleAxis : public RotationBase<AngleAxis<_Scalar>,3> 50 { 51 typedef RotationBase<AngleAxis<_Scalar>,3> Base; 52 53 public: 54 55 using Base::operator*; 56 57 enum { Dim = 3 }; 58 /** the scalar type of the coefficients */ 59 typedef _Scalar Scalar; 60 typedef Matrix<Scalar,3,3> Matrix3; 61 typedef Matrix<Scalar,3,1> Vector3; 62 typedef Quaternion<Scalar> QuaternionType; 63 64 protected: 65 66 Vector3 m_axis; 67 Scalar m_angle; 68 69 public: 70 71 /** Default constructor without initialization. */ 72 AngleAxis() {} 73 /** Constructs and initialize the angle-axis rotation from an \a angle in radian 74 * and an \a axis which \b must \b be \b normalized. 75 * 76 * \warning If the \a axis vector is not normalized, then the angle-axis object 77 * represents an invalid rotation. */ 78 template<typename Derived> 79 inline AngleAxis(Scalar angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {} 80 /** Constructs and initialize the angle-axis rotation from a quaternion \a q. */ 81 template<typename QuatDerived> inline explicit AngleAxis(const QuaternionBase<QuatDerived>& q) { *this = q; } 82 /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */ 83 template<typename Derived> 84 inline explicit AngleAxis(const MatrixBase<Derived>& m) { *this = m; } 85 86 Scalar angle() const { return m_angle; } 87 Scalar& angle() { return m_angle; } 88 89 const Vector3& axis() const { return m_axis; } 90 Vector3& axis() { return m_axis; } 91 92 /** Concatenates two rotations */ 93 inline QuaternionType operator* (const AngleAxis& other) const 94 { return QuaternionType(*this) * QuaternionType(other); } 95 96 /** Concatenates two rotations */ 97 inline QuaternionType operator* (const QuaternionType& other) const 98 { return QuaternionType(*this) * other; } 99 100 /** Concatenates two rotations */ 101 friend inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b) 102 { return a * QuaternionType(b); } 103 104 /** \returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */ 105 AngleAxis inverse() const 106 { return AngleAxis(-m_angle, m_axis); } 107 108 template<class QuatDerived> 109 AngleAxis& operator=(const QuaternionBase<QuatDerived>& q); 110 template<typename Derived> 111 AngleAxis& operator=(const MatrixBase<Derived>& m); 112 113 template<typename Derived> 114 AngleAxis& fromRotationMatrix(const MatrixBase<Derived>& m); 115 Matrix3 toRotationMatrix(void) const; 116 117 /** \returns \c *this with scalar type casted to \a NewScalarType 118 * 119 * Note that if \a NewScalarType is equal to the current scalar type of \c *this 120 * then this function smartly returns a const reference to \c *this. 121 */ 122 template<typename NewScalarType> 123 inline typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type cast() const 124 { return typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type(*this); } 125 126 /** Copy constructor with scalar type conversion */ 127 template<typename OtherScalarType> 128 inline explicit AngleAxis(const AngleAxis<OtherScalarType>& other) 129 { 130 m_axis = other.axis().template cast<Scalar>(); 131 m_angle = Scalar(other.angle()); 132 } 133 134 static inline const AngleAxis Identity() { return AngleAxis(0, Vector3::UnitX()); } 135 136 /** \returns \c true if \c *this is approximately equal to \a other, within the precision 137 * determined by \a prec. 138 * 139 * \sa MatrixBase::isApprox() */ 140 bool isApprox(const AngleAxis& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const 141 { return m_axis.isApprox(other.m_axis, prec) && internal::isApprox(m_angle,other.m_angle, prec); } 142 }; 143 144 /** \ingroup Geometry_Module 145 * single precision angle-axis type */ 146 typedef AngleAxis<float> AngleAxisf; 147 /** \ingroup Geometry_Module 148 * double precision angle-axis type */ 149 typedef AngleAxis<double> AngleAxisd; 150 151 /** Set \c *this from a \b unit quaternion. 152 * The axis is normalized. 153 * 154 * \warning As any other method dealing with quaternion, if the input quaternion 155 * is not normalized then the result is undefined. 156 */ 157 template<typename Scalar> 158 template<typename QuatDerived> 159 AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived>& q) 160 { 161 using std::acos; 162 using std::min; 163 using std::max; 164 Scalar n2 = q.vec().squaredNorm(); 165 if (n2 < NumTraits<Scalar>::dummy_precision()*NumTraits<Scalar>::dummy_precision()) 166 { 167 m_angle = 0; 168 m_axis << 1, 0, 0; 169 } 170 else 171 { 172 m_angle = Scalar(2)*acos((min)((max)(Scalar(-1),q.w()),Scalar(1))); 173 m_axis = q.vec() / internal::sqrt(n2); 174 } 175 return *this; 176 } 177 178 /** Set \c *this from a 3x3 rotation matrix \a mat. 179 */ 180 template<typename Scalar> 181 template<typename Derived> 182 AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const MatrixBase<Derived>& mat) 183 { 184 // Since a direct conversion would not be really faster, 185 // let's use the robust Quaternion implementation: 186 return *this = QuaternionType(mat); 187 } 188 189 /** 190 * \brief Sets \c *this from a 3x3 rotation matrix. 191 **/ 192 template<typename Scalar> 193 template<typename Derived> 194 AngleAxis<Scalar>& AngleAxis<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat) 195 { 196 return *this = QuaternionType(mat); 197 } 198 199 /** Constructs and \returns an equivalent 3x3 rotation matrix. 200 */ 201 template<typename Scalar> 202 typename AngleAxis<Scalar>::Matrix3 203 AngleAxis<Scalar>::toRotationMatrix(void) const 204 { 205 Matrix3 res; 206 Vector3 sin_axis = internal::sin(m_angle) * m_axis; 207 Scalar c = internal::cos(m_angle); 208 Vector3 cos1_axis = (Scalar(1)-c) * m_axis; 209 210 Scalar tmp; 211 tmp = cos1_axis.x() * m_axis.y(); 212 res.coeffRef(0,1) = tmp - sin_axis.z(); 213 res.coeffRef(1,0) = tmp + sin_axis.z(); 214 215 tmp = cos1_axis.x() * m_axis.z(); 216 res.coeffRef(0,2) = tmp + sin_axis.y(); 217 res.coeffRef(2,0) = tmp - sin_axis.y(); 218 219 tmp = cos1_axis.y() * m_axis.z(); 220 res.coeffRef(1,2) = tmp - sin_axis.x(); 221 res.coeffRef(2,1) = tmp + sin_axis.x(); 222 223 res.diagonal() = (cos1_axis.cwiseProduct(m_axis)).array() + c; 224 225 return res; 226 } 227 228 } // end namespace Eigen 229 230 #endif // EIGEN_ANGLEAXIS_H 231