1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This file is part of Eigen, a lightweight C++ template library 27faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez// for linear algebra. 3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 4c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> 5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This Source Code Form is subject to the terms of the Mozilla 7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Public License v. 2.0. If a copy of the MPL was not distributed 8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathnamespace Eigen { 13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Other, 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int OtherRows=Other::RowsAtCompileTime, 16c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int OtherCols=Other::ColsAtCompileTime> 17c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathstruct ei_quaternion_assign_impl; 18c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 19c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \geometry_module \ingroup Geometry_Module 20c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 21c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \class Quaternion 22c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 23c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \brief The quaternion class used to represent 3D orientations and rotations 24c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 25c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param _Scalar the scalar type, i.e., the type of the coefficients 26c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 27c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * This class represents a quaternion \f$ w+xi+yj+zk \f$ that is a convenient representation of 28c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * orientations and rotations of objects in three dimensions. Compared to other representations 29c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * like Euler angles or 3x3 matrices, quatertions offer the following advantages: 30c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \li \b compact storage (4 scalars) 31c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \li \b efficient to compose (28 flops), 32c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \li \b stable spherical interpolation 33c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 34c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * The following two typedefs are provided for convenience: 35c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \li \c Quaternionf for \c float 36c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \li \c Quaterniond for \c double 37c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 38c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa class AngleAxis, class Transform 39c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 40c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 41c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename _Scalar> struct ei_traits<Quaternion<_Scalar> > 42c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 43c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef _Scalar Scalar; 44c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 46c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename _Scalar> 47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathclass Quaternion : public RotationBase<Quaternion<_Scalar>,3> 48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef RotationBase<Quaternion<_Scalar>,3> Base; 50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathpublic: 52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,4) 53c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 54c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath using Base::operator*; 55c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** the scalar type of the coefficients */ 57c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef _Scalar Scalar; 58c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 59c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** the type of the Coefficients 4-vector */ 60c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, 4, 1> Coefficients; 61c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** the type of a 3D vector */ 62c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,3,1> Vector3; 63c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** the equivalent rotation matrix type */ 64c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,3,3> Matrix3; 65c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** the equivalent angle-axis type */ 66c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef AngleAxis<Scalar> AngleAxisType; 67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns the \c x coefficient */ 69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Scalar x() const { return m_coeffs.coeff(0); } 70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns the \c y coefficient */ 71c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Scalar y() const { return m_coeffs.coeff(1); } 72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns the \c z coefficient */ 73c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Scalar z() const { return m_coeffs.coeff(2); } 74c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns the \c w coefficient */ 75c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Scalar w() const { return m_coeffs.coeff(3); } 76c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 77c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns a reference to the \c x coefficient */ 78c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Scalar& x() { return m_coeffs.coeffRef(0); } 79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns a reference to the \c y coefficient */ 80c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Scalar& y() { return m_coeffs.coeffRef(1); } 81c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns a reference to the \c z coefficient */ 82c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Scalar& z() { return m_coeffs.coeffRef(2); } 83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns a reference to the \c w coefficient */ 84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Scalar& w() { return m_coeffs.coeffRef(3); } 85c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 86c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns a read-only vector expression of the imaginary part (x,y,z) */ 87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline const Block<const Coefficients,3,1> vec() const { return m_coeffs.template start<3>(); } 88c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 89c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns a vector expression of the imaginary part (x,y,z) */ 90c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Block<Coefficients,3,1> vec() { return m_coeffs.template start<3>(); } 91c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 92c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns a read-only vector expression of the coefficients (x,y,z,w) */ 93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline const Coefficients& coeffs() const { return m_coeffs; } 94c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 95c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns a vector expression of the coefficients (x,y,z,w) */ 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Coefficients& coeffs() { return m_coeffs; } 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 98c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** Default constructor leaving the quaternion uninitialized. */ 99c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Quaternion() {} 100c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 101c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** Constructs and initializes the quaternion \f$ w+xi+yj+zk \f$ from 102c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * its four coefficients \a w, \a x, \a y and \a z. 103c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \warning Note the order of the arguments: the real \a w coefficient first, 105c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * while internally the coefficients are stored in the following order: 106c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * [\c x, \c y, \c z, \c w] 107c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Quaternion(Scalar w, Scalar x, Scalar y, Scalar z) 109c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { m_coeffs << x, y, z, w; } 110c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 111c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** Copy constructor */ 112c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Quaternion(const Quaternion& other) { m_coeffs = other.m_coeffs; } 113c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 114c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** Constructs and initializes a quaternion from the angle-axis \a aa */ 115c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; } 116c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 117c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** Constructs and initializes a quaternion from either: 118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * - a rotation matrix expression, 119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * - a 4D vector expression representing quaternion coefficients. 120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa operator=(MatrixBase<Derived>) 121c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename Derived> 123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; } 124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternion& operator=(const Quaternion& other); 126c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternion& operator=(const AngleAxisType& aa); 127c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename Derived> 128c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternion& operator=(const MatrixBase<Derived>& m); 129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns a quaternion representing an identity rotation 131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa MatrixBase::Identity() 132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline Quaternion Identity() { return Quaternion(1, 0, 0, 0); } 134c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \sa Quaternion::Identity(), MatrixBase::setIdentity() 136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Quaternion& setIdentity() { m_coeffs << 0, 0, 0, 1; return *this; } 138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 139c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns the squared norm of the quaternion's coefficients 140c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa Quaternion::norm(), MatrixBase::squaredNorm() 141c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 142c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Scalar squaredNorm() const { return m_coeffs.squaredNorm(); } 143c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 144c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns the norm of the quaternion's coefficients 145c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa Quaternion::squaredNorm(), MatrixBase::norm() 146c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 147c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Scalar norm() const { return m_coeffs.norm(); } 148c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 149c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** Normalizes the quaternion \c *this 150c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa normalized(), MatrixBase::normalize() */ 151c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline void normalize() { m_coeffs.normalize(); } 152c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns a normalized version of \c *this 153c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa normalize(), MatrixBase::normalized() */ 154c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Quaternion normalized() const { return Quaternion(m_coeffs.normalized()); } 155c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 156c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns the dot product of \c *this and \a other 157c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Geometrically speaking, the dot product of two unit quaternions 158c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * corresponds to the cosine of half the angle between the two rotations. 159c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa angularDistance() 160c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 161c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Scalar eigen2_dot(const Quaternion& other) const { return m_coeffs.eigen2_dot(other.m_coeffs); } 162c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 163c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Scalar angularDistance(const Quaternion& other) const; 164c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 165c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix3 toRotationMatrix(void) const; 166c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 167c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename Derived1, typename Derived2> 168c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternion& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b); 169c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 170c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Quaternion operator* (const Quaternion& q) const; 171c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline Quaternion& operator*= (const Quaternion& q); 172c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 173c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternion inverse(void) const; 174c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternion conjugate(void) const; 175c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 176c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternion slerp(Scalar t, const Quaternion& other) const; 177c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 178c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename Derived> 179c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector3 operator* (const MatrixBase<Derived>& vec) const; 180c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 181c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns \c *this with scalar type casted to \a NewScalarType 182c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 183c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Note that if \a NewScalarType is equal to the current scalar type of \c *this 184c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * then this function smartly returns a const reference to \c *this. 185c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 186c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename NewScalarType> 187c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline typename internal::cast_return_type<Quaternion,Quaternion<NewScalarType> >::type cast() const 188c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { return typename internal::cast_return_type<Quaternion,Quaternion<NewScalarType> >::type(*this); } 189c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 190c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** Copy constructor with scalar type conversion */ 191c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename OtherScalarType> 192c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline explicit Quaternion(const Quaternion<OtherScalarType>& other) 193c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { m_coeffs = other.coeffs().template cast<Scalar>(); } 194c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 195c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \returns \c true if \c *this is approximately equal to \a other, within the precision 196c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * determined by \a prec. 197c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 198c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa MatrixBase::isApprox() */ 199c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath bool isApprox(const Quaternion& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const 200c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { return m_coeffs.isApprox(other.m_coeffs, prec); } 201c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 202c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathprotected: 203c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Coefficients m_coeffs; 204c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 205c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 206c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \ingroup Geometry_Module 207c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * single precision quaternion type */ 208c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtypedef Quaternion<float> Quaternionf; 209c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \ingroup Geometry_Module 210c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * double precision quaternion type */ 211c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtypedef Quaternion<double> Quaterniond; 212c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 213c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Generic Quaternion * Quaternion product 214c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Scalar> inline Quaternion<Scalar> 215c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathei_quaternion_product(const Quaternion<Scalar>& a, const Quaternion<Scalar>& b) 216c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 217c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return Quaternion<Scalar> 218c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ( 219c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(), 220c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(), 221c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(), 222c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x() 223c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ); 224c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 225c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 226c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \returns the concatenation of two rotations as a quaternion-quaternion product */ 227c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename Scalar> 228c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathinline Quaternion<Scalar> Quaternion<Scalar>::operator* (const Quaternion& other) const 229c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 230c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return ei_quaternion_product(*this,other); 231c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 232c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 233c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \sa operator*(Quaternion) */ 234c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename Scalar> 235c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathinline Quaternion<Scalar>& Quaternion<Scalar>::operator*= (const Quaternion& other) 236c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 237c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return (*this = *this * other); 238c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 239c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 240c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** Rotation of a vector by a quaternion. 241c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \remarks If the quaternion is used to rotate several points (>1) 242c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * then it is much more efficient to first convert it to a 3x3 Matrix. 243c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Comparison of the operation cost for n transformations: 244c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * - Quaternion: 30n 245c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * - Via a Matrix3: 24 + 15n 246c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 247c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename Scalar> 248c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Derived> 249c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathinline typename Quaternion<Scalar>::Vector3 250c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan KamathQuaternion<Scalar>::operator* (const MatrixBase<Derived>& v) const 251c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 252c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Note that this algorithm comes from the optimization by hand 253c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // of the conversion to a Matrix followed by a Matrix/Vector product. 254c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // It appears to be much faster than the common algorithm found 255c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // in the litterature (30 versus 39 flops). It also requires two 256c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Vector3 as temporaries. 257c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector3 uv; 258c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath uv = 2 * this->vec().cross(v); 259c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return v + this->w() * uv + this->vec().cross(uv); 260c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 261c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 262c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Scalar> 263c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathinline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const Quaternion& other) 264c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 265c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m_coeffs = other.m_coeffs; 266c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return *this; 267c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 268c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 269c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** Set \c *this from an angle-axis \a aa and returns a reference to \c *this 270c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 271c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Scalar> 272c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathinline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const AngleAxisType& aa) 273c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 274c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings 275c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath this->w() = ei_cos(ha); 276c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath this->vec() = ei_sin(ha) * aa.axis(); 277c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return *this; 278c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 279c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 280c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** Set \c *this from the expression \a xpr: 281c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * - if \a xpr is a 4x1 vector, then \a xpr is assumed to be a quaternion 282c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix 283c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * and \a xpr is converted to a quaternion 284c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 285c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Scalar> 286c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Derived> 287c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathinline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const MatrixBase<Derived>& xpr) 288c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 289c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ei_quaternion_assign_impl<Derived>::run(*this, xpr.derived()); 290c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return *this; 291c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 292c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 293c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** Convert the quaternion to a 3x3 rotation matrix */ 294c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Scalar> 295c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathinline typename Quaternion<Scalar>::Matrix3 296c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan KamathQuaternion<Scalar>::toRotationMatrix(void) const 297c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 298c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!) 299c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // if not inlined then the cost of the return by value is huge ~ +35%, 300c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // however, not inlining this function is an order of magnitude slower, so 301c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // it has to be inlined, and so the return by value is not an issue 302c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix3 res; 303c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 304c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const Scalar tx = Scalar(2)*this->x(); 305c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const Scalar ty = Scalar(2)*this->y(); 306c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const Scalar tz = Scalar(2)*this->z(); 307c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const Scalar twx = tx*this->w(); 308c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const Scalar twy = ty*this->w(); 309c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const Scalar twz = tz*this->w(); 310c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const Scalar txx = tx*this->x(); 311c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const Scalar txy = ty*this->x(); 312c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const Scalar txz = tz*this->x(); 313c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const Scalar tyy = ty*this->y(); 314c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const Scalar tyz = tz*this->y(); 315c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const Scalar tzz = tz*this->z(); 316c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 317c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res.coeffRef(0,0) = Scalar(1)-(tyy+tzz); 318c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res.coeffRef(0,1) = txy-twz; 319c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res.coeffRef(0,2) = txz+twy; 320c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res.coeffRef(1,0) = txy+twz; 321c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res.coeffRef(1,1) = Scalar(1)-(txx+tzz); 322c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res.coeffRef(1,2) = tyz-twx; 323c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res.coeffRef(2,0) = txz-twy; 324c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res.coeffRef(2,1) = tyz+twx; 325c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath res.coeffRef(2,2) = Scalar(1)-(txx+tyy); 326c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 327c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return res; 328c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 329c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 330c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** Sets *this to be a quaternion representing a rotation sending the vector \a a to the vector \a b. 331c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 332c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \returns a reference to *this. 333c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 334c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Note that the two input vectors do \b not have to be normalized. 335c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 336c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Scalar> 337c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Derived1, typename Derived2> 338c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathinline Quaternion<Scalar>& Quaternion<Scalar>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b) 339c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 340c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector3 v0 = a.normalized(); 341c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector3 v1 = b.normalized(); 342c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar c = v0.eigen2_dot(v1); 343c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 344c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // if dot == 1, vectors are the same 345c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (ei_isApprox(c,Scalar(1))) 346c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 347c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // set to identity 348c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath this->w() = 1; this->vec().setZero(); 349c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return *this; 350c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 351c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // if dot == -1, vectors are opposites 352c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (ei_isApprox(c,Scalar(-1))) 353c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 354c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath this->vec() = v0.unitOrthogonal(); 355c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath this->w() = 0; 356c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return *this; 357c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 358c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 359c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector3 axis = v0.cross(v1); 360c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar s = ei_sqrt((Scalar(1)+c)*Scalar(2)); 361c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar invs = Scalar(1)/s; 362c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath this->vec() = axis * invs; 363c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath this->w() = s * Scalar(0.5); 364c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 365c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return *this; 366c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 367c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 368c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \returns the multiplicative inverse of \c *this 369c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * Note that in most cases, i.e., if you simply want the opposite rotation, 370c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * and/or the quaternion is normalized, then it is enough to use the conjugate. 371c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 372c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa Quaternion::conjugate() 373c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 374c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename Scalar> 375c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathinline Quaternion<Scalar> Quaternion<Scalar>::inverse() const 376c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 377c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite() ?? 378c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar n2 = this->squaredNorm(); 379c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (n2 > 0) 380c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return Quaternion(conjugate().coeffs() / n2); 381c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath else 382c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 383c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // return an invalid result to flag the error 384c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return Quaternion(Coefficients::Zero()); 385c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 386c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 387c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 388c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \returns the conjugate of the \c *this which is equal to the multiplicative inverse 389c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * if the quaternion is normalized. 390c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * The conjugate of a quaternion represents the opposite rotation. 391c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 392c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa Quaternion::inverse() 393c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 394c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename Scalar> 395c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathinline Quaternion<Scalar> Quaternion<Scalar>::conjugate() const 396c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 397c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return Quaternion(this->w(),-this->x(),-this->y(),-this->z()); 398c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 399c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 400c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \returns the angle (in radian) between two rotations 401c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \sa eigen2_dot() 402c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 403c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename Scalar> 404c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathinline Scalar Quaternion<Scalar>::angularDistance(const Quaternion& other) const 405c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 406c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath double d = ei_abs(this->eigen2_dot(other)); 407c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (d>=1.0) 408c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return 0; 409c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return Scalar(2) * std::acos(d); 410c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 411c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 412c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \returns the spherical linear interpolation between the two quaternions 413c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \c *this and \a other at the parameter \a t 414c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 415c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename Scalar> 416c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan KamathQuaternion<Scalar> Quaternion<Scalar>::slerp(Scalar t, const Quaternion& other) const 417c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 418c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static const Scalar one = Scalar(1) - machine_epsilon<Scalar>(); 419c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar d = this->eigen2_dot(other); 420c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar absD = ei_abs(d); 421c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 422c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar scale0; 423c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar scale1; 424c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 425c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (absD>=one) 426c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 427c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath scale0 = Scalar(1) - t; 428c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath scale1 = t; 429c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 430c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath else 431c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 432c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // theta is the angle between the 2 quaternions 433c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar theta = std::acos(absD); 434c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar sinTheta = ei_sin(theta); 435c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 436c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath scale0 = ei_sin( ( Scalar(1) - t ) * theta) / sinTheta; 437c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath scale1 = ei_sin( ( t * theta) ) / sinTheta; 438c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (d<0) 439c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath scale1 = -scale1; 440c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 441c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 442c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs()); 443c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 444c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 445c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// set from a rotation matrix 446c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Other> 447c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathstruct ei_quaternion_assign_impl<Other,3,3> 448c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 449c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename Other::Scalar Scalar; 450c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline void run(Quaternion<Scalar>& q, const Other& mat) 451c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 452c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // This algorithm comes from "Quaternion Calculus and Fast Animation", 453c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Ken Shoemake, 1987 SIGGRAPH course notes 454c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar t = mat.trace(); 455c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (t > 0) 456c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 457c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t = ei_sqrt(t + Scalar(1.0)); 458c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q.w() = Scalar(0.5)*t; 459c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t = Scalar(0.5)/t; 460c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t; 461c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t; 462c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t; 463c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 464c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath else 465c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 466c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int i = 0; 467c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (mat.coeff(1,1) > mat.coeff(0,0)) 468c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath i = 1; 469c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (mat.coeff(2,2) > mat.coeff(i,i)) 470c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath i = 2; 471c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int j = (i+1)%3; 472c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int k = (j+1)%3; 473c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 474c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t = ei_sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0)); 475c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q.coeffs().coeffRef(i) = Scalar(0.5) * t; 476c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t = Scalar(0.5)/t; 477c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t; 478c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t; 479c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t; 480c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 481c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 482c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 483c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 484c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// set from a vector of coefficients assumed to be a quaternion 485c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Other> 486c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathstruct ei_quaternion_assign_impl<Other,4,1> 487c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 488c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename Other::Scalar Scalar; 489c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static inline void run(Quaternion<Scalar>& q, const Other& vec) 490c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 491c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q.coeffs() = vec; 492c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 493c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 494c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 495c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} // end namespace Eigen 496