[136] | 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) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 5 | // Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.fr>
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| 6 | //
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| 7 | // This Source Code Form is subject to the terms of the Mozilla
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| 8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 10 |
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| 11 | #ifndef EIGEN_QUATERNION_H
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| 12 | #define EIGEN_QUATERNION_H
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| 13 | namespace Eigen {
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| 14 |
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| 15 |
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| 16 | /***************************************************************************
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| 17 | * Definition of QuaternionBase<Derived>
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| 18 | * The implementation is at the end of the file
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| 19 | ***************************************************************************/
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| 20 |
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| 21 | namespace internal {
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| 22 | template<typename Other,
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| 23 | int OtherRows=Other::RowsAtCompileTime,
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| 24 | int OtherCols=Other::ColsAtCompileTime>
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| 25 | struct quaternionbase_assign_impl;
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| 26 | }
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| 27 |
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| 28 | /** \geometry_module \ingroup Geometry_Module
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| 29 | * \class QuaternionBase
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| 30 | * \brief Base class for quaternion expressions
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| 31 | * \tparam Derived derived type (CRTP)
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| 32 | * \sa class Quaternion
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| 33 | */
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| 34 | template<class Derived>
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| 35 | class QuaternionBase : public RotationBase<Derived, 3>
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| 36 | {
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| 37 | typedef RotationBase<Derived, 3> Base;
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| 38 | public:
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| 39 | using Base::operator*;
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| 40 | using Base::derived;
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| 41 |
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| 42 | typedef typename internal::traits<Derived>::Scalar Scalar;
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| 43 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 44 | typedef typename internal::traits<Derived>::Coefficients Coefficients;
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| 45 | enum {
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| 46 | Flags = Eigen::internal::traits<Derived>::Flags
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| 47 | };
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| 48 |
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| 49 | // typedef typename Matrix<Scalar,4,1> Coefficients;
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| 50 | /** the type of a 3D vector */
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| 51 | typedef Matrix<Scalar,3,1> Vector3;
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| 52 | /** the equivalent rotation matrix type */
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| 53 | typedef Matrix<Scalar,3,3> Matrix3;
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| 54 | /** the equivalent angle-axis type */
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| 55 | typedef AngleAxis<Scalar> AngleAxisType;
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| 56 |
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| 57 |
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| 58 |
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| 59 | /** \returns the \c x coefficient */
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| 60 | inline Scalar x() const { return this->derived().coeffs().coeff(0); }
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| 61 | /** \returns the \c y coefficient */
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| 62 | inline Scalar y() const { return this->derived().coeffs().coeff(1); }
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| 63 | /** \returns the \c z coefficient */
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| 64 | inline Scalar z() const { return this->derived().coeffs().coeff(2); }
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| 65 | /** \returns the \c w coefficient */
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| 66 | inline Scalar w() const { return this->derived().coeffs().coeff(3); }
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| 67 |
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| 68 | /** \returns a reference to the \c x coefficient */
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| 69 | inline Scalar& x() { return this->derived().coeffs().coeffRef(0); }
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| 70 | /** \returns a reference to the \c y coefficient */
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| 71 | inline Scalar& y() { return this->derived().coeffs().coeffRef(1); }
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| 72 | /** \returns a reference to the \c z coefficient */
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| 73 | inline Scalar& z() { return this->derived().coeffs().coeffRef(2); }
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| 74 | /** \returns a reference to the \c w coefficient */
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| 75 | inline Scalar& w() { return this->derived().coeffs().coeffRef(3); }
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| 76 |
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| 77 | /** \returns a read-only vector expression of the imaginary part (x,y,z) */
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| 78 | inline const VectorBlock<const Coefficients,3> vec() const { return coeffs().template head<3>(); }
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| 79 |
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| 80 | /** \returns a vector expression of the imaginary part (x,y,z) */
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| 81 | inline VectorBlock<Coefficients,3> vec() { return coeffs().template head<3>(); }
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| 82 |
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| 83 | /** \returns a read-only vector expression of the coefficients (x,y,z,w) */
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| 84 | inline const typename internal::traits<Derived>::Coefficients& coeffs() const { return derived().coeffs(); }
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| 85 |
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| 86 | /** \returns a vector expression of the coefficients (x,y,z,w) */
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| 87 | inline typename internal::traits<Derived>::Coefficients& coeffs() { return derived().coeffs(); }
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| 88 |
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| 89 | EIGEN_STRONG_INLINE QuaternionBase<Derived>& operator=(const QuaternionBase<Derived>& other);
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| 90 | template<class OtherDerived> EIGEN_STRONG_INLINE Derived& operator=(const QuaternionBase<OtherDerived>& other);
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| 91 |
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| 92 | // disabled this copy operator as it is giving very strange compilation errors when compiling
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| 93 | // test_stdvector with GCC 4.4.2. This looks like a GCC bug though, so feel free to re-enable it if it's
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| 94 | // useful; however notice that we already have the templated operator= above and e.g. in MatrixBase
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| 95 | // we didn't have to add, in addition to templated operator=, such a non-templated copy operator.
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| 96 | // Derived& operator=(const QuaternionBase& other)
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| 97 | // { return operator=<Derived>(other); }
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| 98 |
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| 99 | Derived& operator=(const AngleAxisType& aa);
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| 100 | template<class OtherDerived> Derived& operator=(const MatrixBase<OtherDerived>& m);
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| 101 |
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| 102 | /** \returns a quaternion representing an identity rotation
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| 103 | * \sa MatrixBase::Identity()
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| 104 | */
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| 105 | static inline Quaternion<Scalar> Identity() { return Quaternion<Scalar>(Scalar(1), Scalar(0), Scalar(0), Scalar(0)); }
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| 106 |
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| 107 | /** \sa QuaternionBase::Identity(), MatrixBase::setIdentity()
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| 108 | */
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| 109 | inline QuaternionBase& setIdentity() { coeffs() << Scalar(0), Scalar(0), Scalar(0), Scalar(1); return *this; }
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| 110 |
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| 111 | /** \returns the squared norm of the quaternion's coefficients
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| 112 | * \sa QuaternionBase::norm(), MatrixBase::squaredNorm()
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| 113 | */
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| 114 | inline Scalar squaredNorm() const { return coeffs().squaredNorm(); }
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| 115 |
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| 116 | /** \returns the norm of the quaternion's coefficients
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| 117 | * \sa QuaternionBase::squaredNorm(), MatrixBase::norm()
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| 118 | */
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| 119 | inline Scalar norm() const { return coeffs().norm(); }
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| 120 |
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| 121 | /** Normalizes the quaternion \c *this
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| 122 | * \sa normalized(), MatrixBase::normalize() */
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| 123 | inline void normalize() { coeffs().normalize(); }
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| 124 | /** \returns a normalized copy of \c *this
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| 125 | * \sa normalize(), MatrixBase::normalized() */
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| 126 | inline Quaternion<Scalar> normalized() const { return Quaternion<Scalar>(coeffs().normalized()); }
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| 127 |
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| 128 | /** \returns the dot product of \c *this and \a other
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| 129 | * Geometrically speaking, the dot product of two unit quaternions
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| 130 | * corresponds to the cosine of half the angle between the two rotations.
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| 131 | * \sa angularDistance()
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| 132 | */
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| 133 | template<class OtherDerived> inline Scalar dot(const QuaternionBase<OtherDerived>& other) const { return coeffs().dot(other.coeffs()); }
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| 134 |
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| 135 | template<class OtherDerived> Scalar angularDistance(const QuaternionBase<OtherDerived>& other) const;
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| 136 |
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| 137 | /** \returns an equivalent 3x3 rotation matrix */
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| 138 | Matrix3 toRotationMatrix() const;
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| 139 |
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| 140 | /** \returns the quaternion which transform \a a into \a b through a rotation */
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| 141 | template<typename Derived1, typename Derived2>
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| 142 | Derived& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
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| 143 |
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| 144 | template<class OtherDerived> EIGEN_STRONG_INLINE Quaternion<Scalar> operator* (const QuaternionBase<OtherDerived>& q) const;
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| 145 | template<class OtherDerived> EIGEN_STRONG_INLINE Derived& operator*= (const QuaternionBase<OtherDerived>& q);
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| 146 |
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| 147 | /** \returns the quaternion describing the inverse rotation */
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| 148 | Quaternion<Scalar> inverse() const;
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| 149 |
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| 150 | /** \returns the conjugated quaternion */
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| 151 | Quaternion<Scalar> conjugate() const;
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| 152 |
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| 153 | template<class OtherDerived> Quaternion<Scalar> slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const;
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| 154 |
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| 155 | /** \returns \c true if \c *this is approximately equal to \a other, within the precision
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| 156 | * determined by \a prec.
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| 157 | *
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| 158 | * \sa MatrixBase::isApprox() */
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| 159 | template<class OtherDerived>
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| 160 | bool isApprox(const QuaternionBase<OtherDerived>& other, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const
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| 161 | { return coeffs().isApprox(other.coeffs(), prec); }
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| 162 |
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| 163 | /** return the result vector of \a v through the rotation*/
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| 164 | EIGEN_STRONG_INLINE Vector3 _transformVector(const Vector3& v) const;
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| 165 |
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| 166 | /** \returns \c *this with scalar type casted to \a NewScalarType
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| 167 | *
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| 168 | * Note that if \a NewScalarType is equal to the current scalar type of \c *this
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| 169 | * then this function smartly returns a const reference to \c *this.
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| 170 | */
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| 171 | template<typename NewScalarType>
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| 172 | inline typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type cast() const
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| 173 | {
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| 174 | return typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type(derived());
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| 175 | }
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| 176 |
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| 177 | #ifdef EIGEN_QUATERNIONBASE_PLUGIN
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| 178 | # include EIGEN_QUATERNIONBASE_PLUGIN
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| 179 | #endif
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| 180 | };
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| 181 |
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| 182 | /***************************************************************************
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| 183 | * Definition/implementation of Quaternion<Scalar>
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| 184 | ***************************************************************************/
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| 185 |
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| 186 | /** \geometry_module \ingroup Geometry_Module
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| 187 | *
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| 188 | * \class Quaternion
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| 189 | *
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| 190 | * \brief The quaternion class used to represent 3D orientations and rotations
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| 191 | *
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| 192 | * \tparam _Scalar the scalar type, i.e., the type of the coefficients
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| 193 | * \tparam _Options controls the memory alignment of the coefficients. Can be \# AutoAlign or \# DontAlign. Default is AutoAlign.
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| 194 | *
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| 195 | * This class represents a quaternion \f$ w+xi+yj+zk \f$ that is a convenient representation of
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| 196 | * orientations and rotations of objects in three dimensions. Compared to other representations
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| 197 | * like Euler angles or 3x3 matrices, quaternions offer the following advantages:
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| 198 | * \li \b compact storage (4 scalars)
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| 199 | * \li \b efficient to compose (28 flops),
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| 200 | * \li \b stable spherical interpolation
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| 201 | *
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| 202 | * The following two typedefs are provided for convenience:
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| 203 | * \li \c Quaternionf for \c float
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| 204 | * \li \c Quaterniond for \c double
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| 205 | *
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| 206 | * \warning Operations interpreting the quaternion as rotation have undefined behavior if the quaternion is not normalized.
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| 207 | *
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| 208 | * \sa class AngleAxis, class Transform
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| 209 | */
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| 210 |
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| 211 | namespace internal {
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| 212 | template<typename _Scalar,int _Options>
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| 213 | struct traits<Quaternion<_Scalar,_Options> >
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| 214 | {
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| 215 | typedef Quaternion<_Scalar,_Options> PlainObject;
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| 216 | typedef _Scalar Scalar;
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| 217 | typedef Matrix<_Scalar,4,1,_Options> Coefficients;
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| 218 | enum{
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| 219 | IsAligned = internal::traits<Coefficients>::Flags & AlignedBit,
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| 220 | Flags = IsAligned ? (AlignedBit | LvalueBit) : LvalueBit
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| 221 | };
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| 222 | };
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| 223 | }
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| 224 |
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| 225 | template<typename _Scalar, int _Options>
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| 226 | class Quaternion : public QuaternionBase<Quaternion<_Scalar,_Options> >
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| 227 | {
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| 228 | typedef QuaternionBase<Quaternion<_Scalar,_Options> > Base;
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| 229 | enum { IsAligned = internal::traits<Quaternion>::IsAligned };
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| 230 |
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| 231 | public:
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| 232 | typedef _Scalar Scalar;
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| 233 |
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| 234 | EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Quaternion)
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| 235 | using Base::operator*=;
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| 236 |
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| 237 | typedef typename internal::traits<Quaternion>::Coefficients Coefficients;
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| 238 | typedef typename Base::AngleAxisType AngleAxisType;
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| 239 |
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| 240 | /** Default constructor leaving the quaternion uninitialized. */
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| 241 | inline Quaternion() {}
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| 242 |
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| 243 | /** Constructs and initializes the quaternion \f$ w+xi+yj+zk \f$ from
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| 244 | * its four coefficients \a w, \a x, \a y and \a z.
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| 245 | *
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| 246 | * \warning Note the order of the arguments: the real \a w coefficient first,
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| 247 | * while internally the coefficients are stored in the following order:
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| 248 | * [\c x, \c y, \c z, \c w]
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| 249 | */
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| 250 | inline Quaternion(const Scalar& w, const Scalar& x, const Scalar& y, const Scalar& z) : m_coeffs(x, y, z, w){}
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| 251 |
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| 252 | /** Constructs and initialize a quaternion from the array data */
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| 253 | inline Quaternion(const Scalar* data) : m_coeffs(data) {}
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| 254 |
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| 255 | /** Copy constructor */
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| 256 | template<class Derived> EIGEN_STRONG_INLINE Quaternion(const QuaternionBase<Derived>& other) { this->Base::operator=(other); }
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| 257 |
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| 258 | /** Constructs and initializes a quaternion from the angle-axis \a aa */
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| 259 | explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }
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| 260 |
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| 261 | /** Constructs and initializes a quaternion from either:
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| 262 | * - a rotation matrix expression,
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| 263 | * - a 4D vector expression representing quaternion coefficients.
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| 264 | */
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| 265 | template<typename Derived>
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| 266 | explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
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| 267 |
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| 268 | /** Explicit copy constructor with scalar conversion */
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| 269 | template<typename OtherScalar, int OtherOptions>
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| 270 | explicit inline Quaternion(const Quaternion<OtherScalar, OtherOptions>& other)
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| 271 | { m_coeffs = other.coeffs().template cast<Scalar>(); }
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| 272 |
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| 273 | template<typename Derived1, typename Derived2>
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| 274 | static Quaternion FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
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| 275 |
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| 276 | inline Coefficients& coeffs() { return m_coeffs;}
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| 277 | inline const Coefficients& coeffs() const { return m_coeffs;}
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| 278 |
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| 279 | EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool(IsAligned))
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| 280 |
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| 281 | protected:
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| 282 | Coefficients m_coeffs;
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| 283 |
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| 284 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 285 | static EIGEN_STRONG_INLINE void _check_template_params()
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| 286 | {
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| 287 | EIGEN_STATIC_ASSERT( (_Options & DontAlign) == _Options,
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| 288 | INVALID_MATRIX_TEMPLATE_PARAMETERS)
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| 289 | }
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| 290 | #endif
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| 291 | };
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| 292 |
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| 293 | /** \ingroup Geometry_Module
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| 294 | * single precision quaternion type */
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| 295 | typedef Quaternion<float> Quaternionf;
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| 296 | /** \ingroup Geometry_Module
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| 297 | * double precision quaternion type */
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| 298 | typedef Quaternion<double> Quaterniond;
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| 299 |
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| 300 | /***************************************************************************
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| 301 | * Specialization of Map<Quaternion<Scalar>>
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| 302 | ***************************************************************************/
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| 303 |
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| 304 | namespace internal {
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| 305 | template<typename _Scalar, int _Options>
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| 306 | struct traits<Map<Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
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| 307 | {
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| 308 | typedef Map<Matrix<_Scalar,4,1>, _Options> Coefficients;
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| 309 | };
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| 310 | }
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| 311 |
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| 312 | namespace internal {
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| 313 | template<typename _Scalar, int _Options>
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| 314 | struct traits<Map<const Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
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| 315 | {
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| 316 | typedef Map<const Matrix<_Scalar,4,1>, _Options> Coefficients;
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| 317 | typedef traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> > TraitsBase;
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| 318 | enum {
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| 319 | Flags = TraitsBase::Flags & ~LvalueBit
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| 320 | };
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| 321 | };
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| 322 | }
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| 323 |
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| 324 | /** \ingroup Geometry_Module
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| 325 | * \brief Quaternion expression mapping a constant memory buffer
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| 326 | *
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| 327 | * \tparam _Scalar the type of the Quaternion coefficients
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| 328 | * \tparam _Options see class Map
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| 329 | *
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| 330 | * This is a specialization of class Map for Quaternion. This class allows to view
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| 331 | * a 4 scalar memory buffer as an Eigen's Quaternion object.
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| 332 | *
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| 333 | * \sa class Map, class Quaternion, class QuaternionBase
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| 334 | */
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| 335 | template<typename _Scalar, int _Options>
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| 336 | class Map<const Quaternion<_Scalar>, _Options >
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| 337 | : public QuaternionBase<Map<const Quaternion<_Scalar>, _Options> >
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| 338 | {
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| 339 | typedef QuaternionBase<Map<const Quaternion<_Scalar>, _Options> > Base;
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| 340 |
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| 341 | public:
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| 342 | typedef _Scalar Scalar;
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| 343 | typedef typename internal::traits<Map>::Coefficients Coefficients;
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| 344 | EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
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| 345 | using Base::operator*=;
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| 346 |
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| 347 | /** Constructs a Mapped Quaternion object from the pointer \a coeffs
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| 348 | *
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| 349 | * The pointer \a coeffs must reference the four coefficients of Quaternion in the following order:
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| 350 | * \code *coeffs == {x, y, z, w} \endcode
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| 351 | *
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| 352 | * If the template parameter _Options is set to #Aligned, then the pointer coeffs must be aligned. */
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| 353 | EIGEN_STRONG_INLINE Map(const Scalar* coeffs) : m_coeffs(coeffs) {}
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| 354 |
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| 355 | inline const Coefficients& coeffs() const { return m_coeffs;}
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| 356 |
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| 357 | protected:
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| 358 | const Coefficients m_coeffs;
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| 359 | };
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| 360 |
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| 361 | /** \ingroup Geometry_Module
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| 362 | * \brief Expression of a quaternion from a memory buffer
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| 363 | *
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| 364 | * \tparam _Scalar the type of the Quaternion coefficients
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| 365 | * \tparam _Options see class Map
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| 366 | *
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| 367 | * This is a specialization of class Map for Quaternion. This class allows to view
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| 368 | * a 4 scalar memory buffer as an Eigen's Quaternion object.
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| 369 | *
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| 370 | * \sa class Map, class Quaternion, class QuaternionBase
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| 371 | */
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| 372 | template<typename _Scalar, int _Options>
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| 373 | class Map<Quaternion<_Scalar>, _Options >
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| 374 | : public QuaternionBase<Map<Quaternion<_Scalar>, _Options> >
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| 375 | {
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| 376 | typedef QuaternionBase<Map<Quaternion<_Scalar>, _Options> > Base;
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| 377 |
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| 378 | public:
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| 379 | typedef _Scalar Scalar;
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| 380 | typedef typename internal::traits<Map>::Coefficients Coefficients;
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| 381 | EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
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| 382 | using Base::operator*=;
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| 383 |
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| 384 | /** Constructs a Mapped Quaternion object from the pointer \a coeffs
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| 385 | *
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| 386 | * The pointer \a coeffs must reference the four coefficients of Quaternion in the following order:
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| 387 | * \code *coeffs == {x, y, z, w} \endcode
|
---|
| 388 | *
|
---|
| 389 | * If the template parameter _Options is set to #Aligned, then the pointer coeffs must be aligned. */
|
---|
| 390 | EIGEN_STRONG_INLINE Map(Scalar* coeffs) : m_coeffs(coeffs) {}
|
---|
| 391 |
|
---|
| 392 | inline Coefficients& coeffs() { return m_coeffs; }
|
---|
| 393 | inline const Coefficients& coeffs() const { return m_coeffs; }
|
---|
| 394 |
|
---|
| 395 | protected:
|
---|
| 396 | Coefficients m_coeffs;
|
---|
| 397 | };
|
---|
| 398 |
|
---|
| 399 | /** \ingroup Geometry_Module
|
---|
| 400 | * Map an unaligned array of single precision scalars as a quaternion */
|
---|
| 401 | typedef Map<Quaternion<float>, 0> QuaternionMapf;
|
---|
| 402 | /** \ingroup Geometry_Module
|
---|
| 403 | * Map an unaligned array of double precision scalars as a quaternion */
|
---|
| 404 | typedef Map<Quaternion<double>, 0> QuaternionMapd;
|
---|
| 405 | /** \ingroup Geometry_Module
|
---|
| 406 | * Map a 16-byte aligned array of single precision scalars as a quaternion */
|
---|
| 407 | typedef Map<Quaternion<float>, Aligned> QuaternionMapAlignedf;
|
---|
| 408 | /** \ingroup Geometry_Module
|
---|
| 409 | * Map a 16-byte aligned array of double precision scalars as a quaternion */
|
---|
| 410 | typedef Map<Quaternion<double>, Aligned> QuaternionMapAlignedd;
|
---|
| 411 |
|
---|
| 412 | /***************************************************************************
|
---|
| 413 | * Implementation of QuaternionBase methods
|
---|
| 414 | ***************************************************************************/
|
---|
| 415 |
|
---|
| 416 | // Generic Quaternion * Quaternion product
|
---|
| 417 | // This product can be specialized for a given architecture via the Arch template argument.
|
---|
| 418 | namespace internal {
|
---|
| 419 | template<int Arch, class Derived1, class Derived2, typename Scalar, int _Options> struct quat_product
|
---|
| 420 | {
|
---|
| 421 | static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived1>& a, const QuaternionBase<Derived2>& b){
|
---|
| 422 | return Quaternion<Scalar>
|
---|
| 423 | (
|
---|
| 424 | a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
|
---|
| 425 | a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
|
---|
| 426 | a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
|
---|
| 427 | a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
|
---|
| 428 | );
|
---|
| 429 | }
|
---|
| 430 | };
|
---|
| 431 | }
|
---|
| 432 |
|
---|
| 433 | /** \returns the concatenation of two rotations as a quaternion-quaternion product */
|
---|
| 434 | template <class Derived>
|
---|
| 435 | template <class OtherDerived>
|
---|
| 436 | EIGEN_STRONG_INLINE Quaternion<typename internal::traits<Derived>::Scalar>
|
---|
| 437 | QuaternionBase<Derived>::operator* (const QuaternionBase<OtherDerived>& other) const
|
---|
| 438 | {
|
---|
| 439 | EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename OtherDerived::Scalar>::value),
|
---|
| 440 | YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
|
---|
| 441 | return internal::quat_product<Architecture::Target, Derived, OtherDerived,
|
---|
| 442 | typename internal::traits<Derived>::Scalar,
|
---|
| 443 | internal::traits<Derived>::IsAligned && internal::traits<OtherDerived>::IsAligned>::run(*this, other);
|
---|
| 444 | }
|
---|
| 445 |
|
---|
| 446 | /** \sa operator*(Quaternion) */
|
---|
| 447 | template <class Derived>
|
---|
| 448 | template <class OtherDerived>
|
---|
| 449 | EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other)
|
---|
| 450 | {
|
---|
| 451 | derived() = derived() * other.derived();
|
---|
| 452 | return derived();
|
---|
| 453 | }
|
---|
| 454 |
|
---|
| 455 | /** Rotation of a vector by a quaternion.
|
---|
| 456 | * \remarks If the quaternion is used to rotate several points (>1)
|
---|
| 457 | * then it is much more efficient to first convert it to a 3x3 Matrix.
|
---|
| 458 | * Comparison of the operation cost for n transformations:
|
---|
| 459 | * - Quaternion2: 30n
|
---|
| 460 | * - Via a Matrix3: 24 + 15n
|
---|
| 461 | */
|
---|
| 462 | template <class Derived>
|
---|
| 463 | EIGEN_STRONG_INLINE typename QuaternionBase<Derived>::Vector3
|
---|
| 464 | QuaternionBase<Derived>::_transformVector(const Vector3& v) const
|
---|
| 465 | {
|
---|
| 466 | // Note that this algorithm comes from the optimization by hand
|
---|
| 467 | // of the conversion to a Matrix followed by a Matrix/Vector product.
|
---|
| 468 | // It appears to be much faster than the common algorithm found
|
---|
| 469 | // in the literature (30 versus 39 flops). It also requires two
|
---|
| 470 | // Vector3 as temporaries.
|
---|
| 471 | Vector3 uv = this->vec().cross(v);
|
---|
| 472 | uv += uv;
|
---|
| 473 | return v + this->w() * uv + this->vec().cross(uv);
|
---|
| 474 | }
|
---|
| 475 |
|
---|
| 476 | template<class Derived>
|
---|
| 477 | EIGEN_STRONG_INLINE QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<Derived>& other)
|
---|
| 478 | {
|
---|
| 479 | coeffs() = other.coeffs();
|
---|
| 480 | return derived();
|
---|
| 481 | }
|
---|
| 482 |
|
---|
| 483 | template<class Derived>
|
---|
| 484 | template<class OtherDerived>
|
---|
| 485 | EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other)
|
---|
| 486 | {
|
---|
| 487 | coeffs() = other.coeffs();
|
---|
| 488 | return derived();
|
---|
| 489 | }
|
---|
| 490 |
|
---|
| 491 | /** Set \c *this from an angle-axis \a aa and returns a reference to \c *this
|
---|
| 492 | */
|
---|
| 493 | template<class Derived>
|
---|
| 494 | EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)
|
---|
| 495 | {
|
---|
| 496 | using std::cos;
|
---|
| 497 | using std::sin;
|
---|
| 498 | Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
|
---|
| 499 | this->w() = cos(ha);
|
---|
| 500 | this->vec() = sin(ha) * aa.axis();
|
---|
| 501 | return derived();
|
---|
| 502 | }
|
---|
| 503 |
|
---|
| 504 | /** Set \c *this from the expression \a xpr:
|
---|
| 505 | * - if \a xpr is a 4x1 vector, then \a xpr is assumed to be a quaternion
|
---|
| 506 | * - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix
|
---|
| 507 | * and \a xpr is converted to a quaternion
|
---|
| 508 | */
|
---|
| 509 |
|
---|
| 510 | template<class Derived>
|
---|
| 511 | template<class MatrixDerived>
|
---|
| 512 | inline Derived& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerived>& xpr)
|
---|
| 513 | {
|
---|
| 514 | EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename MatrixDerived::Scalar>::value),
|
---|
| 515 | YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
|
---|
| 516 | internal::quaternionbase_assign_impl<MatrixDerived>::run(*this, xpr.derived());
|
---|
| 517 | return derived();
|
---|
| 518 | }
|
---|
| 519 |
|
---|
| 520 | /** Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to
|
---|
| 521 | * be normalized, otherwise the result is undefined.
|
---|
| 522 | */
|
---|
| 523 | template<class Derived>
|
---|
| 524 | inline typename QuaternionBase<Derived>::Matrix3
|
---|
| 525 | QuaternionBase<Derived>::toRotationMatrix(void) const
|
---|
| 526 | {
|
---|
| 527 | // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)
|
---|
| 528 | // if not inlined then the cost of the return by value is huge ~ +35%,
|
---|
| 529 | // however, not inlining this function is an order of magnitude slower, so
|
---|
| 530 | // it has to be inlined, and so the return by value is not an issue
|
---|
| 531 | Matrix3 res;
|
---|
| 532 |
|
---|
| 533 | const Scalar tx = Scalar(2)*this->x();
|
---|
| 534 | const Scalar ty = Scalar(2)*this->y();
|
---|
| 535 | const Scalar tz = Scalar(2)*this->z();
|
---|
| 536 | const Scalar twx = tx*this->w();
|
---|
| 537 | const Scalar twy = ty*this->w();
|
---|
| 538 | const Scalar twz = tz*this->w();
|
---|
| 539 | const Scalar txx = tx*this->x();
|
---|
| 540 | const Scalar txy = ty*this->x();
|
---|
| 541 | const Scalar txz = tz*this->x();
|
---|
| 542 | const Scalar tyy = ty*this->y();
|
---|
| 543 | const Scalar tyz = tz*this->y();
|
---|
| 544 | const Scalar tzz = tz*this->z();
|
---|
| 545 |
|
---|
| 546 | res.coeffRef(0,0) = Scalar(1)-(tyy+tzz);
|
---|
| 547 | res.coeffRef(0,1) = txy-twz;
|
---|
| 548 | res.coeffRef(0,2) = txz+twy;
|
---|
| 549 | res.coeffRef(1,0) = txy+twz;
|
---|
| 550 | res.coeffRef(1,1) = Scalar(1)-(txx+tzz);
|
---|
| 551 | res.coeffRef(1,2) = tyz-twx;
|
---|
| 552 | res.coeffRef(2,0) = txz-twy;
|
---|
| 553 | res.coeffRef(2,1) = tyz+twx;
|
---|
| 554 | res.coeffRef(2,2) = Scalar(1)-(txx+tyy);
|
---|
| 555 |
|
---|
| 556 | return res;
|
---|
| 557 | }
|
---|
| 558 |
|
---|
| 559 | /** Sets \c *this to be a quaternion representing a rotation between
|
---|
| 560 | * the two arbitrary vectors \a a and \a b. In other words, the built
|
---|
| 561 | * rotation represent a rotation sending the line of direction \a a
|
---|
| 562 | * to the line of direction \a b, both lines passing through the origin.
|
---|
| 563 | *
|
---|
| 564 | * \returns a reference to \c *this.
|
---|
| 565 | *
|
---|
| 566 | * Note that the two input vectors do \b not have to be normalized, and
|
---|
| 567 | * do not need to have the same norm.
|
---|
| 568 | */
|
---|
| 569 | template<class Derived>
|
---|
| 570 | template<typename Derived1, typename Derived2>
|
---|
| 571 | inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
|
---|
| 572 | {
|
---|
| 573 | using std::max;
|
---|
| 574 | using std::sqrt;
|
---|
| 575 | Vector3 v0 = a.normalized();
|
---|
| 576 | Vector3 v1 = b.normalized();
|
---|
| 577 | Scalar c = v1.dot(v0);
|
---|
| 578 |
|
---|
| 579 | // if dot == -1, vectors are nearly opposites
|
---|
| 580 | // => accurately compute the rotation axis by computing the
|
---|
| 581 | // intersection of the two planes. This is done by solving:
|
---|
| 582 | // x^T v0 = 0
|
---|
| 583 | // x^T v1 = 0
|
---|
| 584 | // under the constraint:
|
---|
| 585 | // ||x|| = 1
|
---|
| 586 | // which yields a singular value problem
|
---|
| 587 | if (c < Scalar(-1)+NumTraits<Scalar>::dummy_precision())
|
---|
| 588 | {
|
---|
| 589 | c = (max)(c,Scalar(-1));
|
---|
| 590 | Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
|
---|
| 591 | JacobiSVD<Matrix<Scalar,2,3> > svd(m, ComputeFullV);
|
---|
| 592 | Vector3 axis = svd.matrixV().col(2);
|
---|
| 593 |
|
---|
| 594 | Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
|
---|
| 595 | this->w() = sqrt(w2);
|
---|
| 596 | this->vec() = axis * sqrt(Scalar(1) - w2);
|
---|
| 597 | return derived();
|
---|
| 598 | }
|
---|
| 599 | Vector3 axis = v0.cross(v1);
|
---|
| 600 | Scalar s = sqrt((Scalar(1)+c)*Scalar(2));
|
---|
| 601 | Scalar invs = Scalar(1)/s;
|
---|
| 602 | this->vec() = axis * invs;
|
---|
| 603 | this->w() = s * Scalar(0.5);
|
---|
| 604 |
|
---|
| 605 | return derived();
|
---|
| 606 | }
|
---|
| 607 |
|
---|
| 608 |
|
---|
| 609 | /** Returns a quaternion representing a rotation between
|
---|
| 610 | * the two arbitrary vectors \a a and \a b. In other words, the built
|
---|
| 611 | * rotation represent a rotation sending the line of direction \a a
|
---|
| 612 | * to the line of direction \a b, both lines passing through the origin.
|
---|
| 613 | *
|
---|
| 614 | * \returns resulting quaternion
|
---|
| 615 | *
|
---|
| 616 | * Note that the two input vectors do \b not have to be normalized, and
|
---|
| 617 | * do not need to have the same norm.
|
---|
| 618 | */
|
---|
| 619 | template<typename Scalar, int Options>
|
---|
| 620 | template<typename Derived1, typename Derived2>
|
---|
| 621 | Quaternion<Scalar,Options> Quaternion<Scalar,Options>::FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
|
---|
| 622 | {
|
---|
| 623 | Quaternion quat;
|
---|
| 624 | quat.setFromTwoVectors(a, b);
|
---|
| 625 | return quat;
|
---|
| 626 | }
|
---|
| 627 |
|
---|
| 628 |
|
---|
| 629 | /** \returns the multiplicative inverse of \c *this
|
---|
| 630 | * Note that in most cases, i.e., if you simply want the opposite rotation,
|
---|
| 631 | * and/or the quaternion is normalized, then it is enough to use the conjugate.
|
---|
| 632 | *
|
---|
| 633 | * \sa QuaternionBase::conjugate()
|
---|
| 634 | */
|
---|
| 635 | template <class Derived>
|
---|
| 636 | inline Quaternion<typename internal::traits<Derived>::Scalar> QuaternionBase<Derived>::inverse() const
|
---|
| 637 | {
|
---|
| 638 | // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite() ??
|
---|
| 639 | Scalar n2 = this->squaredNorm();
|
---|
| 640 | if (n2 > Scalar(0))
|
---|
| 641 | return Quaternion<Scalar>(conjugate().coeffs() / n2);
|
---|
| 642 | else
|
---|
| 643 | {
|
---|
| 644 | // return an invalid result to flag the error
|
---|
| 645 | return Quaternion<Scalar>(Coefficients::Zero());
|
---|
| 646 | }
|
---|
| 647 | }
|
---|
| 648 |
|
---|
| 649 | /** \returns the conjugate of the \c *this which is equal to the multiplicative inverse
|
---|
| 650 | * if the quaternion is normalized.
|
---|
| 651 | * The conjugate of a quaternion represents the opposite rotation.
|
---|
| 652 | *
|
---|
| 653 | * \sa Quaternion2::inverse()
|
---|
| 654 | */
|
---|
| 655 | template <class Derived>
|
---|
| 656 | inline Quaternion<typename internal::traits<Derived>::Scalar>
|
---|
| 657 | QuaternionBase<Derived>::conjugate() const
|
---|
| 658 | {
|
---|
| 659 | return Quaternion<Scalar>(this->w(),-this->x(),-this->y(),-this->z());
|
---|
| 660 | }
|
---|
| 661 |
|
---|
| 662 | /** \returns the angle (in radian) between two rotations
|
---|
| 663 | * \sa dot()
|
---|
| 664 | */
|
---|
| 665 | template <class Derived>
|
---|
| 666 | template <class OtherDerived>
|
---|
| 667 | inline typename internal::traits<Derived>::Scalar
|
---|
| 668 | QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const
|
---|
| 669 | {
|
---|
| 670 | using std::atan2;
|
---|
| 671 | using std::abs;
|
---|
| 672 | Quaternion<Scalar> d = (*this) * other.conjugate();
|
---|
| 673 | return Scalar(2) * atan2( d.vec().norm(), abs(d.w()) );
|
---|
| 674 | }
|
---|
| 675 |
|
---|
| 676 |
|
---|
| 677 |
|
---|
| 678 | /** \returns the spherical linear interpolation between the two quaternions
|
---|
| 679 | * \c *this and \a other at the parameter \a t in [0;1].
|
---|
| 680 | *
|
---|
| 681 | * This represents an interpolation for a constant motion between \c *this and \a other,
|
---|
| 682 | * see also http://en.wikipedia.org/wiki/Slerp.
|
---|
| 683 | */
|
---|
| 684 | template <class Derived>
|
---|
| 685 | template <class OtherDerived>
|
---|
| 686 | Quaternion<typename internal::traits<Derived>::Scalar>
|
---|
| 687 | QuaternionBase<Derived>::slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const
|
---|
| 688 | {
|
---|
| 689 | using std::acos;
|
---|
| 690 | using std::sin;
|
---|
| 691 | using std::abs;
|
---|
| 692 | static const Scalar one = Scalar(1) - NumTraits<Scalar>::epsilon();
|
---|
| 693 | Scalar d = this->dot(other);
|
---|
| 694 | Scalar absD = abs(d);
|
---|
| 695 |
|
---|
| 696 | Scalar scale0;
|
---|
| 697 | Scalar scale1;
|
---|
| 698 |
|
---|
| 699 | if(absD>=one)
|
---|
| 700 | {
|
---|
| 701 | scale0 = Scalar(1) - t;
|
---|
| 702 | scale1 = t;
|
---|
| 703 | }
|
---|
| 704 | else
|
---|
| 705 | {
|
---|
| 706 | // theta is the angle between the 2 quaternions
|
---|
| 707 | Scalar theta = acos(absD);
|
---|
| 708 | Scalar sinTheta = sin(theta);
|
---|
| 709 |
|
---|
| 710 | scale0 = sin( ( Scalar(1) - t ) * theta) / sinTheta;
|
---|
| 711 | scale1 = sin( ( t * theta) ) / sinTheta;
|
---|
| 712 | }
|
---|
| 713 | if(d<Scalar(0)) scale1 = -scale1;
|
---|
| 714 |
|
---|
| 715 | return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs());
|
---|
| 716 | }
|
---|
| 717 |
|
---|
| 718 | namespace internal {
|
---|
| 719 |
|
---|
| 720 | // set from a rotation matrix
|
---|
| 721 | template<typename Other>
|
---|
| 722 | struct quaternionbase_assign_impl<Other,3,3>
|
---|
| 723 | {
|
---|
| 724 | typedef typename Other::Scalar Scalar;
|
---|
| 725 | typedef DenseIndex Index;
|
---|
| 726 | template<class Derived> static inline void run(QuaternionBase<Derived>& q, const Other& mat)
|
---|
| 727 | {
|
---|
| 728 | using std::sqrt;
|
---|
| 729 | // This algorithm comes from "Quaternion Calculus and Fast Animation",
|
---|
| 730 | // Ken Shoemake, 1987 SIGGRAPH course notes
|
---|
| 731 | Scalar t = mat.trace();
|
---|
| 732 | if (t > Scalar(0))
|
---|
| 733 | {
|
---|
| 734 | t = sqrt(t + Scalar(1.0));
|
---|
| 735 | q.w() = Scalar(0.5)*t;
|
---|
| 736 | t = Scalar(0.5)/t;
|
---|
| 737 | q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
|
---|
| 738 | q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
|
---|
| 739 | q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
|
---|
| 740 | }
|
---|
| 741 | else
|
---|
| 742 | {
|
---|
| 743 | DenseIndex i = 0;
|
---|
| 744 | if (mat.coeff(1,1) > mat.coeff(0,0))
|
---|
| 745 | i = 1;
|
---|
| 746 | if (mat.coeff(2,2) > mat.coeff(i,i))
|
---|
| 747 | i = 2;
|
---|
| 748 | DenseIndex j = (i+1)%3;
|
---|
| 749 | DenseIndex k = (j+1)%3;
|
---|
| 750 |
|
---|
| 751 | t = sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
|
---|
| 752 | q.coeffs().coeffRef(i) = Scalar(0.5) * t;
|
---|
| 753 | t = Scalar(0.5)/t;
|
---|
| 754 | q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
|
---|
| 755 | q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
|
---|
| 756 | q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
|
---|
| 757 | }
|
---|
| 758 | }
|
---|
| 759 | };
|
---|
| 760 |
|
---|
| 761 | // set from a vector of coefficients assumed to be a quaternion
|
---|
| 762 | template<typename Other>
|
---|
| 763 | struct quaternionbase_assign_impl<Other,4,1>
|
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| 764 | {
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| 765 | typedef typename Other::Scalar Scalar;
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| 766 | template<class Derived> static inline void run(QuaternionBase<Derived>& q, const Other& vec)
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| 767 | {
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| 768 | q.coeffs() = vec;
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| 769 | }
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| 770 | };
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| 771 |
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| 772 | } // end namespace internal
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| 773 |
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| 774 | } // end namespace Eigen
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| 775 |
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| 776 | #endif // EIGEN_QUATERNION_H
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